High Resolution Infrared Spectroscopy of Slit-Jet Cooled
Radicals and Ions
byMelanie A. Roberts
B.A., Macalester College, 2005

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulﬁllmentof the requirements for the degree ofDoctor of Philosophy
Department of Chemistry and Biochemistry2012This thesis entitled:High Resolution Infrared Spectroscopy of Slit-Jet Cooled Radicals and Ions
written by Melanie A. Roberts
has been approved for the Department of Chemistry and Biochemistry

David J. Nesbitt

G. Barney Ellison

Date

The ﬁnal copy of this thesis has been examined by the signatories, and we ﬁnd that boththe content and the form meet acceptable presentation standards of scholarly work in theabove mentioned discipline.

iii
Roberts, Melanie A. (Ph.D., Chemical Physics)
High Resolution Infrared Spectroscopy of Slit-Jet Cooled Radicals and Ions
Thesis directed by Prof. David J. Nesbitt

This thesis presents high-resolution spectra of supersonically-cooled organic radicals in
the mid-infrared, the details and design of the instruments necessary to obtain the spectra,
and the theory to understand the spectra and the larger context of the results. Speciﬁcally,four organic radicals are studied: singly-deuterated methyl radical (CH2 D), phenyl radical(C6 H5 ), hydroxymethyl radical (CH2 OH), and ethynyl radical (C2 H). All of the spectroscopic
studies presented use an existing mid-infrared high-resolution spectrometer with a frequency
precision of better than 10 MHz. The radicals are generated using a discharge to dissociatea neutral precursor and form the radicals. The discharge is localized at the oriﬁce of a slit
supersonic expansion, which cools the radicals to around 20 K and allows for sub-Doppler
spectral resolution. In addition to the description of the existing spectrometer, the design,
construction, and successful testing of a new, automated mid-infrared spectrometer is presented. The new spectrometer is based upon diﬀerence frequency generation of a scanning
Ti:Sapphire laser and a single-frequency Nd:YAG laser to create high-resolution mid-infrared
radiation. The new system speeds up data-taking by fully automating the scanning process.
The four radicals studied in this thesis are all intermediates in combustion processes ofhydrocarbon fuels. First, the out-of-phase symmetric stretch of phenyl radical is presented.
As the ﬁrst high-resolution infrared study of phenyl, it paves the way for future studies of thisand other aromatic radicals. Second, the two fundamental CH stretches in CH2 D are studied
with full rotational resolution. The narrow linewidth of the transitions reveals resolved
ﬁne structure and partially resolved hyperﬁne structure. This resolution yields additional
information regarding the distribution of electrons in the radical. With this study of CH2 D,a nearly complete set of vibrational frequencies is present in the literature. This inspired us

iv
to develop a comprehensive model that is capable of simultaneously ﬁtting the CH and CD
stretches of all the hydrogenic isotopomers of methyl radical. Third, while ethynyl absorbs
in the mid-infrared, the transition studied are low-lying electronic states. The combinationof a cold source of C2 H and high frequency precision allows us to clarify line assignments
and ﬁnd new transitions. Additionally, localized shifting of transition frequencies allows
for identiﬁcation and partial characterization of the dark perturber states. Fourth, thesymmetric CH stretch of hydroxymethyl radical is studied at high-resolution. The highresolution spectra improve upon band origin and structural information in the radical as well
as set the stage for further experimental studies into potential large amplitude dynamics inthe radical.

Dedication

To My Grandparents

vi

Acknowledgements

First and foremost I would like to acknowledge my advisor, David Nesbitt. I truly
appreciate all the eﬀort he has put into helping me become a scientist and continuallypushing me to grow as a student. He spent many long days in the lab teaching me how thehigh-resolution spectrometer works and guiding me through learning everything from readinga circuit diagram to solving quantum mechanical problems. I am constantly inspired by his
dedication to science and endless energy to think deeply and clearly about even the seemingly
simplest of problems.
I would like to thank the Nesbitt group, past and present members, for creating a
supportive and inspiring atmosphere to work in. While I was working in B212 by myself,
Tom Baker, Brad Perkins, and Alex Zolot were always willing to answer my questions at
any time and I learned a lot from them. I worked with several post-docs in B212 and I
thank them for helping me along the way; Feng Dong, Chandra Savage, Richard Walters,
Chih-Hsuan Chang, and Erin Sharp-Williams. I want to thank Erin for her friendship andconstant support for all problems scientiﬁc and personal, and for always being willing tolaugh about it. I have also enjoyed working with the younger B212-ers Grant Buckingham
and Nathan Hinkley who made sure life in lab was never dull. To the other members of
the Nesbitt group, I have enjoyed working with you: Mike Ziemkiewicz, Mike Deskevitch,
Danny Bell, Rob Roscioli, Julie Fiore, Andrej Grubisic, Andy Gisler, Lora Nugent-Glandorf,
Vasiliy Fomenko, Mia Zutz, Dan Nelson, Larry Fiegland, Monika Gruetter-Kasumaj, Kevin
Early, Nick Dupuis, Eric Holmstrom.

vii
It has been a great honor to have worked in JILA and there are many people helpedme from informal talks of quantum mechanics at cookie time to building a much-needed
piece of equipment. I am grateful to the members of my annual review committee, Roberts
Parson and Carl Lineburger, for their guidance. I also would like to thank the JILA staﬀ
members. I would like to thank the electronics shop, especially Terry Brown, James Fung-AFat, and Paul Beck. The computing group has helped me through many problems, especiallyPete Ruprect, Jim McKown, Mike Paige, Alan Dunwell, and J.R. Raith. J.R. deserves
special thanks for having rebuilt and saved every one of the six computers that run my two
instruments. Hans Green, Blaine Horner, Ariel Paul, and rest of the instrument shop forbuilding integral parts of my instruments and teaching me about machining along the way.
I feel very grateful to have had the opportunity to attend Macalester College since it
was the chemistry faculty (Tom Varberg, Keith Kuwata, Rebecca Hoye, and Ronald Brisbois)
whose classes were so enjoyable that I decided to major in the subject. I would especiallylike to thank my undergraduate research advisor, Tom Varberg, for somehow convincing methat a summer spent in a dark spectroscopy lab would be more fun and rewarding than asummer in the Boundary Waters of Minnesota, a truly life-changing decision.
Finally, I would like to thank my friends and family for supporting me on this long
and, at times, arduous endeavor. I don’t think I would have ﬁnished this process without
my brother, Mike, who trained me to be tough; my sister, Meg, for always being there; andmy parents for their support and love. Last, but not least, I thank my best friend and thelove of my life Ted Reber.

viiiContents

Chapter
1 Introduction

1

2 Experimental Apparatus

92.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

92.2

Generation of Tunable High-Resolution Infrared Light . . . . . . . . . . . . .

9

2.2.1

Dye Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

2.3

Frequency Stabilization and Determination . . . . . . . . . . . . . . . . . . .

18

2.4

Radical Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

2.5

Data Acquisition and Processing . . . . . . . . . . . . . . . . . . . . . . . . .

22

3 A new high-resolution spectrometer for the study of radicals and ions

25

3.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

3.2

Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

3.2.1

Infrared Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29

3.2.2

Scanning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

37

3.3

Frequency Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39

3.4

Molecular Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

43

3.5

Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

3.6

Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

3.7

Test Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

ix
3.7.1

Stability and Reproducibility . . . . . . . . . . . . . . . . . . . . . .

52

3.7.2

HD2 O+ Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

4 Rotationally resolved spectroscopy of phenyl radical in the out-of-phase symmetricCH stretching mode

55

4.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

4.2

Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

4.3

Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

59

4.4

Conclusion and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .

65

5 A complete picture of stretching vibrations in methyl radical and its deuterated isotopomers: a high-resolution study of the CH stretches in CH2 D and a global harmonically coupled Morse oscillator model

67

5.1

Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

5.2

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74

5.3

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

76

5.3.1

Rovibrational Structure . . . . . . . . . . . . . . . . . . . . . . . . .

76

5.3.2

Fine and Hyperﬁne Structure . . . . . . . . . . . . . . . . . . . . . .

82

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

5.4.1

Intensity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

5.4.2

Vibrational Force Constants . . . . . . . . . . . . . . . . . . . . . . .

90Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

5.4

5.5

6 Understanding the 2 Π-2 Σ+ bands in ethynyl radical: from the inclusion of satellite
branches to vibronic coupling

99

6.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

99

6.2

Expectations for 2 Π − 2 Σ+ . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

6.3

Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

x
6.4

6.5

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.4.1

3600 cm−1 Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.4.2

3692 cm−1 Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

6.4.3

3786 cm−1 Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.4.44012 cm−1 Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.4.54107 cm−1 Band . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.5.1

Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6.5.2

Fitting Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.5.3

Perturbation Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 134

6.6

Vibronic Assignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

6.7

Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

7 High-Resolution Direct-Absorption Spectroscopy of Hydroxymethyl Radical in the
CH Symmetric Stretching Region

153

7.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

7.2

Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

7.3

Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7.4

Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

7.5

Conclusion and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

8 Conversion of Coherent 899-29 system into high-accuracy, high-precision automaticallytunable laser: application in a new mid-IR spectrometer for study of transient intermediates

167

8.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

8.2

Precision Automated Scanning of Ti:Sapphire Laser . . . . . . . . . . . . . . 172
8.2.1

Frequency Determination . . . . . . . . . . . . . . . . . . . . . . . . . 172

8.2.2

Integration of Autoscan with larger program . . . . . . . . . . . . . . 177

xi
8.3

Mid-IR spectrometer for studying transient molecules . . . . . . . . . . . . . 180

8.4

Spectrometer test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

8.5

Appendix: YAG Lock Description . . . . . . . . . . . . . . . . . . . . . . . . 184

Bibliography

186

Appendix
A Harmonically Coupled Morse Oscillator (HCMO) ﬁtting routine

198

B LabWindows Code for the New Spectrometer

213

C Data Processing Scripts and Procedures

240

C.1 General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
C.2 Origin Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

xii

TablesTable
4.1

Harmonic B3LYP/AVnZ (n = 2,3,4,5) ab initio predictions as a function ofbasis set size for fundamental CH stretch modes in phenyl radical. Numbers
in parenthesis represent predicted intensities in km/mol. The rightmost column contains anharmonic estimates (∆ν ± 10 cm−1 ) from density functional
B3LYP/6-311g++(3df,3pd) calculations, based on a scale factor of 0.9637(31)benchmarked against CH stretch excitation frequencies for a series of high resolution studies of hydrocarbon radicals[1] . . . . . . . . . . . . . . . . . . . .

4.2

61

Rovibrational spectroscopic constants for gas-phase phenyl radical from a rigid
asymmetric rotor least-squares ﬁt to the out-of-phase symmetric CH stretch
band. Numbers in parentheses represent 1σ uncertainties in units of the leastsigniﬁcant digit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.1

63

Experimental ﬁne- and hyperﬁne-free line centers for the C-H2 symmetricstretch band of CH2 D radical. Estimates of the frequency precision and accuracy are both 15 MHz. The calculated values used are from a global leastsquares ﬁt to Watson’s asymmetric top Hamiltonian of all the symmetricstretch, asymmetric stretch, and the out-of-plane bending mode[2] transitions. 78

xiii
5.2

Experimental ﬁne- and hyperﬁne-free line centers for the C-H2 asymmetricstretch band of CH2 D radical. Estimates of the frequency precision and accuracy are both 15 MHz. The calculated values used are from a global leastsquares ﬁt to Watson’s asymmetric top Hamiltonian of all the symmetricstretch, asymmetric stretch, and the out-of-plane bending mode[2] transitions. 79

5.3

Results from the least-squares ﬁt to asymmetric top Watson’s Hamiltonian(A-Reduction, Ir Representation). The parameters on the top part of thetable are from a global ﬁt including all lines from the symmetric stretch,
asymmetric stretch, and the out-of-plane bending bands. The second part of
the table includes the results of a ﬁt involving the IR data only. The numbers in parenthesis indicate 1-σ uncertainties of the ﬁt; the residual standard
deviation for the global ﬁt is 17 MHz and for the IR-only ﬁt is 66 MHz. . . .

5.4

80

Comparison of ﬁne and hyperﬁne structure parameters from FTIR study[2],scaled estimates based on methyl radical, and least-squares ﬁt results of the
IR experimental line shapes. All values are in MHz. Note that aF (H) was
ﬂoated in the ﬁt, the aF (D) parameter was calculated using the experimentally
determined ratio of 6.541. The numbers in parenthesis are 1-σ uncertainties
from the least-squares ﬁt.

5.5. . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

Results from least-squares ﬁt of the vibrational frequencies to the harmonicallycoupled Morse oscillator model (HCMO) and then to an HCMO model that
includes 2:1 Fermi coupling. The residual standard deviation of the HCMO
plus Fermi coupling ﬁt was 2.0 cm−1 . . . . . . . . . . . . . . . . . . . . . . .

5.6

91

Frequencies of the vibrational fundamentals and ﬁrst overtones obtained fromthe harmonically coupled Morse oscillator model (HCMO) with the addition of
three quanta Fermi coupling. Only the fundamental frequencies were includedin the ﬁt; the overtones were predicted by the model. . . . . . . . . . . . . .

97

xiv
6.1

Experimental lines observed in the 3600 cm−1 2 Π-2 Σ+ band (all frequencies
in cm−1 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

6.2

Experimental combination diﬀerences for the 3600 cm−1 2 Π-2 Σ+ band compared with ground state energy level diﬀerences. . . . . . . . . . . . . . . . . 113

6.3

Experimental lines observed in the 3692 cm−1 2 Π-2 Σ+ band (all frequencies
in cm−1 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

6.4

Experimental combination diﬀerences for the 3692 cm−1 2 Π-2 Σ+ band compared with ground state energy level diﬀerences. . . . . . . . . . . . . . . . . 118

6.5

Experimental lines observed in the 3786 cm−1 2 Π-2 Σ+ band (all frequencies
in cm−1 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

6.6

Experimental lines observed in the 4012 cm−1 2 Π-2 Σ+ band (all frequencies
in cm−1 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6.7

Experimental lines observed in the 4107 cm−1 2 Π-2 Σ+ band (all frequencies
in cm−1 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

6.8

Excited state constants for the 3692 cm−1 2 Π-2 Σ+ band (all in cm−1 ). Numbers in parentheses constitute the error in each reported value. . . . . . . . . 128

6.9

Excited state constants for the 3786 cm−1 , 4012 cm−1 , and 4107 cm−1 2 Π2

Σ+ bands (all in cm−1 ). Numbers in parentheses constitute the error in eachreported value. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.10 Comparing excited state constants for the 4012 cm−1 2 Π-2 Σ+ band (all in
cm−1 ), with and without perturbed 2 Π F1 levels. Numbers in parentheses
constitute the error in each reported value. . . . . . . . . . . . . . . . . . . . 134
6.11 Excited state constants for the 3600 cm−1 2 Π-2 Σ+ band (all in cm−1 ). Numbers in parentheses constitute the error in each reported value. . . . . . . . . 135
7.1

Experimental line positions of the Ka = 0 ← 0 progression with assignments
using the N′ Ka′ Kc′ ← N′′ Ka′′ Kc′′ notation. . . . . . . . . . . . . . . . . . . . . . . 161

xv
7.2

Comparison of molecular constants, all constants in wavenumbers (cm−1 ).
Present work ﬁt to ν + B J(J+1) + DJ [J(J+1)]2 Hamiltonian . . . . . . . . 162

xvi

FiguresFigure2.1

Schematic of the instrument. . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

2.2

Schematic of the ring dye laser. . . . . . . . . . . . . . . . . . . . . . . . . .

12

2.3

Faraday rotator operation, the black arrows represent the state of linear polarization. a) shows the beam propagating in the desired direction. Note thatthe input and output polarizations are the same. b) shows the beam propagating in the backwards direction. Note that the two polarization rotations
add. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.4

Schematic illustrating how the birefringent ﬁlter and Fabry-Perot etalon selectout a single cavity mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.5

13

15

a) The inter-laser Fabry-Perot cavity geometry. b) Scanning galvanometer
plates. Notice that the distance the beam propagates through the plates isdependent upon their angle. . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.1

16

Optical layout of the high-resolution spectrometer. The radiation from atunable Ti:Sapphire laser is overlapped with the single-frequency light of a
Nd:YAG laser in a periodically poled lithium niobate crystal (PPLN) and
via diﬀerence frequency generation to produce the mid-infrared light. The
frequency axis is precise to 10 MHz. . . . . . . . . . . . . . . . . . . . . . . .

29

xvii
3.2

Experimental tuning curves for one PPLN. There are three PPLN’s, each with
7 separate poling periods, necessary to cover the full tuning capability of theTi:Sapphire laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.3

34

Properties of a Herriot cell. Panel a) is a schematic of the U-shaped patternof the laser beams on both the front and back mirror of the Herriot cell. Panelb) plots the beam spot size as a function of pass number both at the centerof the cell and on the front mirror of the cell for a mirror spacing exactly
equal to twice the radius of curvature (60cm). Since the spot size at the front
mirror is continually expanding and will likely not cleanly exit the cell. Panelc) illustrates the optimal mirror spacing so that the exit beam is small enoughto easily exit the cell without clipping the mirror. . . . . . . . . . . . . . . .

3.4

Illustration of the timing of the Autoscan (in blue) and the data acquisition
sequence (green). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3.5

36

40

Sample scan showing the frequency diagnostic tools. Panel a) shows theTi:Sapphire laser fringes from the 250 MHz cavity, panel b) shows the Ti:Sapphirefringes from the 1.5 GHz cavity, and panel c) is the transmission of the IR
through the room temperature reference cell with < 5 Torr D2 O. . . . . . . .

3.6

44

Comparison of the precision of the raw Autoscan axis [panel a)] and the corrected x-axis [panel b)]. The 1.5 GHz and 250 MHz are locked to a frequencystabilized HeNe laser and the emission of the Ti:Sapphire through these twocavities is plotted against the uncorrected and corrected x-axis.

3.7. . . . . . .

51

Illustration of the precision of the new instrument. This region is scanned aminimum of three time and the standard deviation of the measurements foreach line in the region is plotted as a function of the frequency position of theline. The average standard deviation of the measurements is 9.3 MHz. . . . .

3.8

53

Sample HD2 O+ data in the OH stretching region illustrating the ability of the
new instrument to produce molecular ions in appreciable quantities. . . . . .

54

xviii4.1

Geometric structure and highest occupied molecular orbital representation ofphenyl radical, with principal inertial axes as indicated. The out-of-phasesymmetric CH stretch excitation (b2 ) observed in this work has a transition
dipole moment along the A-axis. Note the nodeless, in-plane nature of thesingle ﬁlled HOMO at the radical C center, characteristic of a σ-radical. . . .

4.2

57

A sample 0.5 cm−1 high resolution data scan for phenyl radical in the outof-phase CH symmetric stretch region (with 0.25% peak absorbances), alongwith spectral predictions based on Trot = 15 K and the preliminary rotational
constants reported in Table 4.2. Note the predominance of NK′ a′ Kc′ ← NK′′ a′′ Kc′′
progressions involving N = Kc states, for which the asymmetry splittings innear oblate top phenyl radical are unresolved. . . . . . . . . . . . . . . . . .

5.1

B3LYP/6-311++G(3df,3pd) calculated structure[3] of CH2 D with the HOMO
and principal axes shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.2

60

71

Sample CH symmetric stretch data for CH2 D. Panel a) plots the integrated
absorbance of each of the observed N′Ka′ Kc′ ← N′′Ka′′ Kc′′ rotational lines versus
frequency. Blowups of select transitions, panels b)-d), show additional structure at high resolution due to ﬁne and hyperﬁne interactions. The black dots
are the data and the red lines are simulations base upon constants obtainedin lineshape ﬁts of the ﬁne and hyperﬁne structure. . . . . . . . . . . . . . .

5.3

75

Sample CH asymmetric stretch data for CH2 D. Panel a) plots the integrated
absorbance of each of the observed rotational lines, labeled as N′Ka′ Kc′ ←N′′Ka′′ Kc′′ , versus measured frequency. Details of select transitions, in panelsb)-d), show additional structure at high resolution attributed to ﬁne andhyperﬁne interactions. The black dots are the data and the red lines are
simulations base upon constants obtained in ﬁts to the observed lineshapes. .

76

xix
5.4

CH2 D symmetric stretch rotational structure and ﬁt results. Panel a) is aplot of the experimental data shown as a stick plot with the integrated area
under each rotational peak shown as the y-axis; P-branch transitions are ingreen, Q-branch in blue, and R-branch in red. Panel b) is a simulation based
upon rotational and centrifugal distortion constants from the ﬁt to Watson’s
asymmetric top Hamiltonian. Panel c) plots the observed minus calculated
frequency, in MHz, for each of the observed lines. . . . . . . . . . . . . . . .

5.5

81

CH2 D asymmetric stretch rotational structure and ﬁt results. Panel a) plots
the experimental data as a stick plot with the integrated area under each rotational peak shown as the y-axis; P-branch transitions are in green, Q-branchin blue, and R-branch in red. Panel b) is a simulation based upon rotationaland centrifugal distortion constants from the ﬁt to Watson’s asymmetric top
Hamiltonian. Panel c) plots the observed minus calculated frequency, in MHz,for each of the observed lines. . . . . . . . . . . . . . . . . . . . . . . . . . .

5.6

82

Segmented simulation of ﬁne and hyperﬁne structure of the 110 ← 101 transition for CH2 D in the asymmetric stretch mode. Panel a) shows a simulationand stick spectrum of the transition based upon a 70 MHz Doppler with andno ﬁne or hyperﬁne structure followed by successive inclusion in panel b) of
spin-rotation (εaa ,εbb ,εcc , in panel c) H-atom Fermi contact term (af (H) ), andpanel d) D-atom Fermi contact (af (D) ) terms. Panel e) illustrates how theenergy level structure is split upon each successive addition of terms. . . . .

84

xx
5.7

Comparison of ﬁne structure splitting of the 000 ← 111 transition from theasymmetric stretch mode. Panel a) plots the data, in red dots, and the results of the ﬁt results from the present study (black line). Panel b) plots thedata from the current study, in red dots, and a lineshape simulation based
upon spin-rotation constants from the FTIR study[2] (blue line). In the simulation, the upper and lower state spin-rotation constants are set equal and thehyperﬁne constants are those found in the present study. The high resolutionof the data allows for a reﬁnement of the spin-rotation constants from the
FTIR study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.8

88

A semi-logarithmic plot of experimental integrated line intensities scaled by
the calculated linestrength factors plotted against the rotational energy of thelower state. The symmetric and asymmetric stretch lines are denoted by ﬁlled
and open symbols, respectively with the ortho lines are triangles and the paralines are squares. The solid lines represent least-squares ﬁts of the data to astraight line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.9

89

The experimental values minus the calculated values for all nine of the experimentally known stretches for each of the three models is shown. The black
circles show residuals from a ﬁt to a harmonically coupled harmonic oscillator model, the red squares are the residuals from the harmonically coupled
Morse oscillator model (HCMO), and the blue triangles are residuals from theHCMO model but with 2:1 Fermi interactions added into the model. Panel c)shows diﬀerence between the experimental frequencies for the overtones andthe predicted frequencies based upon the ﬁt to the fundamental modes. . . .

92

xxi
5.10 Graphs showing the fundamental stretching modes nearby overtone and combination bands that are of the correct symmetry to perturb each stretchingmode. CH3 and CD3 , shown in panels a and b, are of D3h symmetry and thestates are labeled with (ν1 , ν2 , ν3l , ν4l ); the symmetric stretch is of A′1 symmetry
and the doubly-degenerate asymmetric stretch is of E′ symmetry. The asymmetrically substituted isotopomers, CH2 D and CHD2 , have three stretches:
two of a1 symmetry, in red, and one of b2 symmetry, in blue. The labels forthese species are (ν3 , ν4 , ν5 , ν6 ), with the stretches labeled explicitly. It is clearthat the CD3 symmetric stretch, the CH2 D CD stretch, and the CD stretches
in CHD2 all have nearby states that could have a Fermi interaction with anearby bending overtone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.1

96

Energy level diagram for both 2 Π and 2 Σ+ states (with spacings exaggerated
for the clearest view) and the possible transitions that can be observed between
them. The energy levels are labeled as F1 or F2 levels and with the J andparity quantum numbers. The transitions are denoted with arrows and belong
to one of four groups: (1) R1 (also P1 and Q1 ), signifying transitions obeying
the selection rule of ∆J = 1 (for R1 branch only) and originating from F1
levels in the 2 Σ+ state and terminating in F1 levels in the 2 Π state; (2) R2(also P2 and Q2 ), signifying transitions obeying ∆J = 1 (for R2 branch only)
and originating from F2 levels in the 2 Σ+ state and terminating in F2 levelsin the 2 Π state; (3) R12 (also P12 and Q12 ) signifying transitions obeying theselection rule of ∆J = 1 (for R12 branch only) and originating from F2 levelsin the 2 Σ+ state and terminating in F1 levels in the 2 Π state; (4) R21 (also P21
and Q21 ) signifying transitions obeying the selection rule of ∆J = 1 (for R21
branch only) and originating from F1 levels in the 2 Σ+ state and terminatingin F2 levels in the 2 Π state. . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

xxii
6.2

Predicted intensities for all possible transition types in 2 Π-2 Σ+ bands as afunction of J′′ . The circle points with solid lines correspond to the mainbranches (R1 , P1 , Q1 , R2 , P2 , Q2 ) and the square points with dashed lines
correspond to the satellite branches (R12 , P12 , Q12 , R21 , P21 , Q21 ). . . . . . . 107

6.3

Sample experimental data for the 3600 cm−1 band. In this 5 cm−1 region,lines from the R1 and Q2 main branches were observed, as well as lines fromthe P21 satellite branch. The downward going red lines were simulated using
our reﬁned excited state constants from Table 6.11 (column 4, excluding the
Coriolis coupling perturbation parameters), the ground state constants determined from previous microwave studies[4], and the energy level expressions
for the unperturbed 2 Σ+ ground state and 2 Π excited state Hamiltonian models discussed in Section 6.5.1. The downward going pink lines were simulated
similarly using our reﬁned excited state constants from Table 6.11 (column 4),
now including the perturbation parameters (β0 , νpert and Bpert ) and the perturbative Σ − Π Coriolis coupling as discussed in Section 6.5.3. The predicted
intensities in both the red and pink traces were calculated using rotational line
strength factors for 2 Π-2 Σ+ bands[5] and a Boltzmann factor for a rotationaltemperature of 12 K, to be the temperature achieved for our C2 H radicals
produced in a slit-discharge of C2 H2 coupled with supersonic expansion. . . . 111

6.4

Sample experimental data for the 3692 cm−1 band. In this 5 cm−1 region, lines
from the R1 and Q2 main branches were observed, as well as lines from the P21
and Q21 satellite branches. The downward going lines were simulated using
our reﬁned excited state constants from Table 6.8, the ground state constants
determined from previous microwave studies[4], and the matrix elements for
the Hamiltonian discussed in Section 6.5.1. The predicted intensities were
calculated using rotational line strength factors for 2 Π-2 Σ+ bands[6] and a
Boltzmann factor for a rotational temperature of 12 K. . . . . . . . . . . . . 114

xxiii
6.5

Boltzmann plot for the 3692 cm−1 band. Sexp are the experimental intensities(in % absorbance) and Sij are the rotational line strength factors from Zare[6].
E′′rot was calculated using the ground state microwave constants[7, 4] and theappropriate energy level expressions for a 2 Σ+ state (see Section 6.5.1. The
points were ﬁt to a line, whose slope is equal to -1/kT. . . . . . . . . . . . . 115

6.6

Sample data for the 3786 cm−1 band showing blow-ups of satellite transitions
appearing as shoulders to main branch transitions. The downward going vertical bars represent simulations of each peak, with predicted frequency positions
determined from excited state constants from Table 6.9, the ground state constants from previous microwave studies,[4] and the corresponding Hamiltonian
expressions discussed in Sec. 6.5.1 for the 2 Σ+ and 2 Π states. . . . . . . . . . 119

6.7

Sample experimental data for the 4012 cm−1 band. In this 5 cm−1 region,lines from the R1 , Q1 , and Q2 main branches were observed, as well as lines
from the R12 , P21 , and Q21 satellite branches. The downward going lines were
simulated using our reﬁned excited state constants from Table 6.8, the groundstate constants determined from previous microwave studies[4], and the matrix elements for the Hamiltonian discussed in Section 6.5.1. The predicted
intensities were calculated using rotational line strength factors for 2 Π-2 Σ+bands[6] and a Boltzmann factor for a rotational temperature of 12 K. . . . . 125

6.8

Sample data for the 4107 cm−1 band showing blow-ups of individual satellite transitions appearing as shoulders to individual main branch transitions.
The downward going gray vertical bars represent simulations of each peak,whereby the predicted frequency positions were determined using the excitedstate constants from Table 6.8, the ground state constants from microwave
studies[4], and the Hamiltonian expressions discussed in Section 6.5.1 for the2

Σ+ and 2 Π states. The intensities of the vertical bars were determined froma rotational line strength factor[6] and a Boltzmann factor for T = 12 K. . . 126

xxiv
6.9

Residuals (observed-calculated) from ﬁt, described in Section 6.5.2, for the2Π-2 Σ+ centered around 3692 cm−1 . The upper graph shows residuals for theR1 (circle points), Q1 (square points), and R12 (diamond points) branches,
while the lower graph shows residuals for the R2 (circle points), Q2 (squarepoints), and P21 (diamond points) branches. . . . . . . . . . . . . . . . . . . 131
6.10 Residuals (observed-calculated) from ﬁt, described in Section 6.5.2, for the 2 Π2

Σ+ band centered around 4012 cm−1 . The upper graph shows residuals for

the R1 (circle points), Q1 (square points), and R12 (diamond points) branches,
while the lower graph shows residuals for the R2 (circle points), Q2 (squarepoints), and P21 (diamond points) branches. . . . . . . . . . . . . . . . . . . 132
6.11 Residuals (νobs -νcalc ) for the 3600 cm−1 band for the Q2 , P21 , R2 , and P2
branches plotted as a function of J′ , where νcalc was determined from theunperturbed Hamiltonian model discussed in Section 6.5.1. These clearly
demonstrate a local perturbation in the Q2 and P21 branches at J′ = 3.5,
evident in not only in the discontinuity in the plot but also in that two lines
are observed at J′ = 3.5 for both of these branches. The residual plots for P2
and R2 reﬂect no such local perturbation. The energy level diagram schematics
to the right demonstrate the transitions being depicted in each plot. Fromthese, it is easy to see that the Q2 and P21 transitions terminate in the upper
parity level in the 2 Π state, while the R2 and P2 transitions terminate in thelower parity level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

xxv
6.12 Energy level diagram illustrating perturbation of the upper parity levels in thebright 2 Π1/2 excited state by a close-lying dark 2 Σ+ state. The Σ-Π Coriolis
perturbation breaks the degeneracy in the 2 Π upper parity energy levels fora given J and gives rise to mixed energy levels (drawn in the center of theexcited state), which contain partial character of the bright and dark states.
The unperturbed 2 Π1/2 energy levels are blue, while the unperturbed 2 Σ+levels in the excited state are red. The mixed states in the center are then
combinations of red and blue, which portrays the predicted intensity for atransition terminating in these levels, based on the percentage of blue (orbright character) depicted in each. At J′ = 3.5, this mixing is approximately
50/50, yielding an integrated intensity ratio of 0.89, and hence, we observetransitions to both J′ = 3.5(-) perturbed levels. The green arrows indicate
the observed transitions in the Q2 branch. . . . . . . . . . . . . . . . . . . . 141
6.13 Energy level diagram for C2 H from the theoretical work of Tarroni and Carter[8,9] revealing the predicted vibronic state densities for each angular momentum
K value. Note the sparse vibronic manifold for a triatomic such as C2 H at
low energies, which provides a novel opportunity to identify the explicit vibrational level(s) involved in the “bright state (2 Π1/2 ) -“dark state (2 Σ+ ) vibronicinteraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

xxvi
6.14 A ≈ 200 cm−1 blow up region of the Tarroni and Carter[8, 9] energy level
diagram for C2 H in the 2 Π-2 Σ+ 3600 cm−1 origin band region, sorted by K
quantum number and clearly identifying the only near-resonant vibrational
states available for strong vibronic interaction via a a local curve crossing.
Near-resonant coupling with the Π, ∆, Φ manifolds can be immediately ruledout (by dashed crosses) since only the upper parity level is selectively perturbed, which leaves only ∆K = ± 1 Π-Σ Coriolis coupling with only one
possible resonant state (blue-green circle) in the 2 Σ+ manifold. The variational calculations by Tarroni and Carter suggest this state is predominantly(0,80 ,0) with partial (0,00 ,2) character. Note the low overall state density(≈ 0.02 states/cm−1 ) in this triatomic molecule, which permits unambiguous
identiﬁcation of the near resonant vibronic interaction. . . . . . . . . . . . . 147
6.15 Overview of the experimentally observed (leftmost, in black) and calculated
vibronic states in C2 H, where the predictions are from Tarroni and Carterand organized by angular momentum projection quantum number Λ. Note theexcellent agreement between the four observed (black) and predicted (blue) 2 Πband origins. Also note the prediction of a highly vibrationally excited 2 ∆ X̃
(1,22 ,0) state in resonance with the 4012 cm−1 band origin, with no other state
inside of a 300 cm−1 window. This makes for unambiguous assignment of thedark state responsible for the J dependent shifts observed in Figure 6.10 to2∆ X̃ (1,22 ,0), i.e., one quantum of CH stretch and 2 quanta of CCH bend,

which couples with the Ã (0,0,0) state by 2 Π-2 ∆ Coriolis interactions. . . . . 150
7.1

Quasiplanar structure of hydroxymethyl radical with HOMO and priciple axis
orientation shown. The equilibrium geometry has a slightly bent methyl groupin the out-of-plane bend coordinate, due to competition between sp3 and sp2
hybridization around the central C atom. . . . . . . . . . . . . . . . . . . . . 156

xxvii
7.2

Comparison of two diﬀerence discharge chemistries for “synthesis” of jet cooled
CH2 OH. The red line represents three sample spectral regions for a discharge
with CH3 OH doped into Ne-70 diluent, with the corresponding black line
representing comparable data scans for a CH3 OH + Cl2 discharge, which
generates hydroxymethyl radical by Cl + CH3 OH → HCl + CH2 OH chemistry. Panel a) illustrates how the CH2 OH number density nearly doubles forchemical formation via H atom abstraction by discharge generated Cl atoms.
Interestingly, panels b) and c) also reveal how the spectral density of undesired species (such as methane and precursor methanol) can be substantiallyminimized under the Cl atom synthetic pathway. . . . . . . . . . . . . . . . . 159

7.3

Sample data shown with simulation based upon least squares ﬁts to a Watson
asymmetric top Hamiltonian. Panel a) reveals a spectral scan region nearthe ν3 symmetric CH stretch band origin, with assignment of the Ka = 0 ←0 progression shown above (in blue). The green arrow indicates the missing spectral line in the progression makes the band origin assignment andJ-labeling unambiguous. Panel b) provides a spectral simulation (in red) of
the A type band Ka = 0 ← 0 progression based upon spectroscopic constantsfrom the least-squares ﬁt. The blow up region in panel c) illustrates a single
101 ← 000 absorption line in the ν3 band, which serves to characterize typicalsignal-to-noise levels of > 10:1 in the current experiment.

7.4. . . . . . . . . . 160

Boltzmann plot analysis of ν3 symmetric CH stretch band spectral line intensities for jet cooled CH2OH radical obtained under both i) CH3 OH doped
discharge (red squares) as well as ii) Cl2 /CH3 OH discharge (blue circles) conditions. Sexp is the integrated line strength in units of absolute absorbance),with Sij and gJ = 2J+1 representing the line strength factor and mJ degeneracy, respectively. The diﬀerence in y-intercepts reﬂects the roughly 60% lower
density of CH2 OH radical in the CH3 OH-only discharge. . . . . . . . . . . . 163

xxviii
8.1

Two sample Ti:Sapphire laser transmission fringes through the two opticaltransfer cavities. Panel a) shows an overlap of the two scans if the frequency
generated by Autoscan is used to overlap two scans. The fringes from the twoscans do not overlap, but there is no ambiguity as to which 1.5 GHz cavity
fringes should overlap while there is ambiguity for the 250 MHz cavity fringes.
Panel b) illustrates the high quality of the overlap between scans when thecorrected frequency axis is used. . . . . . . . . . . . . . . . . . . . . . . . . . 174

8.2

Illustration of nonlinear scanning of the Ti:Sapphire laser system. The plot
is of the diﬀerence between the 250 MHz FSR cavity peak positions andsimulated peak positions for a linear scan plotted as a function of the fringe
count during the segment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

8.3

Plots of the error in counting fringes between two fringe measurements, inunits of fractions of a fringe, as a function of the accuracy of the frequency
measurement and the diﬀerence in frequency between the two fringes. Panela) shows the calculation for the 250 MHz FSR cavity and panel b) plots thecalculation for the 1.5 GHz FSR cavity. Note the diﬀerence in x-axis scale
between the two plots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

8.4

Schematic showing the logic and connectivity of the master scanning program. 179

8.5

Optical layout of the high-resolution spectrometer. The radiation from atunable Ti:Sapphire laser is overlapped with the single-frequency light of a
Nd:YAG laser in a periodically poled lithium niobate crystal (PPLN) and
via diﬀerence frequency generation to produce the mid-infrared light. The
frequency axis is precise to 10 MHz. . . . . . . . . . . . . . . . . . . . . . . . 181

xxix
8.6

Illustration of the precision of the new instrument. This region was scanneda minimum of three time and the standard deviation of the measurements foreach line in the region is plotted as a function of the frequency position of
the line. The average standard deviation of the measurements is 9.3 MHz.
Sample HD2 O+ data in the OH stretching region illustrating the ability of the
new instrument to produce molecular ions in appreciable quantities. . . . . . 183

8.7

Schematic representation of the Nd:YAG locking circuit. . . . . . . . . . . . 185

Chapter 1
Introduction

The existence of infrared radiation was ﬁrst recognized by Hershel by using a thermometer to measure the temperature of diﬀerent regions of the visible spectrum and eventually
mapped out measured temperatures of what we now know to be diﬀerent frequencies of light.
He wasn’t the ﬁrst person to explore diﬀerent spectral regions, a few people had done so in
the 1770’s and again the 1790’s, but he was the ﬁrst to realize the signiﬁcance of his measurements and identify a new region of radiation lower in frequency than the visible spectrum.
He even used mirrors to reﬂect the IR radiation to determine that the new region of radiation
had similar properties to visible radiation. The characterization of this region of light was
furthered with the help of a few technological breakthroughs, speciﬁcally of the thermocouple
by Nobili and Melloni around 1830. The thermocouple allowed faster temperature readings
and avoided the problem of the radiation having to pass through glass, which has variableattenuation as a function of wavelength. With the discovery by Melloni that rock salt transmitted IR radiation without attenuation, researchers began to make rock salt prisms andoptics and subsequently were able to begin to characterize IR radiation.[10] In 1859, Tyndall
did the ﬁrst study of molecular gas absorption by passing IR radiation through four foot-longgas-ﬁlled cells.[11] In the late 1800’s several other researchers explored the IR absorption ofmolecular gases and ascertained that the wavelength-dependant absorptions could be attributed to molecular structure. In the ﬁrst third of the twentieth century, physicists aroundthe world continued to explore and characterize IR absorption of molecules. Many notable2
contributions to the ﬁelds of infrared technology and spectroscopy during this period camefrom Coblentz. One example, in a collaboration with Mabery, who had the largest collectionof puriﬁed hydrocarbon samples, Coblentz took IR spectra of the molecules that could be
used to unambiguously identify each molecule.[12] This was the beginning of the link between the petroleum industry and IR spectroscopy. With World War II came a huge inﬂux
of government and industrial money and interest in the development of IR technology andits use as an indispensable tool for chemical identiﬁcation, often with the added complicationof classiﬁed research and technologies. The British initially invested in the technology to beable to identify the source of German fuel by examining the speciﬁc chemical composition.
The Americans also heavily invested in the technology. The subsequent inﬂux in funds for
IR spectroscopy led to widely used commercial instruments that non-specialists could use
to take IR spectra of samples. Original spectrometers of both Perkin-Elmer and Beckman
were a result of this period and became a tool in chemistry research laboratories around theworld.[13]The work presented in this thesis uses direct absorption spectroscopy in the midinfrared (mid-IR) region using a straight-forward application of Beers law,
A = − ln

I
= Nlσ
I◦

(1.1)

where A is the absorbance, I◦ is the initial intensity of light sent to the sample, I is theintensity of light after passing through the sample, N is the number of absorbing moleculesin the sample, l is the pathlength, and σ is the absorption cross section. In words, we
compare the amount of light before passing through a sample with the amount of light after
passing through a sample as a function of the frequency of the light, yielding the absorption
spectrum of the sample. The energy of the photons in the IR region generally corresponds tofundamental vibrational excitation of molecules, with microwave frequencies corresponding
to rotational excitation and the visible corresponding to electronic excitation. In this thesis,
we study the CH-stretching vibrations of phenyl radical (C6 H5 ), singly-deuterated methyl

3radical (CH2 D) and hydroxymethyl radical (CH2 OH). Ethynyl radical (C2 H) is also studied
in this thesis, but the presence of a low-lying electronic state makes the transitions studied
in this region electronic transitions.
With our high resolution system, we gain more information than only the location of
the vibrational (or electronic) transitions since we fully resolve the rotational structure. We
can then obtain valuable information concerning the structure of the molecule and how itchanges with vibrational excitation. In CH2 D, the coupling between rotational and electron spin angular momentum is large enough to be resolved in the spectra (ﬁne structure).
Additionally, we obtain partial resolution, in the form of broadened lineshapes, of the coupling of electron spin and nuclear spin angular momentum (hyperﬁne structure). In C2 H,
we see transitions out-of and into diﬀerent spin orbit states. Information obtained fromhigh-resolution spectra can lead to many insights; for example, about the speciﬁc nature ofbonding in the molecule, as is the case in CH2 D, or the nature of nearby dark states that
do not have an IR absorption spectra, as happens in C2 H. We therefore work hard to obtainhigh-resolution spectra of these molecules, including a method for creating cold (10-30 K)
molecules with sub-Doppler linewidths and a tunable laser system with a frequency precisionof 10 MHz (30 parts-per-trillion) or better.
There are two high-resolution spectrometers presented in this thesis, both based upondiﬀerence frequency generation to obtain mid-IR light. The spectrometer described in chapter 2 has been evolving since initial development by the ﬁrst students in the Nesbitt group;
this spectrometer is used for all the projects in this thesis except for those in chapters 3 and
8. It is a testament to everyone who has worked on this spectrometer that it remains with somany original elements and design ideas even as improvements and changes were added witheach new generation. For example, the over 100 optics and mounts on the table walks you
through a bit of the history of optical mounts. The dye laser locking setup still employs optics
mounts hand machined by graduate students epoxied to the table; many of the wavemeter
optics use magnetic bases attached to JILA mounts from before set-screw optics mounting

4
became standard; the other frequency locking and diagnostic elements use early generationcommercial mounts with very large optical mounting plates; the IR beampath has some of
the newest mounts with sleek set-screw mounts for the optics and very high turns-per-inch
adjustments. The heart of the instrument is a tunable ring dye laser and a single frequency
argon ion laser that are combined in a periodically poled lithium niobate crystal where difference frequency generation takes place producing mid-IR radiation. The tunability of thedye laser is therefore transferred to the IR light as well as the narrow linewidths of boththe argon ion and dye lasers. The IR light then passes through a 16 pass Herriot cell wherea 4 cm long supersonically expanding slit nozzle ﬂows the gas of interest. The details of
this spectrometer are presented in chapter 2. The molecules studied in this thesis fall under
the category of transient intermediates, short-lived molecules that play important roles inmany chemicals systems such as combustion, atmospheric chemistry, and interstellar space.
Each chapter introduces the historical background, chemical application, and spectroscopic
interest in studying each molecule so the remainder of this chapter is a brief introduction to
the molecule and summary of some of the highlights of each project.
Chapter 3 describes in detail the new high-resolution infrared spectrometer and uses
the OH stretch of doubly deuterated hydronium ion, HD2 O+ , to demonstrate the quality ofthe spectrometer. The HD2 O+ detection is made possible by utilizing the high ion densities formed in supersonically cooled pulsed discharge methods, the sensitive detection fromconcentration modulation techniques, and long absorption path lengths. The spectrometer
utilizes diﬀerence frequency mixing in a periodically poled lithium niobate crystal of a scanning single mode Ti:Sapphire laser and a ﬁxed frequency single mode Nd:YAG laser to create
narrow-linewidth radiation from 1700 - 3900 cm−1 (5.9 - 2.6 µm). The relative frequency ofinfrared light is determined by locking the Nd:YAG laser to a stabilized cavity and tracking
the scanning of the Ti:Sapphire laser on two stabilized cavities. The absolute frequency isdetermined by D2 O absorption in the mid-infrared region. There are two major improvements of this instrument over its predecessor: an increased frequency range and nearly fully

5
automated scanning. The increased frequency range means that we are now able to takedata in the OD stretching region speciﬁcally of HD2 O+ ; however, to test the spectrometer
we record OH stretching lines and compare them to the OH stretch lines taken previouslyon the instrument in chapter 2. Frequency comparisons of many lines over multiple scans on
diﬀerent days resulted in a frequency precision of 10 MHz. With the addition of automatedscanning, data are much faster and easier to obtain with this instrument than with the old
instrument and will hopefully prove to be a great instrument for taking the massive amountsof data required for these high-resolution spectroscopy experiments.
Chapter 4 discusses the rigid nearly symmetric top radical, phenyl radical (C6 H5 ).
Phenyl is one of the largest molecules we have studied at high resolution and yet has arelatively simple spectra. The cyclic structure with largely sp2 hybridized bonds creates a
relatively rigid and planar molecule well described by rigid rotor calculations. Phenyl radical
is formed by homolytic cleavage of a CH bond in the stable benzene molecule and, as such,is highly reactive. Phenyl is of interest in combustion chemistry as an aromatic species since
typical fossil fuels are rich in aromatic species. Furthermore, an unwanted byproduct of
combustion is the formation of soot, which signals incomplete and ineﬃcient combustion.
The formation of soot involves making large ring compounds, as soot is generally a mix oflarge ring and aromatic compounds. Similarly, phenyl radical is of astronomical intereste
as an intermediate in the formation of polycyclic aromatic hydrocarbons. In chapter 4, theν19 out-of-phase CH symmetric stretch mode is presented and analyzed. Using ground state
rotational constants from a microwave study by Thaddeus and coworkers,[14] we are able
to determine the excited state rotational constants for the ﬁrst time. We also obtain theﬁrst gas phase value of the vibrational band origin and, upon comparison with the matrix
values, ﬁnd that there is a remarkably small shift between the matrix value and the gas phasevalues. The ability to resolve the rotational structure of this relatively large prototypicalring molecule is a promising start towards in situ measurement of observation of complex
aromatic species during combustion.

6
In chapter 5, the CH symmetric and asymmetric stretches of mono-deuterated methyl
radical (CH2 D) are presented with full rotational and ﬁne structure resolution and partiallyresolved hyperﬁne structure. CH2 D is smaller and more asymmetric than phenyl radical
and, as a result of the decreased symmetry, the rovibrational spectra doesn’t have the easily
recognizable P-, Q-, and R-branch structure of a symmetric top. Using ab initio predictions
for the structure and a rigid rotor Hamiltonian as an initial guide, we begin to assign the
spectrum. The assignment is conﬁrmed by four line combination diﬀerences. Additionally,
the slit expansion collisionally quenches the transverse velocity distribution along the laser
probe direction, yielding sub-Doppler resolution of spin-rotation structure and even partial
resolution of nuclear hyperﬁne structure for each rovibrational line. The ﬁne and hyperﬁne
structure manifest as a complex lineshape of each rotational line. Global least-squares ﬁts
to the lineshapes provide additional information on spin-rotation and nuclear hyperﬁne constants, which complement and clarify previous FTIR studies of CH2 D in the out-of-planebending region. Finally, analysis of the spectral data from the full isotopomeric CHm D3−mseries based on harmonically coupled Morse oscillators (HCMO) establishes a predictive
framework for describing the manifold of planar stretching vibrations in this fundamental
combustion radical.
In contrast to phenyl and CH2 D where we were exciting CH stretching vibrations, themolecule presented in chapter 6, C2 H, has low lying electronic states that absorb in the
mid-IR region. C2 H, ethynyl radical, is known to be a key intermediate in acetylene (C2 H2 )combustion[15] and has been detected in outer space.[16] Acetylenic combustion is of interestin chemical and industrial applications and in the study of combustion since C2 H4 is a known
intermediate in the combustion of fuel-rich systems of large molecules.[17] High resolution
infrared spectra for ﬁve 2 Π-2 Σ+ bands of jet-cooled C2 H in the gas phase are reported. The
combination of slit-jet cooling (Trot ≈ 12 K) and sub-Doppler resolution (≈ 60 MHz) permits
satellite branches in each 2 Π-2 Σ+ band to be observed and resolved for the ﬁrst time as wellas help clarify a systematic parity misassignment from previous studies.[18, 19] The observed

7lines in each band are least squares ﬁt to a Hamiltonian model containing rotational, spinrotational, spin-orbit, and lambda-doubling contributions for the 2 Π state, from which wereport revised excited state constants and band origins for the observed bands. Three ofthe four bands ﬁt extremely well within a conventional 2 Π model (i.e. σ < 20 MHz), while
one band exhibits a local perturbation due to an avoided crossing with a near resonant darkstate. Vibronic assignments are given for the observed bands, with the dark state clearly
identiﬁed as a highly excited stretch and bending overtone level X̃ (1,22 ,0) by comparison
with high level ab initio eﬀorts.
Additionally, the Ã2 Π- X̃ 2 Σ+ origin band exhibits a strong, parity-speciﬁc local perturbation in the upper 2 Π1/2 state. Based on revised parity assignments of the levels, theperturbing state is unambiguously determined to be 2 Σ+ symmetry, and thus coupled to theÃ2 Π1/2 state by ∆ K = ±1 Coriolis interactions. By incorporating Σ − Π Coriolis coupling
into the unperturbed Hamiltonian (containing only rotational, spin-rotational, spin-orbit,
and lambda-doubling contributions), we are now able to ﬁt the observed 2 Π-2 Σ+ origin band
to a sub Doppler experimental uncertainty of 15 MHz (0.0005 cm−1 ). In addition, the observation of pairs of transitions to mixed states permits determination of the band origin
and rotational constant (Bpert ) for the dark 2 Σ+ state, which prove to be in remarkably
quantitative agreement with full vibronic predictions of Tarroni and Carter[8] as well as UV
dispersed ﬂuorescence studies of Hsu et al.[20] A dark state perturbation is identiﬁed fromshifts in the frequency and intensity of transitions as well as the appearance of an additionaltransition. This represents an important benchmark in mapping out non-BornOppenheimer
vibronic interactions and energy level structure in a polyatomic combustion radical system,
an understanding of which will be key to modeling chemical reactions in both terrestrial andastronomical environments.
Chapter 7 presents the ﬁrst high resolution direct absorption study of hydroxymethyl
radical, CH2 OH, in the infrared CH stretching region. As a result of the low rotationaltemperature and sub-Doppler linewidths obtained in the slit supersonic expansion, the Ka

8= 0 ← 0 band of the symmetric CH stretch for CH2 OH is unambiguously identiﬁed and analyzed. By way of additional chemical conﬁrmation, hydroxymethyl radical is generated via
two diﬀerent chemical synthesis: a pure methanol discharge and a methanol plus molecularchlorine discharge. The identiﬁed transitions are ﬁt to a Watson A-reduced symmetric top
Hamiltonian to yield the ﬁrst precision experimental values for the ground state rotational
constants as well as improved values for the symmetric stretch rotational constants and vibrational band origin. The results both complement and substantially improve upon spectral
eﬀorts via previous double resonance ionization detected IR methods by Feng et al., whichobtained partially rotationally resolved spectra in the CH and OH stretching regions.[21]Chapter 8 presents a novel method for improving the frequency precision and accuracyof the Coherent 899-29 Ti:Sapphire laser and Autoscan system while augmenting the automated scanning capability. This laser system is widely used for high resolution spectroscopy
because of the narrow linewidth, wide tuning range, and automated scanning. To improve
the resolution of the system, we present a solution incorporating two locked cavities, onewith 250 MHz free spectral range (FSR) and one with a 1.5 GHz FSR, to provide a moreaccurate and precise frequency reference for the existing wavemeter. To illustrate the versatility of this system, a method for integrating the Ti:Sapphire and Autoscan system into asophisticated mid-IR high-resolution automated spectrometer for studying transient species
is presented. The spectrometer is based upon diﬀerence frequency generation between thetunable Ti:Sapphire laser and a stabilized, single frequency YAG laser in a Periodically Poled
Lithium Niobate crystal. The precision of the absorption lines of molecular ions generated
by the instrument is 9.3 MHz.

Chapter 2
Experimental Apparatus

2.1

Introduction
Elements of this instrument have been used since the eighties to do spectroscopy andhas been improved upon, added to, and changed with every new post-doc and graduate
student in the lab. While several thesis talk in depth about most of the pieces of the instrument as they were added, there is no thesis that includes it in its current form. Speciﬁcally,
the locking circuits are described in depth in Chris Lovejoy’s thesis[22] and John Farrell’s
thesis[23], the wavemeter and several other aspects of the optical layout are in Scott Davis’s
thesis[24], and the computer programs to process and analyze data are described in Erin
Whitney’s thesis[25]. The components of the instrument that have been discussed in detail
before will only be discussed brieﬂy and emphasis will be places on elements that are not described in detail in other thesis. The most signiﬁcant change that has happened is the switchfrom a lithium niobate crystal to a periodically poled lithium niobate crystal. More minorchanges have been made to certain electronics, parts of the optical layout, and computer
programs.
2.2

Generation of Tunable High-Resolution Infrared Light
The tunable infrared light is generated by diﬀerence frequency generation of a single

frequency argon ion laser (Ar+ ) and a tunable narrow-linewidth dye laser based on an original
design by Pine.[26] An overview of the optical layout of the experiment is shown in Figure

102.1. Brieﬂy, the light from the tunable dye laser is sent through a waveplate to rotate thepolarization 90◦ so that it is vertical to match the vertical polarization of the Ar+ laser andas is required by the nonlinear crystal. The dye light then passes through two telescoping
lenses before being overlapped with the Ar+ light and focused into the non-linear crystal.
The telescoping lens system is necessary to make the dye laser beam, which is expanding
upon exiting the laser, have a beam proﬁle that will match the Ar+ laser beam after theyboth are focused into the crystal. The lenses and lens position are chosen by ﬁrst proﬁling
both laser beams and then using the ABCD law to solve for the two lenses and positions
that will best overlap the dye laser with the Ar+ laser.[27]Figure 2.1: Schematic of the instrument.

The nonlinear crystal used here for diﬀerent frequency generation is a periodicallypoled lithium niobate crystal (PPLN). There are two crystals for use with this experiment,

11
one with 8 poling periods and one with 12 poling periods. The PPLN crystal uses quasi
phase matching for diﬀerence frequency generation of the Ar+ and dye laser frequencies.
A more complete description of diﬀerence frequency generation, quasi phase matching, andperiodic poling are in chapter 3. The single frequency laser can lase at any of the visible Ar+
lines, with 514 nm and 488 nm as the two strongest lines and the ones used in this thesis.
One crystal is for use with the 514 nm line and one is for use with the 488 nm line. Eachpoling period covers about 150 cm−1 with the ability to temperature tune for the proper
phase matching conditions within that 150 cm−1 . Temperature tuning from 100-200 degrees
Celsius is achieved with a commercial brass oven and temperature controller.
As three frequencies of light exit the crystal, a ﬁlter blocks the visible dye and Ar+ lightwhile the infrared radiation gets focused and split into two roughly equal beams. One beam
is directly focused into the reference, liquid nitrogen cooled, InSb detector and the otherbeam goes into the Herriot cell. The Herriot cell consists of two mirrors, both with a 30 cm
radius of curvature, spaced approximately 60 cm apart. This cell is easily conﬁgured for up to
18 passes. The Herriot cell conﬁguration increases the pathlength while continually focusing
the beam as it passes through the sample. Each pass is also sent very nearly overlapping
the previous pass in space. More details of the Herriot cell are found in Chapter 3. Upon
exiting the Herriot cell, the beam is focused onto the signal InSb detector.

2.2.1

Dye Laser

The tunability of the system comes from the dye laser. The layout of the SpectraPhysics model 380A ring dye laser can be found in Figure 2.2, not drawn to scale.. With
the exception of locking elements, all of the necessary elements to create a small linewidth,
tunable laser are found in the laser cavity. A few notes on the cavity in general are in order
before going into each element in more detail. The distance from M1 to M2 is about 8.4 cm
and the distance from M3 to M4 is about 53.1 cm. The second general consideration is that
all relevant surfaces are at Brewster’s angle with respect to the horizontal component. This

12means that the laser will lase purely with horizontal polarization. This is exploited in someof the elements described below.

Figure 2.2: Schematic of the ring dye laser.

The next major design aspect of the cavity is that it is a ring cavity. In a linear cavity,
there is the presence of standing waves due to the superposition of waves traveling in both
directions. In a ring cavity, with the help of a unidirectional device, the waves propagate
in only one direction and are thus traveling waves. The unidirectional device used in thiscase is a Faraday rotator. The Faraday rotator consists of magnetized Faraday plate and aquartz plate and takes advantage of the Faraday eﬀect to create a unidirectional device.[28]Brieﬂy, both the Faraday plate and the quartz plate rotate the polarization of an incoming
beam by 45◦ . When a beam travels in the forward direction, the two rotations cancel and13
the polarization of the outgoing beam is the same as the incoming beam. Conversely, when abeam propagates in the opposite direction, the 45◦ rotations add and the outgoing beam hasa perpendicular polarization to the incoming beam. The perpendicularly polarized beam
is lost through either parallel polarizers on the input and output of the Faraday rotatorassembly or on the Brewster surfaces of the optics in the laser. A schematic of what thiseﬀect looks like is in ﬁgure 2.3 with thin arrows representing the polarization direction. The
Faraday rotator has the eﬀect of suppressing the cavity modes in the opposite direction,
making the cavity unidirectional.

Figure 2.3: Faraday rotator operation, the black arrows represent the state of linear polarization. a) shows the beam propagating in the desired direction. Note that the input
and output polarizations are the same. b) shows the beam propagating in the backwards
direction. Note that the two polarization rotations add.

The cavity longitudinal modes are approximately 200 MHz apart, so it is necessary to14have a way to reliably suppress these modes in order to get single frequency operation. This isdone with two elements, a birefringent ﬁlter and a Fabry-Perot etalon. The birefringent ﬁlter
takes advantage of a birefringent material, whereby the index of refraction of the material,n, is dependant upon the direction of travel through the crystal. The index through thematerial can be described by two diﬀerent values of n, one for the ordinary axis (no ) and
one for the extraordinary axis (ne ) of the crystal. Upon hitting the crystal, the incoming
radiation divides into two components that travel with diﬀerent velocities as a result of thediﬀerent n values. There becomes a phase diﬀerence between the component traveling along
the ordinary axis and the component traveling along the extraordinary axis. This phaseretardation, ϕ, can be expressed as[27, 29, 30]
ϕ = 2π(no − ne )T(sin2 [α])λsin[β](2.1)

where no and ne are the ordinary and extraordinary indices of refraction, β is the Brewster
angle, α is the angle between the fast axis of the plate and the high loss polarization of the
Brewster surfaces, T is the plate thickness, and λ is the wavelength. The β is the incident
angle, Brewsters angle in this case, and α is the angle between the optic axis and the light rayin the plate. The birefringent ﬁlter will be a high loss element in the cavity for wavelengths
that do not have a phase retardation that is an integer multiple of the wavelength. Tuningis achieved by rotation of the ﬁlter. The phase shift from the birefringent ﬁlter is a relatively
broad function of wavelength, illustrated in ﬁgure 2.4.
For spectroscopic applications, an element with better mode selectivity is needed. In
this case, a Fabry-Perot etalon with plane parallel mirrors is used to select out a single cavity
mode. The free spectral range of this etalon is about 75 GHz and the mirrors used have areﬂectivity on the order of 30%. The transmission of a Fabry-Perot is
T = (1 +2πnd −1
4R
sin2 [])
2(1 − R)
λ(2.2)

where R is the reﬂectivity of the mirrors, n is the integer mode number, and d is the cavity
length. Equation 2.2 gives the familiar Fabry-Perot transmission fringes seen in ﬁgure 2.4.

15This form assumes the reﬂectivity, R, of the mirrors to be the same, as they are in thislaser. The elements for longitudinal mode selectivity are now in place. The birefringent
ﬁlter selects only a few Fabry-Perot cavity modes and the Fabry-Perot lock loop keeps thecavity on just one mode, see ﬁgure 2.4. To decrease the potential for mode hops in the
Fabry-Perot cavity, a smaller etalon with a 900 GHz free spectral range originally came withthe laser but is not currently used.

Birefringent Filter

Intracavity Etalon

FSR = 75 GHz

Laser Cavity Longitudinal Modes

FSR = 200 MHz

Figure 2.4: Schematic illustrating how the birefringent ﬁlter and Fabry-Perot etalon selectout a single cavity mode.

As mentioned above, in order to insure that the etalon remains on the same mode,
it is actively stabilized by a “top-of-line” lock loop. A “top-of-line” lock loop does exactly
as the name implies, the lock maintains the laser frequency at the top (instead of the side)of the transmission fringe of the etalon. To accomplish this locking technique, there is a16cylindrical piezo-electric element between the two mirrors that controls the length of thecavity (ﬁgure 2.5). A small voltage 2 KHz sine wave dither is applied to the piezo, whichcauses the intensity of the output to vary by a negligibly small amount. A small percentageof the output of the laser is picked oﬀ by a beamsplitter just after the output coupler of thelaser. The intensity of this pickoﬀ is monitored by the laser control box electronics. The
laser electronics box sends proportional and integral error signals to the laser in the formof correction voltages applied to the piezo. The feedback from this locking circuit keeps the
Fabry-Perot cavity at a distance that corresponds to the peak of a transmission fringe. This
locking circuit is the commercial one that is built into the laser.

a)b)

Figure 2.5: a) The inter-laser Fabry-Perot cavity geometry. b) Scanning galvanometer plates.
Notice that the distance the beam propagates through the plates is dependent upon theirangle.

17
To further stabilize the frequency output of the laser, in addition to the etalon lockloop, the output of the laser is locked to an external cavity and a correction voltage applied
to the piezo element on M2. This loop is a “side-of-line” lock, thus there is no dither voltage
applied to the laser or external cavity. The external cavity is a Fabry-Perot cavity with agalvanometer plate in the center. The principle that this lock loop operates on is as follows.
Part of the dye laser beam is sent to a power detector and another part sent through theexternal cavity and onto a signal detector. The output of the two detectors is divided so thatpower ﬂuctuations in the laser output do not eﬀect the frequency lock loop. The locking
circuit employs a standard feedback loop in which the piezo on the laser M2 is adjusted
to keep the output of the external cavity locked on a side of the Fabry-Perot transmission
fringe.
The last unexplained element in the laser cavity are the two galvo plates, also known as
Brewster plates. These are essentially pieces of glass on rotation motors set at approximately
Brewster’s angle. Figure 2.5 shows how the light will travel through the plates. As theplates rotate, the distance the beam travels through the galvo plates changes. This changes
the length of the cavity slightly and results in a change of wavelength of the laser. The
galvo plates can scan using just the electronics on the laser control box. However for thisexperiment, the galvos are controlled as part of a master-slave scanning system, where thelaser is the slave and an external cavity is the master.
The external master cavity is also used to further stabilize the dye laser. This external
cavity is made from Zerodur material, which has a very low thermal expansion coeﬃcient asa method of stabilization, and aligned in a bowtie conﬁguration. A quartz plate mounted toa galvo is inside the cavity to change the cavity length, making the cavity frequency tunable.
The dye laser is locked to this cavity using a “side-lock” technique. A small amount of the dyelight is sent to the “reference” detector while some light is sent through the cavity and onto
the “power” detector. The signals are then divided, to account for any power ﬂuctuations,and an oﬀset added so that the signal level crosses zero half way up a transmission fringe.

18
The lock then has a zero-crossing to lock on and a directionality in the signal to know how
to correct for the error. Feedback is sent to laser control box to maintain the lock.
As mentioned earlier, the laser control box has the capability to scan the laser over asmall frequency range. It moves the Brewster plates while the internal laser etalon tracks
to maintain lock on the peak of a transmission fringe. However for implementation in this
instrument, we use a step-scan method whereby the laser frequency is stepped by someamount and held at that frequency while recording data. In this case, the scanning iscontrolled via a LabWindows program on a computer. The computer outputs a step voltage,
which is sent to the galvo plates in the master cavity. A feed forward is sent to the laser
galvo plates, via the laser control box, and the laser is able to follow the scanning of themaster cavity.
With the use of an internal etalon stabilization and overall laser stabilization to an
external cavity, the output of the dye laser can have linewidths on the order of 1 MHz.
Internal galvo plates, which follow the scanning of an external master cavity, provide stablecomputer-controlled scanning of the dye laser. The range of this scanning is limited to theability of the galvo plates to change the cavity length without hoping a mode of the internal
etalon or birefringent ﬁlter. Longer frequency scans are obtained by changing internal FabryPerot modes manually by tuning the birefringent ﬁlter. Many of the smaller scans are stitched
together to get continuous data for hundreds of wavenumbers.
2.3

Frequency Stabilization and Determination
The frequency reproducibility of the experiment is arguably the most important piece ofthe experiment, without which the data we take would be useless. The error in the frequencyof the infrared laser is just the quadratic sum of the error of each of the Ar+ and dye lasers,
2
2
2
∆νIR
= ∆νdye+ ∆νAr+ where ∆ν is the error in the frequency. We exploit this by locking

the Ar+ laser to a single frequency and monitoring the dye laser frequency as it scans so thatthe precision of the visible lasers is transferred to the infrared radiation. A known molecular19
absorption line serves to calibrate the frequency axis to make the frequencies absolute. These
components are described in great detail in other thesis and papers, but for completeness, I
will summarize each piece here.
The frequency stabilization starts with a polarization stabilized HeNe laser. The laser
is semi-homebuilt with a purchased laser tube and power supply but assembled here. The
laser lases in two modes with perpendicular polarizations. Since both ends of the laser tube
emit light, one end is sent for use in the experiment and the other output is used for the
HeNe stabilization circuit. The HeNe light is sent through a polarization beam splitter sothat each polarization, hence each mode, is sent to a detector. The subsequent signals fromthe two detectors are sent to the locking circuit where the signals are divided. This creates anerror signal which the circuit uses to lock on and the error is zero when the two polarizationsof the laser have equal magnitude. The laser tube is wrapped in heater tape, which willchange the tube length when heated enough to change the relative intensities of the two
HeNe modes. The HeNe is set to lock at equal magnitudes of both polarizations.
The output of the stabilized HeNe is split with one part sent to a Fabry-Perot cavity(a.k.a. marker cavity or optical transfer cavity)[31] and the other sent to a wavemeter. The
marker cavity consists of two mirrors with a 30 cm focal length that are mounted to a 30 cm
long cylinder consisting of two sections of pyrex glass, a section of stainless steal wrapped inheater tape, and a piezo section. The light is aligned in a bowtie conﬁguration, preventing
feedback into the laser. The free spectral range of this cavity is ≈ 250 MHz. The cavity
is locked to a peak of a HeNe transmission fringe using a “top-of-lock” method with thenecessary small 4.4 KHz dither applied to the piezo. The feedback has a fast, proportional
response delivered to the piezo, on top of the dither, and a slow, integrated response sent
to the heater tape. The cavity length changes to maintain a constant optical path lengthand compensate for changes in temperature and pressure that may occur. The locked cavity
is stable to better than a few MHz over the course of days. This stable cavity provides
the necessary optical tool for being able to stabilize the Ar+ laser and track the dye laser

20
scanning frequency.
A pellicle beam splitter sends ≈ 5% of the Ar+ and dye laser beams to all of thenecessary diagnostics and locks; speciﬁcally the wavemeter, marker cavity, commercial FabryPerot interferometers, and the dye laser lock (dye laser only). Starting with the Ar+ laser
lock, the Ar+ beam is overlapped with the HeNe directly before entering the marker cavity
and a photodiode records the transmission of the Ar+ through the cavity. The locking circuit
here is also a “top-of-line” lock with the same dither signal modulating the cavity for thecavity lock is used to create the error signal for the Ar+ laser. The circuit works to keep
the Ar+ laser lasing with a frequency that corresponds to the peak of a transmission fringe
through the marker cavity. The feedback is in the form of a voltage sent to the piezo mounted
on the back of the Ar+ high reﬂector mirror.
In addition to locking the dye laser and monitoring the scanning, it is necessary todetect when the dye laser mode hops. To detect mode hops, we employ a time-to-amplitude
conversion technique (TAC). We map the change in frequency to make sure it is a linear
function in time so that mode hops become easily recognized as a change from the linear
plot. To accomplish this, we send the dye laser light into the commercial Fabry-Perot cavity
that is changing length in a sawtooth pattern. There is a photodiode at the output of thecommercial cavity that monitors the signal of the laser through the cavity. The TAC signal
measures the time from the start of the FPI ramp until the signal reaches a certain voltage
threshold, corresponding to the presence of a fringe. As the laser scans, the fringe position
relative to the start of the ramp changes, creating the linear function mentioned earlier.
While the FPI is commercial, the ramping and TAC electronics are homebuilt.
The ﬁnal optical piece of the instrument is a homebuilt wavemeter. The wavemeter, a
traveling Michelson interferometer that uses the locked HeNe as a reference, is described indetail in Scott Davis’s thesis[24]. The wavemeter is used to take the starting frequency of thescan, which is always set to be to top of a marker cavity fringe. While not used for absolute
frequency measurements, the wavemeter reading is used to be able to compare marker cavity

21fringes, described fully in Erin Whitney’s thesis[25] and summarized in section 3.6.
2.4

Radical Generation
The speciﬁcs of creating each of the radicals presented in this thesis are found in thechapter pertaining to that radical. However, the same pulsed nozzle, discharge, and vacuum
chamber setup are used and will be described here for completeness. The neutral precursor
is prepared in a holding tank with a buﬀer gas, usually Ne70 (i.e., 70% Ne, 30% He) witha ﬁnal concentration of about 5% precursor. The buﬀer gas choice is important to balanceeﬃcient cooling while minimizing the formation of clusters in the jet[32] and Ne70 is the gas
used in most of the experiments presented here. The buﬀer gas and precursor mixture isfurther diluted to typically ∼ 1.0% in Ne70 using mass ﬂow controllers to regulate the gas
ﬂow into the slit stagnation region.
The slit valve is a JILA-made solenoid-driven pulsed injector with a 4 cm by usually
a 300 µm slit oriﬁce operating at a 19 Hz repetition rate and about a 1000 µs duration.[33]The pressure in the stagnation region is maintained at usually anywhere from 200 - 1000
Torr, with the vacuum chamber kept at < 50 mTorr during operation of the pulsed valve, bya Roots blower (560 liters/sec). During the pulse, a 50 KHz, 50% duty cycle, high negative
voltage (up to -1 KV relative to the nozzle body), high current pulse is applied to the jawsof the nozzle. The jaws are attached to an Ultem insulator, which is attached to the main
body of the nozzle. When the pulsed current is applied, a discharge strikes between thejaws and the main nozzle body. Since the jaws form the limiting oriﬁce of the expansion
and the distance between the jaws can be changed, the slit width is easily adjustable. Lockin detection with double balanced mixers is used to phase sensitively detect concentration
modulation of the radicals produced in the pulsed discharge, thereby greatly minimizing
spectral congestion due to absorption by precursor molecules. Typical rms noise levels are
0.003% in a 10 KHz bandwidth.

22
2.5

Data Acquisition and Processing
The computer program that collects the data is the same program that controls thedye laser scanning. It is written in LabWindows and employs two analogue-digital (A/D)
cards, NI6110 and NI6025E. The triggers that control the pulse valve and discharge are also
generated by the LabWindows program and sent to the respective electronic controls via theNI6110 A/D card. The signal from the lock-in detector is recorded via the NI6025E card.
All of the frequency diagnostics are sent to the computer via the NI6110 card and include
the IR power from the signal detector, the TAC, the dye laser marker cavity fringes, andthe wavemeter readings. The data is recorded coincident with the valve pulse and can beaveraged for any number of pulses the user wishes to specify. The signal is treated slightly
diﬀerently in that it goes through a gated integration process before being averaged overthe speciﬁed number of valve pulses. Brieﬂy, the gated integration process involves a time
average of the signal while the valve is open and an average of a baseline before and after
the gas pulse. The baseline averages are then subtracted from the signal average. This
will correct for the possibility of a rolling baseline and decrease the noise as a result of theaveraging. To approximate the reduction in noise from the gated integration process, justcombine the idea that averaging reduces the noise by √1N , where N is the number of points
averaged, and then propagate the error through the subtraction of the gated regions. The
result of this calculation is that the speciﬁc noise reduction is√1
1 2
σ ′ = σ ( √ )2 + ( √
)
Ns
2Nb

(2.3)

where σ ′ is the new standard deviation of the noise, σ is the noise before averaging, Ns is
the number of points averaged for the signal, and Nb is the number of points in each baseline
gate. The time bin for each of the data points is 1 µs. After the gated integration process,the value of the signal at that point is recorded along with the diagnostics.
The LabWindows data acquisition program stores all of the recorded data as one long
string of numbers for each individual scan. The numbers must be converted from bits to23% absorbance (or voltage for the etalon and TAC signals) as a function of frequency. This
process was described in Erin Whitney’s thesis, but since then the code has been moved toOrigin’s LabTalk language (a C-based language) and C, however the concept of how the axis
is obtained is the same. First, the long string of numbers is broken up into columns of thesignal, etalon, TAC, and IR power as a function of data point number. The scan parameters
are recorded on a separate spreadsheet, called scanlist, and include the wavemeter reading
for the start frequency of the dye and Ar+ lasers. The dye laser marker cavity fringes arecounted and peak positions as a function of data point number are found using the Snyder
peak ﬁnder algorithm[34]. The signal is turned into a % absorbance measurement by dividing
out all sources of gain (A/D gain, gain on the lock-in ampliﬁer, etc) and dividing by the IR
power.
One scan is used as the reference scan, speciﬁcally the reference scan provides the fringe
number that will be labeled as 10000 so that all other fringes taken that day can be assigned
a fringe number relative to 10000. The start frequency of each scan, which corresponds to the
top of an etalon fringe and is the average of ten wavemeter measurements, is subtracted fromthe reference scan start frequency and divided by the free spectral range. The result of thisshould be an exact integer number of fringes. Since we are using experimental measurements,
it will not be exact but should be within about 5% of an integer (ie ± 0.05). Each starting
fringe now has a relative fringe number assigned to it. A new frequency axis is then createdby using the etalon peaks numbers and linearly interpolating between fringes to assign afractional fringe number to each data point. The free spectral range is then used to convert
the fractional fringe number axis into a relative frequency axis, in GHz. At this point,
all of the scans now have a relative frequency axis such that frequency diﬀerences between
absorbance peaks in diﬀerence scans are precise to < 10 MHz or so. The Snyder peak ﬁnder
is used to ﬁnd the frequency of a known absorption line, which is used to convert the relative
frequency axis to an absolute wavenumber axis. Speciﬁc absorption lines used for eachproject are found in the chapter about that project. On the scanlist sheet, the frequency

24of the start and end point for each scan to be added to the concatenated data is entered.
The scans are then combined into one long spreadsheet, or concatenated, and converted toabsolute wavenumbers. The frequency reproducibility usually has a root-mean-squared valueof about 5 MHz.

Chapter 3
A new high-resolution spectrometer for the study of radicals and ions3.1

Introduction
Transient species, such as radicals and ions, play an essential role in a range of chem-

ical systems including atmospheric chemistry, combustion, interstellar chemistry, molecularbiology, pollution processes, and chemical vapor deposition[35]. For example, the chemistryof the interstellar medium involves a variety of ions that, while often short-lived on earth,
are long lived in the conditions found in space[36]. These ions are formed by a variety ofprocesses including particle collisions, UV radiation, or even cosmic rays. Once formed, ionstake part in many reactions, in spite of low concentrations, in part because ion-neutral reactions have no reaction barrier and there are attractive forces between the particles. By
way of an example, H3 O+ is predicted to be one of the more abundant polyatomic species ininterstellar dust clouds and is a key ion for oxygen chemistry. The dissociative recombination
reaction, H3 O+ + e− → OH + H2 O, produces OH, which can react with O to form O2 . In
addition to CO, models predict O2 and H2 O to be the dominant oxygen-containing molecules
in interstellar clouds. Unfortunately, it is often diﬃcult to directly observe O2 and H2 O inmuch of the interstellar medium because of interference from the Earth’s atmosphere, making H3 O+ ion a useful probe of interstellar H2 O and O2 dynamics and concentrations. The
mid-infrared is an especially useful region for probing interstellar chemistry because it is not
limited to studying molecules with permanent electric dipole moments, like the microwave
region, and has less atmospheric interference than the ultraviolet region. Another recent

26
motivation for developing high resolution systems has stemmed from a desire to accurately
measure the Boltzmann constant using molecular transition line proﬁles, which also requires
high accuracy and precision[37, 38]. Additional uses of the mid-IR include remote sensing
applications[39, 40], molecular spectroscopy, and various industrial applications.
The tools used to study the mid-IR region evolved as new and better technology was
introduced. One of the older technologies for creating tunable infrared (IR) light is the color
center laser. While useful, these lasers have a limited tuning range and are experimentallychallenging and delicate. By way of example, the crystals are very hygroscopic and lightsensitive and therefore must be keep under high vacuum, cooled by liquid nitrogen, andaway from light[41]. Another relatively old technology is the use of a continuous-wave (cw)tunable dye lasers. To access the IR region, dye lasers are generally combined with diﬀerence
frequency generation to reach in the mid-IR. Dye lasers are very reliable, but since the gain
medium is liquid, there are some inherent instabilities. Solid state gain mediums are reliable
way to gain stability; lead salt Diode lasers are are possible alternative, but are limited by arelatively small tuning range. Quantum cascade lasers (QCL) are another type of solid statelaser, however currently most QCL’s have a limited continuous tuning range, usually on theorder of several tens of wavenumbers. The external cavity quantum cascade lasers can haveup to 250 cm−1 tuning range, but compared to a 1500 cm−1 tuning range of a dye laser, it
is still quite small[42, 43, 44].
For a versatile high-resolution system with a large continuous tuning range, dye or
Ti:Sapphire lasers, which lase in the visible (the most stable dyes) and near-IR, respectively,
are still the only way to get the large continuous tunability. The best dyes, both for stability
and conversion eﬃciency, lase in the visible and the Ti:Sapphire lases in the near-IR region.
This necessitates the use of a conversion medium to generate light in the mid-IR region.
Miller and coworkers have used Raman stimulation of a gas cell to create mid-infrared light,
but the resolution of that is limited to 200 MHz[45]. The most common way to generate cw
mid-IR light is through diﬀerence frequency generation, ﬁrst implemented for high resolution

27
spectroscopy was ﬁrst reported by Pine et al. in 1974. They mixed a single frequency argon
ion laser with a tunable dye laser in a lithium niobate crystal to create mid-infrared light[26].
Since then, many variations of this have been implemented by groups around the world andincluding the other high resolution spectrometer in the group. The choice of nonlinear crystal
depends upon the desired wavelength region with lithium niobate and AgGaS2 crystals being
the most common until periodic poling of lithium niobate, the advantages of which will be
discussed in section 3.2.1, became a readily available alternative[46].
As a goal of building a new instrument for doing high-resolution spectroscopy in the
mid-IR on many diﬀerence molecular systems we look for i) a large, continuously tunablefrequency range in the mid-IR, ii) frequency precision and accuracy of 10 MHz or better, iii)
an improvement in speed and ease of data acquisition, iv) high detection sensitivity, and v)
ability to create relatively large concentrations of radicals and ions. By way of comparison,
the experiment occupying the other half of the lab satisﬁes most of these requirements,
however it cannot reach the lower frequency region including the OD stretching region anddata taking is still a very slow and manual process. Additionally, the Ar+ and dye lasers
are notoriously unstable and diﬃcult to work with. To our knowledge, there are two other
Ti:Sapphire and YAG DFG systems, but published about the same time, in 2008, for sensing
applications[47, 48] and measuring the Boltzmann constant[49]. They utilized much more
complicated methods to stabilize their YAG laser and were limited by the stability of theTi:Sapphire laser, but still achieved similar resolution to what is reported here. However,their system lacks the scanning infrastructure to scan continuously for long distances andthey are setup to only look at Doppler-limited neutrals. The system presented here is uniquein combining the laser system, with the sub-Doppler radical and ion generation system, withthe machinery for extended and automated continuous scanning.
The instrument presented here does direct absorption spectroscopy using a straight28
forward application of Beer’s law
A = − ln

I
= Nlσ
I◦

(3.1)

where A is the absorbance, I◦ is the initial amount of light sent to the sample, I is theintensity of light after it goes through the sample, N is the number of absorbing moleculesin the sample, l is the pathlength, and σ is the absorption cross section. From this equation,
we see there are two ways to increase in the absorbance signal. Since σ is a property of themolecule, we cannot change that, however we can increase the number of molecules and thepathlength. The slit discharge setup generates radicals and ions in high concentrations andthe Herriot cell and 4 cm long slit increases the pathlength considerably. These concepts
have been used before, including in the other high resolution spectrometer in the group, andare well established as a reliable way to look at radicals and ions.
What separates this spectrometer from its predecessors is most notably the fast andautomated scanning; there are also other improvements including an extended frequency
range, diﬀerent method of obtaining the frequency axis, and the use of solid state lasers
providing a more stable setup. The infrared light is generated by diﬀerence frequency generation in a periodically poled lithium niobate crystal between a Nd:YAG laser and a tunable
Ti:Sapphire laser. A schematic of the experiment is shown in ﬁgure 8.5. The laser system
is described in section 3.2 with the infrared generation described ﬁrst in section 3.2.1 andthe the description of the scanning system in section 3.2.2. The method of accurately andprecisely determining the frequency axis is described in section 3.3 and the molecular sourceand y-axis determination in section 3.4. The data acquisition process and the data processing are described in sections 3.5 and 3.6, respectively. Results from the HD2 O+ test system
are in section 3.7.

29

Figure 3.1: Optical layout of the high-resolution spectrometer. The radiation from a tunable Ti:Sapphire laser is overlapped with the single-frequency light of a Nd:YAG laser in aperiodically poled lithium niobate crystal (PPLN) and via diﬀerence frequency generation
to produce the mid-infrared light. The frequency axis is precise to 10 MHz.

3.2

Laser System

3.2.1

Infrared Generation

The tunable mid-IR light is created through diﬀerence frequency generation using thetunable Ti:Sapphire laser and a single frequency Nd:YAG laser. The Ti:Sapphire laser is avertical ring cavity with most optics mounted directly to an Invar bar for length stability.
The gain medium is an on-axis pumped Titanium-doped sapphire crystal and the pump30
laser is a 6-Watt Coherent Verdi (Nd:YVO4 ) laser. The Ti:Sapphire crystal has a very broad
tuning range (≈ 720-1000 nm) and with this laser requires three sets of optics to cover theentire tuning range; however it is worth noting that there are now optics available that cover
the entire tuning range, which would be a nice upgrade at some point. With a ring laser
design, it is necessary to have an element in place to promote lasing in only one direction,in this case there is an optical diode in the beam path, which uses optical activity and the
Faraday eﬀect, to achieve unidirectional lasing. Single frequency operation achieved withthe combination of a birefringent ﬁlter and two intracavity etalons, similar to the dye laser
described in chapter 2.
The single-frequency laser is a commercial diode pumped Neodymium-doped Yttrium
Aluminum Garnet (Nd:YAG) laser. The basic operation and design is documented in the
manual and will be brieﬂy summarized here. It is a non-planar ring oscillator design, in which
the laser cavity is conﬁned to the Nd:YAG crystal with the cavity mirrors being the polishedsurface of the crystal exploiting either total internal reﬂection or a reﬂective coating. The ring
conﬁguration is made unidirectional by applying a magnetic ﬁeld to the crystal to create aneﬀective optical diode thereby increasing the gain in one direction such that the laser doesn’tlase in the other direction. The laser has a small amount of tunability by changing the crystal
temperature and straining the crystal by way of an attached piezoelectric element. We use
the laser at a single frequency and exploit the tunability features to keep the laser frequency
locked and stabilized, described in detail in section 3.3.
The single frequency Nd:YAG laser overlaps the Ti:Sapphire laser and is sent into thenonlinear crystal for diﬀerence frequency generation. The amount of mid-infrared radiationthat we get out is directly related to amount of light pumping the crystal as well as thequality of overlap of the beams. To insure good spatial overlap, two iris have been placed in
the beampath, on right after the lasers are combined and after the crystal as far down thetable as possible, and both the YAG and Ti:Sapphire lasers are aligned through the irises.
The IR power is also increased by focusing the pump beams in the crystal, to increase the31
power density, and have the beams tightly focused for the entire length of the crystal. The
Rayleigh range is the propagation distance, z, necessary for the beam width to increase from√
ω0 to 2ω0 . The optimum beam proﬁle as the lasers travel through the crystal is going to be
a compromise between a tight focus and long Rayleigh range. Additionally, the beams fromthe two laser are diverging at diﬀerent rates so to get a good spatial overlap it is necessary
to add in a lens or set of lenses. Using the ABCD law, we calculate a solution to not only
make the beams have the same mode, but make it a good compromise between having atight focus and long Rayleigh length. In this case, it is only necessary to add one lens to the
YAG beam path to suﬃciently match to proﬁle of the Ti:Sapphire laser.
The nonlinear crystal used here is a periodically poled lithium niobate crystal, whichtakes advantage of quasi phase matching to generate the mid-IR radiation. To start witha physical picture of diﬀerence frequency generation, the radiation incident on the crystal
causes the charges to accelerate and those accelerating charges generate electromagnetic
radiation. Mathematically it is common to use polarization to describe nonlinear opticalprocesses, which is simply that a polarization changing with time can drive an electromagnetic ﬁeld[50]. More speciﬁcally for diﬀerence frequency generation, incident radiation causes
an oscillating dipole moment with components at each incident frequency with a nonlinear
response. This time-varying polarization can act as a source of new components of the electromagnetic ﬁeld, in this case the diﬀerence frequency. From a mathematical perspective,
the polarization as a function of time is expressed as
→
−
−
→
−
→
→
−
P (t) = ϵ◦ [χ(1) E (t) + χ(2) E 2 (t) + χ(3) E 3 (t) + ...]

(3.2)

−
→
−
→
where P (t) is the time-varying polarization, E (t) is the electromagnetic ﬁeld and χ is thenonlinear optical susceptibility. In a material with only a linear response, the expansion
is truncated after the ﬁrst term and we see that polarization is directly proportional tothe applied electric ﬁeld. The second order term is the nonlinear response that describes
diﬀerence frequency generation. The χ(2) is tensor for materials, but can be simpliﬁed to a

32
3 x 6 matrix for most materials because of the inherent symmetries present in the crystal(2)

lattice such that dil = ( 12 χijk ) where i, j, k are indices and l = j + k. Any given material
will have many dipoles oscillating with the phase of the incident ﬁeld. With correct relative
phase, the radiation produced by each dipole will constructively add and the system will act
like a phased array of dipoles and output radiation, which is described mathematically as
−
→
−
→
−
→
the phase matching condition, k 3 = k 1 + k 2 and is also conservation of momentum. The
other condition necessary for a nonlinear process is one that conserves energy, ω3 = ω1 + ω2 .
By satisfying both the conservation of energy and conservation of momentum conditions, we can describe diﬀerence frequency generation. By writing the magnitude of the
wavevector as nω/c and substituting it into the phase matching condition, an apparent contradiction appears: n3cω3 = n1cω1 + n2cω2 and it seems that phase matching can only occur if
the index of refraction is the same for all wavelengths of light, which is not the case. The
reason this is not a problem is that phase matching occurs in birefringent materials, materials where the index of refraction varies with direction in the crystal. This allows light with
diﬀerent polarizations and/or directions through the crystal to experience diﬀerent indicesand satisfy the phase matching condition. Lithium niobate has a temperature dependant
index of refraction so as the frequency of radiation changes the phase matching condition
can continue to be met by changing the temperature of the crystal. Birefringent phasematching is doable and still commonly used, but it is much easier to use a process called
quasi-phase matching whereby the strict condition of phase matching doesn’t need to be
met. In a material like periodically-poled lithium niobate, the properties of the crystal havebeen periodically reversed so that while the phase is mismatched it is periodically reversed tomismatch the phase in the other direction, thus allowing the light to propagate without perfect phase matching. The poling period is made speciﬁcally for a certain set of wavelengths
and corresponds to the length of crystal at one orientation before it is switched.
Because of the wide tuning range of the Ti:Sapphire laser, we have 3 PPLN’s of 7
poling periods each in order to cover most of the frequency range reachable by the laser.

33
Experimental tuning curves for one of the PPLN crystals is shown in ﬁgure 3.2. The LiNbO3
crystals used here are actually doped with MgO to make them less absorbent at the lower
infrared frequencies. The necessary poling period to generate IR light from any given input
beams is calculated using the Sellmeier equation, which calculates the index of refraction
for a given temperature and involves parameters that are ﬁt experimentally[51, 52]. The
standard expression ﬁnds the index of refraction, ne at a given temperature, T , and a given
wavelength, λ,n2e (λ, T) = a1 + b1 f(T) +a2 + b2 f(T)
a4 + b4 f(T)+2
λ − (a3 + b3 f(T))λ2 − a25(3.3)

where the temperature dependence, in Celsius, enters throughf(T) = (T − T◦ )(T + T◦ + 2 × 273.16)(3.4)

where T◦ is the reference temperature, 24.5◦ here. The other parameters are numerically ﬁtfrom experimental data and can be found in Jundt et al.[51] Once the index of refraction foreach wavelength is calculated at a given temperature, the poling period is easily calculatedusing the phase matching condition or quasi-phase matching:∆k = 2π(

np ns ni1−− − )=0λp λs λi Λ

(3.5)

where np is the extraordinary index of refraction for the pump wavelength as calculated
above and ns and ni are the corresponding values for the signal and idler, respectively. The
poling period needed to satisfy this condition is Λ. The experimental tuning curves for oneof the PPLN crystals at three diﬀerent temperatures is in ﬁgure 3.2. This calculation doesn’t
indicate the eﬃciency of the conversion process. The commonly used expression[53] for theconversion eﬃciency for a diﬀerence frequency generation process isPi =4ωi2 d2eﬀ l2 Ps Pp
np ns ni c3 πϵ◦ (ωs2 + ωp2 )(3.6)

where ωi is the frequency of the idler beam frequency; Ps and Pp are the signal and pumpbeam powers, respectively; ns , np , ni are the appropriate refractive indices for each of the

34signal, pump, and idler beams; l is the length of the crystal, 4 cm here; and def f is the
2π/d33 .

13000

-1

-1

Ti:Sapph Frequency (cm )PPLN #1 Tuning Curves, YAG Frequency= 9394 cm

pp1

12500

pp2
pp3
pp4
pp5
pp6
pp7

12000

11500

100

120

140

160

180

200

PPLN Temperature ( C)

Figure 3.2: Experimental tuning curves for one PPLN. There are three PPLN’s, each with
7 separate poling periods, necessary to cover the full tuning capability of the Ti:Sapphirelaser.

Upon exiting the crystal, the infrared radiation is split into two approximately equalparts, with one portion directed into the liquid-nitrogen cooled InSb reference detector. The
other portion is sent into the vacuum chamber, through a 16-pass Herriot cell before exiting
the chamber and subsequently focused onto the liquid-nitrogen cooled InSb signal detector.
A Herriot cell increases the pathlength of the absorption while probing the center of the slitjet and maintaining a focused laser beam. The Herriot cell consists of two 2” gold mirrors
spaced twice the radius of curvature apart. In this case, the radius of curvature of the

35
mirrors and subsequent size of the Herriot cell is limited by the available vacuum chamber
to be 20 cm, making a 40 cm long cell. The beam enters the cell just below one of themirrors through a CaF2 window, the bottom right of the cell. The beam should be focusedat this point in order for it not to clip the underside of the mirror as it passes through on
the way to the diagonally opposite corner of the other mirror. Upon hitting the top left ofthe mirror, the beam heads to the bottom right of the ﬁrst mirror, just above where thebeam passed through the ﬁrst time. The beam is passed back and forth in this way so as
to make an upside-down U pattern on the mirror by the CaF2 window and a right-side up
U on the other mirror. Figure 3.3 panel a) shows a schematic of the laser beam pattern oneach of the mirrors. At the center of the cell, the beams pass each other in a narrow region
where the 4 cm-long jet of molecules is. The 16 passes through the 4 cm of gas makes for
64 cm for an absorption pathlength. In an ideal design, the laser beams would pass straight
through the slit of gas, at a constant distance from the slit oriﬁce. However, because of thegeometry of laser beams passing through the Herriot cell, the laser beams actually come inat slight angles from the jet. The larger the Herriot cell, the better the approximation thatthe beams pass straight through the gas jet. In a 40 cm cell such as this one, the deviationfrom this linear approximation is signiﬁcant and is the major cause of line broadening in theexperiment. Based upon the geometry, the total vertical span of the jet probed at the ends
is about 7.5 mm and the horizontal span is 2.5 mm. A place for future improvement could
be to extend the arms of the Herriot cell to be 60 or more cm apart.
The second aspect of the Herriot cell involves the focus of the beam due to the curvatureof the mirror. The radius of curvature of the mirror is set to be half the distance between
the two mirrors. Using the ABCD law of Gaussian optics, we simulate what the beam sizefor each pass at one of the mirrors and the center of the cell. Figure 3.3 panel b) shows theresults for a simulation based upon placing the mirrors exactly twice their radius of curvature
apart. While the beam size at the center of the cell, where the slit jet is, remains small the
beam size at the mirror blows up. This is undesirable because after a few passes the light

36

a)

Back Mirror

Front Mirrorb) Mirrors 60 cm apart

20

Front Mirror
Center of Cell

Spot Size (cm)

10
0
4

0

20

40

c) Mirrors 59.3171 cm apart

3
2
1
0
0

20

40

Number of Passes

Figure 3.3: Properties of a Herriot cell. Panel a) is a schematic of the U-shaped pattern of
the laser beams on both the front and back mirror of the Herriot cell. Panel b) plots thebeam spot size as a function of pass number both at the center of the cell and on the front
mirror of the cell for a mirror spacing exactly equal to twice the radius of curvature (60cm).
Since the spot size at the front mirror is continually expanding and will likely not cleanly
exit the cell. Panel c) illustrates the optimal mirror spacing so that the exit beam is smallenough to easily exit the cell without clipping the mirror.

37
wouldn’t ﬁt on the mirror and it would be hard to direct the beam out of the cavity without
it clipping on the mirror. Panel c) of ﬁgure 3.3 shows the calculations for the scenario where
the mirrors are moved 0.687 cm closer together. Now the beam stays relatively focused at
the center of the cell as well as on the mirror. It is advantageous to have the mirrors at
such a distance apart that the beam is most tightly focused as it is exiting the cell because
it maximizes your ability to get the beam cleanly out of the cell. Once the light exits the
Herriot cell, it is focused onto a liquid nitrogen cooled InSb detector.
An important feature of this spectrometer is how sensitive it is, for which the shot noiseon the detectors provides the ultimate lower limit of the detection sensitivity. The amountof IR light generated depends upon the powers of the Ti:Sapphire and YAG lasers on a given
day at a given frequency, in addition to things like quality of the alignment, therefore theamount of light generated has some variation. On a typical day, we might have 2 volts of IR
light on the signal detector. The IR detector has a 100 kΩ transimpedence ampliﬁer followedby an ampliﬁer with a gain of 1, which translates to 20 µA of current. The shot noise on this√amount of current is given by 2ie, where i is the current and e is the charge of an electron.
A typical shot-noise absorbance sensitivity is 2 × 10−5 in a 10 kHz bandwidth.
3.2.2

Scanning

At the heart of the infrared generation system is a cw Ti:Sapphire ring laser, a commercially available system that includes computer controlled scanning and wavemeter. The
Ti:Sapphire laser operation is discussed in detail in the manual, however it is brieﬂy summarized below before discussion of how the labwindows program controls the scanning. The
Ti:Sapphire cavity is a vertical ring cavity with the pump beam, a Coherent Verdi Nd:YVO4 ,hitting the crystal on axis. The Ti:Sapphire crystal has a broad tuning curve and there arethree sets of optics in order to cover the whole range. A birefringent ﬁlter serves to narrow
the tuning range. Then there are two etalons placed inside the cavity in order to obtainsingle-frequency operation. The free spectral range of the cavity is about 280 MHz. The

38
thin etalon has a free spectra range of 225 GHz and the thick etalon has an FSR of 10 GHz.
A small pick-oﬀ of the laser output split into two parts, one goes directly to a detector andthe other goes through the reference cavity and then into a detector. The reference cavity
serves as the master cavity and the laser as the slave cavity while scanning. The reference
cavity has a quartz plate attached to a galvo. The Autoscan computer sends a voltage to thereference cavity galvo to step the size of the reference cavity. The laser cavity is locked to
the reference cavity, so it adjusts the laser cavity galvos and etalons accordingly. A reﬂection
oﬀ the thin etalon is sent to a detector and used to keep the etalon tracking with the laser
frequency. The thick etalon also tracks with the scanning. The locking controls are locatedin the 899 control box and the scanning controls are part of the Autoscan computer.
The Ti:Sapphire laser also has a wavemeter that is attached to the box and is integral
to the automatic scanning system, called Autoscan. The stated accuracy of the wavemeteris ± 200 MHz and the stated precision is ± 50 MHz; we have a good measure of the accuracy
and are usually better than the stated accuracy and precision, depending upon the quality of
the alignment. The Autoscan wavemeter combines the precise measurement from thermallystabilized etalons with an absolute frequency device to obtain the frequency. The absolutemeasurement comes from an optical activity device (OAM) consisting of a crystalline quartz
piece and a spinning polarizer wheel. The light is sent through the optical axis of two
diﬀerent lengths of the quartz crystal; which causes the polarization to rotate by an amount
dependant upon the length traveled through the crystal and the frequency of the light. The
two rotated beams then go through the spinning polarizer wheel to determine the degree ofpolarization. The polarizer wheel is able to determine the polarization angle to about 0.1
degree or about a part in 103 so by comparing the two beams, with diﬀerent rotations, theaccuracy reaches the ± 2.5 cm−1 level necessary for interpreting the etalon data. The light isalso sent to two Zerodur 10 GHz etalons, stabilized to ± 0.03◦ C. The transmission throughthe two cavities is compared and a precise, but inaccurate, frequency is obtained. By using
the OAM to get an absolute measurement and the VET measurement to add precision to39that number, the wavemeter obtains a precise and accurate frequency reading. The frequency
reading from this wavemeter is used for the automatic scanning function, which makes thislaser so nice for scanning large amounts of data quickly.
In order to understand how we obtain a high quality x-axis it is necessary to understanda little about how the Autoscan scans. Figure 3.4 illustrates the logic of Autoscan and how
the rest of the experiments ﬁt in. Autoscans starts by moving the laser to the desired startfrequency and reading the frequency to verify that it is at the correct start frequency. You
can specify how large or small a tolerance you would like on this frequency reading, butsince the accuracy and precision of the wavemeter is 100-200 MHz, it is not meaningful tospecify a tolerance less than that; 100 MHz is usually suﬃcient. After the laser is at thedesired frequency it step-scans 10.2 GHz, the step-size is ﬂexible and speciﬁed by the user.
The laser takes steps by changing the voltage on the galvo; it does not read the frequency
during the 10.2 GHz scans but rather relies on a linearization calibration. This calibration
is imperfect and has systematic deviations from linear by several MHz and is something wewill have to correct for. After the laser has scanned the 10.2 GHz segment, it adds 10.2
GHz to the desired starting frequency and attempts to move the laser to that frequency. It
adjusts the laser until the frequency the wavemeter reads is within the speciﬁed toleranceof the speciﬁed frequency. This has a few important consequences. The ﬁrst consequence isthat if one segment is oﬀ for some reason, that error is not carried over into the rest of thescan. The second consequence is that the laser is resetting itself many times during a scan,so the wavemeter correction needs to be quick and reliable enough to do it numerous times
during each scan. A scan will continue for how ever many segments the user speciﬁed. Moredetails on how we correct for this are found in the following section.
3.3

Frequency Determination
The heart of the precision of the frequency axis is a home-built polarization-stabilized

helium neon laser (HeNe) based upon the design of Niebauer et al[54]. The HeNe laser

40

Experimental Layout
Enter startfrequencyoncomputer

19 Hz
trigger fromcomputer

Autoscanis ready
Computeris ready

Pulse
delay

Step
frequency
10 MHzSolenoid
driver forpulsed valve

Modulate
pulse with
50 kHzSignal!

Gated
integration

Acquiresignal

A/D computer

Repeat for10.2 GHz

Autoscansteps back0.2 GHzand
repeats

Repeatuntil laser
hasscannedspecifiedregionSolenoidSignalInSb
Modulateand pulse
high voltage

Lock-indetector

Jaws

Subtractor

Reference
InSb

Figure 3.4: Illustration of the timing of the Autoscan (in blue) and the data acquisition
sequence (green).

starts with a commercial tube powered by a partially home-built power supply. This HeNelaser has enough gain to support two simultaneously lasing modes, but only enough gain to
support those two modes in perpendicular polarizations. Because of the HeNe gain curve
and the mode spacing of the laser, only one mode of each polarization is present. The way
we achieve a stabilized frequency is by matching the relative intensities of the two modes.
This works because as the frequency of the modes change, they move along the gain curve,
and the relative intensities change. We exploit this by making the relative intensities of thetwo polarizations equal. To do this, at one output of the HeNe is a polarizing beamsplitter41
with the two subsequent beams sent to photodiodes. The signals from the two photodiodes
are subtracted and locked such that the subtracted signal is zero. A piece of heater tapewrapped around the HeNe tube provides the feedback for the locking system in order tomaintain a zero subtracted signal. Once the HeNe is stabilized, it is used to provide a stablesource to lock the cavities needed in the rest of the instrument[31].
To correct for both the nonlinearity in scanning and the inaccurate and imprecise
frequency readings of the Autoscan, we adopted a two cavity solution. At the start of eachsegment the Autoscan wavemeter sets itself to within ± 100 MHz of the desired starting
frequency for that segment and starts to step-scan. As the laser scans, we record the inference
fringes of the Ti:Sapphire laser output through two locked bow-tie confocal cavities, one with
an approximate free spectral range of 1.5 GHz and the other with about a 250 MHz free
spectral range. Since we don’t have control over where each segment begins, we are not able
to always start on the peak of the fringe, which is not an issue with the two cavity method.
The frequency determination can be quantiﬁed with propagation of error calculations. Each
Autoscan wavemeter reading has an error, based upon the speciﬁcation, of 200 MHz; thiserror is usually less than the speciﬁed error and can depend upon how well the wavemeteris aligned and calibrated. This means that every time Autoscan reads the frequency there
is an error of 100 MHz, which is too large for high-resolution spectroscopy. Additionally,
if we wanted to stich together scans the way the old spectrometer does, with a 250 MHz
cavity, we would likely make fringe assignment errors every few segments; since we scan tensof segments a day, this is an unacceptable number of errors.
To get around the limitations of the Ti:Sapphire wavemeter while making full use of
the automated scanning, a two cavity solution is used. Complete details about the design
and implementation are in chapter 8. In short, a locked 1.5 GHz FSR cavity and a locked
250 MHz FSR cavity are used. The wavemeter is accurate enough to assign a fringe number
to the transmission fringes of the 1.5 GHz cavity. The fringe number of the 1.5 GHz cavity
is used to assign a fringe number to the 250 MHz FSR cavity transmission fringes. The 250

42
MHz cavity fringes are then used to stitch together scans. With this method, the frequency
precision is better than 10 MHz. Since the two locked cavities record only the Ti:Sapphiretransmission fringes, and not the mid-IR fringes, it is important that the YAG laser is locked
at a stable frequency.
The 250 MHz cavity is used to stabilize the YAG laser; it is important that the YAG
laser be stable over a day of scanning since the frequency axis is stitched together using
signals from the Ti:Sapphire laser. The YAG laser has a good internal stabilization for fast
frequency noise, however in the long term (minutes and hours) the laser frequency drifts.
To correct for this drift, the laser is locked to the 250 MHz cavity. Because the error thatneeds correcting is just the slow error, the servo-loop has only a integrated error signal; thisis in contrast to the cavity locks, which have proportional and integrated errors. The lock
takes advantage of the dither already being applied to the cavity by using the dither signal
as the local oscillator input on a double balanced mixer, with the signal from the silicon
photodiode as the input. The error signal is then integrated to provide the feedback to thelaser. The laser response is 12 GHz/Volt, so only mV’s are needed to correct for the errors.
A signal on the order of a few volts is sent to a voltage divider, which is attached directly tothe laser control box, to attenuate the signal to give a reasonable change in frequency. Thiseliminates the problem of sending very small voltages along a long wire, which could easily
pick up noise of that magnitude along the way. More details of this lock are in chapter 8.
This lock is stable over a single day of scanning.
As an added check of the absolute frequency, there is a room temperature reference cell
to record a spectra of any reference molecule in the mid-IR in real time. Figure 3.5 showsa small section of a scan with the 1.5 GHz cavity, 250 MHz cavity and the reference cell.
The mid-IR used for the reference cell is just the small amount reﬂected oﬀ of the visible
light ﬁlter just before the reference/signal beamsplitter. Depending upon the gas used, thecell has three diﬀerent pathlength options. The cell has sapphire windows and is followed
by a commercial chopper just before the liquid-nitrogen cooled InSb detector. The signal

43from the detector is passed through a lock-in detector with the reference frequency of thelock-in is the chopper frequency. This signal is recorded along with all of the other scandiagnostics of the NI-6025E card. With proper choice of reference gas and pressure in thecell, this provides a Doppler-limited room-temperature spectra of a well known reference gas
while scanning to have a valuable check of the frequencies.
The instrument also has a commercial Bristol wavemeter used to check and calibrate
the Ti:Sapphire wavemeter and provide the YAG laser frequency. A small amount of YAG
and Ti:Sapphire light is sent to the wavemeter. Because this model of wavemeter can only
read one frequency at a time, there are ﬁlters to either block just the YAG or block just theTi:Sapphire. The light is then coupled into a broadband ﬁber and coupler and sent to thewavemeter. This allows either frequency to be read at any time during the scan without any
disruption of the scan. The Autoscan wavemeter needs periodic (monthly) calibration toremain accurate, so having a quick way to complete the calibration process as well as a daily
check of the accuracy is necessary. At present, the wavemeter interfaces with a secondary
computer and is separate from the data recording process; this is necessary because the main
computer is too old to interface with the new wavemeter. This might be something to change
in the future as it would be advantageous to record the start frequency of the scan with theBristol wavemeter since it is much more accurate and precise than the Autoscan wavemeter.
3.4

Molecular Source
The source of radicals and ions is based upon the designs on the west table with theadditions of some modernization and adaptations. The molecular source is based upon the
JILA-built slit nozzle as in use on the adjacent instrument[55, 33], but there are many
supporting pieces of the instrument that have been modiﬁed, added, and improved before
being implemented in this setup. Large mixing tanks are ﬁlled to usually between 1 and 10% precursor in a buﬀer gas, usually molecular hydrogen or a 70% neon, 30% helium mixture.
The larger of the two welded manifolds is used easily create these tanks and even have

44

Transmissiona) 250 MHz Cavity Fringes

0b) 1.5 GHz Cavity Fringes

0

D O Line
20c) Reference Cavity Signal

2619.62619.82620.0-1Frequency (cm )Figure 3.5: Sample scan showing the frequency diagnostic tools. Panel a) shows theTi:Sapphire laser fringes from the 250 MHz cavity, panel b) shows the Ti:Sapphire fringes
from the 1.5 GHz cavity, and panel c) is the transmission of the IR through the room temperature reference cell with < 5 Torr D2 O.

45several tanks available at one time. The premixed tanks are combined with more buﬀer gas
directly before going into the nozzle stagnation region, thus providing the 0.1% precursor in
buﬀer gas that often provides the best radical or ion signal. To easily change the percentage
of precursor without having to make a new tank, as well as reproduce the same precursor
concentration every time an experiment is run, we use mass ﬂow controllers to regulate theamount of gas from each tank that enters the stagnation region.
The nozzle is completely enclosed in the vacuum chamber, so a single continuous gas
line brings the gas into the vacuum chamber via an ultratorr feedthrough and attaches tothe nozzle using Swagelok. The nozzle is a mirror image of the nozzle in the other chamberand detailed drawings are in several thesis[24, 22, 23] and papers[56, 55, 33]. The nozzle
end has a plate with a 4 cm long slit, most are 500 µm wide, against which the plunger
makes the seal. An Ultem insulator is secured against the plate and has a similar, often
slightly larger, slit cut through it. The two jaws are what actually form the limiting oriﬁceof the slit expansion; they are secured to the insulator and can be adjusted to the desired
slit width. It is the distance between the two jaws, measured and set using metal shims,that forms the limiting oriﬁce for the expansion. The advantage of using a slit, instead ofa pinhole, for the expansion geometry is the expansion is eﬀectively only in one dimension
rather than two dimensions. The laser beam is sent down the axis of the slit, and to a good
approximation for a long slit, the molecules cannot move along the slit axis decreasing the
Doppler broadening of the absorption lines.
While neutral, closed-shell molecules can be studied with the slit jet, we employ adischarge to generate the radicals and ions. The discharge is generated by applying a 50
KHz square-wave voltage to the jaws and since the nozzle is at ground a localized discharge
is created at the slit oriﬁce. The discharge is powered by a 1 kV high voltage power supply,
which sends the voltage to the “oﬀset pulser” where the 2 ms of a 50 KHz square-wave isimprinted on the voltage. The voltage is then sent to a set of ballast resisters before heading
to the jaws. The ballast resisters can easily be switched, but 100 Ω, 200 Ω, and 500 Ω

46
resisters are currently installed. Following Ohms Law, changing the ballast resisters changes
the amount of current sent to the jaws for a given voltage, which even though the current is
the most important indicator of how many radicals or ions will be made, the voltage setting
and ballast choice can eﬀect the stability of the discharge as well as the amount of the target
molecule.
A slit nozzle, even when pulsed, ﬂows much more gas than a pinhole nozzle and consequently is best pumped by a pump that can handle a large throughput of gas. There aresome adjustments to the amount of ﬂow going through the nozzle, they are often made at
the expense of signal, such as shortening the slit length or ﬂowing less gas. The average ﬂow
used for optimum discharge conditions in the generation of radicals and ions is often about
one standard liter per minute (slm). Another way to look at the pumping requirements is
to calculate the average pressure in the chamber during an experiment. The pressure in thechamber is just the gas ﬂow divided by the eﬀective pumping speed. By way of example, for
1 slm of ﬂow (12.7 Torr l/s) and the WS2000 roots blower, which has a pumping speed of 654
l/s, the average pressure in the chamber would be 20 mTorr. This is a good running pressure
for several reasons, for example the pressure is low enough for a supersonic expansion withthe 300 Torr backing pressure in the nozzle and the discharge is nicely localized and stable. It
also allows for an increase in ﬂow without any problem. If we compare that to the option ofpumping with a large turbo pump, which has a pumping speed of 1700 l/s for H2 , a common
buﬀer gas, the pressure in the chamber would be 8 mTorr, which is unfortunately too highfor most turbo pumps. So even though the turbo has a much higher pumping speed, it is
not necessarily the best pump to use for a high gas ﬂow experiment like the slit nozzle. The
gas ﬂow of the nozzle is adjustable, but yield of radicals and ions decreases with decreasing
ﬂow, thus lowering the total signal level.

47
3.5

Data Acquisition
Automation of the instrument is one of the major improvements over the west table

instrument. Even though the nozzles on both tables are pulsed at 19 Hz, dictating how
fast we can take actual data points, the rate of data-taking is also limited by how fast theuser can reset each scan and turn all the knobs that need to be turned. By automating
the scanning and other equipment, it becomes computer controlled and is no longer a ratelimiting step. Automating the system is largely made possible by the addition of a stepper
motor on the birefringent ﬁlter in the laser, electrically controlled tilting of the thin etalon,
and the piezo-controlled thick etalon. These three elements allow electronic control over thefrequency supported by the cavity. The Autoscan setup contains all the code and electronics
to set the laser scanning over an arbitrary frequency distance with the push of a button.
What we have done to automate the entire system is create a LabWindows program that
remotely controls Autoscan as well as most of the other equipment, speciﬁcally the pulse
valve and gas ﬂow manifold, and records all of the relevant data.
The LabWindows program on the main computer communicates with the Autoscan
computer via an RS232 connection. Once the connection is initiated all control over Autoscan
is done through the main LabWindows program. The frequency of the laser is changed bytyping in the desired frequency into the main program. This main program controls thescan parameters, speciﬁcally the scan length and step size, in the form of predeﬁned scan
types; this is necessary because Autoscan needs a ﬁle with all the parameters already on
its computer, so having a set of predeﬁned types avoids the problem of needing to create
a ﬁle with the scan parameters. While the Autoscan computer executes the scan, the hard
work of the scanning is all done by the Autoscan electronics box, which in turn sends info tothe laser control box, which sends the information to the tuning elements in the laser. The
Autoscan electronics box has two trigger and two monitors to control the scanning. Whena scan is started, the LabWindows computer reads the trigger to say Autoscan is ready to48start a segment and then sends an output to signify that LabWindows is ready to scan asegment. This communication occurs each time a new segment is started. Autoscan thensends a signal to say it is ready to take a data point and LabWindows responds by indicating
it is ready to take a data point. All of this communication occurs through BNC cables fromthe NI-6025 breakout box directly into the Autoscan electronics box. The system is thenready to record data.
Once ready to record a data point, after the speciﬁed delay from the trigger, theLabWindows program performes gated integration. It records the average over a speciﬁed
length of both the baseline gates and the signal gate and divides that number by the gate
length. It then takes the signal and subtracts the average of the baseline measurements.
After the signal is recorded, the signal detector voltage is recorded along with the Ti:Sapphiretransmission signal through the 1.5 GHz cavity, the 150 MHz cavity, and the IR referencecell. If signal averaging is being used, it now loops back through acquiring the data andgated integration and averages the values collected. Once all the data acquisition is done fora given data point, the data point signaling between LabWindows and Autoscan repeats,
Autoscan steps the frequency, and the next data point is taken. This repeats for the 10.2
GHz segment length. The communication about the segments is repeated to ready the laser
for the start of the next segment. At the end of a segment, Autoscan changes the laser
frequency to the frequency for the start of the next segment by tilting the birefringent ﬁlter
and the both etalons. The internal wavemeter is used to set the frequency to 10 GHz fromthe start of the previous segment, providing a 0.2 GHz overlap between segments. The scan
ends once the segment loop has gone through the speciﬁed number of segments.
While the main computer and Autoscan coordinate the scanning, there is a whole stringof signals that must be collected and processed to provide the signals eventually recorded
at each data point. The trigger for the pulse valve goes through a homebuilt pulse delay
generater to supply triggers to the pulse valve and the discharge with independent delays.
The pulse valve signal is sent to the solenoid driver box, which sends a large amount of

49
current to the solenoid mounted on the valve and opens the valve, allowing gas to ﬂow.
Simultaneously, the pulse delay generater sends a signal to a modulator box which puts a
50 kHz square-wave on the ﬁrst 2 ms after the trigger. This waveform is then imprinted on
the voltage from a 1 kV high voltage power supply, applied to a set of ballast resisters togenerate the current, which is sent into the vacuum chamber and the jaws of the nozzle. The
amount of current sent to the jaws in controllable by either changing the set voltage on thehigh voltage power supply or by changing the ballast resistors (the current box has 100 Ω
200 Ω and 500 Ω resisters).
In addition to the outgoing triggers, the computer records the absorbance signal, whichgoes through a bit of processing before being recorded on the computer. Both the signal andreference InSb detectors have attached transimpedence ampliﬁers to turn the signal from acurrent into a voltage. The voltages from both detectors are then sent to a subtractor box,
which uses common mode noise subtraction to subtract the signals between the signal andreference detectors. The subtracted signal then goes into a home-built lock-in detector. The
local oscillator for the lock-in detector is the 2 ms of 50 kHz square-wave that was turned
into high voltage and sent to the jaws. Since the signals we are interested in are encodedwith that same waveform, the lock-in ampliﬁer provides a way to look at only the signals weare interested in. The signal from the lock-in ampliﬁer is then sent to the NI-6110 card andrecorded on the computer as described above. The timing and signal ﬂow of the experimentis displayed graphically in Figure 3.4.
3.6

Data Processing
The data as it is recorded by the LabWindows program are in the form of voltages asa function of data point, so there is a bit of processing that needs to happen in order to
get the data to be in terms of percent absorbance as a function of a precise and accurate
frequency axis. After loading the data into the Origin ﬁle, the ﬁrst step is to recreate theaxis according to what Autoscan thinks is correct. To do this, the start frequency is used50
as the frequency of the ﬁrst data point in the ﬁrst segment. The starting frequencies ofeach subsequent segment is just 10 GHz higher in frequency from the start of the previous
segment. A frequency is assigned to each data point after that using the speciﬁed step size.
This is the same algorithm that the Autoscan computer uses to create the frequency axis
if you were to import the frequency axis from Autoscan. Panel a) of ﬁgure 3.6 shows thesignal of the Ti:Sapphire through both the 1.5 GHz cavity and the 250 MHz cavity with theAutoscan axis, illustrating the lack of precision of the Autoscan frequency.
To correct the Autoscan axis, we ﬁnd the peak frequency in terms of the Autoscan
axis of 1.5 GHz peaks using the Snyder peak-ﬁnder algorithm. The 1.5 GHz frequency axis
is then created in the following steps by the program in Origin LabTalk and Origin C. One
segment of one scan is designated as the reference scan. The frequency of the second fringe ofthe reference scan is used to compare the relative frequencies between that scan and the restof the scans taken that day. The Autoscan frequency of the second fringe in each segment
is then subtracted from the reference scan fringe frequency and divided by the free spectral
range of the cavity. This calculation gives a relative fringe number for the second fringein each scan, an oﬀset is added so that there are no negative fringe numbers for ease of
the calculation. If the Autoscan frequency were perfect, each of the relative fringe numbers
would be a perfect integer, which is not the case. The fringe number should, however, bewith 5% or less of a perfect integer to insure a very low uncertainty in the value of the relative
fringe number. The relative fringe number is then rounded to the nearest integer. To begin
to correct for the uncertainly in the step size taken by the laser, linear interpolation is used
to ﬁnd the fractional fringe number for each of the data points between each etalon peak. At
this point, the frequency axis is in terms of a large etalon relative fringe axis. The numbers
are then turned into a frequency using the free spectral range of the cavity. This step has
now made the frequency axis accurate enough for us to ﬁnd the relative fringe number ofthe small etalon peaks. The process used to create a relative frequency axis for the 1.5 GHz
etalon, the large etalon, is repeated for the 250 MHz etalon, the small etalon except the large

51a) Uncorrected Axis

Scan 1

Transmission

Scan 200361108361109361110361111

Uncorrected Autoscan Axis (relative GHz)

Transmissionb) Corrected Axis

0

0
4336

4337

4338

4339

Corrected Axis (relative GHz)

Figure 3.6: Comparison of the precision of the raw Autoscan axis [panel a)] and the corrected
x-axis [panel b)]. The 1.5 GHz and 250 MHz are locked to a frequency-stabilized HeNelaser and the emission of the Ti:Sapphire through these two cavities is plotted against theuncorrected and corrected x-axis.

52
etalon axis is used as the frequency axis instead of the Autoscan axis. Panel b) of ﬁgure
3.6 shows the precision of the corrected frequency axis. After those steps are completed, thefrequency axis is in terms of a very precise relative frequency; to turn the axis into a absolute
frequency, a reference line, such as a methane transition, is used to ﬁnd the oﬀset needed toshift the axis to the correct absolute frequency.
3.7

Test Systems

3.7.1

Stability and Reproducibility

For high resolution spectroscopy, the most important piece of information is the accuracy and precision of the frequency axis. The test the frequency axis, we repeatedly recorded
molecular absorption lines and compared the peak frequency positions obtained on diﬀerent
days. Speciﬁcally, a ∼100 cm−1 region is scanned with D2 O in H2 discharge. The region is
fully scanned at least three times and all lines appearing in each scan are used to compare
how well the spectrometer reproduced the frequencies. Figure 3.7 is a plot of the frequencyof each line on the frequency axis with the standard deviation of the repeated measurementson the absorbance axis. The average standard deviation of all the lines taken is 9.3 MHz,
which is right in the target range. The lines looked at include known D2 O lines and H+
3 lines,
as well as many unidentiﬁed lines, many of which belong to HD2 O+ . This level of frequency
reproducibility is good enough for doing high-resolution studies of radicals and ions.

3.7.2

HD2 O+ Comparison

The initial project for this new spectrometer was to look at the the OD stretches of
HD2 O+ to complement the study of the OH stretch done on the older instrument in thelab[57]. This is also a useful test for the instrument as it was already studied in the lab so wehave a comparison to assess how the new instrument compares to the existing instrument.
As determined by previous spectroscopic studies[57, 58] HD2 O+ is a near-prolate top with

Standard Deviation (MHz)

53

100
80
60
40
20
0
2600

Average Standard
Deviation = 9.3 MHz

2620

2640

2660
-1

Frequency (cm )Figure 3.7: Illustration of the precision of the new instrument. This region is scanned aminimum of three time and the standard deviation of the measurements for each line in theregion is plotted as a function of the frequency position of the line. The average standard
deviation of the measurements is 9.3 MHz.

a low barrier to inversion along the umbrella coordinate. Even with the low temperatureof the slit jet expansion, the ﬁrst excited tunneling level of the ground vibrational state ispopulated, however transitions from the lower tunneling level of the ground state to the lower
tunneling level are the most intense. To test the creation and detection of ions in the new
system, lines from the OH stretch are recorded and checked against the published lineshapes
and intensities. The OH stretch is an b-type transition and the 220 ← 111 and 111 ← 000
transitions are shown in ﬁgure 3.8. The integrated intensity for the 220 ← 111 transition as
published in Figure 5 of Dong et al.[57] is reproduced.

54+

Sample HD O
2

0.2

a) 2

20

+

Transitions, 0

+
1

Band

1

11

% Absorbance

0.1

0.0

3531.16b) 1

113531.18

3531.203512.06

3512.08

0

00

0.2

0.1

0.0

3512.04-1

Frequency (cm )Figure 3.8: Sample HD2 O+ data in the OH stretching region illustrating the ability of the
new instrument to produce molecular ions in appreciable quantities.

Chapter 4
Rotationally resolved spectroscopy of phenyl radical in the out-of-phasesymmetric CH stretching mode

4.1

Introduction
The phenyl radical (C6 H5 ) is a highly reactive 6-membered organic hydrocarbon ringintermediate formed from homolytic cleavage of a CH bond in benzene[59, 14, 60]. By virtue
of its overall reactivity, this radical plays a central role in combustion, speciﬁcally for fossil
fuels which are typically rich in aromatics[61, 62]. Indeed, it is one of the simplest prototypes of an open-shell aromatic species, achieving partial stabilization of the radical due
to resonance structures arising from electron delocalization around the ring. This radical
stabilization also makes it a prime target intermediate for ring formation in complex combustion processes, which makes phenyl a crucial species in mediating the early stages ofsoot formation[63, 64, 65, 66]. From an astronomical perspective, phenyl is a key transientintermediate formed by 2- and 3-carbon-containing ion-molecule reactions in the interstellar
medium, which therefore represents a rate limiting step toward low temperature synthesisof much larger polycyclic aromatic hydrocarbons[67, 68].
There has been considerable eﬀort extended toward detailed spectroscopic characterization of this ubiquitous radical. Early electron spin resonance studies of phenyl by Bennett
The majority of this chapter has been previously published as Sharp, E. N.; Roberts, M. A.; Nesbitt,
D. J. Phys. Chem. Chem. Phys. 2008, 10, 6592-6596

56
et al.[69, 70] revealed electron-proton spin multiplet structures indicative of a C2v radicalwith a 2 A1 ground electronic state, with later studies by Kasai et al.[71] conﬁrming that theunpaired electron resides primarily in a non-bonding s-type orbital centered on the radical
carbon (see Fig. 4.1). Low resolution infrared spectral assignment of phenyl formed by photolysis of acetyl benzoyl peroxide in Ar matrices was ﬁrst obtained in the out-of-plane CH
bending region by Pacansky et al. in the mid 1970s.[72] A higher resolution FTIR matrix isolation study of phenyl was reported by Ellison and coworkers[60] in 1996, followed by a more
systematic study in 2001 addressing all IR active vibrations and multiple partially deuterated isotopomers.[59] During this same time period, multiple electronic bands[73, 74, 75]
for phenyl radical were identiﬁed in the visible (Ã(2 B1 ) ← X̃(2 A1 ), λ ≈ 510 nm) andnear UV ((B̃(2 A1 ) ← X̃(2 A1 )), λ ≈ 235 nm, and (C̃(2 B2 ) ← X̃(2 A1 ), λ ≈ 211 nm).
The weak Ã(2 B1 ) ← X̃(2 A1 ) band in the visible has been exploited by Lin and coworkers
with cavity ringdown spectroscopy for extensive study of phenyl radical H atom abstraction
kinetics.[76, 77, 78, 79] Vibrational frequencies for two totally symmetric (a1 ) low frequency
modes of phenyl radical were deduced from electron photodetachment studies of phenide
anion by Gunion et al.,[80] which both yielded good agreement and permitted a more deﬁnitive assignment to in-plane breathing modes (ν9 and ν10 ) by comparison with the matrix
FTIR work of Ellison and coworkers.[59] Pure rotational spectroscopy of phenyl was maderecently possible with the combination of discharge-excited molecular beams and FT microwave methods by Thaddeus and coworkers, which provided the ﬁrst precise information
on gas-phase rotational constants and molecular structure.[14]This paper presents ﬁrst reports on infrared CH stretch spectroscopy of a jet-cooled
phenyl radical via high resolution direct laser absorption methods in the gas phase. This work
represents the only IR spectroscopy of phenyl in the gas phase with rovibrational resolution,
which has been used to monitor fundamental excitation of the out-of-phase symmetric CH
stretching mode (see Fig. 4.1). Rigorous assignment of rotational structure in the gas-phase
spectra can be obtained from precision 2-line ground-state combination diﬀerences from the57

Figure 4.1: Geometric structure and highest occupied molecular orbital representation ofphenyl radical, with principal inertial axes as indicated. The out-of-phase symmetric CH
stretch excitation (b2 ) observed in this work has a transition dipole moment along the Aaxis. Note the nodeless, in-plane nature of the single ﬁlled HOMO at the radical C center,characteristic of a σ-radical.

58
radio frequency spectroscopy.[14] The analysis yields rotational constants and vibrationalenergy for the excited state, the latter of which proves to be in remarkable agreement withresults from previous matrix isolation studies.[59] The ability to obtain rovibrationally resolved spectra for such a prototypical aromatic species represents an important milestone forspectroscopic study of highly reactive combustion intermediates, and bodes well for direct
spectroscopic detection and analysis of many other complex aromatic radical species in thegas phase.
4.2

Experiment
Our approach for high sensitivity spectroscopic detection of jet-cooled hydrocarbon

radicals via high-resolution infrared laser absorption in a slit-jet cooled supersonic dischargesource is reported elsewhere and will be brieﬂy summarized.[81, 82, 1] High resolution IR
light (<2 MHz linewidth) is produced via diﬀerence-frequency generation (DFG) of a tunable
single mode ring-dye laser (R6G) with a ﬁxed-frequency single mode Ar+ laser (514 nm) in atemperature-controlled, periodically poled LiNbO3 (PPLN) crystal. Transient absorption in
a 16-fold multipass Herriot cell through the long axis (4 cm) of the slit expansion is detectedby diﬀerential change in signal minus reference beam power synchronous with the slit valve
pulse. Absorption sensitivity is achieved via (i) fast electronic subtraction of common-mode
amplitude noise on the split laser beam and (ii) 50 kHz concentration modulation of the DC
discharge. Relative frequencies are obtained to ≈ 10 MHz precision (≈ 0.0003 cm−1 ) via
fringe interpolation on the optical transfer cavity, with absolute frequencies obtained withrespect to the set of CH4 R(4) transitions[83] near 3067.30 cm−1 .
Jet-cooled phenyl radicals are produced by adiabatically expanding a mixture of 0.1%
phenyl bromide (C6 H5 Br) in 70:30 neon-helium buﬀer gas through a pulsed-slit jet (19 Hz,
500 ms pulse duration), with radicals formed by electron associative detachment in a 50 KHz
square wave modulated discharge (575 V, 0.2 A) localized upstream of the expansion oriﬁce.
The slit jet cooled discharge source yields peak absorbances of E 0.25% on typical phenyl

59
rotation-vibration transitions (see Fig. 4.2) which, based on ab initio estimates of integrated
absorption strength (17 km mol−1 ), correspond to radical densities in the probe region of
2 × 1010 cm−3 /quantum state. At noise levels of roughly 1 × 10−4 in a 10 kHz detection
bandwidth, the peak absorption signals in Fig. 4.2 translate into signal-to-noise ratio (SNR)of approximately 10 - 20:1 for the strongest transition lines in the phenyl radical spectra.
4.3

Results and Analysis
By way of initial guidance, we performed quantum chemistry structure and harmonicfrequency calculations for phenyl using density functional methods (B3LYP) over a systematic series of correlation consistent Dunning basis sets (AVnZ, n = 2,3,4,5).[3, 84, 85] The
resulting frequencies, symmetries and intensities in the CH stretch region are summarizedin Table 4.1. Also included are anharmonic predictions from similar series of B3LYP/6311g++(3df,3pd) calculations, which are based on an empirical scaling factor of 0.9637(31)of Dong et al.[1] calibrated by benchmarking against previously observed high resolution gasphase radical spectra in the CH stretch region. As anticipated, the results demonstrate good
convergence with respect to basis set size and are in fundamental agreement with previous
UB3LYP/cc-pVDZ calculations of Ellison and coworkers.[59] Of particular importance is theconsensus frequency and intensity obtained for the strongest CH stretch transition, whichis the out-of-phase symmetric CH stretch mode of b2 symmetry. Based on the orientationof the principal axes shown in Fig. 4.1, this predicts the strongest band in the CH stretch
region to be A-type and near 3067 ± 10 cm−1 . For an asymmetric rotor modeling of thisband as a near oblate top spectrum with small changes in A, B, C rotational constants, one
anticipates a progression of closely overlapped p PK (N) and r RK (N) branch lines (here K =Kc refers to the limiting values for an oblate top) with an approximate spacing of 2C ≈ 0.197
cm−1 , and a moderately prominent Q branch near the band origin.[86]Scans in this region revealed extensive P and R branch progressions with an approximate spacing of 0.196 - 0.198 cm−1 , as well as a more complex Q branch feature near

60

Figure 4.2: A sample 0.5 cm−1 high resolution data scan for phenyl radical in the outof-phase CH symmetric stretch region (with 0.25% peak absorbances), along with spectral
predictions based on Trot = 15 K and the preliminary rotational constants reported in Table
4.2. Note the predominance of NK′ a′ Kc′ ← NK′′ a′′ Kc′′ progressions involving N = Kc states,
for which the asymmetry splittings in near oblate top phenyl radical are unresolved.

3197.65(10.2)
3183.63(5.4)
3164.45(1.1)
3186.46(21.6)
3170.91(4.1)

A1
A1
A1
B2
B2

ν1
ν2
ν3
ν19
ν20

AVDZ

Symmetry mode
3192.85(8.5)
3180.22(3.7)
3160.55(0.8)
3182.58(17.1)
3166.75(4.0)

AVQZ

AV5Z

Anharmonic
Predictions
3189.30(10.4) 3187.64(9.8) 3188.01(9.3) 3071
3175.94(4.3) 3174.53(3.6) 3174.95(3.3) 3065
3157.48(1.0) 3156.52(0.9) 3157.41(0.9) 3046
3178.43(21.6) 3176.76(19.8) 3177.30(18.9) 3067
3163.42(3.5) 3162.20(3.3) 3162.96(3.0) 3052

6-311g++(3df,3pd) AVTZ

Table 4.1: Harmonic B3LYP/AVnZ (n = 2,3,4,5) ab initio predictions as a function of basis set size for fundamental CH stretch
modes in phenyl radical. Numbers in parenthesis represent predicted intensities in km/mol. The rightmost column contains
anharmonic estimates (∆ν ± 10 cm−1 ) from density functional B3LYP/6-311g++(3df,3pd) calculations, based on a scale factorof 0.9637(31) benchmarked against CH stretch excitation frequencies for a series of high resolution studies of hydrocarbon
radicals[1]61623071.80 cm−1 . Sample high resolution data over 0.5 cm−1 in the R-branch region are shownin Fig. 4.2, which indicates the level of signal to noise as well as the approximately 50
MHz sub-Doppler resolution. The complete spectrum exhibits more lines than currently
assigned, which may indicate other transient species formed in the discharge or the presence of vibrationally excited hot bands. For the purposes of this work, therefore, we ﬁrst
restrict our attention to the prominent N = Kc , ∆N = ∆Kc progression out of the groundvibrational state, for which the N-rotational assignment can be obtained unambiguously via
2-line combination diﬀerences from the mm-wave studies of Thaddeus and coworkers.[14]Speciﬁcally, pairs of P(N + 1) and R(N - 1) branch lines to the same upper N state yield
spectral diﬀerences that match frequency predictions to better than 30 MHz. By way offurther conﬁrmation, this choice of N assignment is consistent with a predicted A-type band
origin, as well as in excellent agreement with the position and structure of the experimentallyobserved Q branch feature.
Due to the highly oblate nature of phenyl radical, these strongest lines for an A-type′
band reﬂect a near perfect overlap between the two dominant progressions (N0N
← N0N
′
′
and N1N← N1N ) associated with Kc asymmetry doubling. As a result, these doublets′

remain unresolved even at sub-Doppler resolution and thus provide no information on theasymmetry of phenyl radical in the upper state. Furthermore, the additional conditionof planarity for phenyl radical (B ≈ 2C) yields additional overlapping structure between∆N = ∆Kc = ± 1 transitions out of levels with Kc = N, N-2, N-4, etc. As a result, we
ﬁrst performed an oblate top ﬁt to the main P/R branch progression, based on least squares
adjusting (A′ + B′ )/2 and C′ in the upper state, as well as the band origin, while maintaining
the ground state at microwave values. The phenyl radical asymmetry (A′ B′ ) could then be
estimated from (A′ + B′ )/2 and the assumption of a rigid planar molecule (i.e. 1/C′ ≈1/A′ + 1/B′ ). This ﬁrst order analysis led to very good agreement between predicted andobserved rotational structure in the Q branch, which permitted several additional P, Q, andR branch lines to be rigorously assigned with 2-line ground state combination diﬀerences.

63
As the Q branch transitions sample states with much larger asymmetry splittings, a rigid
rotor least squares ﬁt to the expanded data set permits independent extraction of A′ , B′ ,C′ rotational constants and the band origin ν0 . Results from this preliminary analysis are
summarized in Table 4.2, where, consistent with a rigid rotor model, all contributions due
to centrifugal distortion as well as spin rotation ﬁne structure have been neglected.
Table 4.2: Rovibrational spectroscopic constants for gas-phase phenyl radical from a rigid
asymmetric rotor least-squares ﬁt to the out-of-phase symmetric CH stretch band. Numbers
in parentheses represent 1σ uncertainties in units of the least signiﬁcant digit
Constant
Predictionsa bA(cm−1 )0.211218−1
B (cm )
0.188434
C (cm−1 )0.099588
2
D (amu Å )−1
ν0 (cm )3072

Ground statec
0.209472(10)0.186793(7)0.098714988(20)0.046-

Excited state (ν19 )0.20937(8)0.18655(12)0.098616(20)0.061
3071.8907(10)aRotational constant predictions from B3LYP/AV5Z calculations
ν19 band origin from condensed phase Ar matrix isolation studies of Ellison and coworkers[59]cGround state constants from microwave studies of McMahon et al.[14]bA more complete analysis of the rovibrational spectra is underway and will be presented
elsewhere; however several observations can be made at this time. First of all, the upperstate
rotational constants are in very close agreement with the microwave values,[14] with small
but systematic decreases in all values (∆A/A = 0.05%, ∆B/B = 0.13% and ∆C/C = 1.0%)
qualitatively consistent with CH stretch in-plane excitation. Indeed, this provides a usefulcontext for the quite close but systematically higher rotational constants predicted fromdensity functional theory at the AV5Z level (see Table 4.2), which reﬂect an equilibriumgeometry uncorrected for zero point motion in all 3N - 6 = 27 vibrational modes. Secondly,
the independently ﬁtted upper state rotational constants are consistent with a nearly planar2

radical, with an inertial defect (∆ = 0.061 amu Å ) close to zero and similar to the ground2

state value (∆ = 0.046 amu Å ). The vibrational band origin at 3071.8907(10) cm−1 isin very good agreement (∆ν = +4.8 cm−1 ) with the anharmonic prediction for ν19 shown

64
in Table 4.1, well within the ≈ ±10 cm−1 statistical error. Though also relatively close
in anharmonic predicted frequency, the ν1 symmetric CH stretch can be conclusively ruledout as a possible carrier of the spectral intensity. This would yield a pure B-type rather
than the pure A-type band observed experimentally, which from Fig. 4.1 is consistent with
out-of-phase symmetric CH stretching excitation (ν19 ).[86]The present gas-phase spectral band origin for ν19 is in remarkably good agreementwith the previous matrix isolation studies of phenyl radical by Ellison and coworkers,[59]
who indeed obtained moderate resolution assignments for all IR allowed bands in phenyl
radical. Also by detailed comparison with quantum mechanical calculations, these workers
assigned their strongest band in the CH stretch region at 3072 cm−1 to ν19 , i.e. out-of-phasesymmetric stretching of adjacent pairs of CH groups to either side of the phenyl radical center.
The rotational resolution provided by gas phase spectroscopic techniques permits deﬁnitive
conﬁrmation of this vibrational mode symmetry; this predicts an in-plane transition dipole
moment perpendicular to the C2v radical axis, which is consistent with the observed Atype band rotational structure. The shift (∆ν ≈ 0.1 ± 1 cm−1 ) between condensed andgas phase results is essentially zero for the Ar matrix, which is noteworthy considering themore typical red shift to lower frequencies due to enhanced stabilization interactions in the
excited vibrational state.[87] Comparison with the matrix results[59] suggests that we should
also be able to detect other bands in the CH stretch region, for example, the B-type bandcorresponding to ν1 symmetric CH stretching of all ﬁve H atoms.
As a ﬁnal note, it is worth stressing that the ability to observe a relatively simple
and assignable rovibrational line structure at high resolution in the 3.3 µm infrared CH
stretch region is by no means obvious for such a large hydrocarbon radical. The reason forthis is the presence of weak but ﬁnite anharmonic coupling between the optically allowed
state, corresponding to the CH stretch in this case, and the dense bath of nearly resonant
overtone and combination band states.[88, 89] For a coherently excited initial CH stretch
state, such coupling leads to a time dependent energy ﬂow into lower frequency modes in65
the molecule, resulting in “intramolecular vibrational redistribution” or “IVR”. From acompletely equivalent frequency-domain perspective, such anharmonic coupling results inweak mixing of the zero order oscillator transition strength from the “bright state” into abath of nearly isoenergetic background vibrational states. When this occurs, a transitionout of a single lower state can become spectrally fragmented into a complex overlap of lines
in the high resolution spectrum, with a spectral width that corresponds roughly to theinverse time scale for IVR out of a coherently prepared CH stretch state. Indeed, there havebeen elegant high resolution studies of jet cooled hydrocarbon molecules by several groups
indicating the presence of such spectral fragmentation patterns, as well as direct veriﬁcationof the relaxation dynamics in the time domain.[90, 91, 92, 93, 94]
For the case of a phenyl radical, we can predict the density of total vibrational states
based on the quantum chemical harmonic predictions and direct state counting algorithms[95]to be 510 states per cm−1 at roughly 3000 cm−1 levels of internal excitation, i.e., remarkably
small for a non linear hydrocarbon molecule with 11 atoms. The size is primarily due tothe presence of the ring, which raises the lowest frequency vibrational mode to > 400 cm−1 ,and therefore greatly limits the density of states in the 3000 cm−1 region. The fact that
we can see high resolution sub-Doppler rotational structure (∆ν ≈ 50 MHz) in jet cooled
CH stretch excited phenyl radical, therefore, bodes quite favorably for the feasibility of highresolution IR studies in other radical hydrocarbon ring systems of key importance in both
combustion and interstellar chemistry.
4.4

Conclusion and Summary
The ﬁrst gas-phase high resolution infrared spectral data for phenyl radical havebeen obtained, corresponding to ν = 1 ← 0 excitation of ν19 , the out-of-phase symmetric CH stretch mode. Rovibrational assignment has been unambiguously made based on (i)band type and (ii) 2-line ground state diﬀerences from previous microwave and mm-wave
studies.[14] Density functional predictions of phenyl radical transition frequencies and inten-

66
sities are calculated for a series of Dunning basis sets (AVnZ, n = 2,3,4,5), which indicate
very close agreement with the observed band origin.[84, 85] Rigid asymmetric top A, B,
C rotational constants are obtained for the upper state, which are in good agreement withquantum chemical predictions as well as lower state microwave/mm-wave values by Thaddeus
and coworkers.[14] The measured band origin is in remarkable agreement with the matrix
studies of Ellison,[59] with essentially no shift (∆ν ≈ 0.1 ± 1 cm−1 ) due to the presence ofthe condensed phase environment. Further IR analysis of phenyl radical at higher resolution
as well as detailed line shape modeling of the overlapped transitions is currently underway.
The ability to obtain high resolution IR absorption spectra in the gas phase for such relatively large hydrocarbon radicals represents a signiﬁcant step forward in the spectroscopy oftransient species of particular relevance to complex combustion phenomena,[63] as well as
to detailed modeling of chemistry in the interstellar medium.[68]Chapter 5
A complete picture of stretching vibrations in methyl radical and its
deuterated isotopomers: a high-resolution study of the CH stretches in CH2 D
and a global harmonically coupled Morse oscillator model

Methane, CH4 , is one of the most abundant and strategically important fuel stocks, forwhich, along with other aliphatic hydrocarbon fuels, the critical ﬁrst step in the combustionis the extraction of hydrogen atoms to form sp3 hybridized radical centers on a carbon
atom[96, 97]. This H abstraction reaction from CH4 proceeds with combustion radicals
such as H, O, and OH, to yield methyl radical, CH3 , which propagates the combustion
process forward via a variety of mechanisms. Under low temperature ﬂame conditions, CH3
recombines with O2 to form the relatively stable methyl peroxyl radical CH3 OO adduct.
This can react by H atom abstraction from hydrocarbons to form CH3 OOH, which canfragment to form CH3 O + OH, and thereby regenerating chain radicals. As the temperature
increases, the concentration of OH and O radicals increases relative to the concentration ofO2 , so reactions such as CH3 + O → CH2 O + H and other reactions with CH3 , OH, H, andO radicals dominate[98]. At even high temperatures (T > 1000 K), CH3 is predicted also
to recombine with O2 to form CH3 OO, but now this peroxy radical dissociates to form two
chain radicals CH3 O + O, followed by an additional H atom abstraction and propagation of
the chain reactions.
The majority of this chapter has been previously published as Roberts, M. A.; Savage, C.; Dong, F.;
Sharp-Williams, E. N.; McCoy, A. B.; and Nesbitt, D. J. J. Chem. Phys. 2012, 136, 234308.

68
Methyl radical combustion chemistry also plays a critical role in shaping the end products of combustion reactions. For example, the ﬁnal products of an eﬃcient hydrocarbon
combustion process would ideally be simply CO2 and H2 O, where the product CO2 is usually formed via the reaction CO + OH → CO2 + H. However, this bimolecular reaction
typically requires substantial concentrations of OH and CO, and thus CO2 is not readily
formed without both species relatively abundant. The presence of competing reactions, forexample, CH4 + OH → CH3 + H2 O or CH3 O + OH → CH2 O + H2 O can deplete the OH
and lead to unreacted CO in the ﬁnal products. This results in both ineﬃcient extractionof the combustion enthalpy as well as an undesired pathway to generating CO pollutant
emissions, especially in fuel rich systems[98].
Though clearly ubiquitous in hydrocarbon combustion, methyl radical is also present
in the troposphere, and serves as an intermediate in many important reactions throughout
the lower and upper atmosphere[99, 100]. Methyl radical is formed by oxidative attack of
atmospheric methane, which is present in signiﬁcant quantities from natural gas leakage, incomplete combustion, fermentation, and other biological processes. The relevant chemistry
is initiated by photochemical production of OH radical, followed by hydrogen abstraction reaction from CH4 to form CH3 radical, which then continues to react with nitrogen-containing
compounds to make photochemical smog[98]. By virtue of an appreciably higher C-H bondstrength (∆H = 105 kcal/mol) with respect to any other non-methane hydrocarbons (∆H =96-101 kcal/mol)[101], methane is quite stable, with an approximately 11 year lifetime in the
troposphere and therefore signiﬁcant as a greenhouse gas. Indeed, the only appreciable sourceof chemical removal of methane in the lower atmosphere is via these relatively slow ”scrubbing” reactions with OH radical. Because of the environmental implications, atmosphericreactions involving methane are currently an area of intense investigation, which currently
includes using H/D isotopically substituted species to aid in modeling the chemistry[102].
Methyl radical is also thought to be an important radical intermediate in dense molecular clouds distributed throughout the interstellar medium[103, 104]. One of the most powerful

69
tools for probing reactive chemical species in the interstellar medium is that of microwave
spectroscopy, which requires a permanent electric dipole moment to facilitate dipole allowed
rotational transitions. At its planar equilibrium geometry, methyl radical exhibits D3h point
group symmetry and therefore has a dipole moment (µ) that vanishes identically. However,by asymmetrically deuterating the CH3 radical to make CH2 D radical, the 3-fold symmetry
is reduced to C2v , which generates a weak permanent electric dipole moment and thus anallowed rotational spectrum. While no measurements of µ have been reported to date forCH2 D, the dipole moments of some related molecules have been calculated. For example, theCH2 D+ ion should[105] have a large dipole moment of µ = 0.329 D, while the more closely
analogous CHD2 species has been recently predicted[106] to have a much smaller moment ofµ = 6.5 × 10−3 D.
What makes this issue particularly interesting is that the relative abundance of partiallydeuterated molecular species can be substantially higher in the interstellar medium thanobserved on earth[103]. This is due to the presence of small, but non-negligible zero point
energy diﬀerences between the isotopically shifted vibrational manifolds. These are largely
negligible at typical terrestrial temperatures (300 K), but can become critically important
thermodynamic driving forces at the much lower temperatures (20-50 K) of a dense molecular
cloud. Thus the detection of methyl radical and, in particular, the isotopically substituted
radical species, may provide an indispensable tool in both probing and modeling the complex
chemistry of the interstellar medium.
Though CH3 remains invisible to conventional microwave/mm wave spectroscopy, there
has nevertheless been an exceptionally rich history of methyl radical spectroscopy. The
ﬁrst absorption spectrum of methyl radical was obtained by Herzberg and Shoosmith in
1956[107, 108] in the vacuum ultraviolet region, with the infrared spectrum reported byseveral groups in a matrix[109, 110, 111, 112] and later revisited using isotopic substitution to conﬁrm the band assignments[113]. Observation of methyl radical in the gas phaseproved to be much more challenging, with ﬁrst spectra obtained in pioneering ﬂash kinetic

70
IR spectroscopy studies by Pimentel and coworkers[114]. The development of high resolution
diode lasers in the early 1980’s oﬀered an enormous increase in sensitivity over traditional
IR glow bar sources. This permitted ﬁrst reports of rotationally resolved spectra for gas
phase CH3 radical, with studies of the strongly IR-active out-of-plane umbrella mode (andhot bands thereof)[115] as well as the asymmetric C-H stretch mode[116]. Based on highresolution stimulated Raman methods of Nibler and coworkers, even the IR-inactive C-H
stretching mode of gas phase CH3 was successfully studied in 1991 with complete rotational
resolution[117]. These ideas have been complemented using UV resonance Raman spectroscopy to yield considerable information on methyl radical, in particular with substantial
vibrational excitation in totally symmetric modes. CH2 D has been used in a number of studies to probe complicated dynamics including in kinetic studies[118], studies of vibrationallymediated reactions[119], and a number of EPR studies looking at the dynamics of methyl
radical in matrices[120, 121, 122].
In contrast to the variety of studies on CH3 as well as fully deuterated CD3 species,
there has been some work on the partially H/D isotopically substituted radical species.
Early spectroscopic studies of CH2 D included i) matrix isolation spectroscopy looking at theout-of-plane deformation fundamental[113], ii) resonance enhanced multiphoton ionization
to obtain band origins of all the vibrational fundamental modes for each isotopomer[123],
and iii) photoelectron spectroscopy[124]. Hyperﬁne structure, speciﬁcally the magnitudeof the Fermi contact term, was studied using electron spin resonance (ESR) to look at
methyl radical and all H/D isotopomers in a krypton matrix[125]. The most recent study
involving CH2 D reﬂects combined threshold photoelectron spectroscopy and computationaleﬀorts[126].
The only previous high resolution spectroscopic data on CH2 D in the gas phase comesfrom the group of Kawaguchi in the out-of-place bending fundamental mode, ν4 , obtained by
combined laser photolysis and Fourier transform infrared spectroscopy (FTIR)[2], which wasable to fully resolve the asymmetric top rotational structure as well as partially resolve spin-

71
rotational splitting. Due to equipment limitations, only the Q- and R-branch transitions wereobserved, which nevertheless permitted an unambiguous ﬁt of the rovibrational constants
to Watson’s A-reduced Hamiltonian. The partially resolved spin-rotation splittings wereobserved only in the R-branch but, if one assumes negligible hyperﬁne interactions, still
permitted a ﬁrst estimate of spin-rotation constants in the ground and vibrationally excitedstates. It is important to note that these estimates diﬀer from isotopic scaling of the spinrotation constants for CH2 D from CH3 , as will be discussed in Sec. 5.3.2.

CA
B
Figure 5.1: B3LYP/6-311++G(3df,3pd) calculated structure[3] of CH2 D with the HOMO
and principal axes shown.

To date, there have been no high resolution studies of CH2 D in the C-H stretchingregion, and in particular no measurements whatsoever of gas phase CH2 D radical with suﬃcient resolution for detailed study of rovibrational, ﬁne, and hyperﬁne structure. The focusof the present work is toward the C-H stretching modes on the partially deuterated methyl
radical isotopomers using high-resolution IR spectroscopy. CH2 D is a planar π radical, with

72
the principal axes of the molecule as shown (see Fig. 5.1). CH2 D has six fundamental vibrations, two of which are CH stretching modes. This study looks at the CH antisymmetricand symmetric stretching vibrations using sub-Doppler techniques, which requires treatingrotational as well as both ﬁne and hyperﬁne structure in the analysis[127]. Since CH2 D has
a non-vanishing dipole moment, this work should provide excellent guidance for the very
challenging terrestrial detection of this radical in the microwave/mm wave region of thespectrum.
The organization of the paper is as follows: Sec. 5.1 provides a brief overview of theexperimental apparatus used to obtain the CH2 D spectrum. This is followed by presentationof experimental results for symmetric and asymmetric C-H stretch data in Sec. 5.2. In Sec.
5.3.1, we focus initially on analysis of the high resolution transition frequencies to obtainrovibrational constants. We then take advantage, in Sec. 5.3.2 of sub-Doppler resolution
in the slit-jet spectra to analyze the complex line shape structure on each transition andthereby extract novel information on ﬁne and hyperﬁne interactions. In Sec. 5.4, we discussthese results in the context of previous eﬀorts, as well as develop a simple model of in-planevibrations for all CHm D3−m isotopomers in C2v symmetry, with the results and prospects
for future studies summarized in Sec.5.5.
5.1

Experiment
The radicals are produced and studied with slit supersonic discharge techniques and ahigh resolution infrared spectrometer that have been described in detail elsewhere[128, 129]
and will only be summarized here. The halogenated precursor (CH2 DI, 99.9% Cambridge
Isotope Laboratories) is puriﬁed using freeze-pump-thaw methods and then diluted with
Ne70 (i.e., 70% Ne, 30% He) in a holding tank. This mixture is then further diluted down
to 1.0% in Ne70 using mass ﬂow controllers to regulate the gas ﬂow into the slit stagnation
region. The slit valve is a JILA-made solenoid-driven pulsed injector with a 4 cm by 300µm slit oriﬁce operating at a 19 Hz repetition rate and about a 1000 µs duration. The

73
pressure in the stagnation region is maintained at 300 Torr, with the vacuum chamber kept
at < 50 mTorr during operation of the pulsed valve, by a Roots blower (560 liters/sec).
During the pulse, a 50 kHz, 0.5 A, 50% duty cycle, modulated discharge localized upstreamof the slit oriﬁce achieves eﬃcient electron dissociative attachment at the C-I bond at nearLangevin rates to eﬃciently synthesize the desired CH2 D radicals. Lock-in detection withdouble balanced mixers is used to phase sensitively detect concentration modulation of theradicals produced in the pulsed discharge, thereby greatly minimizing spectral congestion
due to absorption by precursor molecules.
The tunable infrared continuous-wave laser radiation for probing radicals is generated
by diﬀerence-frequency mixing the 514 nm output of a single frequency continuous-wave
argon ion (Ar+ ) laser with the visible output of a tunable ring dye laser (Rhodamine 590,
Exciton dyes) in a periodically poled LiNbO3 crystal. The Ar+ laser is stabilized (< 2 MHz)by locking it to a Fabry-Perot cavity (< 1 MHz), which is in turn locked to a polarizationstabilized helium neon (HeNe) laser. As this fabry-Perot optical transfer cavity is also used tomonitor the dye laser scan, the fringes accurately report on the infrared diﬀerence frequency,
i.e., ωAr+ −ωdye = ωIR . This combination of a locked HeNe laser and a locked optical transfer
cavity yields high reproducibility and precision in the IR frequency diﬀerence measurements,
with excellent agreement between data collected over many months.
The IR radiation is split into a signal and reference beam of roughly equal intensity. The
reference beam is directed onto a liquid nitrogen-cooled InSb detector, with the corresponding
signal beam passing through a 16-pass Herriot cell (l = 4 cm × 16 = 64 cm) before being
focused onto a matched InSb photodiode detector. We then subtract the outputs of thereference detector and the signal detectors and extract the demodulated lock-in signal on
the computer via a fast (1 µs bin time) analogue-to-digital convertor. Absolute frequencies
are obtained by comparison with known methane lines[130], yielding an overall precision andaccuracy of the line center measurements of σ = 15 MHz and 20 MHz, respectively. Suchprocedures yield detection sensitivities of 5 × 10−7 Hz−1/2 , with a peak absorbance of 2%

74
and signal-to-noise ratios of roughly 500:1 on the more intense CH2 D lines.
5.2

Results
The combination of high resolution (∆ν ≈ 0.0001 cm−1 ) and near shot noise limited

sensitivity (5 × 10−7 Hz−1/2 ) of the laser spectrometer comes at the expense of fast spectral
scanning capabilities. Accurate initial estimates for the spectral search region are therefore quite important. The harmonic frequencies of both the symmetric and asymmetric CH
stretch vibrations are calculated using density functional (DFT) methods available in the
GAUSSIAN09 program [B3LYP/6-311++G(3df,3pd) basis set][131]. To account for anharmonicity in the vibration as well as residual method and basis set errors, we improve theseharmonic DFT predictions with a scaling factor, 0.9637(31), which has been quantitatively
benchmarked by comparing theoretical vs. experimental CH stretching frequecies for morethan twenty hydrocarbon radicals[132]. From such calculations, the predicted frequency of
the asymmetric C-H stretch in CH2 D is 3169 cm−1 with a 1-σ standard deviation of about
10 cm−1 . Furthermore, the asymmetric C-H stretch transition dipole moment lies along theB principal axis (see Fig. 5.1) and will have B-type rotational structure. Similarly, thesymmetric C-H stretch vibration is predicted to be an A-type band centered at 3065(10)cm−1 . Recently, a computational study also reported anharmonically corrected ab initio frequencies of 3158 cm−1 and 3062 cm−1 for the asymmetric and symmetric stretch vibrations,
respectively, i.e., in quite good agreement with our predictions[126].
To speed the process, an initial search procedure is performed with a relatively large
step size of 12 MHz. After the CH2 D lines are identiﬁed, they are re-scanned at least two
more times with a 3 MHz step size, which takes full advantage of the sub-Doppler slit jet
spectrometer resolution and allows one to map out the ﬁne and hyperﬁne spectral lineshapes.
Based on ground state rotational constants from the FTIR study[2], two progressions of lines
are readily identiﬁed as CH2 D by comparison with rigid rotor asymmetric top predictions,with details on the assignment conﬁrmation discussed in Sec. 5.3. Figs. 5.2 and 5.3 summa-

202
303

312

212
313

110
211

211

101
202

111

111
110

212

110
111

202
212

101

110

111

211
0.5

000

)
-5

x abs x10

-1

1.0

0.0

3040

% Absorbance

101

a)
101

1.5

(cm

Integrated Absorbance

000

75

0.3

b)

3060

0.3

3080

c)

3100

d)
0.8

0.2

0.2

0.1

0.1

0.0

0.0

0.4

3056.103056.130.0

3063.153063.183083.733083.76-1

Wavenumbers (cm )Figure 5.2: Sample CH symmetric stretch data for CH2 D. Panel a) plots the integrated absorbance of each of the observed N′Ka′ Kc′ ← N′′Ka′′ Kc′′ rotational lines versus frequency. Blowups
of select transitions, panels b)-d), show additional structure at high resolution due to ﬁne
and hyperﬁne interactions. The black dots are the data and the red lines are simulations
base upon constants obtained in lineshape ﬁts of the ﬁne and hyperﬁne structure.

rize data for the symmetric and asymmetric stretch, respectively, indicating the transitions
observed and the high level of S/N. Due to the > 105 -fold disparity between scan size(>
70 cm−1 ) and the transition line widths (< 0.003 cm−1 ), the overview spectrum for eachband is shown simply in Figs. 5.2 and 5.3 as a stick plot, with the height proportional tothe integrated area of the transition. However, sample data transitions (lower panels) for
each band are also shown at high resolution on a greatly expanded frequency scale. This
more clearly reveals the rich presence of highly complex lineshapes, due to the combinationof i) spin-rotation ﬁne structure and ii) electron spin-nuclear spin hyperﬁne structure. In
practice, our analysis procedure is to simultaneously ﬁt the high resolution line contours toa ﬁne/hyperﬁne Hamiltonian, obtain ﬁne/hyperﬁne-free line centers, and then least-squares

212

220

321

331

211

111

322

110

220

212

221

313

303

202

101
212
212
221

111

211
210

202

110

202

0

3140

0.4

% Absorbance

211

110
101

211

111

202

202

000

1

111

212

2

101

(cm

-1

x abs x10-5)Integrated Absorbance

a)

3

111

101

000

76

3160

c)

2

b)

0.2

3180

3200

2

1

d)

1

0.0

0
3152.3003152.33

3171.393178.513171.413178.54-1

W avenumbers (cm )Figure 5.3: Sample CH asymmetric stretch data for CH2 D. Panel a) plots the integrated
absorbance of each of the observed rotational lines, labeled as N′Ka′ Kc′ ← N′′Ka′′ Kc′′ , versus
measured frequency. Details of select transitions, in panels b)-d), show additional structure
at high resolution attributed to ﬁne and hyperﬁne interactions. The black dots are thedata and the red lines are simulations base upon constants obtained in ﬁts to the observedlineshapes.

ﬁt these line centers to a Watson Hamiltonian. However, due to extreme diﬀerences in scaleof rovibrational vs ﬁne/hyperﬁne frequency information, we will ﬁrst present the rovibrational analysis in Sec.5.3.1, followed by a more detailed inspection of the high resolution
ﬁne/hyperﬁne structure in Sec.5.3.2.
5.3

Analysis

5.3.1

Rovibrational Structure

The rotational structure of both the i) symmetric C-H stretch and ii) asymmetricC-H stretch bands are analyzed simultaneously, as they both originate from the ground77
vibrational state. CH2 D is a moderately asymmetric top, κ = -0.2317, which implies thevibrational bands will have a complex structure. If we neglect ﬁne/hyperﬁne coupling forthe moment, the quantum number N for overall molecular rotation is conserved, with thequasi-quantum numbers Ka and Kc approximately representing the projection of N along
the A and C axes, respectively. Additionally, the relatively large rotational constants forCH2 D implies that only a few rotational and/or nuclear spin levels will be populated at therotational temperatures found in the slit jet. The symmetric stretch rotational structure ispredicted to be a nearly pure A-type band, for which the selection rules are ∆Ka = even and∆Kc = odd. Even at high sensitivity, only the most intense ∆K transitions are seen; thus
the selection rules in eﬀect reduce to ∆Ka = 0 and ∆Kc = ± 1. In analogy to previous H/Disotopic studies of H2 DO+ [57, 1], there is in principle also a component of the symmetricC-H stretch dipole transition moment that carries C-type oscillator strength, arising fromlarge amplitude motion over a signiﬁcant barrier in the out of plane bending coordinate.
However, due to absence of a barrier to planarity in CH2 D, these transitions correlate withweak combination band excitation of C-H stretch plus out of plane bending modes, whichshould occur much further to the blue. The asymmetric stretch is a pure B-type band so theselection rules for the allowed rotational transitions are ∆Ka = odd and ∆Kc = odd and,again, the transitions seen here are all ∆Ka and ∆Kc = ± 1.
The frequencies listed in tables 5.1 and 5.2 are the hyperﬁne and ﬁne structure-freeline centers of the symmetric and asymmetric stretch lines, respectively, obtained from a
global ﬁt to the high resolution lineshapes. Correct assignment of these lines has been
unambiguously conﬁrmed by several four-line combination diﬀerences that match to better
than the 15 MHz experimental precision. The 32 line centers are ﬁt simultaneously to a
Watson asymmetric top Hamiltonian (A-reduction, Ir representation)[133], yielding A, B, C
rotational and partial sextic centrifugal distortion constants for the ground state, symmetricstretch, and asymmetric stretch excited state. In a molecule with relatively large rotational
constants and with the low rotational temperatures in the slit jet, only the lowest few N′′

78= 0-2 levels are populated. Therefore, two least squares ﬁts have been pursued in parallel.
The ﬁrst uses only the high resolution rovibrational line centers from the current work,with results presented in the top portions of Table 5.3. The second ﬁt takes additional
advantage of previous mid IR study in the out-of-plane bending mode, for which lower
resolution data are available on a signiﬁcantly higher number of rotational states populated
at room temperature. Speciﬁcally, the line positions from the previous study are added tothe current data set, down-weighted by 100 (i.e., 1/σ 2 ) to account for 10-fold lower precisionand help better determine the ground state[2]. The results of this global ﬁt and residuals
are summarized in the bottom portions of Table 5.3. The resulting molecular constants areused to create a stick plot simulation of each band, as shown in Figs. 5.4 and 5.5.
Table 5.1: Experimental ﬁne- and hyperﬁne-free line centers for the C-H2 symmetric stretch
band of CH2 D radical. Estimates of the frequency precision and accuracy are both 15 MHz.
The calculated values used are from a global least squares ﬁt to Watson’s asymmetric top
Hamiltonian of all the symmetric stretch, asymmetric stretch, and the out-of-plane bending
mode[2] transitions.
N′
1
1
1
0
1
1
1
2
2
2
3
3
3

K′a
1
0
1
0
1
1
0
1
0
1
1
1
0

K′c
0
1
1
0
1
0
1
2
2
1
3
2
3

N′′
2
2
2
1
1
1
0
1
1
1
2
2
2

K′′a
1
0
1
0
1
1
0
1
0
1
1
1
0

K′′c
1
2
2
1
0
1
0
1
1
0
2
1
2

Frequency (cm−1 )3044.12647
3047.31847
3048.68316
3056.10620
3063.16258
3067.74521
3075.11432
3082.10866
3083.73676
3086.71352
3089.89100
3096.61805
3091.16343

Obs - Calc (×10−4 cm−1 )
-1.5
4.8
-1.3
-4.9
2.2
0.5
4.3
1.4
-6.1
-0.3
-1.4
2.2
0.2

79

Table 5.2: Experimental ﬁne- and hyperﬁne-free line centers for the C-H2 asymmetric stretch
band of CH2 D radical. Estimates of the frequency precision and accuracy are both 15 MHz.
The calculated values used are from a global least squares ﬁt to Watson’s asymmetric top
Hamiltonian of all the symmetric stretch, asymmetric stretch, and the out-of-plane bending
mode[2] transitions.

N′
1
1
0
2
1
1
2
2
1
2
2
2
3
3
2
2
3
3
3

K′a
0
1
0
0
0
1
1
2
1
0
2
2
0
1
2
2
2
2
3

K′c
1
1
0
2
1
0
1
0
1
2
1
2
3
3
1
0
2
1
1

N′′
2
2
1
2
1
1
2
2
0
1
2
1
2
2
1
1
2
2
2

K′′a
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
2

K′′c
2
2
1
1
0
1
2
1
0
1
2
1
2
2
0
1
1
2
0

Frequency (cm−1 )3137.83351
3143.59854
3145.13926
3149.11486
3152.31315
3164.13198
3167.04007
3169.60393
3171.39394
3172.73286
3175.67875
3178.51875
3181.68072
3184.78745
3190.15783
3193.22184
3197.17710
3207.46030
3209.46638

Exp - Calc (×10−4 cm−1 )
-0.3
-2.7
3.3
-8.8
5.9
-1.6
3.8
7.7
-7.7
-14.2
-4.8
22.9
13.3
-13.1
-4.7
1.4
1.2
-2.3
0.2

80

Table 5.3: Results from the least-squares ﬁt to asymmetric top Watson’s Hamiltonian (AReduction, Ir Representation). The parameters on the top part of the table are from a global
ﬁt including all lines from the symmetric stretch, asymmetric stretch, and the out-of-planebending bands. The second part of the table includes the results of a ﬁt involving the IRdata only. The numbers in parenthesis indicate 1-σ uncertainties of the ﬁt; the residual
standard deviation for the global ﬁt is 17 MHz and for the IR-only ﬁt is 66 MHz.

Parameter Ground State Symmetric Stretch Asymmetric Stretch Out-of-Plane Vibration[2]Simultaneous Fit of all Three Vibrations
A

9.57436(48)9.398(11)9.46583(26)9.22156(75)B

5.90743(17)5.8739(62)5.86369(34)5.78659(29)C

3.61984(23)3.6049(50)3.59607(32)3.66570(24)δJ /10−4

0.50(13)0.31(42)0.04(14)0.38(14)

δK /10−44.26(54)-71(27)8.5(10)2.45(52)∆J /10−4

1.28(31)-4.2(28)

1.67(18)

1.06(29)∆JK /10−4

4.1(11)34(16)

3.97(62)

3.75(98)∆K /10−4

1.3(11)-246(98)

1.69(69)-0.99(84)3065.63346(55)3158.33273(53)560.5420(29)νoSimultaneous Fit to Present IR Data OnlyA

9.5734(21)9.4190(25)9.46639(85)B

5.90502(41)5.88849(59)5.85986(42)C

3.62098(37)3.59270(39)3.59689(24)∆JK /10−4

8.5(4)

16.2(44)8.8(10)3065.6403(17)3158.3336(17)

νo

1.5
1.0

a) Experiment

P Branch
Q Branch
R Branch

0.5
0.0

Obs - Calc
(MHz)

Relative
Intensity

Integrated Absorbance(cm-1x abs x10-5)81b) Simulation
600c) Residuals

-60

3040

3060

3080

3100

-1

Wavenumbers (cm )Figure 5.4: CH2 D symmetric stretch rotational structure and ﬁt results. Panel a) is a plot of
the experimental data shown as a stick plot with the integrated area under each rotational
peak shown as the y-axis; P-branch transitions are in green, Q-branch in blue, and R-branch
in red. Panel b) is a simulation based upon rotational and centrifugal distortion constantsfrom the ﬁt to Watson’s asymmetric top Hamiltonian. Panel c) plots the observed minus
calculated frequency, in MHz, for each of the observed lines.

3Obs - Calc
(MHz)a) Experiment
P Branch
Q Branch
R Branch210b) Simulation

Relative
Intensity

Integrated Absorbance(cm-1x abs x10-5)8260c) Residuals

0
-60

3140

3160

3180

3200
-1

Wavenumbers (cm )Figure 5.5: CH2 D asymmetric stretch rotational structure and ﬁt results. Panel a) plots theexperimental data as a stick plot with the integrated area under each rotational peak shownas the y-axis; P-branch transitions are in green, Q-branch in blue, and R-branch in red.
Panel b) is a simulation based upon rotational and centrifugal distortion constants from theﬁt to Watson’s asymmetric top Hamiltonian. Panel c) plots the observed minus calculated
frequency, in MHz, for each of the observed lines.

5.3.2

Fine and Hyperfine Structure

As illustrated in Figs. 5.2 and 5.3, each rotational line has a complex lineshape asa consequence of partially resolved ﬁne and hyperﬁne structure. The largest contribution
to the lineshape is the spin-rotation interaction with the hyperﬁne structure manifesting
itself as a general broadening of the peaks seen in Fig. 5.6. Spin-rotation interaction is the83
coupling between molecular rotation, (N), and electron spin, (S) described by:
Hsr = (1/2)∑εα,β (Nα Sβ + Sβ Nα )

(5.1)

α,β

where εα,β is the spin-rotation tensor and α and β are the labels for the principal axis[134].
For molecules with orthorhombic symmetry, only the diagonal terms in the spin-rotation
tensor are non-zero. The ﬁne structure terms for methyl radical ground vibrational state
are known to be εbb = -354(5) MHz and εcc = -3(63) MHz[135, 115]. As a ﬁrst approximation, the spin-rotation tensor values for CH2 D can be estimated by scaling the corresponding
diagonal values for CH3 by the corresponding A, B, C rotational constant ratios. This is
at least a reasonable ﬁrst order anticipation, since spin-rotation interaction couples electron
spin density (i.e., independent of isotopomer) with rotation around each of the three principal axes, whose semiclassical frequency scales inversely with the corresponding moment ofinertia. The scaled values for the spin-rotation constants are εaa = -354 MHz, εbb = -218
MHz, and εcc = -2.3 MHz, which are used as initial estimates in the high resolution lineshapeﬁts.
Similarly, it is also possible to use the known CH3 hyperﬁne constants to make a
prediction for the CH2 D hyperﬁne structure. The nuclear hyperﬁne Hamiltonian consistsof the Fermi contact interaction, the dipole-dipole interaction and the electric quadrupole
interaction, respectively:
Hhf = HF + HDD + HeQ

(5.2)

where
HF = a F I · S(5.3)

HDD = S · TDD · I(5.4)

HeQ = I · TeQ · I(5.5)

where Fermi contact (aF (H) , aF (D) ) represents the largest terms and TDD and TeQ are secondrank traceless tensors smaller in magnitude[134, 136, 137]. The Fermi contact parameter is

84

Asymmetric Stretch

4110a) rotation

e)

110

101

101

NKaKc

2

0
b) spin-rotation

1/2

3/2

1/2

3/2

2

% Absorbance

J
1

0

3/2
c) H-atom Fermi Contact

1/2

5/2

1/2

3/2

2

F1
1

0
d) D-atom Fermi Contact and Data

2

1
Ground State

0

0
.2

.1

.1

-0

0

-1

W avenumbers (cm ).23164.15-03164.12Upper State

Relative Energy (GHz)

Figure 5.6: Segmented simulation of ﬁne and hyperﬁne structure of the 110 ← 101 transition
for CH2 D in the asymmetric stretch mode. Panel a) shows a simulation and stick spectrumof the transition based upon a 70 MHz Doppler with and no ﬁne or hyperﬁne structure
followed by successive inclusion in panel b) of spin-rotation (εaa ,εbb ,εcc , in panel c) H-atom
Fermi contact term (af (H) ), and panel d) D-atom Fermi contact (af (D) ) terms. Panel e)illustrates how the energy level structure is split upon each successive addition of terms.

85
proportional to the nuclear g-factor, so aF (D) can be reliably estimated from aF (H) andthe g-factor ratio of g(H)/g(D) = 6.514 for H vs D nuclei. Indeed, by way of validation,
the Fermi contact parameter for CH2 D has been measured in a krypton matrix using ESR
techniques and found to be aF (H) = -64.74 MHz and aF (D) = -9.896 MHz[125], i.e., in a ratioof aF (H) /aF (D) = 6.541. Since Fermi contact interactions are slightly sensitive (∼ 5%) to thematrix environment[138, 135], rather than use matrix values, we ﬂoat one common aF (H)value for the 3 vibrational states, subject to the constraint that aF (H) /aF (D) = 6.541. The
other two terms in the nuclear hyperﬁne Hamiltonian, dipole-dipole and electric quadrupole,
generate negligibly small splittings (∼ 1 MHz) even at our sub-Doppler resolution in the slit
jet. For example, previous study of CH3 radical in our group attempted to obtain TDD andfound it to be ≤ 1 MHz[135]. Since this tensor also scales proportionally with the nuclear
g-factor, it should decrease upon deuteration[136] and will be too small to resolve in CH2 D.
Similarly, there will be a non-zero electric quadrupole interaction for CH2 D due to nuclear
spin I(D) = 1, but the electric quadrupole coupling constant (eQq) is predicted to be a few
hundred kHz and thus can be safely neglected in the analysis[139, 140, 141].
To extract the relevant information on spin rotation and Fermi contact interactions
from the sub-Doppler IR lineshapes requires coupling diagonalization of the above Hamiltonian with a least squares ﬁtting routine. To achieve this, all ﬁne and hyperﬁne transitions
and intensities are calculated for each N′Ka′ Kc′ ← N′′Ka′′ Kc′′ rovibrational line, convoluted over an
instrumental proﬁle, and compared with experiment, exploiting a lineshape ﬁtting program
developed and extensively tested for analysis of CH2 Cl and CH2 F data[142, 143, 127]. To
minimize correlation issues, the full set of high resolution lineshapes is ﬁt simultaneously,
including a minimum of three scans over each rovibrational line for both the symmetric andasymmetric stretch manifold. All three non-zero elements of the spin-rotation tensor (εaa ,εbb , εcc ) as well as the Fermi contact term (aF ) are varied for each of the three vibrational
states, with a common residual Doppler width for all transitions. The results are summarized in Table 5.4 and will be discussed below in Sec. 5.4. With these ﬁtted lineshapes, it is86then straightforward to extract the pure rovibrational line center frequencies (i.e., ﬁne- andhyperﬁne-free) used in the analysis described previously in Sec.5.3.1.
Table 5.4: Comparison of ﬁne and hyperﬁne structure parameters from FTIR study[2], scaled
estimates based on methyl radical, and least-squares ﬁt results of the IR experimental line
shapes. All values are in MHz. Note that aF (H) was ﬂoated in the ﬁt, the aF (D) parameter was
calculated using the experimentally determined ratio of 6.541. The numbers in parenthesis
are 1-σ uncertainties from the least-squares ﬁt.
Parameter Ground State(from FTIR
study[2])εaa-444(42)εbb-135(13)εcc
aF (H)aF (D)

5.4

Ground State(scaled from
CH3 )
-354
-218
-2.3

Ground State(ﬁt results)

Symmetric
StretchAsymmetricStretch-353.4(3)-226.0(3)-6.7(3)-62.4(2)-9.54-352(2)-220(1)-3.4(8)-68.5(5)-10.47-350.4(2)-224.8(3)-2.5(2)-74.6(2)-11.40Discussion
We ﬁrst compare the experimental ﬁne and hyperﬁne values for CH2 D with our pre-dictions based upon the CH3 radical. As shown in Table 5.4, the spin-rotation tensor values
for each of the three vibrational states are in remarkably close agreement with the εaa =-354 MHz, εbb = -218 MHz, and εcc = -2.3 MHz estimates discussed above, with a rms deviation of < 4 MHz. By way of additional conﬁrmation of the ﬁt quality, even the considerably
smaller magnitude Fermi contact parameters for the H/D nuclei are also in consistently good
agreement with our expectations based on CH3 . Interestingly, our reported spin rotation values diﬀer by 50-100 MHz from an earlier study of the out-of-plane umbrella mode (εaa =-444(42) MHz and εbb = -135(13) MHz[2]), which clearly deserves further discussion. By way
of example, Fig. 5.7b displays i) experimental data for the 000 ← 111 asymmetric stretchtransition in CH2 D along with ii) a lineshape simulation using the current spin-rotation
constants, revealing deviations well outside of experimental S/N and resolution constraints.
By way of contrast, Fig. 5.7a shows a similar plot based on predictions from the present

87
study, which ﬁts the experimental data extremely well. The source of this discrepancy isunclear; however, one possibility is that the previous analysis did not include Fermi contact
interaction terms in the Hamiltonian, which for incompletely resolved transitions could skew
the spin-rotation parameters in a least squares ﬁt. A second issue is that the previous studies
were performed at room temperature and with Doppler limited resolution, which requires
sampling spin rotation ﬁne structure in a set of much higher rotational states than populated in a supersonic jet. Both the higher resolution of a sub-Doppler slit jet study and theexcellent agreement with scaled predictions based on CH3 generate strong conﬁdence in thepresent ﬁne/hyperﬁne analysis for CH2 D radical.
5.4.1

Intensity Analysis

The intensity of a given transition depends upon a nuclear spin weight, a Boltzmann
factor, and a Hönl-London Factor. The two hydrogen atoms in CH2 D are fermions eachwith nuclear spin I = 12 ; thus the overall wavefunction of the molecule, ψtotal = ψelectronicψvibrational ψrotational ψnuclearspin , must be antisymmetric with respect to exchange of thesehydrogen nuclei. As the electronic wave function can be thought of as a p-like orbital
perpendicular to the plane of the molecule, ψelectronic must be antisymmetric with respect
to 180◦ rotation about the C-D axis (for a C2v planar reference geometry). The vibrational
wave function, ψvibrational , is always symmetric with respect to H atom exchange for themolecule in the ground vibrational state. Since the A-axis is the same as the C2v axis, therotational wave function, ψrotational , is symmetric for even Ka values and antisymmetric for
odd Ka values. Of the four possible nuclear spin wave functions, ψnuclearspin , three (ortho, I =√ √1) have even symmetry (αα, ββ, 1/ 2 (αβ + βα)), and one (para, I=0) has odd symmetry√ √(1/ 2 (αβ − βα)). This implies that states with even/odd Ka quantum numbers willcorrespond to 3:1 nuclear spin weights.
A second contribution to relative intensity comes from thermal population of the lower
rotational state. The experimental integrated line intensity, Sexp , for a rovibrational transi-

88

a)

Asymmetric Stretch

0.6

111 line

000
Data
Fit

% Absorbance

0.3

0.0
b)

Data

0.6

Simulation (based
upon Kawaguchi, 2001)

0.3

0.0

3145.133145.15-1
Wavenumbers (cm )Figure 5.7: Comparison of ﬁne structure splitting of the 000 ← 111 transition from theasymmetric stretch mode. Panel a) plots the data, in red dots, and the results of the ﬁt
results from the present study (black line). Panel b) plots the data from the current study,
in red dots, and a lineshape simulation based upon spin-rotation constants from the FTIR
study[2] (blue line). In the simulation, the upper and lower state spin-rotation constants
are set equal and the hyperﬁne constants are those found in the present study. The highresolution of the data allows for a reﬁnement of the spin-rotation constants from the FTIR
study.

tion, from lower state, i, to upper state, j, is[132]Sexp = Ni l(So )ij

(5.6)

where
Ni = NvibogNS gJ −(Ei )/kTrot
e
QNS
rot

(5.7)

where the absorption pathlength is l = 64 cm, (So )ij is the line strength per rotational state,

89
Nvib
o is the population in the ground vibrational state, gN S and gJ are the nuclear spin andSmagnetic quantum number degeneracies, and QN
rot is the rotational partition function fora given nuclear spin symmetry. Fig. 5.8 shows the experimental integrated line intensity,
scaled by the line strength factors, plotted semi-logarithmically against the ground state
rotational energy. The slope of the graph reveals that the molecules are well described by arotational temperature of 23(1) K.

Symmetric Stretch

ln[Sexp Q/(Sij gNS gJ fNS)]

gNS = 3gNS = 1

-9

Asymmetric Stretch
gNS = 3gNS = 1

-10

-11

-12

Trot = 23(1) K

0

10

20

30

40

-1

Erot (cm )Figure 5.8: A semi-logarithmic plot of experimental integrated line intensities scaled by thecalculated linestrength factors plotted against the rotational energy of the lower state. The
symmetric and asymmetric stretch lines are denoted by ﬁlled and open symbols, respectively
with the ortho lines are triangles and the para lines are squares. The solid lines represent
least-squares ﬁts of the data to a straight line.

Information about the relative intensities of the bands can also be extracted from this90
Boltzmann plot. In particular, the y-intercept diﬀerence between asymmetric and symmetric CH stretches is the logarithm of the associated IR intensity ratio, which is found to be
Iasym /Isym = 1.93(22). By way of comparison, the calculated ([B3LYP/6-311++G(3df,3pd)
basis set][3]) relative intensity of the two bands is 2.38, i.e., slightly higher than the experimental ratio but smaller than the standard 3:1 bond-dipole prediction for a 120 degree HCH
bond angle[143]. It is worth noting that this behavior is quite diﬀerent from what was observed for both CH2 F and CH2 Cl radicals in our group[143, 142], where the symmetric stretch
was found to be anomalously strong compared to the asymmetric stretch (i.e., Iasym /Isym <1) due to vibrationally induced charge ”sloshing” of electron charge along the carbon-halidebond direction. The vibrational transition strength behavior in CH2 D is clearly unaﬀectedby any strongly dipolar C-X bond, yielding results within 50% of the simple bond-dipole
picture.

5.4.2

Vibrational Force Constants

There has been a rich history of spectroscopic analysis and modeling of CH3 radical vibrations. In 1967, Pimentel and coworkers used force constants from analysis of CH3
bending spectra to predict frequencies for CD3 bending modes and to analyze out-of-plane
and in-plane bending motion using a normal coordinate analysis[109, 114]. With inclusionof the CH3 gas phase C-H stretching data, Hirota et al. exploited the known frequencies
to calculate an approximate harmonic force ﬁeld for the molecule[144]. Soon thereafter,
Nibler and coworkers obtained the IR inactive symmetric C-H stretch in CH3 by narrow
band laser Raman methods, and with this inclusion used the high-low frequency separation method of Wilson[145] to predict the stretching frequencies for all four H/D methyl
radical isotopomers[117]. Meanwhile, Spirko and coworkers developed nonrigid inverter
Hamiltonian methods capable of describing the umbrella and C2v vibrations of ammonia
simultaneously[146, 147, 148, 149, 150, 151], which were subsequently applied to CH3 andCD3 [152, 153, 154]. Soon afterwards, Westre et al. obtained data on the Raman active

91
stretches and ﬁrst overtones for all four isotopic species. This inﬂux of new overtone data
facilitated an analysis based on the harmonically coupled anharmonic oscillator (HCAO)
model developed by Child[155] and Mills[156, 157] but it was still necessary to treat the CH
and CD stretch manifolds separately for the four isotopomers[158]. With the additional highresolution for CH2 D from this work, we now have 9 of 10 in-plane CH and CD stretching frequencies, covering all 4 H/D isotopomers of methyl radical, with the symmetric CD stretchof CHD2 as the only missing fundamental mode. With this more comprehensive body of highresolution data, our goal is to provide a predictive model for CH and CD in-plane stretching
dynamics in all four H/D isotopomeric species.
Table 5.5: Results from least-squares ﬁt of the vibrational frequencies to the harmonicallycoupled Morse oscillator model (HCMO) and then to an HCMO model that includes 2:1
Fermi coupling. The residual standard deviation of the HCMO plus Fermi coupling ﬁt was
2.0 cm−1 .
Parameter
De (∗10−10 ergs)a (Å−1 )frr′ (cm−1 )Scaling Factor

HCMO
HCMO and Fermi Interaction
7.9(5)
7.1(4)
1.9(7)
2.02(6)2606.8065()
2211(280)
0.79 (7)

We approach this analysis with three increasing levels of complexity. As the simplest
level, we model each of the three stretches as harmonic oscillators (i.e., frr and fθθ ) and withharmonic coupling between each of the stretches (i.e., frr′ ). This is essentially a normal mode
analysis for the high frequency in-plane vibrations, with results analytically expressible interms of the G matrix elements from Wilson et al.[145]. Indeed, a similar high-low frequency
separation analysis was performed by Nibler and coworkers[117], who used the force constantobtained from CH3 stretching frequencies to predict frequencies for all stretching vibrationsof the H/D isotopomeric species. The results of our ﬁt are in Table 5.5 and the ﬁt residuals
are shown in Fig. 5.9. Note that the CH stretch data ﬁt signiﬁcantly better to the harmonicmodel than the CD stretches; this trend had been noted previously by several groups andattributed to anharmonicity in the CH and CD bonds[117, 158]. As we shall see below,

92
a more likely explanation is that CD stretch vibrations prove to be more susceptible toresonant interactions with the bending overtones.

20a) CH Stretching Region

HCMO
HCMO + Fermi
HCHO

Experimental - Calculated (cm

-1

)

0

-20
2950

3000

3050

3100

3150

3200

b) CD Stretching Region

20

0

-20
2150

2200

2250

2300

2350

2400

20

0

-20

c) 1st Stretching Overtone Region

4350

4500

6000

6150

-1

Wavenumbers (cm )Figure 5.9: The experimental values minus the calculated values for all nine of the experimentally known stretches for each of the three models is shown. The black circles show
residuals from a ﬁt to a harmonically coupled harmonic oscillator model, the red squares are
the residuals from the harmonically coupled Morse oscillator model (HCMO), and the blue
triangles are residuals from the HCMO model but with 2:1 Fermi interactions added into
the model. Panel c) shows diﬀerence between the experimental frequencies for the overtones
and the predicted frequencies based upon the ﬁt to the fundamental modes.

This modest level of agreement motivates our second level of attack, using harmonicallycoupled Morse oscillators (HCMO). In this model, each CH bond is represented by a simple
Morse oscillator, with potential coupling between stretches described within the harmonic

93
approximation. The Morse oscillator model takes into account the diﬀerence in anharmonicity between the CH and CD bonds. This can easily be seen by looking at the Morse oscillator√
2 2
Denergy level expression: E(nα ) = ω(nα + 21 ) − ωx(nα + 12 )2 with ω = 2a~ ( 2µ) and ωx = a2µ~
noting that ω and ωx scale diﬀerently with mass. The full model employed was ﬁrst developed by Halonen and Child and used on a variety of tetra-atomic systems including methaneand fully deuterated methane[159]. The Hamiltonian is
3
3 ∑
3
∑
∑
1
2
−arα 2
Htot =[ Gαα pα + D(1 − e) ]+[−Gαβ pα pβ + frr′ rα rβ ]2α=1α=1 β>α(5.8)

where the sums over α and β run over the three local mode bonds, rα are the bond displacement coordinates, D and a are the Morse oscillator dissociation energy and range parameter,
respectively, and the Gαα and Gαβ are the corresponding Wilson G-matrix elements divided
by hc to keep the expression in cm−1 . The ﬁrst summation simply represents the Morseoscillator Hamiltonian, for which the analytic solutions are well known and therefore provide
a convenient 3D product basis of Morse oscillator eigenfunctions. The second summation
contains both kinetic and potential energy coupling terms in the harmonic approximation,
the matrix elements of which we can obtain in a Morse basis from expressions provided by
Halonen and Child[159]. However, it is possible to simplify these matrix elements further
using recursion relations[160] and eliminate any need for calculating gamma functions altogether. The required matrix elements of the p and r operators can then be expressedas:√a< n + j | p | n >= (ı~(−1)j+1 ) (k − 2n − 1)(k − 2(n + j) − 1)2j∏(n + m) 1] 2 (1 − δj0 );
j≥0
[
(k
−
n
−
m)
m=1
(−1)j+1< n + j | r | n >=
a

(5.9)

√

(k − 2n − 1)(k − 2(n + j) − 1)j(k − 2n − j − 1)j
∏ (n + m) 1
j≥1
[
]2 ;
(k
−
n
−
m)
m=1

(5.10)

94n∑

1(1 − δn0 ))].
(5.11)k−n−mm=1√
where n labels the Morse oscillator eigenfunctions, k = 2 (2µD)/(a~), µ is the reduced< n | r | n >= a−1 [ln(k) − Φ(k − 1 − 2n) +(mass, a and D are the Morse oscillator range parameter and dissociation energy. Diagonal
matrix elements in r (i.e., < n | r | n >) contain the digamma function, Φ , which can becalculated for one value of k - 1 - 2n numerically and then readily extended to all otherarguments via recursion relations[160]. The results converge quickly with basis set size;
speciﬁcally, it is only necessary to include up to n = 5 quanta in each of the three stretches
to achieve convergence out to 5 digits (≈ 0.1 cm−1 )With eigenvalues from the harmonically coupled Morse oscillator model, we simultaneously ﬁt the 9 planar stretching modes for which the gas phase experimental frequencies
are known. The resulting Morse oscillator and harmonic coupling constants from the ﬁt arelisted in Table 5.5, with the residuals between experimental and calculated frequencies fromthe harmonically coupled Morse oscillator model are shown in red squares in Fig. 5.9. The
Morse oscillator model does a qualitatively better job than a simple harmonic treatment,
yielding an rms deviation of ≈ 5.2 cm−1 vs 14 cm−1 . However, it is still clear that theﬁt quality is much better for CH than CD stretches, which thus suggests the presence ofadditional terms still necessary to include in our Hamiltonian treatment.
To investigate this, we consider the eﬀect of the inclusion of such cubic coupling terms in
our third level of analysis. As a starting point, we need energies for the bend overtones, which
we calculate using the harmonic frequencies reported by Cunha de Miranda et al.[126] The
resulting energies of these states along with the CH and CD stretch fundamental frequencies
are shown in Fig. 5.10. The labeling used for the CH3 and CD3 levels is (ν1 , ν2 , ν3l , ν4l ) andthe notation used to label the states for CH2 D and CHD2 is (ν3 , ν4 , ν5 , ν6 ) with ν1 and ν2labeled separately. The planar bending overtone and combination frequencies are calculated
in the harmonic approximation based on fundamental frequencies of Cunha de Miranda etal.[126]. Noticeably, the CD stretch manifolds for many of the isotopomers have nearby two

95
quanta states of the correct symmetry for a strong 2:1 Fermi interaction. This contrasts
strikingly with the CH stretch manifolds, which do not have such candidate states withinseveral hundred wavenumbers. This plot makes it clear that the energy diﬀerences between
the CD stretch fundamental and the CD bend overtone is smaller than for the CH stretch
fundamental, i.e., consistent with a greater impact of Fermi resonances in the CD stretch
than for the CH stretch manifold.
Since the dataset we are ﬁtting includes only the fundamentals in the CH and CD
stretches, we are reluctant to introduce many more parameters into the model. Even though
we lack exact frequencies for the perturbing states, it seems clear that there are consistently
states that give rise to a Fermi interaction. Therefore we added a Fermi interaction to theMorse oscillator model using a simple two-state perturbation matrix as a qualitative way totest the idea. This is not such an unreasonable assumption, since the states that appear to bepoorly described by the unperturbed coupled Morse oscillator model have nearby two-quantabending states. To account for this perturbation, Herzbergs’ classic model[86] is used,
En0 − EWW

Ei0 − E=0(5.12)

where W is the coupling matrix element and E0i and E0n are the unperturbed energy levels. Based on the above analysis and to minimize the number of additional parameters,
we therefore start from theoretically predicted coeﬃcients of the (a†s ab ab + as a†b a†b ) and(a†s ab ab′ + as a†b a†b′ ) terms in the cubic expansion of the normal mode Hamiltonians for CH3 ,CH2 D, CHD2 , and CD3 , evaluated at the MP2/aug-ccpVTZ level with GAUSSIAN 09 forthe equilibrium methyl radical structure.[131] Here a and a† represent harmonic oscillator
raising and lowering operators, respectively, with the s and b subscripts denoting stretching
and bending modes.
We then ﬁt the full set of observed CH and CD fundamental frequencies using a suitably
augmented Hamiltonian and in a Morse oscillator basis, scaling the theoretical stretch/bend
cubic terms obtained from the electronic structure calculation by a single adjustable param-

'0103

'0020

'0020

'0203
2000
'0401
'0003

'0003
'0202

96

'0103

3500

CH3

a)

v
v

CD3

b)

'0010
3

'0600

3000

0

3

1

1000

'1003

1

03

'0003
03

'0003

'0202

'0202
'1003
'0203
'0401

2

02

02

'0400
'0002
'0004

'0002

'0600

21

'0202

1

'0203
'0201

-1

Wavenumbers (cm )

'0004

'0004

'0202

2500

v
v

'0010
'3000

0
'4000
''320002(0400)
2000

A'

1

E'

'1002

CH2D
'0006
'0200

'1002
'0003
'0401
'0001

v
v

d)

CHD2

'000010
5
'3000

'2200
'1400
'0006
3000

100000

3000

E'

1

'0202

c)

02

'0002
'0201
'0003

A'

'1400

3500

2

1

(0002)

'2001

'2200

3

1000

1

2001

'2001
'0401

v

1000001'0001(0200)

2000

'2000

1001

'1001

1200

2500

'1200

'0002
0002
'0400

v

'0002
0002

0201

2

2000
1200

'2000
'1200
'0400

2000

A

B

1

v
v

'000010'0201'010000

2

A

1001
'1001
'0201
0201

5

'010000

2

B

1

2

'0200
'0200

Figure 5.10: Graphs showing the fundamental stretching modes nearby overtone and combination bands that are of the correct symmetry to perturb each stretching mode. CH3
and CD3 , shown in panels a and b, are of D3h symmetry and the states are labeled with
(ν1 , ν2 , ν3l , ν4l ); the symmetric stretch is of A′1 symmetry and the doubly-degenerate asymmetric stretch is of E′ symmetry. The asymmetrically substituted isotopomers, CH2 D and
CHD2 , have three stretches: two of a1 symmetry, in red, and one of b2 symmetry, in blue.
The labels for these species are (ν3 , ν4 , ν5 , ν6 ), with the stretches labeled explicitly. It is clearthat the CD3 symmetric stretch, the CH2 D CD stretch, and the CD stretches in CHD2 allhave nearby states that could have a Fermi interaction with a nearby bending overtone.

eter, γ. The results of the ﬁt, as well as predicted frequencies for the ﬁrst overtones and theas yet unobserved CHD2 asymmetric stretch fundamental are listed in Table 5.6 with theﬁtting parameters in Table 5.5. This model now yields a 2.5-fold improvement in ﬁtting thefundamental frequency data (σ = 2.0 cm−1 vs. 5.2 cm−1 ). Of equal importance, it appears to
predict the overtone transitions reasonably well (see Table 5.6), even though these data are

97
not included in the least-squares analysis. It is also noteworthy that the dissociation energy
and other Morse parameters are consistent with experimental data for CH bond strengths,
further indicating that the model provides a physically reasonable description of the stretches
in methyl radical.[101] Finally, this improved treatment clearly suggests that the lower quality ﬁt of the CH and CD stretch frequencies to the ﬁrst two models is not dominated byisotopic anharmonicity eﬀects, but rather due to a greater proximity of bending states in the
CD manifold able to participate in resonant 2:1 Fermi interactions.
Table 5.6: Frequencies of the vibrational fundamentals and ﬁrst overtones obtained fromthe harmonically coupled Morse oscillator model (HCMO) with the addition of three quantaFermi coupling. Only the fundamental frequencies were included in the ﬁt; the overtones
were predicted by the model.
Isotopomer
CH3

CH2 D

CHD2

CD3

5.5

Stretch Experimental Frequency Results From Fit
ν13004.436
3005.532ν15959.7ν33160.82118
3157.67ν13065.63346
3065.332ν16059.4
ν22283.32283.372ν24509.3
ν53158.33273
3159.17ν13114.577
3116.182ν16114.9ν2
2221.52220.772ν24412.5
ν5
ν12156.52155.222ν14294.1
ν3
2381.0886
2382.76

Predicted By Fit
5962.666058.634505.426107.52
4413.312384.60
4294.69

Conclusion
First high-resolution IR spectra of supersonically cooled singly-deuterated methyl radi-cal has been obtained, which has permitted investigations of both the A-type symmetric C-Hstretch and B-type antisymmetric C-H stretch vibrations. Band origins, rotational constants

98and centrifugal distortion constants have been ﬁt to a Watson asymmetric top Hamiltonian,with ﬁne structure and hyperﬁne parameters determined using a least-squares-ﬁtting program previously developed in the group. The spin-rotation constants for the ground, symmetric, and asymmetric stretch states are obtained, with Fermi contact terms for each of thethree states as well.
Since the spectroscopy of CH3 radical has been extensively studied, this allows us tomake simple predictions on the CH2 D constants, which in most cases proved to be in very
good agreement with experiment. The predicted band origins of the symmetric and asymmetric CH stretches are each within one standard deviation of 10 cm−1 from the experimental
value. This illustrates the utility of a scaling factor based upon analysis of previous C-Hstretches in a family of radicals, combined with high level B3LYP calculations for predicting
the band origin of new radical species. The spin-rotation constants have been demonstrated
to scale with the A, B, C rotational constants upon deuteration. This again proved a usefulapproximation, with all predicted spin-rotation constants within 10 MHz of experimental
values.

Chapter 6
Understanding the 2 Π-2 Σ+ bands in ethynyl radical: from the inclusion ofsatellite branches to vibronic coupling

6.1

Introduction
The ethynyl radical (C2 H) is known to be a key intermediate in the combustionof acetylene (C2 H2 ),[15] which is of considerable interest both in chemical and industrial
applications.[161] Additionally, acetylene is known to be produced as an intermediate in
the combustion of fuel-rich mixtures of larger hydrocarbons.[17] Therefore, the formationof C2 H and its further reactions with other intermediates likely play an important role inmodeling combustion mechanisms. Because of this, much experimental work has focused on
elucidating the kinetic rate constants for the reaction of C2 H with a variety of species, witha recent review by Laufer and Fahr summarizing experimental ﬁndings.[162] Of particularinterest is the formation of soot as a byproduct of the combustion of hydrocarbon fuels.
While it is known that soot formation occurs through a nucleation process of larger andlarger polycyclic aromatic hydrocarbons (PAHs) until solid particulates form, it is still not
clear which mechanistic steps in combustion initiate PAH formation in the ﬁrst place. One
postulated mechanism[163] involves the reaction of free radical intermediates, such as phenyl
Portions of this chapter have been previously published as Sharp-Williams, E. N.; Roberts, M. A.;
Nesbitt, D. J. J. Chem. Phys. 2011, 134, 064314. and Sharp-Williams, E. N.; Roberts, M. A.; Nesbitt, D.
J. Phys. Chem. Chem. Phys. 2011, 13, 1747417483.

100
radical (C6 H5 ), with small unsaturated hydrocarbons such as C2 H2 and C2 H.
The ethynyl radical has also been detected in outer space[16] and is thought to participate in similar reaction chemistry there, even though the environment of the interstellar
medium is quite diﬀerent from that of a ﬂame. Speciﬁcally, C2 H has been postulated to contribute to the formation of larger hydrocarbons and carbon clusters, particularly in denseinterstellar clouds.[164] Additionally, Vuitton et al. proposed the following mechanism forthe formation of haze particles in the atmosphere of Titan:[165]C2n H2 + hν → C2n H + H(6.1)

C2n H + C2m H2 → C2(n+m) H2 + H(6.2)

net : C2n H2 + C2m H2 → C2(n+m) H2 + 2H

(6.3)

The above reaction sequence shows the potential involvement of C2 H (and other acetylenelike species) in the nucleation process in space, i.e., the transformation of gas-phase molecules
to particulate-sized species. Given the key role that ethynyl radical plays in both combustionand space chemistry, it is no surprise that there have been many theoretical and experimental
studies conducted to fully understand its ground and excited states. Accurate kinetic modeling of reaction chemistry occurring both on earth and in space rests largely on the quality of
the laboratory data available for the molecules present in that chemistry, including reactive
intermediates such as C2 H.
Previous experimental work on C2 H has been quite extensive, with many studies measuring rate coeﬃcients for reactions of C2 H with a variety of neutral molecules.[162, 166,
167, 168, 169, 170, 171] In addition, there has been a large amount of spectroscopic work,with studies aimed at understanding the vibrationless ground state,[16, 172, 7, 4] the excited
vibronic levels of the X̃ state,[173, 174, 175, 176, 177, 178, 179, 20, 180] and the electronically
excited Ã state.[181, 182, 183] To summarize the most important results, these gas-phase
experimental studies conﬁrmed that (i) the ground state of C2 H is 2 Σ+ symmetry,[7] (ii)the lowest energy vibration, the CCH bending vibration, is located at 371.6034 cm−1 above

101
the vibrationless level of the ground state,[174] and (iii) the C-C stretching vibration is located at 1840.5711 cm−1 above the vibrationless level.[175] The location of the third andﬁnal vibrational frequency, that of the C-H stretch, is still under some debate, althoughcurrently the leading candidate[173] has been a band observed near 3299 cm−1 . What makes
this interesting is that the electronically excited Ã state of 2 Π symmetry is very low-lying
with respect to the ground state, located only approximately 3600 cm−1 higher.[181] It is
speculated that diﬃculties in assigning the C.H stretch mode may be due to anomalous Ã
state coupling with vibrational levels in the X̃ state.
Indeed, multiple challenges arise from vibronic coupling of the three lowest electronic
states in C2 H, namely, 2 Σ+ (A′ ), 2 Π (A′ ), and 2 Π (A′′ ). The 2 Π electronic state of linear
C2 H splits into two potential energy curves of A′ and A′′ symmetries as the molecule bends,
due to the interaction of electronic and vibrational angular momenta, i.e., the Renner-Teller
eﬀect. The potential energy surfaces for these three electronic states are expected to lie
close in energy, again with the 2 Π curves located approximately 3600 cm−1 above that of the2

Σ+ ground state. The 2 Π (A′′ ) and 2 Π (A′ ) components of the Renner-Teller pair become

nondegenerate as the molecule bends, with the 2 Π (A′′ ) state lower in energy. While the
Wigner noncrossing rule permits the X̃ 2 Σ+ (A′ ) state to cross the 2 Π (A′′ ) curve, there
is an avoided crossing of the same symmetry X̃ 2 Σ+ + (A′ ) and 2 Π (A′ ) curves for bent,
C-C stretch excited geometries, which yields a conical intersection (often termed a “pseudo”
Jahn-Teller interaction) between these two states. Additionally, crossing of the X̃ and Ã
state potential energy curves is expected to occur near the equilibrium Ã state geometry.
This can promote strong vibronic mixing between the lowest energy vibrational levels of theexcited state with excited vibrational levels of the ground state, which may account for aweak fundamental C-H stretching vibration.
As a direct consequence of the strong non-Born-Oppenheimer eﬀects present in C2 H,
there have been numerous theoretical studies focused on unraveling the spectral complexity
and accurately calculating vibronic level positions for the ground and ﬁrst excited states.[184,102
185, 186, 187, 188, 189, 190, 8, 9] Speciﬁcally, recent work by Tarroni and Carter[8, 9]
has predicted the frequencies, intensities, and identities of all the vibronic and electronictransitions in C2 H up to 6400 cm−1 . This variational method[191] requires diagonalizing
the full Hamiltonian in a basis of electronic, vibrationally, and spin-rotational symmetry
adapted functions, in conjunction with high level ab initio diabatic potential energy surfaces
for all three electronic states: 2 Σ+ (A′ ), 2 Π (A′ ), and 2 Π (A′′ ).[8] Of considerable interest withregard to the this work, their calculations found that the Ã 2 Π electronic character is actually
spread over as many as ﬁve Π levels in the 3300.4300 cm−1 range, with the largest fraction(0.301) contained in a state located at 3604.4 cm−1 . Indeed, their assignments for many
levels in the 3300.4300 cm−1 region reﬂect Ã 2 Π character in addition to highly vibrationallyexcited X̃ state contributions, indicating signiﬁcant mixing between states probed at typicalfrequencies in the near IR.
Of particular relevance to this work, there have been several observations of 2 Π-2 Σ+bands in C2 H, both in the matrix[192, 193, 194] and in the gas phase,[195, 18, 19, 196, 197,
198] as well as high resolution gas phase studies of C2 H hot bands[181] and 13 C2 H/C2 D
isotopomers.[177, 182] Speciﬁcally, Curl and co-workers[18, 19] were ﬁrst to observe andidentify four 2 Π-2 Σ+ bands in C2 H between 3675 and 4125 cm−1 . Using color center laser
absorption spectroscopy with magnetic rotation for sensitivity enhancement, they observed
rotationally resolved IR bands with origins at 3692.606, 3786.096, 4012.259, and 4107.874
cm−1 . This magnetic rotation technique generates small shifts in observed peak positions,[19]which required detailed corrections in order to infer ﬁeld free line frequencies in each of the2

Π-2 Σ+ bands. Their production of C2 H by discharging pure argon over polyacetylene de-posits created near room temperature radicals, which allowed them to observe rovibrationaltransitions originating from N′′ levels up to as high as N′′ = 19. Reported accuracy in determining line center positions was claimed to be 0.001 cm−1 (30 MHz),[18] with overalllineshapes broadened to approximately 0.01 cm−1 (300 MHz).
Later, Forney et al.[194] observed the same four 2 Π-2 Σ+ bands, previously reported

103
in the gas phase, in a matrix of solid neon at 3685.8, 3759.4, 3983.9, and 4085.4 cm−1 ,respectively. These spectra were taken using a Fourier transform interferometer with 0.1
cm−1 (3 GHz) resolution and accuracy. Shepherd and Graham[193] veriﬁed these same 2 Π2Σ+ absorption bands in an argon matrix and conﬁrmed their assignment to ethynyl radical

via similar studies of its isotopomers, C2 D and 13 C2 H. Vervloet and Herman[196] observed
these four 2 Π-2 Σ+ bands via Fourier transform emission spectroscopy of C2 H in the gas
phase. Later, Hsu et al.[197] observed three of the four aforementioned bands using laser
induced ﬂuorescence spectroscopy, exciting gas-phase C2 H radicals to their B̃ electronic state
and recording emission down to many of the vibronic levels in the X̃ state. Zhou et al.[198]reported multiple vibronic bands of C2 H and C2 D, including the four previously reported2Π-2 Σ+ bands between 3675 and 4125 cm−1 , with slow electron velocity-map imaging. Of

particular interest, this work provided Neumark and co-workers report updated assignments
for their observed vibronic bands, based largely on the theoretical results of Tarroni andCarter,[8, 9] to which we will refer later.
The organization of this chapter is as follows. In Sec. 6.2, we present an overview offundamental spectroscopic expectations for 2 Π-2 Σ+ bands, followed in Sec. 6.3 by a brief
discussion of the slit jet discharge experimental apparatus for making jet cooled C2 H. In Sec.
6.4 we present high resolution infrared C2 H radical absorption spectra of ﬁve 2 Π-2 Σ+ bands
reported by Curl and co-workers,[18, 19] and others,[193, 194, 197, 198] for which the current
experimental combination of (i) low radical temperatures (Trot ≈ 12 K), (ii) sub-Doppler
resolution (∆ν ≤ 0.002 cm−1 (60 MHz)), and (iii) high measurement precision (∆νexp ≈0.00033 cm−1 (10 MHz)) signiﬁcantly augment and clarify the previous eﬀorts. In Sec. 6.5.2,
we report reﬁned excited state constants as well as make vibronic assignments for each of the2

Π states, guided by previous experimental and theoretical work mentioned above. Finally,in Sec. 6.6 we explore vibronic coupling interactions, introducing the idea of near resonant
dark states aﬀecting energy levels in the 2 Π upper states as well as discussing prospects ofextending our Hamiltonian model to include this coupling. The chapter is summarized and104
concluded in Sec. 6.7.
6.2

Expectations for 2 Π − 2 Σ+
Figure 6.1 demonstrates the allowed transitions expected for a 2 Π-2 Σ+ band, with theenergy levels rigorously described by a total rotational quantum number (J) and parity (+or -). The additional F1 /F2 labels indicate whether the state corresponds to a lower/higher
energy eigenvalue of the secular determinant for the same J, respectively. Here K = N(end-over-end) + L (electronic orbital) represents angular momentum exclusive of electron
spin, which couples with electron spin S to yield the total angular momentum J = K + S.
(To minimize confusion, we also note the use of other popular notational conventions,[199]
whereby K and N are replaced by N and R, respectively.)
For the lower 2 Σ+ state with L = 0 and S = 0.5, the ground state rotational level (i.e.,
N = K = 0) is nondegenerate with J = 0.5 and labeled F1 . By way of contrast, there are
two possible values of J for K > 0, giving rise to nearly degenerate pairs of F1 (J = K +0.5) and F2 (J = K - 0.5) levels, respectively, of the same parity. Whether the F1 state isabove or below the F2 state for the same K value must be determined experimentally, as
has been done for 2 Σ+ C2 H from high precision microwave measurements.[7, 4] The orderingin Figure 6.1 is consistent with the reported ground state constants from these microwave
studies, with the diﬀerence between the F1 and F2 levels for each K state corresponding tospin-rotation splitting in the lower electronic state. Finally, the overall parity builds on the
ground electronic 2 Σ+ symmetry; thus, the K = 0 (F1 , J = 0.5) level must be + parity, withparity alternating as (-1)K . Note that this implies the presence of nearly degenerate spinrotation levels of the same parity for any K > 0.
For the 2 Π state, energy levels are again described by rotational quantum number(J) and parity (+ or -). The 2 Π state has two manifolds of energy levels, now more widely
separated due to a stronger spin-orbit interaction term in the Hamiltonian. This generates F1(lower) and F2 (upper) manifolds, split roughly by the magnitude of the spin-orbit coupling

105

Figure 6.1: Energy level diagram for both 2 Π and 2 Σ+ states (with spacings exaggerated
for the clearest view) and the possible transitions that can be observed between them. Theenergy levels are labeled as F1 or F2 levels and with the J and parity quantum numbers.
The transitions are denoted with arrows and belong to one of four groups: (1) R1 (also P1and Q1 ), signifying transitions obeying the selection rule of ∆J = 1 (for R1 branch only)
and originating from F1 levels in the 2 Σ+ state and terminating in F1 levels in the 2 Π state;(2) R2 (also P2 and Q2 ), signifying transitions obeying ∆J = 1 (for R2 branch only) andoriginating from F2 levels in the 2 Σ+ state and terminating in F2 levels in the 2 Π state; (3)R12 (also P12 and Q12 ) signifying transitions obeying the selection rule of ∆J = 1 (for R12
branch only) and originating from F2 levels in the 2 Σ+ state and terminating in F1 levels in
the 2 Π state; (4) R21 (also P21 and Q21 ) signifying transitions obeying the selection rule of∆J = 1 (for R21 branch only) and originating from F1 levels in the 2 Σ+ state and terminatingin F2 levels in the 2 Π state.

106
constant, |A|. This work conﬁrms that the spin orbit constant A is negative for each of thefour C2 H 2 Π-2 Σ+ bands; therefore, the 2 Π3/2 spin orbit state (F1 ) lies below the 2 Π1/2 spin
orbit state (F2 ) in Figure 6.1. Every J value in a 2 Π state gives rise to two widely spaced
pairs (F1 , F2 ) of closely spaced energy levels of opposite parity, the diﬀerence between whichcorresponds to lambda-doubling in the 2 Π state. The sign of this lambda-doubling splitting
and thus the ordering of parity labels in the 2 Π state can only be determined from experiment.
It is important to note that the parity labeling in Figure 6.1 speciﬁcally corresponds to thatwhich has been determined in this work for the 2 Π-2 Σ+ band observed at 3692 cm−1 , which
diﬀers from previous studies obtained at slightly lower resolution.
Along with the 2 Σ+ and 2 Π energy levels depicted in Figure 6.1, arrows are drawn into illustrate all allowed transitions in a 2 Π-2 Σ+ band. While previous work of Curl et al.[19]reported observed lines from six main branches, e.g., Ri , Qi , Pi (i = 1,2), corresponding
to ∆J = 1, 0, -1 transitions between Fi levels in 2 Σ+ and Fi levels in 2 Π), there are also six
additional branches indicated in Figure 6.1, often called satellite branches.[200] These satellite branches cross over from F1 ←F2 or F2 ← F1 and are labeled by both states accordingly.
For example, R12 signiﬁes transitions obeying ∆J = 1 that go from F2 levels in 2 Σ+ up to F1
levels in 2 Π. Figure 6.2 shows the predicted intensities for each of these branches, both mainand satellite, as a function of J′′ , where predicted rotational line strengths[6] are functionsof J′′ and the ratio of spin-orbit coupling constant to the rotational constant, Y = A/B. The
predicted intensities in Figure 6.2, therefore, reﬂect the A and B values determined in our
analysis of the 3692 cm−1 2 Π-2 Σ+ C2 H band reported herein.
It is easy from Figure 6.2 to appreciate why previous experimental studies at room
temperature were relatively insensitive to these satellite transitions, with appreciable population mostly in high J′′ (N′′ ) levels.[19] The intensity drops oﬀ quickly with J for thesesatellite transitions, such that above J′′ = 4.5, there is little observable intensity. However,there is considerable oscillator strength in the blowup region from J′′ = 0.5 to J′′ = 4.5 in
Figure 6.2, which are preferentially populated at low rotational temperatures. Thus, it is the

107

Figure 6.2: Predicted intensities for all possible transition types in 2 Π-2 Σ+ bands as a function of J′′ . The circle points with solid lines correspond to the main branches (R1 , P1 , Q1 ,R2 , P2 , Q2 ) and the square points with dashed lines correspond to the satellite branches(R12 , P12 , Q12 , R21 , P21 , Q21 ).

combination of (i) jet-cooled C2 H radicals (12 K) and (ii) high resolution IR spectroscopic
techniques that permits observation of both main branch and satellite branch transitions
with high signal to noise (S/N). Most importantly, this permits much higher frequency pre-108
cision and unambiguous assignment of the transitions, which in turn allows more detailed
characterization of the upper state energy level structure.
6.3

Experiment
The approach for high sensitivity spectroscopic detection of jet-cooled hydrocarbon

radicals via high resolution infrared laser absorption in a slit-jet cooled supersonic dischargesource is reported elsewhere[82, 201, 1] and will be only brieﬂy summarized here. High
resolution IR light (< 2 MHz linewidth) is produced by diﬀerence-frequency generation ofa tunable single mode ring-dye laser (operated with R6G dye) with a ﬁxed frequency single
mode Ar+ laser (operated at 488 nm) in a temperature-tuned, periodically poled LiNbO3(PPLN) crystal. This IR light is split onto a reference InSb detector (cooled to 77 K) anddirected into the vacuum can, where it intersects the jet-cooled beam of radicals 16 times
via a Herriot cell conﬁguration, yielding an absorption path length of 64 cm (16 × 4 cm slit
width). Light coming out of the vacuum can is directed onto a signal InSb detector (alsocooled to 77 K), with transient absorption detected by the diﬀerential change in signal minus
reference beam IR power, synchronous with the 50 kHz modulation of the slit valve pulsed
discharge. Absorption sensitivity is achieved by fast electronic subtraction of common-mode
amplitude noise on the laser beam as well as by phase sensitive lock-in detection at the
50 kHz dc discharge modulation frequency. Relative frequencies are obtained to 10 MHz
precision via a λ-meter and fringe interpolation from the transmission of a marker cavity
with a free spectral range of 250 MHz, whose free spectral range is stabilized absolutely bylocking onto a polarization stabilized HeNe laser. Absolute frequencies are obtained withrespect to known reference lines of stable molecules. Speciﬁcally, for the 3692 and 3786 cm−1
bands, the 111 ← 000 (ν1 = 1←0) and 101 ← 000 (ν3 = 1←0) reference transitions of H2 O
at 3600.95753 and 3779.49376 cm−1 are used, whereas for the 4012 and 4108 cm−1 bands,
the R(0) and R(1) transitions of HF(ν = 1←0) at 4000.9894 and 4109.9363 cm−1 provide asuitable absolute frequency reference.[202, 203]

109
Jet-cooled C2 H radicals are produced by adiabatically expanding a mixture of ≈ 0.04%
acetylene in a 70%:30% neon. helium buﬀer gas through a pulsed slit-jet (operated at 19
Hz, ≈ 1 ms pulse duration), with a square wave modulated discharge (50 kHz) to form
radicals by collisional electron induced dissociation. Optimum discharge conditions are 0.2
A and -450 V bias, utilizing lock-in detection in order to extract the absorption signal
component synchronous with the modulation. For the C2 H lines reported herein, the slit-jet
cooled discharge source yields absorbances from 0.01% to as high as 0.5% on the strongest
C2 H lines. With typical rms noise levels of 0.0025% in a 10 kHz detection bandwidth, thistranslates into signal to noise ratios of 4:1 on the weakest and 200:1 on the strongest lines.
6.4

Results

6.4.1

3600 cm−1 Band

Figure 6.3 shows sample data for the C2 H Ã2 Π ← X̃ 2 Σ+ origin band centered around3600 cm−1 taken with the high resolution slit-jet infrared spectrometer. The black trace isthe experimental data, while the red and pink traces are inverted simulations of the origin
band, using diﬀerent Hamiltonian models for the 2 Π state in each discussed in more detaillater (see Section 6.5.1). The predicted intensities of the simulated lines correspond to
the product of a rotational line strength factor[6] and a Boltzmann factor for a rotationaltemperature of 12 K. Lines from three diﬀerent branches appear in the sample data, thoseof R1 and Q2 (main branches), as well as P21 (satellite branch). As evident in Figure
6.1, the P21 lines appear as blue-shifted shoulders to the corresponding Q2 lines. Typicaltransitions correspond to sub-Doppler absorptions with essentially Gaussian proﬁles and an
experimental linewidth of roughly 60 MHz. The transitions, which are comprised of two
overlapping features (e.g., one main branch line and one satellite line in most cases), areleast squares ﬁt to a superposition of two Gaussian proﬁles, which also yields a comparable
roughly 60 MHz sub-Doppler linewidth.

3596.4721

3610.5429

4.5

4

R1
R12
Q1
3598.9852 3596.0801
3602.2549 3596.4603 3596.0822
3605.2336 3596.5677 3596.4654
3607.9834
3596.5751

J′′ N′′
0.5 0
1.5 1
2.5 2
3.5 3
P1

R2
Q21
3607.2254 3605.3733
3590.2412
3607.2286
3587.6815 3590.2461 3611.3015 3611.3091
3587.6888 3613.3711 3613.3801

Q12

Q23602.4637
3601.4132
3600.5101
3599.3240
3600.1404
3599.0963

P2

3599.3330
3600.1494

3602.4657 3596.6281
3601.4187 3592.6550
3600.5160

P21

Table 6.1: Experimental lines observed in the 3600 cm−1 2 Π-2 Σ+ band (all frequencies in cm−1 ).

110

111

Figure 6.3: Sample experimental data for the 3600 cm−1 band. In this 5 cm−1 region, lines
from the R1 and Q2 main branches were observed, as well as lines from the P21 satellite
branch. The downward going red lines were simulated using our reﬁned excited state constants from Table 6.11 (column 4, excluding the Coriolis coupling perturbation parameters),
the ground state constants determined from previous microwave studies[4], and the energy
level expressions for the unperturbed 2 Σ+ ground state and 2 Π excited state Hamiltonianmodels discussed in Section 6.5.1. The downward going pink lines were simulated similarly
using our reﬁned excited state constants from Table 6.11 (column 4), now including the
perturbation parameters (β0 , νpert and Bpert ) and the perturbative Σ − Π Coriolis coupling
as discussed in Section 6.5.3. The predicted intensities in both the red and pink traces were
calculated using rotational line strength factors for 2 Π-2 Σ+ bands[5] and a Boltzmann factor
for a rotational temperature of 12 K, to be the temperature achieved for our C2 H radicals
produced in a slit-discharge of C2 H2 coupled with supersonic expansion.

Table 6.1 lists the observed line positions for the 2 Π-2 Σ+ origin band. All frequencies
reported in this paper represent an average of three measurements for each experimental line,with a standard deviation of approximately 10 MHz in the three measurements. In Table 6.1,
individual rovibrational lines from each of the six main branches are reported, as well as from112
four of the six possible satellite branches (all observed branches are pictured in Figure 6.1).
Assignments of the observed lines are conﬁrmed by using two-line ground state combination
diﬀerences, based on the previous high accuracy microwave studies.[7, 4] Table 6.2 shows
all possible 2-line combination diﬀerences of the observed lines in Table 6.1, and compares
these to the corresponding ground state energy level diﬀerences (calculated using B, D, andγ constants determined from microwave studies). The experimental combination diﬀerences
agree with the ground state energy level diﬀerences < 20 MHz in most cases. It should be
noted that there are two lines reported in Tables 6.1 and 6.2 for both Q2 (3.5) and P21 (4.5).
Curl and coworkers[182] similarly reported two Q2 (3.5) lines, which they attributed to thepresence of a local perturbation with a crossing at N′ =4. Assignments in the present caseare further conﬁrmed by ground-state combination diﬀerences, which agree with microwave
predictions to better than 10 MHz for both pairs of lines. The implications of the multiple
line shifts in this curve crossing at J′ = 3.5 (or N′ = 4) will be discussed in more detail in
Section 6.5.3.

6.4.2

3692 cm−1 Band

Figure 6.4 shows sample data for the 2 Π-2 Σ+ band centered around 3692 cm−1 takenwith the high resolution slit-jet discharge infrared spectrometer. The black trace is experimental data, while the inverted red trace is a simulation of the 3692 cm−1 band, based on(i) revised excited state constants from this work discussed in more detail later in Sec. 6.5
and (ii) ground state energy levels from previous microwave studies.[7, 4, 173] The intensities of the simulated lines are obtained from the product of (i) rotational line strengths[6]and (ii) jet cooled populations for a rotational temperature of 12 K determined from theBoltzmann analysis of the data (see Figure 6.5). Lines from four diﬀerent branches appear
in this sample data scan, that of R1 and Q2 (main branches) as well as Q21 and P21 (satellite
branches). Most of the observed satellite branch transitions appear as weak shoulders to
main branch transitions, which conﬁrms why these were not resolved/observed in previous

113
−1 2

Table 6.2: Experimental combination diﬀerences for the 3600 cm
with ground state energy level diﬀerences.
Lines
R1 (0.5)
P1 (2.5)R1 (1.5)
P1 (3.5)R1 (0.5)
Q12 (1.5)R1 (1.5)
Q12 (2.5)
P1 (2.5)
Q12 (1.5)
P1 (3.5)
Q12 (2.5)Q1 (1.5)
R12 (0.5)
Q1 (2.5)
R12 (1.5)
Q1 (3.5)
R12 (2.5)R2 (0.5)
P2 (2.5)
R2 (0.5)
Q21 (1.5)R2 (2.5)
Q21 (3.5)
R2 (3.5)
Q21 (4.5)
P2 (1.5)
Q21 (0.5)
P2 (2.5)
Q21 (1.5)Q2 (0.5)
P21 (1.5)Q2 (1.5)
P21 (2.5)
Q2 (2.5)
P21 (3.5)
Q2 (3.5)
P21 (4.5)
Q2 (3.5)
P21 (4.5)

J′′
0.5
2.5
1.5
3.5
0.5
1.5
1.5
2.5
2.5
1.5
3.5
2.5
1.5
0.5
2.5
1.5
3.5
2.5
0.5
2.5
0.5
1.5
2.5
3.5
3.5
4.5
1.5
0.5
2.5
1.5
0.5
1.5
1.5
2.5
2.5
3.5
3.5
4.5
3.5
4.5

ν (cm−1 ) Comb. Diﬀ. (∆ν) (cm−1 ) E′′ (cm−1 )3598.9852
8.739103598.2461
8.738737
3602.2549
14.5661
2.912593
3587.6888
17.478260
3598.9852
8.744003590.2412
8.743957
3602.2549
14.5733
2.912593
3587.6815
17.485569
3590.2461
0.00508.738737
3590.2412
8.743957
3587.6888
0.007317.478260
3587.6815
17.485569
3596.0822
0.00212.912593
3596.0801
2.915725
3596.4654
0.00518.738737
3596.4603
8.743957
3596.5751
0.007417.478260
3596.5677
17.485569
3607.2254
14.5704
2.915725
3592.6550
17.485569
3607.2254
0.00322.915725
3607.2286
2.912593
3611.3015
0.007617.485569
3611.3091
17.478260
3613.3711
0.009129.140304
3613.3801
29.130907
3596.6281
8.74528.743957
3605.3733
03592.6550
14.5735
17.485569
3607.2286
2.912593
3602.4637
0.00202.915725
3602.4187
2.912593
3601.4132
0.00528.743957
3601.4187
8.738737
3600.5101
0.005917.485569
3600.5160
17.478260
3599.3240
0.009029.140304
3599.3330
29.130907
3600.1404
0.009029.140304
3600.1494
29.130907

2+

Π- Σ band compared∆E′′ (cm−1 ) ∆ν-∆E′′ (MHz)8.73873710
14.565668

128.743957

3

14.572977

100.005221-8

0.007309-1

0.00313232

0.005221-3

0.0073093

14.569844

160.0031321

0.007309

90.009397-108.743957

37

14.572977

170.003132-34

0.00522190.007309-43

0.009397-110.009397-11a

The ground state energy levels were calculated using the B, D and γ constants from previous microwave
studies[7, 4].

gas-phase experimental studies.[18, 19] It is straightforward to predict from Figure 6.1 that
the P21 progression should appear as blue-shifted shoulders on the Q2 progression, with the114

Figure 6.4: Sample experimental data for the 3692 cm−1 band. In this 5 cm−1 region, lines
from the R1 and Q2 main branches were observed, as well as lines from the P21 and Q21
satellite branches. The downward going lines were simulated using our reﬁned excited state
constants from Table 6.8, the ground state constants determined from previous microwave
studies[4], and the matrix elements for the Hamiltonian discussed in Section 6.5.1. The
predicted intensities were calculated using rotational line strength factors for 2 Π-2 Σ+ bands[6]and a Boltzmann factor for a rotational temperature of 12 K.

diﬀerence between Q2 (0.5) and P21 (1.5) lines, for example, equaling spin-rotation splittingin the K = 1 2 Σ+ ground state level. Blowup examples for each type of satellite line areshown in Figs. 6.6 and 6.8 for two other 2 Π-2 Σ+ bands centered around 3786 and 4107 cm−1 ,respectively. Typical linewidths correspond to sub-Doppler absorption proﬁles, i.e., Gaussian ﬁts determine an experimental linewidth of roughly 60 MHz and frequency precision of
approximately 10 MHz in the Ne/He expansion. Those transitions comprised of an overlapof two lines (one main branch line and one satellite line in most cases) are well-represented by

115
a simple superposition of two Gaussian proﬁles with individual linewidths of approximately
60 MHz.

Figure 6.5: Boltzmann plot for the 3692 cm−1 band. Sexp are the experimental intensities(in % absorbance) and Sij are the rotational line strength factors from Zare[6]. E′′rot wascalculated using the ground state microwave constants[7, 4] and the appropriate energy level
expressions for a 2 Σ+ state (see Section 6.5.1. The points were ﬁt to a line, whose slope isequal to -1/kT.

Table 6.3 lists line positions for the 2 Π-2 Σ+ band centered around 3692 cm−1 observedin this work. Frequencies reported represent an average of three measurements for eachexperimental line, with a typical rms standard deviation of ≈ 10 MHz. From inspectionof Table 6.3, individual rovibrational lines from each of the six main branches are observed
as well as from four of the six possible satellite branches. Transitions from the P12 andR21 branches are not seen which were predicted to have the lowest transition intensities
even at low J′′ (see Figure 6.2). Since the ground state is known to high accuracy,[7, 4]

116
assignments of observed lines can be unambiguously conﬁrmed by using two-line groundstate combination diﬀerences. Table 6.4 displays all possible combination diﬀerences fromthe observed lines listed in Table 6.3, compared against corresponding ground state energy
level diﬀerences from microwave studies.[7, 4] The experimental combination diﬀerences (CD)agree with precision ground state energy level diﬀerences to ≈ 10 MHz rms, with 19 out of
20 2-line CD’s < 20 MHz. Indeed, the only 2-line CD in excess of 20 MHz involves theweakest satellite line R12 (2.5) at the S/N limit, which introduces an additional 20-30 MHz
uncertainty in determining frequency diﬀerences.
Figure 6.5 shows a Boltzmann plot of the peak absorbance data used to determine
the rotational temperature of the slit-jet generated C2 H radicals, which yields a rotationaltemperature of 12(1) K. A corresponding plot based on integrated versus peak intensities
yields a rotational temperature of 11(1) K, i.e., the same within experimental uncertainty.
This rapid drop oﬀ in population with energy at such low rotational temperatures explains
why lines higher than J′′ = 4.5 are not observed. However, the resulting lower spectralcongestion and higher resolution provide valuable new information on C2 H, as described in
more detail in Sec. 6.5.
It is also of interest to predict the radical densities at the slit jet oriﬁce, based on a
total absorbance of A = 0.0048(1) summed over all lines. The integrated cross-section permole for this band, as calculated by Tarroni and Carter,[9] is 302 km/mol, which implies
5.0 × 10−17 cm/molecule or a peak cross section of 2.5 × 10−14 cm2 /molecule for a typical
60 MHz sub-Doppler linewidth. Based on a 64 cm Herriot cell absorption path length (4cm × 16 passes), Beer’s law predicts the concentration of C2 H radicals in the probe region
to be ≈ 3.0 × 109 radicals/cm3 . If we correct for the 1/r drop oﬀ of radical density 5-10mm downstream from a 300 µm slit width, this translates into roughly 1011 radicals/cm3
at the slit oriﬁce. This is notably lower than the 1014 radicals/cm3 densities often observed
from electron dissociative attachment of alkyl halides in the slit jet expansion, likely, due
to C2 H being rapidly lost by reactive collisions with acetylene to make longer carbon chain

Q12

P1

R2

Q21

Q2

P21

P2

3689.5367
3689.4304

3.5 3 3700.9092

4.5 4 3703.4859

3680.6822

3703.0175 3691.5404 3692.1807

2.5 2 3698.1755 3689.5308 3689.4685 3680.6747 3683.3196 3703.0102 3700.8098 3692.1739 3692.8956 3684.0917

3700.8051 3698.6650 3692.8900 3693.8020 3687.9497

Q1

1.5 1 3695.2475 3689.4632 3689.1587 3683.3140

R123698.6620 3696.6940 3693.8000

R1

0.5 0 3692.0582 3689.1566

J′′ N′′

Table 6.3: Experimental lines observed in the 3692 cm−1 2 Π-2 Σ+ band (all frequencies in cm−1 ).

117

118
−1 2

Table 6.4: Experimental combination diﬀerences for the 3692 cm
with ground state energy level diﬀerences.
Lines
R1 (0.5)
P1 (2.5)R1 (1.5)
P1 (3.5)R1 (0.5)
Q12 (1.5)R1 (1.5)
Q12 (2.5)
P1 (2.5)
Q12 (1.5)
P1 (3.5)
Q12 (2.5)Q1 (1.5)
R12 (0.5)
Q1 (2.5)
R12 (1.5)
Q1 (3.5)
R12 (2.5)R2 (0.5)
P2 (2.5)
R2 (0.5)
Q21 (1.5)R2 (1.5)
Q21 (2.5)R2 (2.5)
Q21 (3.5)
P2 (1.5)
Q21 (0.5)
P2 (2.5)
Q21 (1.5)Q2 (0.5)
P21 (1.5)Q2 (1.5)
P21 (2.5)
Q2 (2.5)
P21 (3.5)
a

J′′
0.5
2.5
1.5
3.5
0.5
1.5
1.5
2.5
2.5
1.5
3.5
2.5
1.5
0.5
2.5
1.5
3.5
2.5
0.5
2.5
0.5
1.5
1.5
2.5
2.5
3.5
1.5
0.5
2.5
1.5
0.5
1.5
1.5
2.5
2.5
3.5

ν (cm−1 ) Comb. Diﬀ. (∆ν) (cm−1 ) E′′ (cm−1 )3692.0582
8.738603683.3196
8.738737
3695.2475
14.5652
2.912593
3680.6822
17.478260
3692.0582
8.744303683.3140
8.743957
3695.2475
14.5728
2.912593
3680.5747
17.485569
3683.3196
0.00578.738737
3683.3140
8.743957
3680.6822
0.007617.478260
3680.6747
17.485569
3689.1587
0.00212.912593
3689.1566
2.915725
3689.4685
0.00538.738737
3689.4632
8.743957
3689.5367
0.006017.478260
3689.5308
17.485569
3698.6620
14.57032.915725
3684.0917
17.485569
3698.6620
0.00302.915725
3698.6650
2.912593
3700.8051
0.00478.743957
3700.8098
8.738737
3703.0102
0.007317.485569
3702.0175
17.478260
3687.9497
8.74438.743957
3696.6940
03684.0917
14.5733
17.485569
3698.6650
2.912593
3693.8000
0.00212.915725
3693.8020
2.912593
3692.8900
0.00568.743957
3692.8956
8.738737
3692.1739
0.006817.485569
3692.180717.4782602+

Π- Σ band compared∆E′′ (cm−1 ) ∆ν-∆E′′ (MHz)8.738737-4
14.565668-18.743957

914.572977-60.00522113

0.007309

80.00313230

0.0052212

0.007309-41

14.56984

140.003132-50.005221-17

0.007309

08.743957

11

14.57298

100.003132-32

0.00522111

0.007309-16

The ground state energy levels were calculated using the B, D and γ constants from microwave studies[7,4].

species such as C4 H, C6 H, etc. In any event, the densities are clearly high enough to achieve
excellent signal to noise on all 2 Π-2 Σ+ rovibrational bands reported in this work.

119

Figure 6.6: Sample data for the 3786 cm−1 band showing blow-ups of satellite transitions appearing as shoulders to main branch transitions. The downward going vertical bars represent
simulations of each peak, with predicted frequency positions determined from excited state
constants from Table 6.9, the ground state constants from previous microwave studies,[4]and the corresponding Hamiltonian expressions discussed in Sec. 6.5.1 for the 2 Σ+ and 2 Πstates.

120
6.4.3

3786 cm−1 Band

Figure 6.6 shows sample data for the 2 Π-2 Σ+ vibronic band observed near 3786 cm−1
via high resolution IR absorption spectroscopy, with examples of stronger and weaker transitions. The two panels each show two lines corresponding to main and satellite branchtransitions. For example, the top panel shows the main branch line, Q1 (2.5), with the satellite branch line, R12 (1.5), appearing as a red-shifted shoulder to the Q1 line. From Figure
6.1, these two transitions terminate in the same J′ = 2.5 level in the 2 Π3/2 upper state,
and therefore they are spaced by the ground state spin-rotation splitting in K′′ = 2. The
downward going gray vertical bars represent simulations of each peak, where predicted frequency positions are determined from the excited state constants in Table 6.9 (column 2),
the ground state constants from previous microwave studies,[4] and the appropriate matrix
element expressions discussed in Sec. 6.5 for the 2 Σ+ and 2 Π states. The intensities of thesimulated vertical bars are determined from the product of rotational line strength [6] andBoltzmann factors at T = 12 K, with Table 6.5 summarizing all observed lines in this band.
As discussed in Sec. 6.4, the assignments of these lines are conﬁrmed by 2-line combination
diﬀerences, which agree with microwave predictions[7, 4] to approximately 10 MHz rms.

6.4.4

4012 cm−1 Band

Figure 6.7 shows sample high resolution IR data for the 2 Π-2 Σ+ vibronic band centeredaround 4012 cm−1 . The black and red traces reﬂect experimental data and simulation, thedetails of which will be discussed in Sec. 6.5. Brieﬂy, the predicted frequency positions are
determined from least squares ﬁtted excited state constants reported in Table 6.9 (column
3) and ground state constants from previous microwave studies,[4] with predicted intensities
based on line strengths and Boltzmann population analysis. The assignments of these lines(summarized in Table 6.6) are conﬁrmed by 2-line combination diﬀerences, which agree to ≤20 MHz (10 MHz rms) with ground state energy level diﬀerences from microwave studies.[7, 4]

P1

R2

Q21

Q2

P21

P2

4.5 4

3.5 3 3795.0307

2.5 2 3792.4220

3783.9134

3783.9995

3784.6626

3795.7767 3784.6580 3784.9627

3777.9840 3795.7700 3793.3773 3784.9551 3785.3101

3793.3720 3790.9739 3785.3050 3785.8468 3779.9588

Q12

1.5 1 3789.6689 3783.9937 3783.8582 3777.9776

Q13790.9716 3788.7031 3785.8444

R12

0.5 0 3786.7216 3783.8552

J′′ N′′ R1Table 6.5: Experimental lines observed in the 3786 cm−1 2 Π-2 Σ+ band (all frequencies in cm−1 ).

121

122
Interestingly, the higher signal to noise in Figure 6.7 reveals several strong lines in the black
trace neither due to C2 H nor the precursor acetylene molecule C2 H2 . Given the reactivityof C2 H and its proclivity to form longer chain species with C2 H2 , this is not surprising.
Indeed, C2 H in the jet will lead to a range of possible radicals as well as stable long chainhydrocarbon species. As an evidence of this, for example, we have obtained high resolution
jet-cooled spectra of larger chain species such as diacetylene and triacetylene, which are
currently under analysis. The presence of such C4 and C6 species provides evidence for richbimolecular chemistry taking place, even on the 5-10 µs time scale of the slit jet expansion
reaching the laser probe region.

6.4.5

4107 cm−1 Band

Figure 6.8 shows sample data for the ﬁnal 2 Π-2 Σ+ band presented in this work. The twopanels in Figure 6.8 each show two experimentally observed lines, one line corresponding toa main branch transition and one to a satellite branch transition (the upper panel shows two
members of a progression). The downward going gray vertical bars represent simulations ofeach peak, where the predicted frequencies are determined using the excited state constantsfrom Table 6.9 (column 4), the ground state constants from previous microwave studies,[4]and the appropriate matrix element expressions discussed in Sec. 6.5 for the 2 Σ+ and 2 Πstates. Intensities are determined from rotational line strengths[6] and Boltzmann factors at
T = 12 K. Observed lines are listed in Table 6.7, where assignments have been conﬁrmedby 2-line combination diﬀerences which agree to ≤ 20 MHz (10 MHz rms). This band is thestrongest of the four reported in this study, which permits us to observe transitions out toJ′′ = 5.5. Even at S:N ≈ 200:1 for the strongest lines, we still do not observe either the P12
or R21 satellite branches, which are predicted from Figure 6.2 to be the weakest.

J′′ N′′
0.5 0
1.5 1
2.5 2
3.5 3
4.5 4

R1
R12
Q1
4013.0237 4010.1831
4015.9505 4010.3518 4010.1849
4018.7740 4010.5068 4010.3567
4021.4712
4010.5140
4010.6225
4004.2798
4001.3785

Q12

R2
Q21
4017.1221 4014.7656
4019.6241 4017.1243
4004.2849 4022.1393 4019.6291
4001.3851

P1

Q2
P21
P2
4011.9363
4011.5397 4011.9384 4006.0219
4011.3739 4011.5447 4002.5515
4011.3020 4011.3813

Table 6.6: Experimental lines observed in the 4012 cm−1 2 Π-2 Σ+ band (all frequencies in cm−1 ).

123

J′′ N′′
0.5 0
1.5 1
2.5 2
3.5 3
4.5 4
5.5 5

R1
R12
Q1
4108.1850 4105.3033
4111.1875 4105.4674 4105.3054
4113.9629 4105.4490 4105.4720
4116.5719
4105.4559
4119.0456
4105.3186
4105.0915
4099.4415
4096.6149

Q12

R24113.0433
4115.3346
4099.4460 4117.6418
4096.6220 4119.9066
4093.5710 4122.1030

P1

Q214110.9019
4113.0453
4115.3396
4117.6488

Q2
P21
P2
4108.0465
4107.3677 4108.0484 4102.1579
4106.8849 4107.3725 4098.4727
4106.4642 4106.8924 4094.9383
4106.0492

Table 6.7: Experimental lines observed in the 4107 cm−1 2 Π-2 Σ+ band (all frequencies in cm−1 ).

124

125

Figure 6.7: Sample experimental data for the 4012 cm−1 band. In this 5 cm−1 region, lines
from the R1 , Q1 , and Q2 main branches were observed, as well as lines from the R12 , P21 ,and Q21 satellite branches. The downward going lines were simulated using our reﬁned
excited state constants from Table 6.8, the ground state constants determined from previous
microwave studies[4], and the matrix elements for the Hamiltonian discussed in Section 6.5.1.
The predicted intensities were calculated using rotational line strength factors for 2 Π-2 Σ+bands[6] and a Boltzmann factor for a rotational temperature of 12 K.

6.5

Analysis

6.5.1

Hamiltonian

The eﬀective Hamiltonian used for ﬁtting the ground 2 Σ+ state is
H = BN2 − DN4 + γ(N·S)

(6.4)

126

Figure 6.8: Sample data for the 4107 cm−1 band showing blow-ups of individual satellite
transitions appearing as shoulders to individual main branch transitions. The downward
going gray vertical bars represent simulations of each peak, whereby the predicted frequency
positions were determined using the excited state constants from Table 6.8, the ground state
constants from microwave studies[4], and the Hamiltonian expressions discussed in Section
6.5.1 for the 2 Σ+ and 2 Π states. The intensities of the vertical bars were determined from arotational line strength factor[6] and a Boltzmann factor for T = 12 K.

127
which gives the following energy level expressions
E(F1 ) = BN(N + 1) − DN2 (N + 1)2 + γN/2

(6.5)

E(F2 ) = BN(N + 1) − DN2 (N + 1)2 − γ(N + 1)/2

(6.6)

Since the B′′ , D′′ , and γ ′′ rotational and spin-rotational ground state constants have been
determined to high accuracy from microwave data, we simply ﬁx these to the literature
values[4] in all ﬁts, namely, B′′ = 1.456 825 10, D′′ = 3.519 60 × 10−6 , and γ ′′ = -0.002 088
45 cm−1 .
The Hamiltonian utilized for ﬁtting the upper 2 Π state is[199]H = Hrot + Hso + Hsr + HLD(6.7)

Hrot = BR2 , where R = ((J − S) − L)2(6.8)

Hso = A(L·S)(6.9)

Hsr = γ((J − S)·S)(6.10)

HLD = q/2(J+ + J− )2 − (q/2 + p/4)[(J+ + J− )(S+ + S− )(6.11)

2+(S+ + S− )(J+ + J− )] + q/2 + p/2(S+ + S− )Note that unlike previous rotational analysis,[195, 19, 197] we have adopted a case (a) basis
for describing the 2 Π state, since we are safely in this limit with only low J states populated
in the jet. Additionally, we have omitted higher order terms in the Hamiltonian due tocentrifugal distortion of lambda doubling (i.e., pD and qD ), since this should be a negligible
eﬀect at the low J levels we observe. Furthermore, Curl and coworkers noted the presenceof signiﬁcant deviations between observed and ﬁtted line positions either for an isolated J′
level (local perturbation) or over a series of high J′ levels (global perturbation).[181, 19] It is
possible that the anomalous magnitudes of such pD and qD terms reﬂect partial compensation
for such perturbing eﬀects in the 2 Π states. Therefore, these terms have been excluded tosee if the low J′ data can be explained and understood by this simpler Hamiltonian model.

128
Evaluated in a Hund’s case (a) basis, this results in a fourth order secular determinant
yielding values of (i) F1 , F2 and (ii) parity (+/-) for a given total J, the solutions of which
are detailed elsewhere.[199]6.5.2

Fitting Results

The 3692 cm−1 band data are least squares ﬁt to the matrix eigenvalue expressions forthe eﬀective 2 Π Hamiltonian described above to determine revised excited state constants.
Table 6.8 reports ﬁt results for the present jet cooled data (column 5) along with the resultsfrom previous room temperature studies (column 2) of Curl et al.[19] Note that the residual
standard deviation (σ = 13 MHz) of the high resolution ﬁt to the simpliﬁed Hamiltonianis extremely good, consistent with experimental uncertainty in frequency measurement and5 × smaller than previous studies. The results for B, D, γ, and A are also in excellent
agreement with Curl’s reported values but with an apparent sign reversal in the extracted
lambda doubling parameters.
Table 6.8: Excited state constants for the 3692 cm−1 2 Π-2 Σ+ band (all in cm−1 ). Numbers
in parentheses constitute the error in each reported value.
Excited State
Constants
ν0B
D (x 105 )γApqpD (x 105 )qD (x 105 )st devaCurl’s Fitof Curl’s Data
3692.606(1)1.41171(2)-0.51(1)0.0158(1)-5.405(1)0.0044(4)0.00967(3)-1.1(4)0.02(3)0.002

Revised Fitof Curl’s Data
3692.604(2)1.41187(7)-0.37(4)0.0157(5)-5.406(5)-0.005(1)-0.0094(1)2.6(1.3)-0.37(8)0.0079

Revised Fit IIThis work

3692.606(2)1.41178(8)-0.45(4)0.0162(5)-5.407(6)-0.0033(8)-0.00981(5)3692.6084(2)1.41169(4)-0.34(15)0.0164(1)-5.4018(4)-0.0021(1)-0.00950(2)0.00940.00042

From Curl et al.[19].
Revised fit of all Curl’s reported lines[19] for the 3692 cm−1 band, excluding lines indicated as strongly
overlapped.
c
Revised fit of Curl’s data[19] with the revised Hamiltonian in this work, discussed in Section 6.5.1, i.e.,
no centrifugal distortion of lamda doubling terms.
b

129
To test for possible errors in the Hamiltonian treatment, we also have performed tworevised ﬁts of data of Curl et al. for this band.[19] Revised ﬁt I (column 3) uses Curl’s originalcase (b) eﬀective Hamiltonian expression, with higher order pD and qD distortion constants
explicitly included. We also pursue a revised ﬁt II (column 4) to Curl’s data, which uses
the case (a) Hamiltonian given above, but neglecting pD and qD distortion constants. In an
attempt to minimize eﬀects due to perturbations, Curl et al.[19] ﬁtted only an unspeciﬁed
subset (53 out of 59), whereas our work ﬁts all unblended reported lines. Nevertheless, thereasonable zeroth order expectation would be that revised ﬁts I and II should yield essentially
identical results as the original analysis.[19]Immediately clear from Table 6.8 is that there is a sign reversal for p and q between
results of Curl et al. and the revised ﬁts as well as a suggestion of an additional sign
reversal in pD and qD between the two nominally identical ﬁts (columns 2 versus 3) to thesame case (b) Hamiltonian. By way of contrast, there is an excellent agreement between
ﬁts to the current high resolution results with jet cooled C2 H (column 5) and the tworevised ﬁts for data of Curl et al. (columns 3 and 4). Speciﬁcally, each treatment yields
lambda doubling constants p and q < 0, in contrast yet consistent with a systematic parity
misassignment in the previous work.[19] Interestingly, Hsu et al.[197] also inferred negative
signs for the lambda doubling constants in this 2 Π state from dispersed ﬂuorescence excitation
spectroscopy but had ascribed this diﬀerence to use of l -doubling versus lambda doublingterms in the Hamiltonian.[197] The current high resolution analysis clearly conﬁrms that
this is due to an early parity misassignment in the 2 Π state, as conﬁrmed by subsequentdiscussions with Curl. Indeed, sign changes in the lambda doubling Hamiltonian were later
introduced by Curl and co-workers in their analysis of C2 D spectra, though without revisiting
the analysis of the C2 H bands currently under consideration. Note that since parity reversal
is numerically equivalent to a sign change in p, q, pD , qD , such an error would have had
no inﬂuence on quality of ﬁts originally reported by Curl et al. However, this can and does
have a major impact on using high resolution data to identify the correct symmetry of dark

130states perturbing the Ã state spectrum, as will be demonstrated elsewhere.
In summary, the ﬁt to high resolution data at low J states shows that the simpliﬁed
Hamiltonian treatment describes the 2 Π-2 Σ+ band at 3692 cm−1 very well, with a standard
deviation on the order of experimental precision (≈ 10 MHz). Additionally, the excited state
constants for this Hamiltonian (after appropriate sign reversal in p, q) are in good agreementwith those found by Curl et al.,[19] with ﬁvefold smaller residuals than ﬁts to the much larger(albeit lower resolution) data sets in previous works.[19, 197] To make this more explicit,
Figure 6.9 displays a plot of deviations from best ﬁt parameter predictions as a function of J
and branch. The upper panel in Figure 6.10 shows residuals (observed-predicted) for the R1(circles), Q1 (squares), and R12 (diamonds) branches, while the lower graph shows residuals
for the R2 (circles), Q2 (squares), and P21 (diamonds) branches. In all cases, the points are
clustered tightly around zero, with an rms value of 0.0003 cm−1 (10 MHz) and the largest
deviations ≤ 0.001 cm−1 (30 MHz).
Similar least squares ﬁts have been carried out on the high resolution 2 Π-2 Σ+ bands
centered around 3786, 4012, and 4107 cm−1 , based on the simpliﬁed Hamiltonian for the 2 Πstates discussed above and with results presented in Table 6.9. Both the 3786 and 4107 cm−1
bands (columns 2 and 4) are very accurately described, as evidenced by standard deviations(≈ 0.0003 cm−1 ) close to experimental precision. However, this is not the case for the 4012
cm−1 band, which is clearly not as well ﬁt by the eﬀective Hamiltonian for the excited state.
This is evident in the 30 × larger standard deviation (σ = 0.01 cm−1 (300 MHz)) of the leastsquares ﬁt for the 4012 cm−1 band, which even though small by typical Doppler broadened
infrared standards, corresponds to 30 × higher than our sub-Doppler experimental precision.
This point is clearly illustrated in Figure 6.10, which plots the residuals (observed.predicted)
from the least squares ﬁt of our data, where again the upper graph is a plot of the residuals
for the R1 (circles), Q1 (squares), and R12 (diamonds) branches, and the lower graph is aplot of the residuals for the R2 (circles), Q2 (squares), and P21 (diamonds) branches. Notethe tenfold increase in the scale from Figure 6.9, and that the residuals are now scattered

131

Figure 6.9: Residuals (observed-calculated) from ﬁt, described in Section 6.5.2, for the 2 Π2 +
Σ centered around 3692 cm−1 . The upper graph shows residuals for the R1 (circle points),
Q1 (square points), and R12 (diamond points) branches, while the lower graph shows residuals
for the R2 (circle points), Q2 (square points), and P21 (diamond points) branches.

132

Figure 6.10: Residuals (observed-calculated) from ﬁt, described in Section 6.5.2, for the 2 Π2 +
Σ band centered around 4012 cm−1 . The upper graph shows residuals for the R1 (circle
points), Q1 (square points), and R12 (diamond points) branches, while the lower graph shows
residuals for the R2 (circle points), Q2 (square points), and P21 (diamond points) branches.

133
−1

−1

−1 2

Table 6.9: Excited state constants for the 3786 cm , 4012 cm , and 4107 cm
Π- Σ+
bands (all in cm−1 ). Numbers in parentheses constitute the error in each reported value.
Excited State 3786 cm−1
Constants
Bandν03786.0910(2)B
1.42266(6)D (x 105 )2.3(3)
γ
0.00254(10)A-2.4406(4)p-0.0016(1)q-0.02735(2)st dev
0.000424012 cm−1
Band
4012.284(4)1.437(1)-16(6)-0.011(2)-2.16(1)-0.0023(28)-0.0411(4)
0.011

2

4107 cm−1
Band4107.8753(5)1.41429(9)-1.2(2)0.0006(3)-3.286(1)-0.0171(3)-0.02195(4)0.0016around zero by on the order of 0.01-0.02 cm−1 . It is particularly evident in the upper panelin Figure 6.10 that there is a precipitous dip at J′ = 2.5, indicative of a “local” perturbationin the F1 manifold caused by a close-lying dark state of C2 H. By way of contrast, note theextremely tight clustering of residuals for each of the three transitions to the same upper J
state, a point we will return to in Sec. 6.5.3. Part of this is to be expected; since Q2 andR12 (as well as Q1 and P21 for the lower panel) transitions reach the same ﬁnal parity level,
this agreement is completely consistent with 2-line combination diﬀerences for the groundstate and thus experimental precision. However, the fact that we also see a similar tightclustering of the Q1 and R1 transitions, which necessarily access states of opposite parity, isparticularly noteworthy. Speciﬁcally, this means that the local perturbation of the F1 J′ =2.5 parity levels must arise from a near resonant state also with both +/- parity levels inclose proximity. From Figure 6.1, this implies that the dark state cannot be 2 Σ; i.e., it must
be a state with Λ > 0.
To rule out that this eﬀect at J′ = 2.5 is caused by a global perturbation, a leastsquares ﬁt has been performed on the 4012 cm−1 data, but with the lines terminating in
J′ =2.5, F1 manifold, namely, R1 (1.5), P1 (3.5), Q1 (2.5), R12 (1.5), and Q12 (2.5), removed
from the data set. The results for this revised ﬁt are presented in Table 6.10 (column 3),compared with those presented earlier in Table 6.9 and summarized in column 2 of Table

134
6.10. Already by leaving out transitions to this more strongly perturbed upper state, thestandard deviation of the ﬁt improves ﬁvefold from 0.01 to 0.002 cm−1 . Interestingly, there
is an additional manifestation of this local perturbation in the F2 manifold in the vicinityof J′ = 3.5, as evident in the lower panel of Figure 6.10. Similar to what is seen in the F1
manifold, the tight clustering of the Q2 /P21 and R2 transitions (which by symmetry must
access diﬀerent parity levels) conﬁrms the presence of local vibronic mixing from a darkstate with closely spaced levels of both + and - parities, i.e., 2 Π, 2 ∆, etc. Based on the (i)quality of high level ab initio vibronic calculations and (ii) sparse vibrational level density
for C2 H at only 3500-4000 cm−1 of internal energy, this bodes well for being able to identify
the actual vibrational state responsible, as discussed below.
Table 6.10: Comparing excited state constants for the 4012 cm−1 2 Π-2 Σ+ band (all in cm−1 ),with and without perturbed 2 Π F1 levels. Numbers in parentheses constitute the error ineach reported value.
Excited State
Constants
ν0B
D (x 105 )γApq
st dev

4012 cm−1 Revised Fit for 4012 cm−1
Band
Band
4012.284(4)4012.2867(9)1.437(1)1.4393(3)-16(6)-5.7(1.3)-0.011(2)-0.0093(5)-2.16(1)-2.148(2)-0.0023(28)-0.0035(6)-0.0411(4)-0.04094(9)0.011
0.0022

Revised fit of the 4012 cm−1 band as discussed in Section 6.5.2, whereby the lines that terminated in
F1 J = 2.5 were removed from the data input to the fit.
a

′

6.5.3
6.5.3.1

Perturbation Analysis
3600 Band

The present least squares ﬁt to the unperturbed Hamiltonian in Table 6.11 (column 2
with σ = 0.13 cm−1 ) fails to reproduce the 10 MHz (0.0003 cm−1 ) experimental accuracy of

135
our sub-Doppler measurements. At ﬁrst glance, this would appear to be an even worse ﬁtquality than the results of Curl and coworkers (σ = 0.004 cm−1 ). However, it is important tonote that the previous analysis was for room temperature spectra with strongly perturbed
low J transitions selectively removed from the analysis, thus precluding a direct comparison
with the current treatment of all lines in the jet cooled spectrum.
Table 6.11: Excited state constants for the 3600 cm−1 2 Π-2 Σ+ band (all in cm−1 ). Numbers
in parentheses constitute the error in each reported value.
Excited State Constants Curl’s Fit This work Iν03600.353(1) 3600.38(5)B
1.40529(1)1.40(1)D (x 105 )
1.710(5)-31.4(34.4)
γ-0.0127(1)-0.005(29)A-7.219(2)-7.2(1)p-0.0016(4)0.03(3)q
0.00816(2)-0.009(5)5pD (x 10 )1.7
qD (x 105 )-0.407(9)
νpert
Bpert
β0
st dev
0.004
0.13This work II
3600.3521(2)1.40499(5)1.6(2)-0.0092(1)-7.2191(1)0.0083(1)-0.00748(2)3611.45(2)1.450(2)0.11765(7)0.00051a

From Curl and coworkers[181].
Fit of all lines given in Table 6.1 to the unperturbed model.
cFit of all lines given in Table 6.1 to the perturbed model presented in Section 6.5.3, which includes the
local perturbation of the 2 Π1/2 state.
b

The data in column 2 of Table 6.11 clearly indicate that the sub-Doppler high resolution
spectrum is poorly ﬁt by the unperturbed Hamiltonian model for the 2 Π state. This point
is further emphasized in Figure 6.3, which compares a sample scan region of high resolution
spectral data (in black) with unperturbed predictions (in red) calculated using the energy
level expressions from the Hamiltonian model for the 2 Π state given above and the constants
determined in column 4, along with the energy level expressions for the 2 Σ+ state (given
in eqn (2) and (3)) and the ground state constants determined from previous microwave
studies.16 While the experimental R1 lines and the ﬁrst two members of the Q2 and P21

136
progressions agree, deviation between experiment and the unperturbed simulation becomemuch more prominent at Q2 (2.5)/P21 (3.5) and Q2 (3.5)/P21 (4.5). To highlight the source of
discrepancy in our model, Figure 3 displays plots of the residuals for the Q2 , P21 , R2 , andP2 branches for the unperturbed model ﬁtting results versus J′ . Particularly evident is thatthe residuals (νobs − νcalc ) for the R2 and P2 branches are scattered closely around zero(∆ν = 0.0005 cm−1 ), while those of Q2 and P21 deviate by as much as 1000-fold more fromzero, particularly in the vicinity of the doubled set of lines observed for Q2 (3.5), each ofwhich is nearly symmetrically pushed away from the residuals at lower J. This doubling of
the spectral lines was also observed in the Curl data and tentatively assigned as Q2 (3.5).
As an important additional piece of evidence, the jet cooled IR spectrum reveals thisdoubling of lines to be replicated for P21 (4.5), which terminates in the same upper state(i.e., 2 Π1/2 F2 (J0 = 3.5)) as Q2 (3.5). This permits unambiguous conﬁrmation of the J state
assignment by 2-line ground state combination diﬀerences that agree to within experimental
precision ( < 10 MHz). In the residuals for our data in Figure 6.11, there is a striking
discontinuity from J′ = 3.5 to J′ = 4.5 in the case of the Q2 branch (and from J′ = 2.5 toJ′ = 3.5 in the case of P21 ). This behavior is consistent with a strong local perturbation in
the upper state manifold near J′ = 3.5, which therefore both (i) vibronically mixes opticallybright and dark state of the same overall rovibronic symmetry and parity to yield additional
mixed state lines in the spectrum, as well as (ii) introduces systematic shifts in adjacentrotational levels in the vicinity of J′ = 3.5. Each of these eﬀects are evident and can bequantitatively analyzed in the high resolution jet cooled spectrum, as described in detailbelow.
The energy level diagram insets in each residual plot given in Figure 6.11 demonstratethat the noticeably perturbed bands (i.e. Q2 and P21 ) have transitions that only terminate
in the upper parity level for a given value of J′ in the 2 Π1/2 state. Conversely, R2 and P2 ,which exhibit no such perturbation and are well ﬁt with the unperturbed Hamiltonian, havetransitions that terminate exclusively in the lower parity level for a given value of J′ . Since J137

Figure 6.11: Residuals (νobs -νcalc ) for the 3600 cm−1 band for the Q2 , P21 , R2 , and P2 branchesplotted as a function of J′ , where νcalc was determined from the unperturbed Hamiltonianmodel discussed in Section 6.5.1. These clearly demonstrate a local perturbation in the Q2
and P21 branches at J′ = 3.5, evident in not only in the discontinuity in the plot but also inthat two lines are observed at J′ = 3.5 for both of these branches. The residual plots for P2
and R2 reﬂect no such local perturbation. The energy level diagram schematics to the rightdemonstrate the transitions being depicted in each plot. From these, it is easy to see that
the Q2 and P21 transitions terminate in the upper parity level in the 2 Π state, while the R2
and P2 transitions terminate in the lower parity level.

138
and parity are good quantum numbers and must be rigorously conserved in a unimolecularinteraction, this permits the symmetry of the perturbing state to unambiguously identiﬁed.
First of all, since only one of the two closely spaced parity levels for every J in the 2 Π1/2
state is perturbed, this implies that the perturbing manifold must belong to a state withoutparity doubling, i.e. a 2 Σ state. Secondly, since overall parity in a 2 Π1/2 manifold necessarily
alternates with J, the fact that only the negative parity 2 Π1/2 level with J′ = 3.5 is perturbed
requires that the associated ground state 2 Σ J′ = 0.5 level (i.e., ∆J = odd) must be of positive
parity, therefore identifying the perturbing state to be of 2 Σ+ symmetry. This non-adiabaticinteraction therefore represents a heterogeneous perturbation between states with diﬀerent
vibronic symmetries and projection of angular momentum along the molecular axis, which
can be treated isomorphically as ∆K = ± 1 Σ − Π Coriolis coupling.
It is relatively straightforward to include this local perturbation into our Hamiltonianmodel. To do this, we form the 2 × 2 coupling matrix EΠ β 
β EΣ(6.12)

where EΠ and EΣ represent the zeroth order unperturbed energies for the optically bright2

Π1/2 and dark 2 Σ+ state, and β is the associated rovibronic matrix element, which for ∆K= ±1, Σ − Π coupling scales asβ = β0√N(N + 1)

(6.13)

As we shall see, the deperturbed 2 Π1/2 state energies are extremely well described by the
eigenvalue solutions to the equations in section 6.5.1. Though the spectral data clearly
contain less quantitative information on the dark perturbing 2 Σ+ state, the unperturbed
energy levels can be adequately approximated by a simple rigid rotor (Bpert ) built on a band
origin energy (νpert ):E1 = νpert + Bpert (N (N + 1))(6.14)

where only the lowest order contributions to a 2 Σ+ state have been included for simplicity.

139
Subsequent matrix diagonalization yields the two coupled state energies, E+ and E−
as analytic functions of EΠ , EΣ , and β:√

E1 + E2
E± =±2

E1 −E22+ 4β 22(6.15)

By least squares ﬁtting the observed bright and dark state transition frequencies to thismodel, we thereby extract improved excited state parameters for both 2 Π1/2 and 2 Π3/2 states,
as well as new information on the dark 2 Σ+ state, speciﬁcally βO , Bpert , and νpert .
Results from such least squares ﬁts to the perturbed model incorporating Σ−Π Coriolis
coupling are summarized in Table 6.11, column 4. First of all, the standard deviation of thisﬁt is dramatically improved over 100-fold to σ = 0.00051 cm−1 (15 MHz), i.e., now comparable to the experimental precision of ± 10 MHz. The visual quality of this ﬁt is illustrated
in the simulation trace (in pink) in Figure 6.3 labeled perturbed, where the frequencies andintensities are predicted from the eigenvalues and eigenvectors of the 2 × 2 matrix. In contrast with the unperturbed simulation (in red), the perturbed trace accurately predicts allof the experimental C2 H lines, and in particular, the strongly split pair of Q2 (3.5)/P21 (4.5)
lines.
There is additional conﬁrmation of the model in the relative intensities of the brightand dark state transitions, which can be predicted from the matrix eigenvectors. Speciﬁcally,
the mixing angle θ is determined from β, EΠ , and EΣ byθ =arctan E1 2β− E2
2(6.16)In terms of this mixing angle, the new eigenfunctions can be expressed as
ψ+ = sin θψu + cos θψp(6.17)
ψ− = cos θψu + sin θψpwhere ψb and ψd represent the unperturbed bright and dark state wavefunctions, respectively.
For example, in our ﬁt, we determined β0 = 0.11765 cm−1 (see column 4 of Table 6.11).
Therefore, at J = 0.5 (N = 0 in terms of the 2 Σ state), β = 0 according to Eq. 6.13, and140
θ = 0 according to Eq. 6.16, so the perturbed energy levels (E+ and E− ) look exactly likethe unperturbed J = 0.5 levels for the 2 Σ and 2 Π1/2 states, respectively. Whereas, for J = 1.5(N = 1), β = 0.1665 cm−1 and θ = 2.275◦ . Therefore, the perturbed wavefunctions are
ψ+ = 0.0397ψu + 0.999ψp ψ− = 0.999ψu + 0.0397ψp(6.18)

for J = 1.5. Obviously then, the transitions observed in our spectrum must be to E± levels
that have a sizeable amount of ψu or bright state character, and so the Q2 (1.5) transition
terminates in the E− level.
This determines relative transition intensities to coupled pairs of upper levels observedin the spectrum,
I(E+ )= tan2 θI(E− )(6.19)

which in turn reﬂects the fractional bright state character in the E+ vs. E− upper state. Thisis represented in Figure 6.12 by red vs. blue fraction for a given J, which corresponds to thepredicted intensity ratio for a pair of transitions terminating in the upper perturbed level.
This expression also explains why we measure appreciable frequency shifts at high resolution
over a wide series of transitions, but only with suﬃciently strong local mixing to see thedark state at J = 3.5. For example, the mixing angle (θ ≈ 43.4◦ ) at N = 3 from equation
6.19 predicts an intensity ratio of 0.89; this agrees well with the two, nearly equally strong
Q2 (3.5) lines that are observed, terminating in the E− level or E+ level. However, even for
one J higher or lower, the intensity ratios for the corresponding dark state lines according
to equation 6.19 are down by 420-fold and thus not observed above the experimental noiselevel.
6.5.3.24012 Band

Figure 6.10, which plots the residuals (observed.predicted) from the least squares ﬁtof our data, where again the upper graph is a plot of the residuals for the R1 (circles), Q1(squares), and R12 (diamonds) branches, and the lower graph is a plot of the residuals for

141

Figure 6.12: Energy level diagram illustrating perturbation of the upper parity levels in thebright 2 Π1/2 excited state by a close-lying dark 2 Σ+ state. The Σ-Π Coriolis perturbation
breaks the degeneracy in the 2 Π upper parity energy levels for a given J and gives rise
to mixed energy levels (drawn in the center of the excited state), which contain partial
character of the bright and dark states. The unperturbed 2 Π1/2 energy levels are blue, while
the unperturbed 2 Σ+ levels in the excited state are red. The mixed states in the center arethen combinations of red and blue, which portrays the predicted intensity for a transition
terminating in these levels, based on the percentage of blue (or bright character) depicted ineach. At J′ = 3.5, this mixing is approximately 50/50, yielding an integrated intensity ratioof 0.89, and hence, we observe transitions to both J′ = 3.5(-) perturbed levels. The green
arrows indicate the observed transitions in the Q2 branch.

the R2 (circles), Q2 (squares), and P21 (diamonds) branches. Note the tenfold increase in thescale from Figure 6.9, and that the residuals are now scattered around zero by on the orderof 0.01-0.02 cm−1 . It is particularly evident in the upper panel in Figure 6.10 that there is a
precipitous dip at J′ = 2.5, indicative of a “local” perturbation in the F1 manifold caused by

142
a close-lying dark state of C2 H. By way of contrast, note the extremely tight clustering ofresiduals for each of the three transitions to the same upper J state, a point we will return
to in Sec. 6.6. Part of this is to be expected; since Q2 and R12 (as well as Q1 and P21 forthe lower panel) transitions reach the same ﬁnal parity level, this agreement is completely
consistent with 2-line combination diﬀerences for the ground state and thus experimental
precision. However, the fact that we also see a similar tight clustering of the Q1 and R1
transitions, which necessarily access states of opposite parity, is particularly noteworthy.
Speciﬁcally, this means that the local perturbation of the F1 J′ = 2.5 parity levels must arise
from a near resonant state also with both +/- parity levels in close proximity. From Figure
6.1, this implies that the dark state cannot be 2 Σ; i.e., it must be a state with Λ > 0.
To rule out that this eﬀect at J′ = 2.5 is caused by a global perturbation, a leastsquares ﬁt has been performed on the 4012 cm−1 data, but with the lines terminating in
J′ =2.5, F1 manifold, namely, R1 (1.5), P1 (3.5), Q1 (2.5), R12 (1.5), and Q12 (2.5), removed
from the data set. The results for this revised ﬁt are presented in Table 6.10 (column 3),compared with those presented earlier in Table 6.9 and summarized in column 2 of Table
6.10. Already by leaving out transitions to this more strongly perturbed upper state, thestandard deviation of the ﬁt improves ﬁvefold from 0.01 to 0.002 cm−1 . Interestingly, there
is an additional manifestation of this local perturbation in the F2 manifold in the vicinityof J′ = 3.5, as evident in the lower panel of Figure 6.10. Similar to what is seen in the F1
manifold, the tight clustering of the Q2 /P21 and R2 transitions (which by symmetry must
access diﬀerent parity levels) conﬁrms the presence of local vibronic mixing from a darkstate with closely spaced levels of both + and - parities, i.e., 2 Π, 2 ∆, etc. Based on the (i)quality of high level ab initio vibronic calculations and (ii) sparse vibrational level density
for C2 H at only 3500-4000 cm−1 of internal energy, this bodes well for being able to identify
the actual vibrational state responsible, as discussed below.

143
6.6

Vibronic Assignments
One important issue to address is vibronic assignment of the four C2 H 2 Π-2 Σ+ bands

observed in this work. There has been excellent theoretical eﬀort on this topic, most notably
the recent predictions by Tarroni and Carter,[8, 9] which make detailed assignments forboth energies and vibronic transition intensities throughout the 3000-6000 cm−1 region.
For example, they predict a strong band at 3690.5 cm−1 which is in remarkably good ﬁrst
principles agreement with experimental observation at 3692.6084 cm−1 . Similar quality
predictions are also made for the other three strong bands, i.e., (i) 3790.9 versus 3786.0910
cm−1 (obs), (ii) 4011.4 versus 4012.2840 cm−1 (obs), and (iii) 4093.6 versus 4107.8753 cm−1(obs). In particular, they oﬀer general assignment of the upper states for these four bands
to complex admixtures of electronic and vibrational excitation. As one example, theory
suggests the upper state character of the 3690.5 cm−1 band to be a superposition of Π statesÃ(0,0,0) and X̃(0,11 ,2) and X̃(1,11 ,0), where (ν1 , ν2 , ν3 ), corresponds to the C-H stretching,
CCH bending, and C-C stretching vibrations, respectively, and the superscript indicatesquanta in vibrational angular momenta, l. Given that the Ã state manifold is embedded in
the X̃ manifold at relatively low energy, one might well anticipate strong ﬁrst order vibronic
mixing between (i) high lying 2 Π symmetry vibrational levels in the ground state X̃ manifold
and (ii) low lying levels of the excited 2 Π electronic Ã state.
This picture can be further tested by experimental band intensities, which also agree
well with the predicted absorption cross-sections of Tarroni and Carter.[9] For a common
rotational temperature, relative oscillator strengths for each band can be quantitatively
obtained by comparing intercepts in Boltzmann plots such as in Figure 6.5. Normalized tothe 3962 cm−1 band, the experimental band intensities are found to be 1.0 (3692 cm−1 ): 1.5(3786 cm−1 ): 2.7 (4012 cm−1 ): 4.9 (4107 cm−1 ). This is in excellent qualitative agreementwith the corresponding 1.0 : 1.2 : 2.8 : 3.2 band strength ratios predicted by Tarroni andCarter, lending further credence to a picture of extensive vibronic coupling between 2 Π states

144in the Ã and X̃ manifolds.
The perturbed 3600 cm−1 2 Π-2 Σ+ origin band has been analyzed and the high resolution slit-jet-cooled data successfully ﬁt using the zero-order (unperturbed) Hamiltonian
for the 2 Π upper state along with Σ - Π Coriolis coupling terms. We can now incorporate
the previous high J data, reported by Yan et al.,[181] into our ﬁt and see if these high J
lines are still well characterized with our perturbed model. As mentioned earlier, Curl andcoworkers[182] reported evidence for (i) a strong local perturbation at N′ = 4 as well as (ii)increasing frequency shifts away from the least squares ﬁts with increasing rotational state(N′ > 19) in the 3600 cm−1 band data. We have clearly identiﬁed this local vibronic couplingat low N′ in the supersonic jet data, but in addition this may also be responsible for whatlooks a more global interaction at higher N′ . Speciﬁcally, second order perturbation theory
predicts that the resulting frequency shifts due to bright state-dark state coupling shouldgrow approximately as ±β/|∆E|, where ∆E = EΠ - EΣ is the diﬀerence in unperturbed en√ergies. For Σ-Π Coriolis coupling (i.e.,β = β0 N (N + 1)) and an energy spacing dominatedby diﬀerences in a rigid rotor progression (i.e., ∆ ≈ ∆B[N (N + 1]), these level shifts will
asymptotically approach a constant displacement of β 2 /|∆E| ≈ β02 /∆B, which therefore
could explain the gradual perturbation in the residuals reported by Yan et al.[181] at high N.
Indeed, the magnitude of this shift β02 /∆B = 0.31 cm−1 is directly predicted from our leastsquares ﬁtted values in the low N regime, which is consistent with the oﬀsets observed byCurl and coworkers in their original study. More quantitatively, a combined ﬁt of our low J
data with the previously reported high J data[182] using the perturbed Hamiltonian model
discussed in detail in Section 6.5 yields residuals for the Q2 (J) branch consistent within experimental error for all J, suggesting that only one Σ-Π Coriolis interaction with a single
dark state plays a role in the high resolution spectroscopic analysis. This makes much better
sense, as the density of vibrational states for a simple triatomic such as C2 H in the 3600
cm−1 region is predicted to be ≈ 0.02 states/cm−1 , i.e. yielding typical energy spacings morethan an order of magnitude higher than typical Coriolis coupling matrix elements at low J

145
values in the supersonic jet.[8, 9] One immediate corollary of this low density of backgroundstates is that the extent of vibronic state mixing and therefore perturbations in the spectra are much more isolated (and thus analyzable and assignable) than perhaps previously
appreciated.

Figure 6.13: Energy level diagram for C2 H from the theoretical work of Tarroni and Carter[8,9] revealing the predicted vibronic state densities for each angular momentum K value. Notethe sparse vibronic manifold for a triatomic such as C2 H at low energies, which provides anovel opportunity to identify the explicit vibrational level(s) involved in the “bright state(2 Π1/2 ) -“dark state (2 Σ+ ) vibronic interaction

As one example, this unusual combination of (i) a high resolution jet cooled spectral
data analysis and (ii) the relatively low density of states in a triatomic such as in C2 H
provides a rather novel opportunity for unambiguously determining the vibrational identityof the vibronically perturbing dark state in a highly reactive radical species. For this purpose
we take advantage of the theoretical work by Tarroni and Carter,[8, 9] which provides an146excellent ﬁrst order description of the complete set of background states. The relevant
results are summarized in Figure 6.13, which list the predicted energies from 06000 cm−1for all vibronic states in C2 H as a function of electronic/vibrational angular momentum K
along the molecular axis. Also listed in the left most column are the vibronic energy levels
thought to be largely dominated by the Ã(2 Π) electronically excited state, the lowest ofwhich is nominally the band origin of the Ã(2 Π) ← X̃(2 Σ+ ) transition, as indicted by thearrow. It is worth noting that the states appear relatively discrete and well separated evenon such a coarse energy scale, particularly when labeled by angular momentum symmetry.
The simple patterns in the lowest Σ+ , Π, ∆, Φ states reﬂect a regular progression in the CCH
bend, which has a 2 Π ← 2 Σ+ fundamental transition at 371 cm−1 . The pattern becomesslightly more complex with the additional states arising from CC stretch excitation, starting
around the 2 Σ+ ← 2 Σ+ fundamental band at 1840 cm−1 . Finally, the CH stretch excitation
predicted at 3298 cm−1 contributes state density in the vicinity of the Ã(2 Π) ← X̃(2 Σ+ )electronic transition, though the assignment of this vibration is still a matter of controversy.
The CCH bending[175] and CC stretching[174] fundamentals have been deﬁnitively assigned
previously, while there is still uncertainty in the CH stretching fundamental, hence thefrequency for the best candidate for this fundamental[177] in Figure 6.13. The Π -2 Σ+ band
reported here has previously[181, 192] been assigned as the origin of the Ã-X̃ electronictransition. However, the calculations by Tarroni and Carter[8] illustrate that the coupling
between the Ã and X̃ states is so strong that there is no pure origin transition, but rather
their assignment for the level calculated to be at 3604.4 cm−1 is a complex admixture of X̃
(0,11 ,2), X̃ (1,11 ,0), Ã (0,0,0)1 , where (ν1 , ν2 , ν3 ), correspond to the CH stretching, CCH
bending, and the CC stretching vibrations, respectively, and the superscript indicates quantain vibrational angular momenta, l. Their calculations predict that while the origin of the Ãstate is vibronically distributed among several 2 Π levels, the largest amplitude is calculated
for the level predicted at 3604.4 cm−1 . Hence, the 2 Π-2 Σ+ band located at 3600.3521 cm−1
can be reasonably assigned as the origin band of the Ã-X̃ electronic transition in C2 H.

147

Figure 6.14: A ≈ 200 cm−1 blow up region of the Tarroni and Carter[8, 9] energy level
diagram for C2 H in the 2 Π-2 Σ+ 3600 cm−1 origin band region, sorted by K quantum number
and clearly identifying the only near-resonant vibrational states available for strong vibronicinteraction via a a local curve crossing. Near-resonant coupling with the Π, ∆, Φ manifolds
can be immediately ruled out (by dashed crosses) since only the upper parity level is selectively perturbed, which leaves only ∆K = ± 1 Π-Σ Coriolis coupling with only one possible
resonant state (blue-green circle) in the 2 Σ+ manifold. The variational calculations by Tarroni and Carter suggest this state is predominantly (0,80 ,0) with partial (0,00 ,2) character.
Note the low overall state density (≈ 0.02 states/cm−1 ) in this triatomic molecule, which
permits unambiguous identiﬁcation of the near resonant vibronic interaction.

One can take this considerably further in Figure 6.14, which shows an expanded region
around the Ã-X̃ spectral band origin. At this higher spectral resolution, the calculations of
Tarroni and Carter now predict only ﬁve states total in the ± 100 cm−1 window surrounding
the band origin region between 3500 and 3700 cm−1 . Furthermore, of these ﬁve states,
three are of Π or higher character (i.e., K > 1), and therefore rigorously unable to mix withthe upper 2 Π state by ∆ K = ±1, Σ - Π Coriolis interactions. Interestingly, there are no148
states whatsoever of Σ− symmetry within the nearby ± 500 cm−1 region. Indeed, based on
the earlier parity assignment, this symmetry state would have been necessarily implicated in
Coriolis coupling, the complete absence of which conﬁrms the correctness of the revised parity
labeling. This leaves only two Σ+ states within a ± 100 cm−1 window and of the correct
symmetry determined in the perturbation analysis. This immediately supports assignmentof the 2 Σ+ state at 3604.6 cm−1 as the dark perturbing species, which is essentially resonant(≈ + 0.2 cm−1 ) with their predicted 2 Π band origin at 3604.4 cm−1 . From the variational
calculations of Tarroni and Carter, this state is predominantly X̃ (0,80 ,0), i.e. the 7th
overtone of the CCH bending vibration, but also with contributions from the X̃ (0,00 ,2)state ≈ 57.5 cm−1 lower in energy at 3546.9 cm−1 . Based on these theoretical predictions,the dark state at 3611.4(1) cm−1 from our spectral deperturbation can be conﬁdently assigned
to the zeroth order X̃ (0,80 ,0) vibrational level. Given the small error (≈ 7 cm−1 or 0.3%) of
these predictions, this speaks to the remarkable accuracy of the ab initio surfaces, coupling
matrix elements and variational treatment of Tarroni and Carter.[8, 9]
As a ﬁnal comment, there is additional conﬁrmation from Hsu et al., who have performed extensive studies on C2 H using laser induced ﬂuorescence (LIF) techniques.[197, 20,
180] Speciﬁcally, these studies used 193 nm excimer light to fragment HCCH into C2 H + H
under both cell and supersonic jet conditions, followed by tunable UV LIF to excite the C2 H
on a series of UV transitions to K = 03 levels in the upper electronic state. Rotationallyresolved spectroscopic data on high lying vibrational levels in the electronic ground state
were then obtained from dispersed ﬂuorescence (DF) back down to the X̃ manifold. Of
interest to the present work, these studies were able to probe DF down to both X̃ (0,00 ,2)and X̃ (0,80 ,0) vibrational levels, thus yielding term values of 3546.75 cm−1 and 3611.54
cm−1 , respectively, above the X̃ (0,00 ,0) ground electronic state. The upper term value(3611.54 cm−1 ) of Hsu et al. is clearly in excellent agreement with the value (3611.4(1)cm−1 ) obtained from the present high resolution deperturbation analysis.[197, 20, 180] Indeed, by way of additional conﬁrmation, the rotational constant for the perturbing state from149
our high resolution analysis is found to be Bpert = 1.45(1) cm−1 , i.e., again in quantitative
agreement[197] with the reported Hsu et al. value of B = 1.441 cm−1 . Furthermore, theappearance of vibronic coupling facilitated by high quanta in the ν2 and ν3 vibrations also
makes excellent physical sense in light of the potential surface crossing predicted between
the electronically excited Π state and ground Σ states as a function of both CC stretching
and CCH bending coordinates.[8, 9, 184, 185, 186, 187, 188, 189, 190]
In summary, high resolution infrared spectroscopy in a slit supersonic discharge has
yielded evidence for outstanding ﬁrst principles agreement between both theory and experiment for the identiﬁcation and assignment of resonantly coupled states in the vibronic
manifold of C2 H. This provides strong encouragement that the powerful combination of abinitio and high resolution methods will enable further spectroscopic exploration of this critically important combustion radical as well as establish a solid benchmark for understanding
non-adiabatic vibronic interactions between multiple Born Oppenheimer potential surfaces.
In addition to strong global mixing between 2 Π states of the same projection (|Λ| = 1)of electronic/vibrational angular momentum, the data also show clear indications of much
weaker, local mixing between isolated rotational states of same J and parity, which come
accidentally into resonance, as illustrated nicely by the 4012 cm−1 band in Figure 6.10.
This much weaker coupling almost certainly implies states of diﬀerent angular momentum
projection, mixing, for example, by Λ-Π Coriolis interactions with ∆Λ = ±1. In conjunction
with high quality ab initio predictions by Tarroni and Carter, the unusually low state density
in the X̃ manifold for C2 H oﬀers a rare opportunity to assign such local vibronic interactions
as well.
Figure 6.15 illustrates this with a blow up region around 4012 cm−1 , where the zerothorder symmetries and energies are taken directly from Tarroni and Carter. From the above
discussion, we argued that the source of local coupling at J′ = 3.5 in F1 and J′ = 2.5 in
F2 manifolds, respectively, required that the “dark” state responsible for the coupling beof 2 Π, 2 ∆, . . . (i.e., non-Σ) symmetry. This was based on the high resolution evidence

150

Figure 6.15: Overview of the experimentally observed (leftmost, in black) and calculated
vibronic states in C2 H, where the predictions are from Tarroni and Carter and organized byangular momentum projection quantum number Λ. Note the excellent agreement between
the four observed (black) and predicted (blue) 2 Π band origins. Also note the prediction of ahighly vibrationally excited 2 ∆ X̃ (1,22 ,0) state in resonance with the 4012 cm−1 band origin,with no other state inside of a 300 cm−1 window. This makes for unambiguous assignmentof the dark state responsible for the J dependent shifts observed in Figure 6.10 to 2 ∆ X̃
(1,22 ,0), i.e., one quantum of CH stretch and 2 quanta of CCH bend, which couples with theÃ (0,0,0) state by 2 Π-2 ∆ Coriolis interactions.

151
in Figure 6.10 for perturbations involving both + and - parity levels, which implies thatthe dark state must also have both parity levels in close proximity. Furthermore, since ∆Λ= 0 state mixing with the 2 Π electronic manifold is too strong to be consistent with 0.01
cm−1 displacements of only a single rotational level, one anticipates the perturber to be 2 ∆symmetry (∆Λ = 1) or possibly higher. Interestingly, Tarroni and Carter[8, 9] predict two
states (Π and ∆) in the 4012 cm−1 region, with no other states of any symmetry predicted
inside of a 300 cm−1 window. The one state (Π) is the vibronically mixed state to which thestrong 2 Π - 2 Σ+ band is already assigned. This leaves the remaining ∆ state, X̃ (1,22 ,0),
speciﬁcally one quantum of C-H stretch and two quanta of CCH bend, as the sole culprit for
local vibronic interactions, coupling with the Π state via ∆-Π Coriolis interactions (i.e. ∆Λ= ± 1). With good signal to noise, the mixed states can acquire suﬃcient oscillator strength
to be observed, which permits such an analysis to be taken even further. For example, we seea particularly clear example of highly localized crossing of manifolds in what is nominally theÃ ← X̃ band origin near 3600 cm−1 , which has permitted a detailed spectroscopic analysisof the dark state, as discussed elsewhere. In any event, the present high resolution data
already oﬀers a rigorous benchmark for understanding vibronic interactions in Renner-Teller
systems as well as a rare glimpse into relatively high vibrational states of the Ã manifold forsuch a fundamentally important combustion radical.
6.7

Summary and Conclusion
Infrared spectra for ﬁve 2 Π - 2 Σ+ bands of jet-cooled ethynyl radical (C2 H) in thegas phase have been reported at sub-Doppler resolution, which permits ﬁrst observationof resolved main and satellite branches in each 2 Π - 2 Σ+ band. Parity state assignments
have been corrected, with the observed lines nonlinearly least squares ﬁt to a Hamiltonianmodel containing rotational, spin-rotational, spin-orbit, and lambda-doubling contributions
for the 2 Π state. Three of the ﬁve bands can be quantitatively well-described by this simple
Hamiltonian to within an experimental precision is 10 MHz rms. From these ﬁts, we report152
revised excited state constants and band origins for each of the bands. Vibronic assignments
are revisited for the four observed bands and the dark perturbing state in the 4012 cm−1 2 Π- 2 Σ+ band is unambiguously assigned to the X̃ 2 ∆ (1,22 ,0) state, based on parity labelingand previous frequency and intensity predictions by Tarroni and Carter.[8, 9]
For the 3600 cm−1 band, this analysis reveals that the 2 Π1/2 upper parity levels arestrongly and selectively perturbed by a close-lying dark state of 2 Σ+ symmetry, which limits
the quality of such ﬁts to > 100-fold worse than expectations. However, incorporation of
Σ-Π Coriolis coupling into the spectral model allows one to successfully ﬁt the upper state
to 15 MHz, i.e. comparable to experimental accuracy. Additionally, high resolution analysis of the spectral shifts and additional bright and dark state transitions has permitted aband origin (νpert ) and rotational constant (Bpert ) for the perturbing 2 Σ+ state to be determined, as well as the magnitude of the Coriolis coupling constant β0 . Finally, this facilitates
unambiguous vibronic assignments to be made for the bright 2 Π as well as the dark 2 Σ+state, guided by previous theoretical[8, 9] and experimental[197, 181] work. Identifying thelocations of these perturbing dark states helps map out the complicated energy level structure in ethynyl radical, which represents a crucial step toward understanding and accurately
modeling combustion and interstellar chemistry.

Chapter 7
High-Resolution Direct-Absorption Spectroscopy of Hydroxymethyl Radical in
the CH Symmetric Stretching Region

7.1

Introduction
Hydroxymethyl radical, CH2 OH, has been the subject of over 100 experimental andtheoretical papers in the last 40 years,[204] in large measure due to the important role itplays as a reactive intermediate in combustion and environmental chemistry. As one example, the combustion initiation step for oxygenated hydrocarbon fuels such as methanol isthought to be hydrogen abstraction by O2 to produce hydroxymethyl radical, i.e., CH3 OH+ O2 ← CH2 OH + HO2 .[205, 206] There is also key hydroxymethyl radical in many of thesubsequent chain reaction kinetics, for example, a fundamental chain propagation step in theoxidative combustion of methanol is CH3 OH + HO2 ← CH2 OH + H2 O2 . Indeed, real time
monitoring capabilities for CH2 OH radical in methanol combustion, as well as a detailed
understanding of the underlying kinetics would be invaluable to optimizing the combustion
process. Signiﬁcantly complicating this task is the ubiquitous presence of methoxy radical(CH3 O) in many combustion systems, which has the same chemical composition as hydroxymethyl radical and consequently makes mass spectrometry sampling much less powerful formonitoring the underlying radical kinetics.
Roberts, M. A.; Sharp-Williams, E. N.; Nesbitt, D. J. in preparation

154
In addition to fundamental combustion processes, hydroxymethyl radical is an important intermediate for oxidative reactions occurring in the troposphere. Indeed, atmosphericscrubbing reactions of alkanes, alkenes, and alcohols all involve hydroxymethyl radical as areactive intermediate. As one example, alkenes account for about 10 % of the non-methaneorganic compound concentration in many urban areas as a result of gasoline-based fuels
and motor vehicle exhaust emissions. The initial oxidative scrubbing reactions of the simplest alkene (such as ethene) are initiated by hydroxyl (OH) radical attack, which features
several steps involving CH2 OH as an intermediate.[207] Furthermore, methanol itself has a
non-trivial concentration in the troposphere, ranging from 400-700 ppt depending upon thelatitude, with about 85 % of atmospheric oxidative scrubbing reactions producing hydroxymethyl radical as a transient intermediate.[208]The above examples provide strong motivation for development of high resolution nearIR experimental tools for spectroscopic identiﬁcation of hydroxymethyl radical, as a key
reactive intermediate in combustion and atmospheric reactions. Such keen levels of interest
have spurred signiﬁcant spectroscopic eﬀorts. The earliest such studies on hydroxymethyl
radical were based on electron spin resonance (ESR) detection, which, in conjunction withhigh level ab initio theoretical eﬀorts, predicted a quasi-planar structure of the radical.[125]Low resolution infrared detection of CH2 OH radical was ﬁrst obtained via matrix isolation
spectroscopy and UV photolysis of methanol, which identiﬁed several vibrational modesin the ﬁngerprint region.[209] These pioneering eﬀorts stimulated a plethora of additional
theoretical, kinetic, and spectroscopic studies.[210, 211, 212, 213, 214] Of particular relevanceto our work is a series of resonance enhanced multiphoton ionization (REMPI) studies by
Hudgens and coworkers, which identiﬁed multiple Rydberg states and Franck-Condon active
vibrational progressions in these lower and upper state manifolds.[215, 216, 217]
In order to facilitate interpretation of their spectral data, Hudgens and coworkers
calculated a 2-dimensional potential energy surface (MP2/6-311G(2df,2p) level) of the OH
torsion (ν8 ) and CH2 (ν9 ) wag coordinates, yielding detailed energy/frequency predictions for155
these two coupled modes. By way of example, their potential surface calculations predict thefrequency of the ﬁrst excited ν9 wag mode at 238 cm−1 , which is in excellent agreement withthe observed value at 234 ± 5 cm−1 . Furthermore, these studies determined that quantum
state labels for the two modes remained approximately separable, at least for vibrationalenergies suﬃciently low with respect to the roughly 1700 cm−1 OH torsion barrier height.
Most importantly, the presence of such a torsional barier predicts closely spaced tunnelinglevels, speciﬁcally with splittings between the ground and ﬁrst excited torsional modes (ν8 )lower than the 1 cm−1 precision of the calculations.[204] Based on such an upper limit forthese torsional splittings, one expects both ground and ﬁrst excited tunneling levels to be
populated even under jet-cooled conditions and thus the possibility for doubling of the nearIR spectra.
More recently, Reisler and coworkers did a number of studies on dissociation dynamics
and the spectroscopy of hydroxymethyl radical.[218, 219, 220, 221, 222, 21, 223] In particular, these studies elucidated the spectroscopy of low lying electronic states including the 3s,
3px , and 3pz Rydberg levels as well as the CH symmetric stretch, CH asymmetric stretch,and OH stretch fundamental and ﬁrst overtone. Speciﬁcally, Feng et al. exploited double resonant ionization detected IR spectroscopy via the 3pz Rydberg state to probe both
CH and OH stretches with a roughly 0.4 cm−1 laser linewidth and thus achieving partial
rotational resolution. Least squares analysis of the rovibrational band contours yielded i)vibrational band origins and ii) A, B, and C rotational constants for the upper states, based
upon ab initio estimates for the ground state. The CH asymmetric stretch and OH stretch
spectra closely matched theoretical predictions of pure B-type, and A\B mixed type bands,
respectively, as predicted by ab initio calculations. In contrast, the CH symmetric stretch
was theoretically predicted to be predominantly A-type, but in fact required a more mixed
60% A-type \ 40% B-type character to adequately ﬁt the data. Additionally, Feng et al.
did not see any evidence of additional structure in their data due to the OH torsional mode,
which also provided an upper limit of 0.1 cm−1 for the ground state tunneling splitting.

156

A

B

C

Figure 7.1: Quasiplanar structure of hydroxymethyl radical with HOMO and priciple axis
orientation shown. The equilibrium geometry has a slightly bent methyl group in the outof-plane bend coordinate, due to competition between sp3 and sp2 hybridization around thecentral C atom.

In the current study, we have built on the pioneering work of Reisler and coworkers to
help guide a near-IR search for hydroxymethyl radical with sub-Doppler, fully rovibrationallyresolved spectral splitting. Figure 7.1 shows the equilibrium structure and principal axes ofhydroxymethyl radical and the highest occupied molecular orbital (HOMO), calculated at
the B3LYP/6-311g++(3df,3pf) level[3]. Although we have very good estimates from previous studies for all three H-stretching bands, we have chosen ﬁrst to focus on the symmetricCH stretch spectral region near 3043 cm−1 , which is predicted to have the highest integrated
band intensity. Indeed, we observe a surprisingly rich spectrum in this region, partially congested by discharge-induced hot band transitions in methanol and presently under analysis.

157
However, as ﬁrst high resolution data on this critical combustion radical, we have been able
to unambiguously identify and assign the Ka = 0 ← 0 progression of symmetric stretch
excited CH2 OH, and which serves as the primary focus of this report.
7.2

Experiment
The high-resolution infrared spectrometer used in these experiments has been describedin detail elsewhere and will only be brieﬂy summarized here.[82, 81, 1] Narrow-linewidth (<2 MHz), high-precision infrared light is generated by diﬀerence frequency generation of asingle frequency argon ion laser (Ar+ ) and a tunable cw dye laser (R6G, Exciton dyes)
in a temperature-tuned periodically-poled lithium niobate (LiNbO3 ) crystal. The infrared
radiation is split into reference and signal beams, with the reference beam directed onto aliquid-nitrogen cooled InSb detector. The signal beam is directed through a CaF2 window
into a 16-pass Herriot cell mounted in the slit jet discharge expansion vacuum chamber, witheach pass sampling a 4 cm long path length of jet of radicals. Spectra of CH2 OH radical
are recorded via transient depletion of the transmitted IR light monitored by the signal
InSb detector. The signals from the two detectors are combined in a common mode noise
subtractor before being sent to a lock-in detector and subsequently recorded on a computer(via a NI-6025E analogue-digital card). Relative frequency precision (10 MHz) is obtainedby monitoring dye laser fringes through an actively stabilized (< 1 MHz rms) Fabry-Perot
etalon, with the Ar+ laser actively locked to the same Fabry-Perot cavity to provide single
frequency operation and stability while scanning. Absolute frequency calibration is achievedby comparison with well characterized ν3 CH stretch absorptions of jet cooled methane doped
into the expansion and monitored in the same spectral region.[83]Jet-cooled hydroxymethyl radicals are produced by supersonic expansion of trace amounts
of precursor in 70% neon, 30% helium (Ne70) buﬀer gas mixture through a pulsed slit jet
nozzle (19 Hz, 500 s duration). Radicals are generated via electron associative detachment ina square-wave modulated (50 KHz) discharge at the expansion oriﬁce. For the many radicals

158
previously studied with this apparatus, the precursor has been designed to contain a weakbond cleavage point (typically C-Br or C-I) to form the desired target radical, typically by
dissociative detachment. Such precursors for hydroxymethyl radical are unstable, which led
us to develop two recipes based on methanol, though this requires cleavage of a strong CH
bond. Our ﬁrst approach, i.e., simply a Ne70 discharge with trace methanol, was successful
in generating suﬃcient concentrations of hydroxymethyl radical but also generated spectralinterferences from methane and vibrationally excited methanol. Our second approach was
based on doping Cl2 into the Ne70/methanol discharge expansion, which generates hydroxymethyl radical my selective CH bond abstraction reactions of Cl + CH3 OH → CH2 OH +HCl and, more importantly, yields fewer spectral interferences. Similar chemistry has beenused before by several groups, but they used photolysis to generate Cl radicals to react with
CH3 OH and generate CH2 OH.[224, 225, 226]
Figure 7.2 shows traces of three diﬀerent species generated with the two diﬀerent
synthesis, with the black line showing the CH3 OH in Ne70 discharge and the red line showing
the CH3 OH + Cl2 + Ne70 discharge. The ﬁrst panel plots the CH2 OH 404 ← 303 (N′ Ka′ Kc′← N′′ Ka′′ Kc′′ labeling) line, which shows an appreciable percent increase in absorbance withaddition of Cl2 (assignment will be discussed in detail in section 7.3). The second panel
illustrates that methane is produced in a methanol discharge, but with the addition of thechlorine, no methane is detectable. The third panel is a methanol absorption line to illustrate
the decrease in precursor absorption with the addition of molecular chlorine. The measured
linewidths of the transition is 80 MHz in both syntheses. While both spectra are congested
in this region, the synthesis with Cl2 makes CH2 OH with fewer other molecules.
7.3

Results and Analysis
A sample region of the CH2 OH symmetric stretch is shown in Figure 7.3. A represen-tative section of experimental data is plotted in panel a), with the assignment above the line,
panel b) shows the predictions based upon the constants obtained in the ﬁt, discussed below,

159

CH3OH Discharge
CH3OH + Cl2 Discharge% Absorbance

0.3a) Hydroxymethylb) Methane

Symmetric Stretch

CH Stretch

4

04

3

03

line

0.2

R(2) line
0.6

0.2

0.1

0.4

0.1

0.0

3049.100.3c) Methanol R(4) line

0.2

0.0

3049.153049.200.03048.153048.20

Energy (cm3037.403037.45-1)

Figure 7.2: Comparison of two diﬀerence discharge chemistries for “synthesis” of jet cooled
CH2 OH. The red line represents three sample spectral regions for a discharge with CH3 OH
doped into Ne-70 diluent, with the corresponding black line representing comparable data
scans for a CH3 OH + Cl2 discharge, which generates hydroxymethyl radical by Cl + CH3 OH→ HCl + CH2 OH chemistry. Panel a) illustrates how the CH2 OH number density nearly
doubles for chemical formation via H atom abstraction by discharge generated Cl atoms.
Interestingly, panels b) and c) also reveal how the spectral density of undesired species (suchas methane and precursor methanol) can be substantially minimized under the Cl atom
synthetic pathway.

and an inset highlighting the signal-to-noise is in panel c). The identiﬁed hydroxymethyl
radical lines are the Ka = 0←0 progression, which is predicted to be the highest intensity
progression based upon nuclear spin statistics and will be discussed in Section 7.4. The spacing between the Ka = 0 lines is approximately (B+C)/2. Using ab initio rotational constants
to guide the search, we are able to identify a clear progression of lines with this spacing. As

160
an additional conﬁrmation of the assignment, we compare the spectrum with two diﬀerent
mechanisms of generating hydroxymethyl radical. While the progression appears with bothchemistries, it is much more intense with the Cl2 synthesis. This allows us to identify thelines that are most likely due to CH2 OH based upon an increase in intensity upon adding
Cl2 and ignore the lines from other species.

0.25

0.20

% AbsorbanceN'a) Experiment

Ka'Kc'

1

01

0

2
00

02

1

N''

01

Ka''Kc''3

Labels

03

2

02

0.15

0.10

0.05

Relative Intensity

0.00

0.15

c)
0.10

0.05

0.00

b) Simulation
3042

3043

3043.603044

3043.65

3045

3046

3047

-1

Energy (cm )Figure 7.3: Sample data shown with simulation based upon least squares ﬁts to a Watson
asymmetric top Hamiltonian. Panel a) reveals a spectral scan region near the ν3 symmetricCH stretch band origin, with assignment of the Ka = 0 ← 0 progression shown above (inblue). The green arrow indicates the missing spectral line in the progression makes the band
origin assignment and J-labeling unambiguous. Panel b) provides a spectral simulation (inred) of the A type band Ka = 0 ← 0 progression based upon spectroscopic constants fromthe least-squares ﬁt. The blow up region in panel c) illustrates a single 101 ← 000 absorption
line in the ν3 band, which serves to characterize typical signal-to-noise levels of > 10:1 inthe current experiment.

161
There will rigorously be no Q-branch for the Ka = 0 band, which makes the identiﬁcation of the band origin straightforward. As is seen in Figure 7.3, there is a line missing in
the progression unambiguously identifying the band origin. In the study by Feng et al,[21]the band origin they list is 3043.4 cm−1 , which diﬀers from the band origin obtained in thisstudy by approximately (B+C)/2. With the high-resolution of the present work, we areable to resolve the lack of a Ka = 0 line. Without the ability to identify a missing line it isreasonable to have an assignment shifted by J, as in the study by Feng et al. Table 7.3 shows
the list of lines and assignments. The Ka = 0 ← 0 progression is ﬁt to a Watson asymmetric
top Hamiltonian. Because of the nature of the progression, there is not enough information
to ﬁt the A-constants, so those are ﬁxed at ab initio values. Speciﬁcally, the constants varied′′′in the ﬁt are B , D′′J , B , and D′J and the Hamiltonian used is ν + B J(J+1) + DJ [J(J+1)]2. The ﬁt results are summarized in Table 7.3 and the predictions based upon these constants
are shown in panel b of Figure 7.3.
Table 7.1: Experimental line positions of the Ka = 0 ← 0 progression with assignments using
the N′ Ka′ Kc′ ← N′′ Ka′′ Kc′′ notation.
Frequency (cm−1 ) N′ Ka′ Kc′
3034.31828
303
3036.17478
202
3038.03187
101
3039.89590
000
3043.61368
101
3045.46667
202
3047.31135
303
3049.14586
404
3050.96781
505
3052.77492
606
3054.56541
707

N′′ Ka′′ Kc′′
404
303
202
101
000
101
202
303
404
505
606

162
−1

Table 7.2: Comparison of molecular constants, all constants in wavenumbers (cm ). Present
work ﬁt to ν + B J(J+1) + DJ [J(J+1)]2 HamiltonianB′scaled ab initio values
0.9371B
D′J × 10−4ν3022(10)′D′′J × 10−4′

Previous Work[21] Present Work0.9305(2)0.91(2)0.93(2)0.9291(2)0.95(2)3043.33041.7560(5)aCalculated at the B3LYP\6-311++g(3df,3pd) level[3], band origin frequency scaled by 0.9637 (scaling
factor from Dong et al[1]).

7.4

Discussion
The intensity of the lines is used to characterize the rotational temperature of themolecules in the slit-jet and in this case verify that the two chemistries have the same rotational temperature. The intensity of any one rotational line is a function of the appropriate
Hönl-London factor, degeneracies, and a Boltzmann factor of lower state energy and jet
rotational temperature. Figure 7.4 presents a standard semilogarithmic Boltzmann plot of
the experimental populations vs. rotational energy of the lower state. The red squares arefrom the CH3 OH + Cl2 synthesis and the blue circles are from the CH3 OH only discharge.
The diﬀerence in total quantity of CH2 OH produced in the two syntheses is reﬂected in
the diﬀerent y-intercepts. Not only do the points ﬁt to a straight line, indicating that therotational population distribution is well described by a temperature, but it also shows thatboth methods of producing CH2 OH produce it at the same rotational temperature, within
the error of the ﬁts, of about 29 K.
One thing to notice is that, based upon intensity predictions, we should be able tosee clearly the Ka = 1 ← 1 progression. In the absence of other eﬀects, the Ka = 1 ←1 progression would be comparably intense as the Ka = 0 ← 0 progression. However, inhydroxymethyl radical there is the possibility of seeing the eﬀects of nuclear spin statistics as a result of the two equivalent hydrogen atoms bonded to the carbon atom. In this

163

-7.0
CH OH + Cl
32

discharge

Linear fit of CH OH + Cl
3

-7.5

2

discharge data

CH OH discharge
3Linear fit of CH OH discharge data

-8.0

o

ln[S

exp

ij

J

/(S *g )]

3

-8.5
T

-9.0
T

rot

rot

= 30(6) K= 28(3) K

-9.5
0

5

10

15

20

-1

Energy (cm )Figure 7.4: Boltzmann plot analysis of ν3 symmetric CH stretch band spectral line intensities
for jet cooled CH2OH radical obtained under both i) CH3 OH doped discharge (red squares)
as well as ii) Cl2 /CH3 OH discharge (blue circles) conditions. Sexp is the integrated line
strength in units of absolute absorbance), with Sij and gJ = 2J+1 representing the line
strength factor and mJ degeneracy, respectively. The diﬀerence in y-intercepts reﬂects theroughly 60% lower density of CH2 OH radical in the CH3 OH-only discharge.

case, the two hydrogen atoms are equivalent via a 180◦ rotation along the CO axis and arotation of the OH torsional motion. At the energies accessible in this experiment, it isexpected that the hydrogen bonded to the oxygen is not interchangeable with the othertwo hydrogen atoms so it does not need to be included in the nuclear spin statistics calculation. Hydrogen atoms are Fermions with a nuclear spin of 21 and as such, the overall
wavefunction of the molecule must be antisymmetric with respect to exchange of those twohydrogen nuclei. The overall wavefunction, Ψtot , is a product of the individual components,

164
Ψelectronic Ψtorsion Ψvibrational Ψrotational Ψnuclearspin . The electronic component, Ψelectronic , canbe visualized as the orbital shown in ﬁgure 7.1 and is antisymmetric with respect to the180◦ rotation. The vibrational wavefuntion, broken into two parts for clarity, Ψtorsion andΨvibrational , are symmetric in the ground vibrational state and lowest tunneling state. From
the ab initio predictions, the A-axis of the molecule is approximately along the CO bond, as
shown in ﬁgure 7.1 and consequently the rotational wavefunction, Ψrotational , is symmetricfor even Ka values and antisymmetric for odd Ka values. Therefore, the ground tunnelingstate has a 3:1 intensity pattern for Ka = 0 : Ka = 1 states. The ﬁrst excited tunneling level
will an antisymmetric Ψtorsion and will therefore have the opposite nuclear spin statistics.
Furthermore, if we are able to resolve the transitions out of the diﬀerent tunneling levels,
not only might we see two progressions, but the two progressions will have diﬀerent nuclear
spin statistics.
The observed transition out of the ground vibrational state and ground torsional stateis to the ground torsional level of the ﬁrst excited CH symmetric stretch. The transitionout of the ﬁrst excited torsional level of the ground vibrational state would go to the ﬁrst
excited torsional level of the CH symmetric stretch. Consequently, the diﬀerent in band
origin between the two bands is equal to the diﬀerence in tunneling splitting between the
ground vibrational state and the CH symmetric stretch state, which is likely quite small. If
the splitting between the two bands is too small to be resolved, no nuclear spin statistics
will be observed and the Ka = even and Ka = odd progressions will be of equal nuclear spinweight. Given the prominence of the Ka = 0 ← 0 progression, in the case of overlapping
torsional bands, there would be a prominent Ka = 1 ← 1 progression. Since we do not see
a Ka = 1 ← 1 progression, it is quite possible that we can resolve the splitting between the
two torsional bands. We have looked for, but not yet identiﬁed, transitions originating fromthe ﬁrst excited torsional level. This is quite reasonable considering the likely decrease inpopulation between the ground and ﬁrst excited torsional level in a supersonic jet. Adding
to this decrease in signal is that the now 1:3 (Ka = 0: Ka = 1) nuclear spin statistics decrease

165
the signal of the most prominent Ka = 0 ← 0 band. It is not surprising then, that the band
originating out of the ﬁrst excited torsional level is not seen.
At this point, we are unable to see the Ka = 1 ← 1 progression, in spite of predictions
indicating it should be visible. One possibility for this is that there is an anomalously largechange in the A constant upon vibrational excitation, shifting the Ka 1 ← 1 progression
farther from the Ka 0 ← 0 progression than initially predicted. Even in with this scenario,
we might expect to ﬁne the Ka = 1 ← 1 progression within several wavenumbers, which
we don’t see. The identiﬁcation of the Ka = 1 ← 1 progression as well as any B-type
progression and progressions out of the upper tunneling state are ongoing. Even thoughpredictions indicate that the Ka = 1 ← 1 band should be detectable based upon the signalto-noise levels and that the band should be close to the Ka = 0 ← 0 band, we are not able toﬁnd it even with a larger search region. This clearly indicates that the rigid rotor predictions
are somewhat inadequate for describing the rotational structure of hydroxymethyl radical.
The identiﬁcation of B-type transitions is contingent upon obtaining 2-line combination
diﬀerences that either form 4-line combination diﬀerences with other B-type transitions ormatch energy levels from the identiﬁed A-type band. Even with the estimate of 40% of Btype character, the p-branch transitions will have very low signal-to-noise due to unfavorable
Hönl-London factors, which precludes using internal B-type 4-line combination diﬀerences.
With only the A-type Ka 0 ← 0 band identiﬁed, no inter-band 4-line combination diﬀerences
have been found. This could be because the contribution of the B-type band is small thanreported previously or with the congested spectra we do not yet have enough information to
make a positive identiﬁcation.
7.5

Conclusion and SummaryFirst fully rotationally resolved high resolution spectra of hydroxymethyl radical havebeen obtained in the Ka = 0 ← 0 symmetric CH stretch region, resulting in much improved experimental values for ground state rotational constants and vibrational band ori-

166
gin. Additional conﬁrmation of the spectra arising from hydroxymethyl radical is achievedby synthesizing the radical in two diﬀerent ways: i) via electron bombardment cleavage of
methanol doped in a supersonic discharge expansion (CH3 OH → CH2 OH + H) and ii) selective chemical H atom removal by Cl + CH3 OH → CH2 OH + HCl reactions in a Cl2 andmethanol doped discharge. The precision of the ground state rotational constants provide
reliable frequency predictions to minimize spectral search and thereby enable further laboratory detection and characterization of this highly reactive radical in the microwave, mm
wave, far-IR and near-IR spectroscopic region. The large amplitude COH torsional tunneling and out of plane CH2 wagging motion provide important state-of-the-art challenges forbenchmarking high quality potential energy surfaces as well as furthering the developmentof eﬃcient computational methods for multidimensional QM dynamics calculations. It is ourhope that such synergism between high resolution spectroscopic eﬀorts, ab initio chemistry
and rigorous dynamical theory will help elucidate the role of this important radical in diverse
venues ranging from combustion chemistry to atmospheric chemistry.

Chapter 8
Conversion of Coherent 899-29 system into high-accuracy, high-precision
automatically-tunable laser: application in a new mid-IR spectrometer forstudy of transient intermediates

8.1

Introduction
High resolution spectroscopy has proven a powerful technique for the structure andbonding of molecules.[227] For example, in vibrational spectroscopy increasing the resolution often reveals rich rotational structure that allows for direct experimental observation of
the molecular structure. Sometimes even smaller eﬀects, such as energy level shifts due toelectron-spin nuclear-spin interaction can be resolved and tell even more about the electronic
structure.[35] For molecular spectroscopy, knowing the frequency of a transition with a precision of 10 MHz permits unambiguous assignment of the rotational and vibrational transitions
for many molecules. Another recent motivation for developing high resolution systems has
stemmed from a desire to accurately measure the Boltzmann constant by measuring molecular transition line proﬁles, which also requires high accuracy and precision[37, 38]. A popular
tool for high-resolution spectroscopy is the Coherent 899-29 Ti:Sapphire laser system. This
commercial system was designed for automated scanning at high-resolution and is commonlyused in the ﬁeld of spectroscopy. The laser system includes a wavemeter, electronics, andcomputer system to automatically scan the desired frequency range. The laser has a stable
Roberts, M. A.; Sharp-Williams, E. N.; Nesbitt, D. J. in preparation

168
narrow linewidth that lends itself to high-resolution work. However the achievable resolution
is only about 200 MHz, limiting the quality of the spectroscopic data that can be obtainedwith the system. In this paper, we provide a cost eﬀective and straightforward solution to
improve the resolution of this laser system to <10 MHz, while improving upon the automatedscanning capability of the laser. To demonstrate the new capability of the laser system, weincorporate it into a new mid-IR automated scanning spectrometer with improvements overpreviously published spectrometers. One aspect that separates this spectrometer from its
predecessors is the fast and automated scanning; there are also other improvements including
an extended frequency range, diﬀerent method of obtaining the frequency axis, and the useof solid state lasers providing a more stable setup.
In creating a mid-IR spectrometer, there are many experimental challenges that need
to be overcome and subsequently the technology used to mid-IR spectroscopy has changed astechnology improved. One of the older technologies for creating tunable infrared (IR) lightis the color center laser. These lasers have a limited tuning range and are experimentallychallenging and delicate; the crystals are very hygroscopic and light sensitive and therefore
must be keep under high vacuum, cooled by liquid nitrogen, and away from light[41]. Leadsalt Diode lasers can be used, but are limited by a relatively small tuning range of tensof wavenumbers. Quantum cascade lasers (QCL) also reach the mid-IR, however currently
most QCL’s have a limited continuous tuning range, usually on the order of several tensof wavenumbers. The external cavity quantum cascade lasers can have up to 250 cm−1
tuning range, but compared to a 1500 cm−1 tuning range of a dye laser, it is still quite
small[42, 43, 44]. Frequency conversion is the most frequently used method for generating
mid-IR radiation. Miller and coworkers have used Raman stimulation of a gas cell to create
mid-infrared light, with a resolution of about 200 MHz[45]. Diﬀerence frequency generationof a single frequency argon ion laser with a tunable dye laser in a lithium niobate crystal tocreate mid-infrared light[26] was ﬁrst reported by Pine et al. in 1974. Pine’s system is very
versatile and has been very successfully adapted, with modiﬁcation, by many groups [53]169
including our group but still requires partial manual scanning.[57] The spectrometer in ourgroup uses a tunable ring dye laser and a single frequency argon ion laser to generate mid-IR
light via diﬀerence frequency generation in a periodically poled lithium niobate crystal andhas a frequency precision of better than 10 MHz. An optical parametric oscillator (OPO)
conﬁguration is a very common way to generate mid-IR radiation and there are many inthe literature as well as commercial models.[228] One advantage of just DFG over an OPO
is that with DFG all of the frequency diagnostics, locks, and scanning mechanisms can beapplied to the visible (or near-IR) lasers and not the mid-IR, making ﬁnding optics anddetectors easier, cheaper, and extendible to other frequencies with the change of a crystal or
single-frequency laser.
In order to improve upon existing mid-IR spectrometers, this system needs i) a large,
continuously tunable frequency range in the mid-IR, ii) frequency precision and accuracyof 10 MHz or better, iii) an improvement in speed and ease of data acquisition, iv) highdetection sensitivity, and v) ability to create relatively large concentrations of radicals andions. The technique presented in this paper combines an actively stabilized Nd:YAG laser
and the tunable Ti:Sapphire laser in a periodically poled lithium niobate crystal where,
via diﬀerence frequency generation, tunable mid-IR light is generated. To our knowledge,
there are two other Ti:Sapph and YAG DFG systems published, both in 2008, for sensing
applications[47, 48] and measuring the Boltzmann constant[49]. They utilized much more
complicated methods to stabilize their YAG laser and were limited by the stability of theTi:Sapph laser. Those systems also lack the scanning infrastructure to scan continuously
for long distances and they are setup to only look at Doppler-limited neutrals. The systempresented here is unique in combining the laser system, with the sub-Doppler radical and ion
generation system, with the machinery for extended and automated continuous scanning.
Since the scanning functionality used is heavily based upon the Ti:Sapphire and Autoscan system, a brief introduction is useful. The Ti:Sapph laser is set up in a vertical ring
conﬁguration with a Faraday Rotator in the cavity to ensure unidirectional lasing. A bire-170
fringent ﬁlter and two intracavity etalons narrow the laser linewidth to a single cavity mode.
The thick intracavity etalon consists of two mirrors separated by a piezo cylinder and islocked to peak transmission output and therefore tracks with the laser cavity length change.
The thin intracavity etalon, consisting of a single optic, also tracks with the laser scanning,but tracks by tilting. All of the electronics necessary to achieve locking and scanning up to
30 GHz are contained in the laser control box. For increased stability, the laser is locked
to an external cavity with feedback sent to a piezo-mounted cavity mirror. Tunability of
the laser is achieved by galvo-controlled rotation of a quartz plate that changes the cavity
length. The laser achieves tunability by rotation of a plate in the external cavity changing
that cavities length, which causes the laser to follow the scanning by changing the laser
cavity length by rotation of the quartz plate in the laser cavity.
The laser system also includes an attached wavemeter and system for automated scanning of large frequency regions, called Autoscan, and consists of a separate set of electronic
controls and a computer. The Autoscan computer provides an interface to read the frequencyof the laser, change the laser frequency to any speciﬁed frequency, and automatically scan
the laser any speciﬁed frequency range. Scanning of the laser is achieved through control
over the laser elements listed above and a stepper motor attached to the birefringent ﬁlter.
This allows the Autoscan system and laser move to any speciﬁed frequency at which thelaser lases. Autoscan contains algorithms to check the laser frequency, move the elements inthe laser (birefringent ﬁlter, etalons, etc.), check the frequency again and repeat until thedesired laser frequency is reached. To scan, the system ﬁrst moves to the speciﬁed starting
position. It then scans by moving the reference cavity plate, forcing the laser to follow. In
step-scan mode, the mode used here, the user speciﬁes the frequency step in between eachdata point. The laser has a linearization procedure to determine what voltage to apply tothe reference cavity plate to generate the most linear scan. This continues for 10.2 GHz
and is called a segment. At the end of a segment, the laser uses the wavemeter to moveto a frequency that is 10 GHz from the starting frequency of the previous segment. Once171
the laser reaches the new frequency, it scans another 10.2 GHz segment. This procedure isrepeated until the desired frequency region is scanned, completing what is referred to as ascan. The frequency associated with each data point is given as the starting frequency plus
10 GHz times the segment number (with zero corresponding to the ﬁrst segment) plus the
step-size times the data point number for the segment. The wavemeter used to measure thefrequencies at the start of each segment has a stated accuracy of 200 MHz and that means
there is a 200 MHz uncertainty at the start of each segment. To obtain the frequency foreach data point, the step size is deﬁned as the frequency length between data points and is
added to the start frequency. This means that each data point has a 200 MHz uncertainty,
plus any diﬀerence between the stated step size and the actual step size (found to be usually
within a few MHz). This large uncertainty in the frequency of each 10.2 GHz segment is thecrux of the problem with the Autoscan system.
There are two major improvements needed before the Autoscan system can be used
for high-resolution mid-IR spectroscopy. Since the wavemeter is integral to the automatedscanning system, we are motivated to keep as much of the system as possible. The ﬁrst
problem that needs to be address is the precision and accuracy of the frequency axis provided
by the Autoscan system. The second problem is the integration of the laser system into alarger system. In this paper, we present a novel implementation to improve upon the accuracyof the Coherent 899-29 laser system such that is can be used to high-resolution spectroscopy
with frequency precision of about 10 MHz. Using a set of locked cavities, we are able totake advantage of the frequency readings provided by the associated wavemeter and thefrequency axis provided by the Autoscan system but correct the frequency such that the
precision is improved more than 10-fold. This solution means that we are taking advantage
as much of the existing machinery as possible in order to minimize the work needed improve
the frequency precision. To illustrate the use of the improved system, we integrate the laser
into a fully automated mid-IR scanning spectrometer that has several improvements frompreviously published mid-IR spectrometers.

172
The organization of the chapter is as follows: In section 8.2 the two major modiﬁcationsof the Coherent Autoscan system are discussed. First the modiﬁcations necessary to the
Autoscan system are described: the procedure for correcting the Autoscan-generated axis
is in section 8.2.1 and the remote operation of the laser and Autoscan is in section 8.2.2.
The mid-IR spectrometer for studying transient species is presented in section 8.3 and somesample data illustrating the success of the spectrometer are in section 8.4.
8.2

Precision Automated Scanning of Ti:Sapphire Laser

8.2.1

Frequency Determination

The frequency axis needs to be corrected in order to obtain high-precision scans. The
two problems that need to be ﬁxed are i) lack of frequency accuracy causing errors when
stitching together segments and scans and ii) nonlinear scanning during a segment. To
ﬁx these problems we will use the Autoscan wavemeter, with accuracy of 200 MHz, andtwo stabilized optical transfer cavities, one with a 1.5 GHz FSR and another with a 250
MHz FSR. While the Ti:Sapphire laser is scanning, we record the Ti:Sapphire transmission
through each cavity. At the start of each segment, the Autoscan wavemeter reading isused to assign a fringe number to the 1.5 GHz FSR cavity fringe. A Snyder peak-ﬁnder
algorithm[34] is used to ﬁnd the peak positions of each fringe. The fringe number on the
1.5 GHz FSR cavity is used to assign a fringe number to the 250 MHz FSR cavity. The
Autoscan wavemeter is not accurate enough to unambiguously assign a fringe number to the
250 MHz cavity but is accurate enough to assign a fringe number to the 1.5 GHz FSR cavity.
To correct for the nonlinearity in scanning, we deﬁne the frequency diﬀerence between each
250 MHz FSR etalon peak to be the precise value of the FSR and then linearly interpolate
the data points between each peak. Using a relatively small (250 MHz) FSR cavity for thisstep minimizes the number of data points to be interpolated. Once a peak from the 250
MHz FSR cavity in each segment of each scan is assigned a fringe number and the scan is173linearized, it is possible to precisely stitch together scans and assign an absolute frequency
using a molecular reference line. A sample scan showing fringes from the locked 250 MHz
cavity before and after the correction process is is Fig. 8.1. The choice of 1.5 GHz and 250
MHz is discussed in section 8.2.1.1.
The 250 MHz optical transfer cavity consists of two curved dielectric mirrors mounted
to a hollow tube. The tube has 2.5 cm of piezo material on one end, a section of pyrex
glass, a section of stainless steel wrapped in a resistive heater, and ﬁnally another section ofpyrex. The piezo allows for fast changes of cavity length and the heated steel responds to slow
changes. The cavity is aligned in a confocal bowtie conﬁguration. A home-built polarizationstabilized HeNe laser[54] is sent through the cavity and the peak of the transmission fringe
is used to lock the frequency of the cavity mode. Once the HeNe is stabilized, it is used toprovide a stable source to lock the cavities needed in the rest of the instrument[31]. The 1.5
GHz cavity is similar, but does not have the stainless steel segment, the heater is wrapped
directly around the pyrex glass tube, and the piezo material is only 1.5 cm long. Thesechanges are only necessary because of the diﬀerence in distance changes necessary to correct
for errors in a physically shorter cavity are small than for a physically longer cavity. Oncethe two optical transfer cavities are locked to the HeNe, the free spectral range of the cavity
is precisely determined. While the Ti:Sapphire laser is scanning the transmission fringes
through both the 250 MHz cavity and 1.5 GHz cavity are recorded; sample data from two
diﬀerent scans is shown in panel a) of Fig. 8.1.
To correct for both the nonlinearity in scanning and the inaccurate and imprecise
frequency readings of the Autoscan, we adopted a two cavity solution. At the start of eachsegment the Autoscan wavemeter sets itself to within ± 100 MHz of the desired starting
frequency for that segment and starts to step-scan. As the laser scans, we record the inference
fringes of the Ti:Sapphire laser output through two locked bow-tie confocal cavities, one with
an approximate free spectral range of 1.5 GHz and the other with about a 250 MHz free
spectral range. Since we don’t have control over where each segment begins, we are not able

174a) Overlap of scans using Autoscan-generated frequencies

Cavity Transmission

250 MHz FSR Cavity

0
1.5 GHz FSR Cavity

Scan 1
Scan 20361108361109361110361111

Ti:Sapphire Frequency from Autoscan (GHz)

Cavity Transmissionb) Overlap of scans using cavity-corrected frequencies

0
4336

4337

4338

4339

Corrected Axis (relative GHz)

Figure 8.1: Two sample Ti:Sapphire laser transmission fringes through the two optical transfer cavities. Panel a) shows an overlap of the two scans if the frequency generated by Autoscan is used to overlap two scans. The fringes from the two scans do not overlap, but there
is no ambiguity as to which 1.5 GHz cavity fringes should overlap while there is ambiguity
for the 250 MHz cavity fringes. Panel b) illustrates the high quality of the overlap between
scans when the corrected frequency axis is used.

175

Difference From Linearity (MHz)Nonlinear Scanning Illustrated Using 250 MHz FSR Cavity Fringes
Sample Scan 1

15

Sample Scan 2

10
5
0
-5
-10
-15
0

10

20

30

40

Fringe Number

Figure 8.2: Illustration of nonlinear scanning of the Ti:Sapphire laser system. The plot is of
the diﬀerence between the 250 MHz FSR cavity peak positions and simulated peak positions
for a linear scan plotted as a function of the fringe count during the segment.

to always start on the peak of the fringe, which is not an issue with the two cavity method.
The frequency determination can be quantiﬁed with propagation of error calculations. Each
Autoscan wavemeter reading has an error, based upon the speciﬁcation, of 200 MHz; thiserror is usually less than the speciﬁed error and can depend upon how well the wavemeteris aligned and calibrated. This means that every time Autoscan reads the frequency there
is an error of 100 MHz, which is too large for high-resolution spectroscopy. Additionally,
if we wanted to stich together scans the way the old spectrometer does, with a 250 MHz
cavity, we would likely make fringe assignment errors every few segments; since we scan tensof segments a day, this is an unacceptable number of errors.

176
8.2.1.1

Choice of Cavity Size

The design of the 2-cavities is motivated by understanding the precision and accuracy of
the wavemeter and propagating that error. The functionality of the optical transfer cavities
is twofold, i) accurately reference the start frequency of each segment and ii) correct for
the nonlinearity of the scanning. In order to linearize the scan, we interpolate between thefringes and want to minimize the number of points to be interpolated between the peak of
the fringes. At the same time, we need the FSR to be large enough to unambiguously assign
a mode number to the fringe. Therefore we need one cavity with a small enough FSR tominimize possible inaccuracies while interpolating and a second cavity with a large enough
FSR so that if the Autoscan frequency is used to assign a fringe number there is no ambiguity
to the fringe count.
The choice of the large FSR cavity is based upon the ability to assign a number tothe cavity mode, with an acceptable level un uncertainty. The stated level of accuracy of
the Ti:Sapph wavemeter is 200 MHz. Accuracy is the correct number here because of themethod by which the Ti:Sapph starts each scan. At the start of each segment, the laser
takes an absolute frequency number and uses that to set the starting point for the scan;
therefore the start of every segment involves an absolute frequency reading. In order to get
the relative fringe number for the experiment, we take the diﬀerence between two fringe
readings. Speciﬁcally,Fn =peak A − peak B
FSR

(8.1)

where Fn is the diﬀerence between the two fringes in units of fringe number. The error
associated with calculating Fn is calculated by propagating the error associated with thiscalculation. The result of propagating the error on this process, the uncertainty in the fringe
number, is√ √∆Fn = (

step
δFSR 2
2 × acc2 2
) (
) +(
)
FSR
step
FSR

(8.2)

where acc is the accuracy in the measurement, step is the diﬀerence in frequency between

177
the two measurements (peak A - peak B), F SR is the free spectral range of the cavity,and δF SR is the uncertainly in the free spectral range. For the 1.5 GHz cavity, the term
involving the error in the FSR becomes almost negligible. Fig. 8.3 illustrates these ideas fora sample cavity with a 250 MHz free spectral range and a 2 MHz uncertainly in the FSR
with the uncertainly in the fringe number shown with the contours, the distance between two
frequency measurements, and the accuracy of the absorbance measurements. The important
thing to notice about this graph is that with an uncertainty in the accuracy of a frequency
measurement of 100 MHz (a lower limit of the Autscan accuracy), there will always be an
uncertainly of half a fringe in any given measurement, irrespective of the distance between
the two measurements. This illustrates the need to use a cavity with a much larger FSR in
order to accurately stitch scans together, especially scans from diﬀerent frequency regions.
This type of error propagation analysis led to the choice of a 1.5 GHZ cavity to be able toconﬁdently assign a relative fringe number to the start of each scan.

8.2.2

Integration of Autoscan with larger program

The second problem with the Autoscan system is that it is not sophisticated enough to
run the entire high resolution system and must be integrated into a program that can run allof the necessary equipment while maintaining the scanning functionality. The approach taken
to control the Autoscan system, and subsequently the laser system, splits the control into
two parts, i) complete remote control of Autoscan computer program and ii)coordinate stepscan with pulse valve and data recording. Figure 8.4 shows a brief outline of the master scan
program and the ﬂow of information to and from the program. Using A/D output channels
connected directly to the Autoscan electronics and RS232 communication to the Autoscan
computer, control over the Ti:Sapphire laser and Autoscan system is entirely through themaster program. In addition to controlling the laser system, this program coordinates theuse of all lab equipment necessary to take data. The program triggers the pulsed nozzle anddischarge, controls the gas ﬂow and discharge, laser scanning and timing of recording data.

178

200
180

1.4

a) Fractional
Fringe Error

160

250 MHz Cavity

1.2

Accuracy of Wavemeter Measurement (MHz)

140
120

1.0

0.8

100
80

0.6

60

0.4

40

0.2

20
0
0.0

0.2

0.4

0.6

0.8

1.0

200

0.175

b) Fractional
Fringe Error
150

0.150

1.5 GHz Cavity

0.125
0.100

100

0.075
0.050

50

0.025
0
10

20

30

40

50

60

70

80

90

100

-1

Difference Between Measurements (cm )Figure 8.3: Plots of the error in counting fringes between two fringe measurements, in unitsof fractions of a fringe, as a function of the accuracy of the frequency measurement and thediﬀerence in frequency between the two fringes. Panel a) shows the calculation for the 250
MHz FSR cavity and panel b) plots the calculation for the 1.5 GHz FSR cavity. Note thediﬀerence in x-axis scale between the two plots.

179
This requires control over the laser scanning machinery, timing and triggers for the pulsed
valve and discharge, and data and diagnostics recording processes. Figure 8.4 diagrams
the connectivity between the computer dedicated to running the scannew program and theother lab equipment. To communicate with the lab equipment, two analogue-to-digital cards(NI-6110 and NI-6025E) are used as well as several RS232 ports.

Logic and Information Flow
Scan Program

Scan setuporange = digital 2-way communication
green = digital to analogue output
purple = analogue to digital input

Gas flow control
Trigger to pulse valve and discharge voltage

Start of scan

Laser wavelength change, scan setup and start

Loop over segments
Data point loop
Average overvalve pulses
Record data

Step-scan triggers
SignalFrequency Diagnostics

Coherent 899-29 System

AutoscanControl Box

Laser
Control
Box
Wavemeter
Ti:Sapphire Laser

Figure 8.4: Schematic showing the logic and connectivity of the master scanning program.

The computer program piece of the Autoscan system has the ability to be controlled
through a series of RS232 commands. For our purpose, these commands are used to change
and read the laser frequency, start and end a scan, and specify what type of scan to execute,180such as scan length and step size. Once a scan is in progress, the computer program takes
over control of the Autoscan scanning electronics through analogue connections. The laser
is operated in step-scan mode, more speciﬁcally that the laser pauses at each point until
told to step by the designated step size and then pauses again until told to take anotherstep. This is repeated for 10.2 GHz, at which point the laser ends the segment and moves
back 0.2 GHz while peaking the power. Once the laser has reached the new frequency, itsignals to the computer and waits for the signal to begin the step-scan. To achieve this levelof communication, the programs employs nested while loops and dig in line LabWindows
command to monitor the status of the communication from the laser, and dig out line tosend commands to the laser indicating the computer is done recording data and is readystep in frequency. Fig. 8.4 also shows an outline of the logic of the computer program. The
combination of analogue and digital communication between the Autoscan system and main
computer are all that is needed to transfer the frequency control and scanning functionalityof Autoscan to a master program where it is incorporated into a larger instrument.
8.3

Mid-IR spectrometer for studying transient molecules
The advantage of putting so much eﬀort into creating a high-resolution, high-precision

frequency axis with the visible/near-IR laser is that when we use DFG to generate mid-IR
light, the precision, resolution, tunability, and automation is transferred to the mid-IR light
as long as the second laser is a locked, stable, single frequency source. This setup could easily
be adapted to other IR frequencies of light by simply changing the single-frequency laser,
nonlinear crystal, and potentially the detectors. This ﬂexibility provides a huge advantage
over systems where the frequency precision and tunability are tied to an IR laser or an
IR-speciﬁc OPO.
The mid-IR light is generated via diﬀerence frequency generation (DFG) of the tunable Ti:Sapphire light with the single-frequency Nd:YAG light in a temperature-tuned,periodically-poled lithium niobate crystal. The Nd:YAG laser frequency is stabilized by

181

Wavemeter+
TI:SAPPHIRE

Common Mode
Noise Subtraction

VERDI

A-D Card/
ComputerLock-inDetection
Gas Inlet

Slit Jet
NozzleYAG
Polarization
Stabilized
HeNe

InSb
Herriott Cell

PD

50/50
BeamSplitter

PD
PD

Vacuum Chamber

InSb
PD

Wavemeter

PD
Stabilized Marker
Cavities

Lock-in Detection

Chopper

InSb

Reference Cell

PPLN

Figure 8.5: Optical layout of the high-resolution spectrometer. The radiation from a tunable Ti:Sapphire laser is overlapped with the single-frequency light of a Nd:YAG laser in aperiodically poled lithium niobate crystal (PPLN) and via diﬀerence frequency generation
to produce the mid-infrared light. The frequency axis is precise to 10 MHz.

182
active locking to the 250 MHz optical transfer cavity discussed previously. Details of the
YAG locking are found in the appendix. The radiation resulting from the DFG is split into
two beams of roughly equal intensity, a signal and a reference beam, and detected withmatched InSb photovoltaic detectors. The signal beam is directed through a CaF2 window
and into the vacuum chamber where it passes 16 times through the long axis of the slit oriﬁce(4 cm) in a Herriot cell conﬁguration, increasing the pathlength to 64 cm. The Herriot cellconsists of two 2” gold mirrors with a 40 cm radius of curvature, mounted just under 40 cm
apart in the vacuum chamber.
The transient species, in this case molecular ions such as HD2 O+ , are produced by adiabatically expanding a mixture of D2 O in H2 . The ﬂow and mixture percentage is controlled
through the use of mass ﬂow controllers just before passing through a slit nozzle(4cm by
300 µm) pulsing at 19 Hz with an adjustable opening time of 1-2 ms. The limiting oriﬁceof the slit is a pair of adjustable steal jaws, attached to an Ultem insulator plate that is
attached to the body of the nozzle. This nozzle setup is a near-replica of the one describedin detail elsewhere[33, 55] and the discharge setup is similar to the setup described in Daviset al.[56]. Absorbance signals are generated by automatic subtraction electronics and then,if a discharge is being used, sent to a homebuilt lock-in detector. The lock-in detector takes
advantage of the concentration modulation with the 50 KHz discharge frequency serving as
the local oscillator so that the output contains signal only from species produced in the modulating discharge. This signal is sent to the computer via a A/D card (NI6110E). The time
trace of the signal is gated and integrated in coincidence with the pulse valve and discharge.
8.4

Spectrometer test results
For high resolution spectroscopy, the most important piece of information is the accu-racy and precision of the frequency axis. The test the frequency axis, we repeatedly recorded
molecular absorption lines and compared the peak frequency positions obtained on diﬀerent
days. Speciﬁcally, a ∼100 cm−1 region was scanned with D2 O in H2 discharge. The region

183
was fully scanned at least 3 times and all lines appearing in each scan were used to compare
how well the spectrometer reproduced the frequencies. Figure 8.6 is a plot of the frequencyof each line on the frequency axis with the standard deviation of the repeated measurementson the absorbance axis. The average standard deviation of all the lines taken is 9.3 MHz,
which is right in the target range. The lines looked at include known D2 O lines and H+
3 lines,
as well as many unidentiﬁed lines, many of which belong to HD2 O+ . This level of frequency
reproducibility is good enough for doing high-resolution studies of radicals and ions.
25a) Reproducibility of Line Positions
Average Standard Deviation of 9.3 MHz+20b) Sample HD O
2++Transition, 0

1

Band

% Absorbance

0.2# of Lines

15

10

2

20

1

11

0.1

0.0
3531.18

3531.20-1Frequency (cm )
5

0
0

5

10

15

20

25

30

35

40

80

85

Standard Deviation (MHz)Figure 8.6: Illustration of the precision of the new instrument. This region was scanned aminimum of three time and the standard deviation of the measurements for each line in theregion is plotted as a function of the frequency position of the line. The average standard
deviation of the measurements is 9.3 MHz. Sample HD2 O+ data in the OH stretchingregion illustrating the ability of the new instrument to produce molecular ions in appreciable
quantities.

The initial project for this new spectrometer was to look at the the OD stretches of
HD2 O+ to complement the study of the OH stretch done on the older instrument in the184
lab[57]. This is also a useful test for the instrument as it was already studied in the lab
so we would have some nice benchmarks to assess how the new instrument compares tothe existing instrument. As determined by previous spectroscopic studies[57, 58] HD2 O+
is a near-prolate top with a low barrier to inversion along the umbrella coordinate. Even
with the low temperature of the slit jet expansion, the ﬁrst excited tunneling level of theground vibrational state is populated, however transitions from the lower tunneling level ofthe ground state to the lower tunneling level are the most intense. To test the our ability
to create ions and detect them with the new setup, we began by taking some lines from the
OH stretch and checking against the published lineshapes and intensities. The OH stretch
is an b-type transition and the 220 ← 111 and 111 ← 000 transitions are shown in ﬁgure 8.6.
The integrated intensity for the 220 ← 111 transition is the same as that in Figure 5 of Donget al.[57].
8.5

Appendix: YAG Lock Description
The concept and method for locking the YAG laser to a single frequency is based upon

methodology successfully used for many years for locking an Ar+ laser to a single frequency.
To the best of our knowledge, the literature does not include application of these methods forlocking a YAG laser. The YAG laser is use here is a Lightwave Electronics Series 126. The
laser is a non-planar ring oscillator with the crystal interface acting as the cavity mirrors.
There are two ways to tune the crystal: piezo-induced strain and temperature variance using
a thermoelectric cooler attached to the crystal. The frequency of the laser is stable in the
short term, but tends to drift over long times so it is only necessary to correct for slow
ﬂuctuations in frequency. The response of the temperature tuning of the laser results inabout -3.1 GHz change per degree Celsius and continuous tuning is achievable for about 10
GHz before a laser mod hop occurs.
A small portion of the YAG light is sent through the locked 250 MHz FSR cavity andrecorded on a photodiode. Fig. 8.7 is a schematic of the locking circuit. The 4 KHz dither

185
applied to the 250 MHz cavity is used as the local oscillator for the top-of-line locking circuit.
Since only slow errors need to be corrected, the servo-loop only has integrated feedback. With
the GHz/◦ C conversion of the laser, only mV level corrections generally need to be made.
Therefore directly at the input to the laser is a voltage divider to ensure that the voltages
passed through cables are large but that the voltage corrections supplied to the laser areappropriate. With this circuit, the Nd:YAG laser frequency is stabilized for an entire day ofscanning.

Nd:YAG
Laser

Piezo Locked Optical

Transfer Cavity

Heater Input
4 KHz Dither
Phase
AdjustDetector

AC Filter

Integrator
Double Balanced
Mixer
Figure 8.7: Schematic representation of the Nd:YAG locking circuit.

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Appendix A
Harmonically Coupled Morse Oscillator (HCMO) fitting routineThis is the full ﬁtting program, with sample input ﬁle, for the Harmonically Coupled
Morse Oscillator model presented in chapter 5.
Sample Input File:

3004.436
3160.82118
3160.82118

1
1
1

1
0
1

2283.33065.63346
3158.33273

2
2
2

1
1
1

2221.52381
3114.577

3
3
3

1
0
1

2156.52381.08860
2381.08860

4
4
4

1
0
1

-999

0

0

1.007825,2.014102,12.0000,120.,1.0818
7,7,7
1
4
7.8794175d-12
1.903033d8
2580.1732d0
0.72
0
0
0
0

Main Program:

PROGRAM wgtLSQIMPLICIT double precision(A-H,O-Z)
CHARACTER*16 DATAFILEDIMENSION XM(25,2),wt(250),RES(250),SCRAT(5000),
x COEF(10),SPLST(10),STAT(10),PV(250,2),SDPV(250),SDRES(250),
x VCV(10,10),STEP(10),DSTAK(20000),SCALE(10),STP(10),IFIXED(10),. spec(100),coefp(5),F(12),y(25),ctemp(10),ytmp(25),fcm(12)COMMON/CSTAK/DSTAK
common/flag/iflag,ieflag

199
common/constants/hconstant(10),ihconstant(10),gmat(3,3,4)
EXTERNAL MODELc ************************************************************************cc this version will also fit overtone bands and print out thec eigenfunctions.
LDSTAK = 20000
IXM=250
THE FOLLOWING WERE ADDED TO ACCESS THE NLSWS VERSION OF NLSQ
THIS VERSION USES WEIGHTED LEAST SQUARES FITTING OF <= 10 PARAMSDELTA = -1.0
IVAPRX=1
MIT = 100
IVCV = 25
NPRT = 22222
do i=1,10c
SCALE(i)=-1.0d-5
STP(i)=1.0d-5
enddo
SCALE(1)=-1.
c SCALE(3)=1.d-5c
STP(1)=-1.0d0
STOPP = 1.d-7
STOPSS = 1.d-7
m=3CC

iflag=0c this routine will fit the predicted frequencies from a harmonicallyc coupled morse oscillator model to experimental frequencies of allc the methyl radical isotopes.
c I will make it general so that I can change the hamiltonian and basis
c set if that is needed.
c first set up some of the constants that will be needed in the modelc some idiot first programmed this shit in cgs units, evidently it should bec in atomic units if one wants to have reasonable numbers.
c hbar = 1.054571628d-27
c cms = 2.99792458d10
hbar=1.
cms=137.036
C
DATAFILE=’mfrinput.dat’
OPEN(UNIT=7,FILE=DATAFILE,IOSTAT=IOS,STATUS=’OLD’)REWIND 7
N=0
10 READ (7,*) y(N+1),spec(N+1), WT(N+1)
IF(y(N+1).EQ.-999.) GO TO 15
N=N+1
GO TO 1015 continuec read in the hydrogen mass, deuterium mass, carbon mass, thec bond angle, and the bond length
read (7,*) hmass,dmass,cmass,ba,blc read in the basis set parameters you want to use for the fit
c specifically, the max quanta you want in each stretchc and store the values in hconstantread(7,*) nq1, nq2, nq3
c read in the ifit, which is 1 if you want to fit or 0 if you justc want to predict the spectra based on the input force constantsread(7,*) ifitc read in the stuff about the variables that you will have starpact fit
READ(7,*) NPAR
C the parameters are (in this order):c
De, aa, Frr,wni
c where De is the dissociation energy, aa is the morse parameterc and Frr is the force constant coupling the different stretches

READ(7,*) (coef(J), J=1,NPAR)
READ(7,*) (IFIXED(J), J=1,NPAR)
close(unit=7)
c turn the parameters into atomic units from cgs units
c de in energy, a in 1/length, frr in cm-1/ang^2c enau=4.35974394d-18

200
c ajscgs=1.0d-7
c alenau=0.52917720859d0
c erghar=4.35974820000e-11
c cmhar=219474.6313705
c coef(1)=ctemp(1)*ajscgs/enau
c coef(2)=ctemp(2)*alenau*1.0d-8
c coef(3)=ctemp(3)*alenau*alenau/(cmhar)c print *,ctemp(1),ctemp(2),ctemp(3)c print *,coef(1),coef(2),coef(3)c write the info that will be passed on to model via common blocks
ihconstant(1) = nq1
ihconstant(2) = nq2
ihconstant(3) = nq3
hconstant(4) = hbar
hconstant(5) = cms
c now calculate the g-matrix and write that to gmat so it can getc passed on to model
amug=1.66053886d-24
emassg=9.10938215d-28
acm=1.0d8
hmcgs=hmass*amug/emassg
dmcgs=dmass*amug/emassg
cmcgs=cmass*amug/emassg
c print *,hmcgs,dmcgs,cmcgs
blcgs=bl/acm
call gmiso(hmcgs,dmcgs,cmcgs,blcgs,ba)
c this is the output file for the eigenvalues and vectors
open(unit=8,file=’output.dat’,status=’unknown’)ieflag=0
c now split between the fitting and the modeling part of program
if (ifit.eq.1) then
CALL NLSWS(Y,WT,XM,N,M,IXM,MODEL,COEF,NPAR,RES,LDSTAK,
X IFIXED,STP,MIT,STOPSS,STOPP,SCALE,DELTA,IVAPRX,NPRT,X NNZW,NPARE,RSD,PV,SDPV,SDRES,VCV,IVCV)
ieflag=1
call model(coef,npar,XM,N,M,IXM,F)
print *,fCelse
c this is to correct the the dimensions of coef
do i=1,npar
coefp(i) = coef(i)enddo
ieflag=1
call model(coefp,npar,XM,N,M,IXM,F)
print *,’F list’
print *,fendifclose(8)call exitend

c **********************************************************************
c **********************************************************************SUBROUTINE MODEL(P,NPAR,XM,N,M,IXM,F)IMPLICIT double precision (A-H,O-Z)
DIMENSION P(NPAR),XM(IXM,M),F(N),pcoef(npar),.
gmatiso(3,3),freq(1000),temp(3,4),. unpert(10),dkpert(10),pertu(10),pertl(10),ftmp(N)COMMON/constants/hconstant(10),ihconstant(10),gmat(3,3,4)
common/flag/iflag

HBAR = hconstant(4)cms = hconstant(5)pi=4.d0*atan(1.d0)
hh=hbar*2.d0*pi

201
c
c

enau=4.35974394d-18
ajscgs=1.0d-7
alenau=0.52917720859d-8
erghar=4.35974394e-11
cmhar=219474.6313705
c
pcoef(1)=p(1)*ajscgs/enau
pcoef(1)=p(1)/erghar
pcoef(2)=p(2)*alenau
pcoef(3)=p(3)*alenau*alenau/(erghar)ccprint *,p(1),p(2),p(3)print *,pcoef(1),pcoef(2),pcoef(3)C I will have to loop over this calculation for each isotope
do i=1,4
c for each isotope, I will put the gmatrix into gmatiso and send toc the matrix elements routine
do j=1,3
do k=1,3
gmatiso(j,k)=gmat(j,k,i)
enddo
enddo
c now calculate the eigenvalues for that isotope
call trans(pcoef,gmatiso,freq)
c store the frequencies in a temporary place
do j=1,3
temp(j,i)=freq(j)enddo
c end loop over isotopes
enddo
c now add the correction for the fermi interaction
c first pull out the relevant perturbed frequencies
c ch2d,chd2,cd3
c unpert(1)=temp(1,2)
c unpert(2)=temp(1,3)
c unpert(3)=temp(1,4)
c then make the matrix containing the perturbing frequencies
c dkpert(1)=2338d0/cmhar
c dkpert(2)=2054d0/cmhar
c dkpert(3)=2056d0/cmharc then send each to have the energies corrected for the pertebationc the wni term is the off diagonal matrix element that we will be fittingc wni=p(4)c do i=1,3
c en=unpert(i)c ei=dkpert(i)c call fermi(en,ei,wni,outu,outl)c pertu(i)=outu
c pertl(i)=outl
c enddoc put all of the frequency data into the F-matrix
c and turn them form hartrees to wavenumbers
cmhar=219474.6313705
scale=p(4)do i=1,4
do j=1,3k=(i-1)*3+j
Ftmp(k)=temp(j,i)*cmhar
enddo
enddo
c call the new fermi routine that takes all the stretches and calculatesc the Fermi interaction
call fermi2(Ftmp,F,scale)c now replace the perturbed frequencies
c F(4)=pertl(1)*cmharc F(7)=pertu(2)*cmharc F(10)=pertu(3)*cmhar

202
c print *, ’perturbed states’
c do i=1,3c print *,pertl(i)*cmhar,pertu(i)*cmharc enddoENDc **********************************************************************
c **********************************************************************
subroutine trans(p,gmatiso,freq)
IMPLICIT double precision (A-H,O-Z)
DIMENSION freq(1000),p(10),eigval(1000),gmatiso(3,3),. eigvecmat(1000,1000),ibasis(1000,4),hmat(1000,1000)
COMMON/constants/hconstant(10),ihconstant(10),gmat(3,3,4)
common/flag/iflag
c this is the maximum number of basis sets that can be used
nmax=1000
C THIS SUBROUTINE CALCULATES ENERGY LEVELS FOR A HAMILTONIAN USING MORSEC OSCILLATOR BASIS SET USING THE EXACT EXPRESSIONS FOR A MORSE OSC.
C GENERATE BASIS SET LABELLING SCHEME
CALL MAKEBASIS(iBASIS,NMAX,nbasis)c print *,’basis made’
C CALCULATE THE HAMILTONIAN MATRIX ELEMENTS
C AND RETURN THEM IN THE HERMITIAN MATRIX HMAT(NTOT,NTOT)CALL MATRIXEL(iBASIS,HMAT,nbasis,nmax,p,gmatiso)
c print *,’matrixel done’
C NOW CALL THE DIAGONALIZATION ROUTINESCALL hmatdiag(nbasis,hmat,nmax,EIGVECMAT,EIGVAL)
c print *,’hmatdiag done’
C THIS RETURNS...
C THE NTOT ASCENDING EIGENVALUES IN EIGVAL(J=1,NTOT)C THE CORRESPONDING MATRIX OF EIGENVECTORS IN EVECMAT(I=1,NTOT,J)C WHERE EIGENVAL(J) CORRESPONDS TO THE JTH COLUMN VECTOR

C sort and store the values for further analysis
call store(ibasis,EIGVECMAT,EIGVAL,nbasis,NMAX,freq)
c do i=1,3c print *,freq(i)c enddoreturnENDc *********************************************************************
c *********************************************************************SUBROUTINE MAKEBASIS(iBASIS,nmax,nbasis)
IMPLICIT double precision (A-H,O-Z)
DIMENSION iBASIS(NMAX,4)
COMMON/constants/HCONSTANT(10),ihconstant(10),gmat(3,3,4)
common/flag/iflag
C
C

THIS SUBROUTINE GENERATES THE BOOKKEEPING FOR HOW BASISFUNCTIONS ARE LABELLEDC READ IN BASIS SET PARAMETERS, STORED IN ICONSTANT
C the basis is labeled by the bond number and the number of quanta
C in each bond. basis(n,1) holds the quantum numbers for bond 1, etc.
nq1 = ihconstant(1)nq2 = ihconstant(2)nq3 = ihconstant(3)NBASIS = 0
ni=nq1+1
nj=nq2+1
nk=nq3+1
do i = 1,ni
do j = 1,nj
do k = 1,nk
nbasis = nbasis + 1
ibasis(nbasis,1) = nbasis
ibasis(nbasis,2) = i-1
ibasis(nbasis,3) = j-1
ibasis(nbasis,4) = k-1
enddo

203
enddo
enddo
c PRINT OUT THE BASIS SET LIST IF IFLAG = 1
if (iflag.eq.1) thenDO I = 1,nbasis
PRINT *, iBASIS(I,1),iBASIS(I,2),iBASIS(I,3),iBASIS(I,4)
ENDDO
ENDIF
RETURNEND
C *****************************************************************************
C **********************************************************************SUBROUTINE MATRIXEL(iBASIS,HMAT,nbasis,NMAX,p,gmatiso)
IMPLICIT double precision (A-H,O-Z)
DIMENSION HMAT(NMAX,NMAX),iBASIS(NMAX,4),p(10),gmatiso(3,3),. delta(10),energyr(10),energyp(10),emorse(10)COMMON/constants/HCONSTANT(10),ihconstant(10),gmat(3,3,4)
c print *,’entered matrixel’
C THIS SUBROUTINE HAS THE RESPONSIBILITY TO CALCULATE THE
C MATRIX ELEMENTS OF HMAT(NTOT,NTOT)c the matrix elements are explicit matrix elements of a morse oscillator
C SET UP HAMILTONIAN CONSTANTS
hbar = hconstant(4)cms = hconstant(5)pi=4.*atan(1.)
hh=hbar*2.*pi

c read in the parameters for the hamiltonian that are being fit by starpac
De = p(1)aa = p(2)frr = p(3)c now for the actual expressions for the matrix elementsc loop through the list of basis fcns
do n=1, nbasis
do nn=1,nbasis
c first make the necessary matrix elements
do m=1,3
gmu=1./gmatiso(m,m)
ak=fcnk(gmu,de,aa,hbar)
nl=ibasis(n,m+1)
nu=ibasis(nn,m+1)
c print *,nu,nl
energyr(m)=rcoupling(gmu,nu,nl,aa,de,ak)
energyp(m)=pcoupling(gmu,nu,nl,aa,de,ak,hbar)
delta(m)=deltakron(nu,nl)emorse(m)=dmorse(hbar,de,gmu,cms,aa,nl)
c print *,nu,nl,delta(m),energyr(m),energyp(m),emorse(m)enddoc then combine them to make the hmat entry
fm=emorse(1)*delta(1)*delta(2)*delta(3)sm=delta(1)*emorse(2)*delta(2)*delta(3)tm=delta(1)*delta(2)*emorse(3)*delta(3)totmorse=(fm+sm+tm)
c print *,fm,sm,tm,totmorse
first=energyr(1)*energyr(2)*delta(3)second=energyr(1)*energyr(3)*delta(2)third=delta(1)*energyr(2)*energyr(3)potential=frr*(first+second+third)
c print *,frr,first,second,third,potential
c the -1 here is for the i^2 term
fk=-1.d0*energyp(1)*energyp(2)*delta(3)fkp=gmatiso(1,2)
sk=-1.d0*energyp(1)*delta(2)*energyp(3)skp=gmatiso(1,3)
tk=-1.d0*delta(1)*energyp(2)*energyp(3)tkp=gmatiso(2,3)
ekinetic=(fk*fkp+sk*skp+tk*tkp)
c print *,fk,sk,tk
c sum up each piece of the matrix element and store in the proper placec in the hmat matrix
tot=totmorse+potential+ekinetic
hmat(n,nn)=tot

204
c end the loop over the basis functions
enddo
enddo

c print *,’end loop in matrixel’
c print out hamiltonian matrix for debuggingc
IF(IFLAG.EQ.1) THENc
DO N1=1,nbasisc
DO N2=1,nbasis
c if (abs(hmat(n1,n2)).gt.(1.0d-10)) thenc
PRINT *, iBASIS(N1,2),ibasis(n1,3),iBASIS(N1,4),c. iBASIS(N2,2),ibasis(n2,3),iBASIS(N2,4),HMAT(N1,N2)
c endif
c
ENDDO
c
ENDDO
c
ENDIF
END
C ****************************************************************
C ****************************************************************SUBROUTINE hmatdiag(nmat,AMAT,nmax,EVEC,EIG)IMPLICIT double precision (A-H,O-Z)
DIMENSION AMAT(nmax,nmax),EVEC(nmax,nmax),. Work(2*nmat**2+6*nmat+1),. IWORK(5*nmat+3),EIG(nmax)
CHARACTER job,uplo
EXTERNAL sSYEVD

c
C
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c

THIS SUBROUTINE DIAGONALIZES THE HAMILTONIAN WITHDSYEVD ROUTINE FROM MKL LIBRARY
Integer IA,N,IV,IFAILReal AMAT(IA,NMAT),EIG(NMAT),EVEC(IV,NMAT),WORK(3*NMAT)Parameters
AMAT
a real array of dimension at least NMAT X NMAT
IA initial dimension of A, at least N
NMAT
order of matrix
EIG
real array, dim’n at least NMAT
on exit, contains
eigenvalues in ASCENDING order
EVEC
real array, at least NMAT X NMAT.
on exit, contains
eigenvectors in ascending order, such that
EVEC(I,J), I=1,2,...,N correspond to EIG(J)
WORK
real array, used as scratch
IFAIL must be set=0 before entry; if IFAIL<>0 on exit,
an error has occurred
ia=Nmax
lwork=2*nmat**2+6*nmat+1
liwork=5*nmat+3
IFAIL=0
job = ’V’
uplo = ’L’ccfirst need to write AMAT into EVEC, since the input matrix
is replaced with the eigenvector matrix anyway
do i=1,nmat
do j=1,nmat
evec(i,j) = amat(i,j)
enddo
enddo

.

CALL DSYEVD(JOB,UPLO,nmat,evec,ia,eig,work,lwork,
IWORK,liwork,IFAIL)
IF(IFAIL.NE.0) THEN
PRINT *, ’PROBLEMS IN MATRIX DIAGONALIZATION ROUTINE’PRINT *, ’IFAIL = ’,IFAIL
ENDIF

c print *, ’nmat=’,nmat
c do i=1,nmat
c print *,eig(i)c enddo
RETURNEND
c *****************************************************************
c *****************************************************************
subroutine store(iBASIS,EIGVECMAT,EIGVAL,nbasis,NMAX,Fiso)
implicit double precision (a-h,o-z)205dimension ibasis(nmax,4),eigvecmat(nmax,nmax),eigval(nmax),. fiso(nmax)
common/flag/iflag,ieflag
c this takes the list of eigenvalues and puts them in the f-matrix
c so that it can be least-squares fit
c the eigenvalues come out sorted in ascending orderc the first number is the zpe and will be subtracted off
c the complete list of values and eigenfunctions will bec written in another file. the 3 ch stretch data will be put
c in the f-matrix

do i=1,3j=i+1
temp=eigval(j)-eigval(1)Fiso(i)=temp
enddo
c print out to a new file the list of eigenvalues and corresponding eigenvector
if (ieflag.eq.1) thenccc

DO I = 1,nbasis
write(8, *) iBASIS(I,1),iBASIS(I,2),iBASIS(I,3),iBASIS(I,4)
ENDDO

do i=1,20
temp2=(eigval(i)-eigval(1))*219474.6313705
write(8,*) eigval(i),temp2
do j=1,nbasis
aa=ibasis(j,2)
bb=ibasis(j,3)
cc=ibasis(j,4)
tot=aa+bb+cc
if (abs(eigvecmat(j,i)).ge.1.e-2) thenwrite(8,*) eigvecmat(j,i),ibasis(j,2),ibasis(j,3),ibasis(j,4)
endif
enddo
enddo
endif
c

10 format(’’,D10.8)

returnend
c *****************************************************************
c *****************************************************************
subroutine gmiso(hmass,dmass,cmass,bl,ba)
implicit double precision (a-h,o-z)
dimension ch3m(10),ch2dm(10),chd2m(10),. chd3m(10),cd3m(10),ch3c(10),ch2dc(10),chd2c(10),cd3c(10),. ch3gm(10,10),ch2dgm(10,10),chd2gm(10,10),cd3gm(10,10)
COMMON/constants/HCONSTANT(10),ihconstant(10),gmat(3,3,4)
common/flag/iflag

c this is the bookkeeping routine for the calculating all of thec g-matrices for each of the isotopesc this is the number of coordinates in the g-matrix

ncoord=3
c separate the data by species and create masses and coordinates for eachcmasses in amu for CH3
ch3m(1)=hmass
ch3m(2)=hmass
ch3m(3)=hmass
ch3m(4)=cmassccenter coords (ang and degrees)
r12, r13, r14, phi142, phi143ch3c(1) = blch3c(2) = blch3c(3) = blch3c(4) = bach3c(5) = ba

c calculate the g-matrix elements for this isotope
call gmatrix(ch3m,ncoord,ch3c,ch3gm)

206
c now repeat for the second species, CH2D
cmasses for CH2D
ch2dm(1)=hmass
ch2dm(2)=hmass
ch2dm(3)=dmass
ch2dm(4)=cmassccenter coords (ang and degrees)
r12, r13, r14, phi142, phi143
ch2dc(1) = bl
ch2dc(2) = bl
ch2dc(3) = bl
ch2dc(4) = ba
ch2dc(5) = ba

c calculate the g-matrix elements for this isotope
call gmatrix(ch2dm,ncoord,ch2dc,ch2dgm)
c now for the third species, CHD2cmasses in amu for CHD2
chd2m(1)=hmass
chd2m(2)=dmass
chd2m(3)=dmass
chd2m(4)=cmassccenter coords (ang and degrees)
r12, r13, r14, phi142, phi143
chd2c(1) = bl
chd2c(2) = bl
chd2c(3) = bl
chd2c(4) = ba
chd2c(5) = ba

c calculate the g-matrix elements for this isotope
call gmatrix(chd2m,ncoord,chd2c,chd2gm)
c repeat for the fourth species, CD3cmasses in amu for CD3
cd3m(1)=dmass
cd3m(2)=dmass
cd3m(3)=dmass
cd3m(4)=cmassccenter coords (ang and degrees)
r12, r13, r14, phi142, phi143
cd3c(1) = bl
cd3c(2) = bl
cd3c(3) = bl
cd3c(4) = ba
cd3c(5) = ba
c calculate the g-matrix elements for this isotope
call gmatrix(cd3m,ncoord,cd3c,cd3gm)
c compile all the gmat data into the gmat matrix

do i=1,3
do j=1,3
gmat(i,j,1)=ch3gm(i,j)
enddo
enddo
do i=1,3
do j=1,3
gmat(i,j,2)=ch2dgm(i,j)
enddo
enddo
do i=1,3
do j=1,3
gmat(i,j,3)=chd2gm(i,j)
enddo
enddo
do i=1,3
do j=1,3
gmat(i,j,4)=cd3gm(i,j)
enddo
enddo
returnend

207c *****************************************************************
c *****************************************************************
subroutine gmatrix(amass,ncoord,coord,gmat)
implicit double precision(a-h,o-z)
dimension gmat(10,10), amass(10), coord(10)ccthis subroutine calculates the Wilson G matrix as per
the elements listed in WDC appendix VI

c
c
c
c

we assume a planar 4-atom molecule with atom 4 as the central atom
the coordinates are 3 bond lengths and 2 angles
the unique atom is number one, and the two angles surroundthat atom. this g-matrix is only for the 3 stretchesc first, define all the parameters
am1=amass(1)am2=amass(2)am3=amass(3)am4=amass(4)rmu1 = 1./am1
rmu2 = 1./am2
rmu3 = 1./am3
rmu4 = 1./am4
pi = 4.*atan(1.)
r14 = coord(1)r24 = coord(2)r34 = coord(3)ro14 = 1./r14
ro24 = 1./r24
ro34 = 1./r34
phi142rad = coord(4)*pi/180.
phi143rad = coord(5)*pi/180.
phi243rad = 2.*pi-phi142rad-phi143radc

cospsi321 = cospsi123

c print *,’cos coords’
c print *,cospsi132,cospsi312,cospsi321c

now calculate the Gij matrix elements
gmat(1,1) = rmu1+rmu4
gmat(1,2) = rmu4*cos(phi142rad)gmat(1,3) = rmu4*cos(phi143rad)gmat(2,2) = rmu2 + rmu4
gmat(2,3) = rmu4*cos(phi243rad)gmat(3,3) = rmu3 + rmu4

c complete the matrix
do i=1,ncoord
do j=1,i
gmat(i,j)=gmat(j,i)
enddo
enddo
returnend
C *****************************************************************
c *****************************************************************
function dmorse(hbar,de,gmu,cms,aa,nn)
implicit double precision (a-h,o-z)
c this calculates the morse oscillator energy levels, the Ho partc of the Hamiltonian
pi=4.*atan(1.)
hh=hbar*2.*pi
rnn=nnww=2.*aa*hbar*sqrt(de/(2.*gmu))
wa=2*log(aa)wh=2*log(hbar)
wb=log(2.)
wc=log(gmu)wx=exp(wa+wh-wb-wc)
temp=(rnn+0.5)*ww-wx*(rnn+0.5)**2.
dmorse=temp
returnend
c **********************************************************************
c**********************************************************************

208
function deltakron(nu,nl)
implicit double precision (a-h,o-z)
c kronicker delta function
c this function returns 0.0 if nu is not equal to nl and 1.0 if nu=nl
if (nu.eq.nl) thentemp=1.0d0
else
temp=0.0d0
endif
deltakron=temp
returnend
c **************************************************************************
c *************************************************************************
FUNCTION digamma(dgx)
IMPLICIT double precision (A-H,O-Z)
DATA cs,d1/100.d0,-0.5772156649d0/
c this calculates the digamma function for values greater than -1 to anc accuracy of better that 1 part in 10^8 (this can be changed by changing
c where you start using the stirling approximation - ie change cs)
c This uses the stirling approximation at large values (eq 6.3.18 ofc Abromowitz and Stegun) and then uses the recurrence formula (6.3.5) toc get the smaller values of the function.
c This algorithm was inspired by Appl. Statistics (1976) vol. 25 no. 3
c algorithm AS 103 by JM Bernado
y = dgxs3 = 1.d0/12.d0
s4 = 1.d0/120.d0
s5 = 1.d0/252.d0
if (y.le.0.0) thentemp = 0.0
endif
temp = 0.0
10 if (y.ge.cs) go to 20
temp = temp -1.0d0/y
y = y + 1.0d0
go to 1020 rr = 1/y
temp = temp+dlog(y)-0.5d0*rr
rr = rr*rr
temp = temp-rr*(s3-rr*(s4-rr*s5))
digamma = temp
returnENDc **************************************************************************
c **************************************************************************

FUNCTION fcnk(fmu,dd,aa,hbar)
IMPLICIT double precision (A-H,O-Z)
p1 = 2.d0/(aa*hbar)
p2 = dsqrt(2.d0*fmu*dd)
tmp = p1 * p2
fcnk = tmp

RETURNEND
c *************************************************************************
c *************************************************************************
FUNCTION pcoupling(rmu,nu,nl,aa,de,ak,hbar)
IMPLICIT double precision (A-H,O-Z)
c this function returns the matrix element for the momentum operator whenc the upper state is not equal to the lower state, as per Halonene and Childc print *,nu,nl
rnu = nu
rnl = nl
inu = nu
inl = nl209
cc=1.0d0
c taking advantage of the Hermitian operators
if (inu.lt.inl) thentp = rnu
rnu = rnl
rnl = tp
inn = inu
inu = inl
inl = inn
cc = -1.0d0
endif
rj = rnu-rnl
jj = inu-inl
if (inu.eq.inl) thentemp=0.0
else
p1 = hbar* (-1.d0)**(rj+1.)*aa/2.d0
p2= dsqrt((ak-2.d0*rnl-1.d0)*(ak-2.d0*(rnl+rj)-1.d0))
prod=1.d0
do m=1,jj
rm=float(m)prod= prod*(rnl+rm)/(ak-rnl-rm)
enddo
temp=p1*p2*dsqrt(prod)
endif
pcoupling = temp*cc
c print *,nu,nl,pcoupling
RETURNEND

c *************************************************************************
c *************************************************************************
FUNCTION rcoupling(fmu,nu,nl,aa,de,ak)
IMPLICIT double precision (A-H,O-Z)
c this function calculates the off diagonal matrix elements for non-zeroc changes in n for the potential energy cross term
c print *,’entered rcoupling’
rnu = nu
rnl = nlknu = nu
knl = nlc taking advantage of the Hermitian operators
if (nu.lt.nl) thentp = rnu
rnu = rnl
rnl = tpknn = knu
knu = knl
knl = knn
endif
rj = rnu-rnl
jj = knu-knl
if (knu.eq.knl) thentemp=0.0d0
if (knl.eq.0) thenp1 = dlog(ak)arg2 = ak-1.d0-2.d0*rnl
p2 = digamma(arg2)
temp= (p1-p2)/aa
else
p1 = dlog(ak)arg2 = ak-1.d0-2.d0*rnl
p2 = digamma(arg2)
sum = 0.0d0
do i=1,nl
ri = float(i)sum = sum+1.d0/(ak-rnl-ri)
enddo
p3 = sum
temp = (p1-p2+p3)/aa
endif
elseif (knu.gt.knl) then210
p1=(-1.d0)**(rj+1)/aa
p2= dsqrt((ak-2.d0*rnl-1.d0)*(ak-2.d0*(rnl+rj)-1.d0))
prod=1.d0
do m=1,jj
rm=float(m)prod= prod*(rnl+rm)/(ak-rnl-rm)
enddo
p3=rj*(ak-2.d0*rnl-rj-1.d0)
temp = p1*p2*dsqrt(prod)/p3
elseif (knu.lt.knl) thenprint *,error
temp = 0.0
endif
rcoupling = temp
RETURNEND
c *******************************************************************
c *******************************************************************
subroutine fermi(en,ei,wni,outu,outl)
implicit double precision (a-h,o-z)

eniave=(en+ei)*0.5d0
del=en-ei
outu=eniave+0.5d0*dsqrt(4.d0*wni*wni+del*del)outl=eniave-0.5d0*dsqrt(4.d0*wni*wni+del*del)c print *,en,ei,eniave,del,wni
returnend
c ******************************************************************
c ******************************************************************
subroutine fermi2(ftmp,f,scale)
implicit double precision (a-h,o-z)
dimension ftmp(12),f(12),ach2d(4,4),achd2(4,4),. eigchd2(4),eigch2d(4),evch2d(4,4),evchd2(4,4),. ach3(4,4),eigch3(4),evch3(4,4),. acd3(4,4),eigcd3(4),evcd3(4,4)
c this subroutine calculates the effect of all coupling withc 2 quanta states for all isotopomers
c print *,’before coupling’c print *,ftmp
c print *,’after coupling’c first CH3

ach3(1,1)=ftmp(2)ach3(1,2)=185.593*0.5d0*scale/2.d0
ach3(1,3)=-185.556*0.5d0*scale/2.d0
ach3(1,4)=0.d0
ach3(2,2)=2795.
ach3(2,3)=0.d0
ach3(2,4)=191.746*0.5d0*scale/2.d0
ach3(3,3)=2795.d0
ach3(3,4)=191.746*0.5d0*scale/2.d0
ach3(4,4)=ftmp(1)c make it symmetrical
do i=1,4
do j=i,4ach3(j,i)=ach3(i,j)
enddo
enddo
nmch3=4
call hmatdiag(nmch3,ach3,nmch3,evch3,eigch3)c now pull out the stretches and put them in the f matrix
f(1)=eigch3(3)f(2)=eigch3(4)f(3)=f(2)c end alternate way to get ch3 couplingc then ch2d, start with symmetric stretches
ach2d(1,1)=ftmp(4)ach2d(1,2)=-104.598*0.5d0*scale/2.d0
ach2d(1,3)=10.315*0.5d0*scale/2.d0

211
ach2d(1,4)=0.0
ach2d(2,2)=2338.
ach2d(2,3)=0.
ach2d(2,4)=159.268*0.5d0*scale/2.d0
ach2d(3,3)=2774.
ach2d(3,4)=262.485*0.5d0*scale/2.d0
ach2d(4,4)=ftmp(5)c make it symmetrical
do i=1,4
do j=i,4ach2d(j,i)=ach2d(i,j)
enddo
enddo
nmch2d=4
call hmatdiag(nmch2d,ach2d,nmch2d,evch2d,eigch2d)c now pull out the stretches and put them in the f matrix
f(4)=eigch2d(1)f(5)=eigch2d(4)c ch2d asymmetric stretch
en=ftmp(6)ei=2556
wni=-264.846*(1.d0/dsqrt(8.d0))*scaleeniave=(en+ei)*0.5d0
del=en-ei
outu=eniave+0.5d0*dsqrt(4.d0*wni*wni+del*del)outl=eniave-0.5d0*dsqrt(4.d0*wni*wni+del*del)f(6)=outu

c next: chd2 the symmetric stretches
achd2(1,1)=ftmp(7)achd2(1,2)=163.879*0.5d0*scale/2.d0
achd2(1,3)=10.267*0.5d0*scale/2.d0
achd2(1,4)=0.0
achd2(2,2)=2054
achd2(2,3)=0
achd2(2,4)=-47.064*0.5d0*scale/2.d0
achd2(3,3)=2554
achd2(3,4)=383.853*0.5d0*scale/2.d0
achd2(4,4)=ftmp(9)c make it symmetrical
do i=1,4
do j=i,4
achd2(j,i)=achd2(i,j)
enddo
enddo
nmchd2=4
call hmatdiag(nmchd2,achd2,nmchd2,evchd2,eigchd2)
c now pull out the stretches and put them in the f matrix
f(7)=eigchd2(2)f(9)=eigchd2(4)c chd2 asymmetric stretchc just print out the uncoupled values so we can couple it later
f(8)=ftmp(8)
c
c
c
c
c
c
c
c

en=ftmp(8)ei=2304
wni=72.942*scaleeniave=(en+ei)*0.5d0
del=en-ei
outu=eniave+0.5d0*dsqrt(4.d0*wni*wni+del*del)outl=eniave-0.5d0*dsqrt(4.d0*wni*wni+del*del)f(8)=outu

c finally, cd3
c the 2v4 state perturbes both the stretches, separtely
c first the symmetric stretch
c
c
c
c
c
c
c
c

en=ftmp(10)ei=2056
wni=-127.945*0.5d0*scaleeniave=(en+ei)*0.5d0
del=en-ei
outu=eniave+0.5d0*dsqrt(4.d0*wni*wni+del*del)outl=eniave-0.5d0*dsqrt(4.d0*wni*wni+del*del)f(10)=outu

212
c cd3 asymmetric stretch
c
c
c
c
c
c
c
c
c

en=ftmp(11)ei=2056
wni=131.35*0.5d0*scaleeniave=(en+ei)*0.5d0
del=en-ei
outu=eniave+0.5d0*dsqrt(4.d0*wni*wni+del*del)outl=eniave-0.5d0*dsqrt(4.d0*wni*wni+del*del)f(11)=outu
f(12)=f(11)c alternate frequency method cds
acd3(1,1)=ftmp(11)acd3(1,2)=120.069*0.5d0*scale/2.d0
acd3(1,3)=-120.041*0.5d0*scale/2.d0
acd3(1,4)=0.d0
acd3(2,2)=2056.d0
acd3(2,3)=0.d0
acd3(2,4)=117.625*0.5*scale/2.d0
acd3(3,3)=2056.d0
acd3(3,4)=117.625*0.5*scale/2.d0
acd3(4,4)=ftmp(10)c make it symmetrical
do i=1,4
do j=i,4
acd3(j,i)=acd3(i,j)
enddo
enddo
nmcd3=4
call hmatdiag(nmcd3,acd3,nmcd3,evcd3,eigcd3)
c now pull out the stretches and put them in the f matrix
f(10)=eigcd3(3)f(11)=eigcd3(4)f(12)=f(11)c end alternate method
returnend
c ******************************************************************
c ******************************************************************

Appendix B
LabWindows Code for the New Spectrometer

Included here is the LabWindows code used to run the new spectrometer presented inchapter 3.

/* ****************************************************************************************************************************************************
SCAN.C*NB See Quicknotes for updates and Settings
This is the first working version of the data acquisition program written
in C language that interfaces to NI 6110 and 6025 cards in a pentium-based PC
The main subroutines in this program are as follow:
MAIN is the first subroutine accessed.
and set up the user interface panels

It defines global variables (static)

Main_Done is the subroutine for quitting out of the program
Measure is the subroutine that acquires the data (IR absorbance, etalon, ref cell,and IR power) and displays them to the screen
The Wave_Form subroutine captures and displays the time dependent waveform of thesignal. It is used to set gates and maximize signals.
Save_Data subroutine saves the data as a binary file to be passed to the array offortran programs developed to plot and analyze data.
New_Scan resets the counter variables for a new data scan.

This version of the program generates pulses on the 6110 card. The rising edgeof the pulse is used to trigger the pulse valve and the falling edge, which comes
after some delay, is used to start the data acquisition of the signal wave formon the 6110 card which usesthe internal 20 MHz counter to set the rate. 2000 data
points are acquired at 1 MHz covering 2 ms of signal. The waveform is integrated
with a signal and two baseline gates. This integral is averaged for the number of
averages specified.
Multiple other channels are read on the 6025 card and plotted and stored.
#include "ScanUI.h"#include <cvirte.h>#include <userint.h>#include <analysis.h>#include <formatio.h>#include <ansi_c.h>#include <utility.h>#include <easyio.h>#include <Dataacq.h>#include <stdlib.h>#include <NIDAQEX.h>#include <string.h>

*/

214
#include <rs232.h>#include <math.h>#include <time.h>#define MaxScanSize 4100
#define TACres 64#define NTraces 5
struct traces{
double *ACSig; /* AC Coupled Signal (Gated) */double *DCSig; /* DC Voltage from Signal Detector */double *DCRef; /* DC Voltage from Reference Detector */double *TAC1; /* TAC for syncing with AutoScan */double *Fr1500;
double *Fr250;};
char *Newdir(char *currdir,char *append_this ,int *Ierror); // Creates a directory and updates stringchar *strrchr(const char *save_file, int c);/* AutoScan I/O */static int iDIOSegOut = 1;
static int iDIODataOut = 2;
static int iDIOSegIn= 3;
static int iDIODataIn = 4;// Blue// Red// Yellow// Orange

const int iPCI6110 = 1; // PCI-6110
const int iPCI6025 = 2; // PCI-6025E
const int iAutoscan = 1; //RS232 port, COM1 connected to Autoscan
const int iMFC = 3;//RS232 port, COM3, connected to CCR Mass Flow Controler box
static int isPulsing=0; // Status of Pulse Valvestatic int iChangeWFGates=0;// Triggers update of the gates in the waveform
static int iChangeWFGain =0; // Triggers update of the A2D gain for the waveform
static int iSaveWaveform =0; // Triggers the saving of the waveform
double *adScan; // Array for storing the data (now dynamic)// Data is stored in sequential blocks
unsigned long ulDataPoints; // # X Data Points Expected// static double adData[4*MaxScanSize];// Old array for storing data - deprecatedstatic double dOffsetDCSig, dOffsetDCRef, dOffsetVSaw, dOffsetFr250, dOffsetFr1500;

const char sINITfile[10]="b212.ini";char sdate[88]="MM-DD-YYYY";
char sDirDefDate[MAX_PATHNAME_LEN];
char sDirDef[MAX_PATHNAME_LEN];
char DirDef[MAX_PATHNAME_LEN];
static int isigamp=2, ietamp=2, iTACamp=1, iIRamp=1;
static int iADamp=2; /* Gain changed from 20 to 2 on 06/25/06 by FD */static int isigoffset=200, ietoffset=1600, iTACoffset=500, iIRoffset=1000;
static long lB1Start, lB1Length, lB2Start, lB2Length;
static long lSigStart, lSigLength, ulPulseRate;static int panel0, panel1, panel2, panel3, panel4, panel5, panel6;
static int istopflag=0, iControl, iautocount, iexit=0;
static int imenubar, iloopcount;static double LSB0=2.44; /* Least Significant Bit in mV. */static double FreqStepSize=12.5; /* in MHz *//*Variables that can be changed to alter the waveform acquisition and length of scanconst unsigned int uMaxPoints=4096; /*max. number of data points acquired in full scan */const static int ArraySize=4100; /* dimension must be greater than uMaxPoints */static short uladata[16400]; /* dimension must be greater than 4*uMaxPoints */static double dlpdata[10000];
static double dlpdatan[10000];*/const int iPoints_Per_Screen=1024; /* 683 => 6-screen scan, 1024 => 4-screen,1365 => 3-screen */const double dSampleRate=1000000.0; /*frequency at which sample waveform points are taken*/const unsigned long ulCount=2000; /*number of points in sample waveform */static double pdVoltBuffer[2001]; /* dimension must be greater than ulCount */static short piBuffer[2001]; /* dimension must be greater than ulCount */static long icounter=0, ibreakflag=0;
static int iOldPlot, iOldV1, iOldV2, iOldV3;
static long uPulseAve;
static short sboard2, sboard1; /* 1: PCI-6110 2: PCI-6025E */static short LamReadStep=10;
static double dLam[4][20], dTemp[5], dLamMeas[4][410];
static char save_file[MAX_PATHNAME_LEN], asave_file[MAX_PATHNAME_LEN], asave[MAX_PATHNAME_LEN];
static char Default_Directory[12]="C:Scan_Data";
int SendAutoscan(char command[50],char reading[50], int iType);
int ReadAutoscan(char reading[50]);

215
char ScanFileName[20];int iStepSize, ulNumSeg;
char allocbuf[85];/* MAIN */int main (int argc, char *argv[]){
int i;
int iStatus, iRetVal, iexclaim, iIgnoreWarning;char sError[6];char message[MAX_PATHNAME_LEN];
double dPulseDelay, dVmin, dVmax, dRefOffset, dSigOffset;
float fPulseDelay, fVmin, fVmax, fRefOffset, fSigOffset;
int iScanStep;
int iPulseRate, iPulseAve;
int iB1start, iB2start, iSstart;
int iB1length, iB2length, iSlength;
int iWFgain;
int iASgain;
int iTrashAS, iTrashMFC;

const char sINITfile[10]="b212.ini";
FILE *fINITfile;
if (InitCVIRTE (0, argv, 0) == 0)
return -1; /* out of memory */if ((panel0 = LoadPanel (0, "ScanUI.uir", PANEL_0)) < 0)return -1;
if ((panel1 = LoadPanel (0, "ScanUI.uir", PANEL_1)) < 0)return -1;
if ((panel2 = LoadPanel (0, "ScanUI.uir", PANEL_2)) < 0)return -1;/* Initialize DAQ and set default values; read calibration data */if (Init_DA_Brds (2, &sboard2)){
iexclaim = MessagePopup ("Fatal Error","Fatal Error: DAQ Boards not operating");
return -1;}
if (Init_DA_Brds (1, &sboard1)){
iexclaim = MessagePopup ("Fatal Error","Fatal Error: DAQ Boards not operating");
return -1;}/* Initialize the RS232 communication with Autoscan and the Mass Flow Controllers// Must open the rs323 port connection and configure it to match params.as*/

iTrashAS = OpenComConfig (iAutoscan, "COM1", 9600, 0, 8, 1, 512, 512);
if (iTrashAS < 0){
MessagePopup ("Fatal Error","Fatal Error: Autoscan RS232 not working");};
iTrashMFC = OpenComConfig (iMFC, "COM3", 9600, 0, 8, 1, 512, 512);
if (iTrashMFC < 0){
MessagePopup ("Fatal Error","Fatal Error: MFC RS232 not working");};/* Setup Digital I/O lines for communication with AutoScan */DIG_Line_Config (iPCI6025, 0, iDIOSegOut, 0);
DIG_Line_Config (iPCI6025, 0, iDIODataOut, 0);
DIG_Line_Config (iPCI6025, 0, iDIOSegIn,
1);
DIG_Line_Config (iPCI6025, 0, iDIODataIn, 1);/* Set initial values to LOW */DIG_Out_Line (iPCI6025, 0, iDIOSegIn, 0);
DIG_Out_Line (iPCI6025, 0, iDIODataIn, 0);

SetPanelAttribute (panel0, ATTR_VISIBLE, 1);/* the startup panel */SetPanelAttribute (panel1, ATTR_VISIBLE, 0);/* the difference freq signal panel - data */SetPanelAttribute (panel2, ATTR_VISIBLE, 0);/* the panel to display the waveform in real time// SetPanelAttribute (panel3, ATTR_VISIBLE, 0);/* the panel with end of scan options */

*/

216
/* Load the Initialization File with the saved values */if ( (fINITfile = fopen(sINITfile,"r+")) == NULL){
iexclaim = MessagePopup ("File Error","Intialization file b212.ini missing \n Execution Aborted");return -1;}
else{
fscanf(fINITfile,"%d\n",&iScanStep);
fscanf(fINITfile,"%d\n",&iPulseRate);
fscanf(fINITfile,"%f\n",&fPulseDelay);
fscanf(fINITfile,"%d\n",&iPulseAve);fscanf(fINITfile,"%d\n",&iB1start);
fscanf(fINITfile,"%d\n",&iB1length);fscanf(fINITfile,"%d\n",&iSstart);
fscanf(fINITfile,"%d\n",&iSlength);fscanf(fINITfile,"%d\n",&iB2start);
fscanf(fINITfile,"%d\n",&iB2length);fscanf(fINITfile,"%f\n",&fVmin);fscanf(fINITfile,"%f\n",&fVmax);
fscanf(fINITfile,"%f\n",&fSigOffset);
fscanf(fINITfile,"%f\n",&fRefOffset);
fscanf(fINITfile,"%d\n",&iWFgain);fscanf(fINITfile,"%d\n",&iASgain);fgets(sDirDef, 256, fINITfile);
fclose(fINITfile);
i = 0;
while (isprint(sDirDef[i]) != 0){
DirDef[i] = sDirDef[i];i++;}// iStatus = MakeDir(DirDef);if ( (iStatus = 0) || (iStatus = -9) ){ // Successmemcpy(sdate, DateStr(),88);
strcpy(sDirDefDate,Newdir(DirDef,sdate,&iStatus));}else{// Failure
strcat(message,"Directory Issues \n MakeDir error = ");Fmt(sError,"%s<%i[w5p0]",iStatus);
strcat(message, sError);strcat(message,"\n Execution Aborted");iexclaim = MessagePopup ("Directory Error",message);
return -1;}
SetCtrlVal (panel0, PANEL_0_STRING_directory,sDirDefDate);// SetCtrlVal (panel0, PANEL_0_RING_StepSize, iScanStep);
SetCtrlVal (panel0, PANEL_0_NUMERIC_pulse_rate, iPulseRate);
SetCtrlVal (panel0, PANEL_0_NUMERIC_time_delay, (double) fPulseDelay);
SetCtrlVal (panel0, PANEL_0_NUMERIC_Average, iPulseAve);
SetCtrlVal (panel0, PANEL_0_NUMERIC_B1_GATE, iB1start);
SetCtrlVal (panel0, PANEL_0_NUMERIC_B1_LENGTH, iB1length);
SetCtrlVal (panel0, PANEL_0_NUMERIC_S_GATE, iSstart);
SetCtrlVal (panel0, PANEL_0_NUMERIC_S_LENGTH, iSlength);
SetCtrlVal (panel0, PANEL_0_NUMERIC_B2_GATE, iB2start);
SetCtrlVal (panel0, PANEL_0_NUMERIC_B2_LENGTH, iB2length);
SetCtrlVal (panel1, PANEL_1_NUMERIC_Vmin, (double) fVmin);
SetCtrlVal (panel1, PANEL_1_NUMERIC_Vmax, (double) fVmax);
SetCtrlVal (panel1, PANEL_1_NUMERIC_offsetDCSig, (double) fSigOffset);
SetCtrlVal (panel1, PANEL_1_NUMERIC_offsetDCRef, (double) fRefOffset);
SetCtrlVal (panel2, PANEL_2_RINGSLIDE_Gain, iWFgain);
SetCtrlVal (panel0, PANEL_0_RING_ADgain, iWFgain);
SetCtrlVal (panel0, PANEL_0_RING_ASGain, iASgain);}
RunUserInterface ();/* Update the ini file when closing . . .*/if ( (fINITfile = fopen(sINITfile,"r+")) == NULL){
iexclaim = MessagePopup ("File Error","Intialization file b212.ini missing \n Execution Aborted");return -1;}
else{// GetCtrlVal (panel0, PANEL_0_RING_StepSize, &iScanStep);
GetCtrlVal (panel0, PANEL_0_NUMERIC_pulse_rate, &iPulseRate);
GetCtrlVal (panel0, PANEL_0_NUMERIC_time_delay, &dPulseDelay);
GetCtrlVal (panel0, PANEL_0_NUMERIC_Average, &iPulseAve);
GetCtrlVal (panel0, PANEL_0_NUMERIC_B1_GATE, &iB1start);
GetCtrlVal (panel0, PANEL_0_NUMERIC_B1_LENGTH, &iB1length);
GetCtrlVal (panel0, PANEL_0_NUMERIC_S_GATE, &iSstart);

217
GetCtrlVal (panel0, PANEL_0_NUMERIC_S_LENGTH, &iSlength);
GetCtrlVal (panel0, PANEL_0_NUMERIC_B2_GATE, &iB2start);
GetCtrlVal (panel0, PANEL_0_NUMERIC_B2_LENGTH, &iB2length);
GetCtrlVal (panel1, PANEL_1_NUMERIC_Vmin, &dVmin);
GetCtrlVal (panel1, PANEL_1_NUMERIC_Vmax, &dVmax);
GetCtrlVal (panel1, PANEL_1_NUMERIC_offsetDCSig, &dSigOffset);
GetCtrlVal (panel1, PANEL_1_NUMERIC_offsetDCRef, &dRefOffset);
GetCtrlVal (panel0, PANEL_0_RING_ADgain, &iWFgain);
GetCtrlVal (panel0, PANEL_0_RING_ASGain, &iASgain);

fprintf(fINITfile,"%d\n",iScanStep);
fprintf(fINITfile,"%d\n",iPulseRate);
fprintf(fINITfile,"%10.3f\n",dPulseDelay);fprintf(fINITfile,"%d\n",iPulseAve);fprintf(fINITfile,"%d\n",iB1start);
fprintf(fINITfile,"%d\n",iB1length);fprintf(fINITfile,"%d\n",iSstart);
fprintf(fINITfile,"%d\n",iSlength);fprintf(fINITfile,"%d\n",iB2start);
fprintf(fINITfile,"%d\n",iB2length);fprintf(fINITfile,"%10.3f\n",dVmin);fprintf(fINITfile,"%10.3f\n",dVmax);
fprintf(fINITfile,"%10.3f\n",dSigOffset);
fprintf(fINITfile,"%10.3f\n",dRefOffset);
fprintf(fINITfile,"%d\n",iWFgain);
fprintf(fINITfile,"%d\n",iASgain);fputs(DirDef,fINITfile);
fclose(fINITfile);}
if (adScan) free(adScan);DiscardPanel (panel0);
DiscardPanel (panel1);
DiscardPanel (panel2);
return 0;}/******************************************************* */int CVICALLBACK Main_Done (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
int query=0;
int iStatus;
unsigned int ulGpctr0 = ND_COUNTER_0;
char command[10],reading[10];switch (event){case EVENT_COMMIT:
query = ConfirmPopup ("Quit", "if (query){
iStatus=AO_VWrite (1, 0, 0);
iStatus=AO_VWrite (2, 0, 0);

Are you sure?");ibreakflag = 1;
istopflag = 1;/* Reset GPCTR. */iStatus = GPCTR_Control(iPCI6110, ulGpctr0, ND_RESET);/* Close COM1 RS232 communication */strcpy(command,"END");
SendAutoscan(command, reading, 4);// CloseCom(iAutoscan);
QuitUserInterface (0);}}return 0;}/* **************************************************************** */// This subroutine will use the RS232 to communicate with the// Autoscan computer/* ***************************************************************** */int CVICALLBACK ChangeWavelength (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){

218
int iTrash;double dwavelength;char send_data[50],wavelength_data[20],send_data2[50];char *read_data = allocbuf;
char *read_data2=allocbuf;// char read_error[100];

switch (event){case EVENT_COMMIT:

iTrash = GetCtrlVal (panel0, PANEL_0_NUMERIC_Wavelength, &dwavelength);if (dwavelength < 1.0){
MessagePopup ("Error", "Must Input Initial Wavelength");return 0;}
SetXMode(iAutoscan,0);
SetCTSMode (iAutoscan, 0);
SetComTime (iAutoscan, 5.0);//this moves the laser to specified wavelength
strcpy(send_data,"GOK ");Fmt(wavelength_data, "%s<%f[p4]",dwavelength);strcat(send_data,wavelength_data);
SendAutoscan(send_data,read_data,0);// now to read the wavelength
strcpy(send_data2,"READK");
SendAutoscan(send_data2,read_data2,1);// SetCtrlVal(PANEL_0,PANEL_0_CONSTANT_kvalue,read_data2);

break;}
return 0;}/* ************************************************************** *//* The ReadAutoscan subroutine reads the output of RS232 */int ReadAutoscan(char reading[50]){int bytes_read;
bytes_read = ComRd(iAutoscan,reading,50);
return 0;}/*************************************************************** *//* The SendAutoscan Subroutine actually sends the Macro/* commands to the Autoscan computer. I set it up this way because/* it gets around the fact that the subroutine must end in order for/* the command to get sent across the RS232 cable/* **************************************************************** */int SendAutoscan (char command[50],char reading[50], int iType){// int iAutoscan, bytes_sent;// char command[500];
int bytes_sent,bytes_read;char *string;char *pch;// double Num;char *ans = allocbuf;
char *strNum;

strcat(command,"\r");bytes_sent = ComWrt(iAutoscan,command, StringLength(command));bytes_read = ComRd(iAutoscan,ans,85);

219
SetCtrlVal(PANEL_0,PANEL_0_STRING_output,ans);

switch (iType){// case 0:/* GOK *//* bytes_read = ComRd(iAutoscan,reading,50);// this checks to make sure the laser moved successfullyif (bytes_read!=25){
MessagePopup ("Warning","Wavelength Change Failed.");return -1;}
break;*/

case 1:/* READK */// bytes_read = ComRd(iAutoscan,ans,50);
pch = strtok (ans," ");pch = strtok (NULL," ");strNum = strtok (NULL," ");// Num = atof(strNum);
SetCtrlVal(PANEL_0,PANEL_0_CONSTANT_kvalue,strNum);break;// case 2: /* SCAN filename *//* bytes_read = ComRd(iAutoscan,ans,50);// FlushInQ(iAutoscan);break;
case 3: /* EXECUTE *//* break;case 4: /* END */// FlushInQ(iAutoscan);// break;}return 0;}/* ***************************************************************** *//* this routine reads what type of scan you want to do, accesses*//* scan filename , and makes the step size and number of segments*//* global variables. If you make a new scanfile, just add the info *//* here and on the actual button on the GUI *//* ***************************************************************** */int CVICALLBACK ScanSpecs (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
int iScanType;switch(event){case EVENT_COMMIT:
GetCtrlVal(panel0,PANEL_0_RING_ScanType, &iScanType);

switch(iScanType){case 1:
strcpy(ScanFileName, "SCANA");
iStepSize = 2;
ulNumSeg = 1;
break;
case 2:
strcpy(ScanFileName,"SCANB");
iStepSize = 10;
ulNumSeg = 3;
break;
case 3:
strcpy(ScanFileName,"SCANC");
iStepSize = 10;
ulNumSeg = 1;
break;
case 4:
strcpy(ScanFileName,"SCAND");
iStepSize = 10;
ulNumSeg = 15;
break;}
break;}

220
return 0;}/* *************************************************************** *//* ** This sets up the flow controller *************************** *//* *************************************************************** */int CVICALLBACK MFCStart (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
int iTrash;char mfcsetting[20], setpoint[12], mfcreply[100];
int bytes_sent, bytes_read;switch (event){case EVENT_COMMIT:
switch (control){case PANEL_0_COMMANDBUTTON_omfc1:
GetCtrlVal(panel0,PANEL_0_STRING_ch1,setpoint);
strcpy(mfcsetting, "SP1");
strcat(mfcsetting,setpoint);
break;
case PANEL_0_COMMANDBUTTON_omfc2:
GetCtrlVal(panel0,PANEL_0_STRING_ch2,setpoint);
strcpy(mfcsetting, "SP2");
strcat(mfcsetting,setpoint);
break;
case PANEL_0_COMMANDBUTTON_omfc3:
GetCtrlVal(panel0,PANEL_0_STRING_ch3,setpoint);
strcpy(mfcsetting, "SP3");
strcat(mfcsetting,setpoint);
break;
case PANEL_0_COMMANDBUTTON_omfc4:
GetCtrlVal(panel0,PANEL_0_STRING_ch4,setpoint);
strcpy(mfcsetting, "SP4");
strcat(mfcsetting,setpoint);
break;}

if (StringLength(mfcsetting)!= 9){
MessagePopup("Error","Incorrect number of digits for flow meter");
return -1;};

strcat(mfcsetting,"\r");bytes_sent = ComWrt(iMFC,mfcsetting, StringLength(mfcsetting));
bytes_read = ComRd(iMFC,mfcreply,100);
SetCtrlVal(PANEL_0,PANEL_0_STRING_mfcoutput,mfcreply);

break;}
return 0;}/* ************************************************************ *//* *****This stops the flow of gas to the flow controller****** *//* ************************************************************ */int CVICALLBACK MFCClose (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
int bytes_read, bytes_sent;char mfcsettingc[20], mfcreplyc[100];
switch (event){case EVENT_COMMIT:

221
switch (control){case PANEL_0_COMMANDBUTTON_cmfc1:
strcpy(mfcsettingc, "SP1");
break;
case PANEL_0_COMMANDBUTTON_cmfc2:
strcpy(mfcsettingc, "SP2");
break;
case PANEL_0_COMMANDBUTTON_cmfc3:
strcpy(mfcsettingc, "SP3");
break;
case PANEL_0_COMMANDBUTTON_cmfc4:
strcpy(mfcsettingc, "SP4");
break;}

strcat(mfcsettingc, "0.0000");
strcat(mfcsettingc,"\r");bytes_sent = ComWrt(iMFC,mfcsettingc, StringLength(mfcsettingc));
bytes_read = ComRd(iMFC,mfcreplyc,85);
SetCtrlVal(PANEL_0,PANEL_0_STRING_mfcoutput,mfcreplyc);

break;}
return 0;}/* **************************************************************** *//* ********* This function allows you to send any command ********* *//* ********* to the mass flow controller box that you want ******** *//* **************************************************************** */int CVICALLBACK MFCMessage (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
char fcmessage[50], mfcreplyc[85];int bytes_sent,bytes_read;switch (event){case EVENT_COMMIT:
GetCtrlVal(PANEL_0,PANEL_0_STRING_message,fcmessage);
strcat(fcmessage,"\r");bytes_sent = ComWrt(iMFC, fcmessage,StringLength(fcmessage));bytes_read = ComRd(iMFC,mfcreplyc,85);
SetCtrlVal(PANEL_0,PANEL_0_STRING_mfcoutput,mfcreplyc);

break;}
return 0;
}

/*
/*
/*
/*
/*
/*

**************************************************************** The Measure subroutine sets up a counter, A/D and D/A**** conversions. The signal waveform is acquired and**** integrated with signal and baseline gates. Supporting **** other data such as etalons are also acquired.
****************************************************************

int CVICALLBACK Measure (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
int iStatus=0, iRetVal, iIgnoreWarning, iEventLoc=-1, ipanelloc;
short sTimeBase=1;
short iDAQstopped=0;
unsigned int ulGpctr0 = ND_COUNTER_0;
unsigned int ulGpctr1 = ND_COUNTER_1;
unsigned int ulLOWcnt1, ulHIGHcnt1;
unsigned int ulLOWcnt2, ulHIGHcnt2;
unsigned int ulRun1, ulRun2;
unsigned short uSampInt=0;
unsigned long ulRetrieved;
double dTimeDelay;
int iADgain;

*/
*/
*/
*/
*/
*/

222
int iASgain;
double dwavelength;
short iSegOut=0, iDataOut=0;
int iLPulse, iLSeg;// LCVint iLBase1, iLBase2, iLSig;// LCV

double dBase1Length, dBase2Length, dSignalLength;
longlBase1Sum=0, lBase2Sum=0, lSigSum=0, lSumInt=0;
double dBase1Sum,
dBase2Sum,
dSigSum,dSumInt,
dIntPlot;double dBase1VSum,dBase2VSum,dSigVSum, dSumVInt, dIntVPlot;
double dcheck, dfraction, dtrash;unsigned long ulPointsPerSeg;
int iCountSeg,iAnswer;

double dVmin, dVmax;
double dLastPlot, dLastVPlot, dLastDCSig, dLastDCRef, dLastFr250, dLastFr1500;
int iMax, iADmax;
int iScanType;double dDCSig, dDCRef,dFr1500, dFr250;
double dVTACstep;
double dASVout;char execute[50], reading[50], FileSend[50];char sCount[7];char message[MAX_PATHNAME_LEN]="";
dVTACstep = 10.0 / TACres;
istopflag=0;
ibreakflag=0;
iADmax = -2048;
switch (event){case EVENT_COMMIT:/* DiscardPanel (panel0);*/if (!isPulsing){MessagePopup ("Smooth Move Exlax", "Pulse Valve Not Running");
return 0;}
GetCtrlVal (panel0, PANEL_0_NUMERIC_Wavelength, &dwavelength);if (dwavelength < 1.0){
MessagePopup ("Error","Must Input Initial Wavelength");return 0;}
SetCtrlVal (panel1, PANEL_1_NUMERIC_Wavelength, dwavelength);
GetCtrlVal (panel0, PANEL_0_RING_ADgain, &iADgain);
GetCtrlVal (panel0, PANEL_0_RING_ASGain, &iASgain);ulDataPoints = ulNumSeg * (1 + 10200 / iStepSize);// ulPointsPerSeg = 10200 / iStepSize;// Missing data points on the overlap. This should get the count right now. (4/23/08 - TAB)
ulPointsPerSeg = 1 + 10200 / iStepSize;

if (adScan) free(adScan);adScan = malloc ((ulDataPoints*(NTraces+1))*sizeof(double));if (!adScan){
MessagePopup ("Memory Allocation Failure", "Insufficient Memory for adScan.\nScan Aborted!");return 0;}
SetCtrlVal (panel1, PANEL_1_NUMERIC_ADmax, iADmax);
SetCtrlVal (panel1, PANEL_1_LED_A2D, 0);
SetCtrlVal (panel1, PANEL_1_NUMERIC_LSB, 2. * 10. / iADgain / uMaxPoints * 1000.);
SetCtrlVal (panel1, PANEL_1_RING_ADgain, iADgain);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Return, ATTR_DIMMED, 1);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Save,
ATTR_DIMMED, 1);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Stop,
ATTR_DIMMED, 0);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_GetXY, ATTR_DIMMED, 1);223
SetPanelAttribute (panel0, ATTR_VISIBLE, 0);
SetPanelAttribute (panel1, ATTR_VISIBLE, 1);
SetPanelAttribute (panel2, ATTR_VISIBLE, 0);
icounter=0;/* Read Values off the Setup Control Panel */GetCtrlVal (panel0, PANEL_0_NUMERIC_Average, &uPulseAve);/*
Read the Baseline1 start and length*/
GetCtrlVal (panel0, PANEL_0_NUMERIC_B1_GATE, &lB1Start);
GetCtrlVal (panel0, PANEL_0_NUMERIC_B1_LENGTH, &lB1Length);dBase1Length = (double) lB1Length;/*
Read the Baseline2 start and length*/
GetCtrlVal (panel0, PANEL_0_NUMERIC_B2_GATE, &lB2Start);
GetCtrlVal (panel0, PANEL_0_NUMERIC_B2_LENGTH, &lB2Length);dBase2Length = (double) lB2Length;/*
Read the Signal start and length*/
GetCtrlVal (panel0, PANEL_0_NUMERIC_S_GATE, &lSigStart);
GetCtrlVal (panel0, PANEL_0_NUMERIC_S_LENGTH, &lSigLength);dSignalLength = (double) lSigLength;
SetCtrlVal (panel1, PANEL_1_NUMERIC_AR_Display, dLam[1][11]);
SetCtrlVal (panel1, PANEL_1_NUMERIC_Dye_Display, dLam[2][11]);
SetCtrlVal (panel1, PANEL_1_NUMERIC_IR_Display, dLam[3][11]);
SetCtrlVal (panel1, PANEL_1_NUMERIC_Sig_Amp, isigamp);
SetCtrlVal (panel1, PANEL_1_NUMERIC_Et_Amp, ietamp);
SetCtrlVal (panel1, PANEL_1_NUMERIC_Sig_Offset, isigoffset);
SetCtrlVal (panel1, PANEL_1_NUMERIC_Et_Offset, ietoffset);/*
Set up the graph on which to show data */SetCtrlAttribute (panel1, PANEL_1_GRAPH_signal, ATTR_DATA_MODE,
VAL_DISCARD);/* The following call is needed to clear the plot before the next begins
GetCtrlVal (panel1, PANEL_1_NUMERIC_Vmin, &dVmin);
GetCtrlVal (panel1, PANEL_1_NUMERIC_Vmax, &dVmax);
GetCtrlVal (panel1, PANEL_1_NUMERIC_offsetDCSig, &dOffsetDCSig);
GetCtrlVal (panel1, PANEL_1_NUMERIC_offsetDCRef, &dOffsetDCRef);*/

DeleteGraphPlot (panel1, PANEL_1_GRAPH_signal, -1, VAL_IMMEDIATE_DRAW);
SetAxisScalingMode (panel1, PANEL_1_GRAPH_signal, VAL_XAXIS,
VAL_MANUAL, 0.0, ulPointsPerSeg);
SetAxisScalingMode (panel1, PANEL_1_GRAPH_signal, VAL_LEFT_YAXIS,
VAL_MANUAL, dVmin, dVmax);
SetCtrlAttribute (panel1, PANEL_1_GRAPH_signal, ATTR_REFRESH_GRAPH, 1);
SetCtrlAttribute (panel1, PANEL_1_GRAPH_signal, ATTR_XGRID_VISIBLE, 0);
SetCtrlAttribute (panel1, PANEL_1_GRAPH_signal, ATTR_YGRID_VISIBLE, 0);
SetCtrlAttribute (panel1, PANEL_1_GRAPH_signal, ATTR_PLOT_BGCOLOR,VAL_WHITE);/*
Set up fast data acquisition for external start and use of internal clock forcycle of other conversions*/
iIgnoreWarning = 0;
iStatus = DAQ_Config (iPCI6110, 1, 0);
iRetVal = NIDAQErrorHandler(iStatus, "DAQ_Config", iIgnoreWarning);/*
Set trigger source for AI initiation - Triggers on falling edge on PFI6 */iStatus = Select_Signal (iPCI6110, ND_IN_START_TRIGGER, ND_PFI_6,ND_HIGH_TO_LOW);
iStatus = DAQ_Rate (dSampleRate, 0, &sTimeBase, &uSampInt);/* To time the speed of the program, call the clock() routine at two times
ulRun1=clock();*/

SetCtrlAttribute (panel1, PANEL_1_LED_SegOut, ATTR_CTRL_VAL, 0);/* Now that everything is set up, we can start scanning. The scanning is started by/* A macro sent over the RS232 cable that tells the laser what file to load in order/* to start scanning. */strcpy(FileSend,"SCAN ");strcat(FileSend,ScanFileName);
SendAutoscan(FileSend, reading, 2);
strcpy(execute,"EXECUTE");
SendAutoscan(execute,reading,3);

224/* This for loop, loops over each segment that autoscan puts together/* Each segment is 10.2 GHz as defined by Autoscan*/*/for (iLSeg = 1; (iLSeg <= ulNumSeg && !istopflag); iLSeg++){
SetCtrlVal(panel1, PANEL_1_NUMERIC_SegNum,iLSeg);/* Display Active Segment Scanning */DeleteGraphPlot (panel1, PANEL_1_GRAPH_signal, -1, VAL_IMMEDIATE_DRAW);
SetAxisScalingMode (panel1, PANEL_1_GRAPH_signal, VAL_XAXIS, VAL_MANUAL,
ulPointsPerSeg*(iLSeg-1), ulPointsPerSeg*iLSeg);/* Need to keep icounter in sync with segments */icounter = (iLSeg-1)*ulPointsPerSeg;
iCountSeg = 0;
DIG_Out_Line(iPCI6025,0,iDIOSegIn,0); // Reset SegIn
SetCtrlAttribute (panel1, PANEL_1_LED_SegOut, ATTR_CTRL_VAL, 0);iSegOut = 0;

while (!iSegOut && ! istopflag){
DIG_In_Line(iPCI6025,0,iDIOSegOut,&iSegOut);
ProcessSystemEvents();}

SetCtrlAttribute (panel1, PANEL_1_LED_SegOut, ATTR_CTRL_VAL, 1);/* AutoScan Ready for a Segment */DIG_Out_Line(iPCI6025,0,iDIOSegIn,1); // Tell AutoScan, we too are ready// May need to delay a call to set iDIOSegIn to 0 to pause between segments

while (iSegOut && !istopflag){iDataOut = 0;
while (!iDataOut){
DIG_In_Line(iPCI6025,0,iDIODataOut,&iDataOut);}/* AutoScan Ready for a data point */// if (ibreakflag==1) /*//break;

gets out of measure loop is "quit program" button is pressed

if (istopflag!=1) /* continue to scan until "stop scan" button is pressed{/* Read system event once every 10 points - it takes time to do this*/dcheck = (double) icounter/10.;
dfraction = modf (dcheck, &dtrash);if ((icounter!=0)&&(dfraction)<0.05){
GetUserEvent (0, &ipanelloc, &iEventLoc);
if (iEventLoc!=-1)
ProcessSystemEvents ();}/* Loop over the number of pulses to signal averagedSumVInt = 0.0;
dSumInt = 0.0;*/*/

for (iLPulse=1; iLPulse <=uPulseAve; iLPulse++){/* Obtain ulCount data points on CH0 of 6110 board *//* The gain is set at 2 for a -5V - +5V range. */iStatus = DAQ_Start (iPCI6110, 0, iADgain, piBuffer, ulCount, sTimeBase, uSampInt);
iStatus = DAQ_Check (iPCI6110, &iDAQstopped, &ulRetrieved);
while ((iDAQstopped != 1) || (iStatus != 0)){/* Loop until acquisition is complete. */iStatus = DAQ_Check(iPCI6110, &iDAQstopped, &ulRetrieved);}/* Convert the Digital Number to its Analog Voltage ch0 or 6110 board*/
iStatus = DAQ_VScale (iPCI6110, 0, iADgain, 1, 0, 2000, piBuffer, pdVoltBuffer);/* Calculate the average of baselines and signal and subtractdBase1VSum= 0;
dBase1Sum = 0;lBase1Sum = 0;

*/

*/

225
if (lB1Length > 0){for (iLBase1=lB1Start; iLBase1<=(lB1Start+lB1Length); iLBase1++){dBase1VSum += pdVoltBuffer[iLBase1];lBase1Sum += piBuffer[iLBase1];}dBase1Sum = (double) lBase1Sum / dBase1Length;
dBase1VSum = dBase1VSum/dBase1Length;}dSigVSum=0;
lSigSum =0;
iMax = -2048;
for (iLSig=lSigStart; iLSig<=(lSigStart+lSigLength); iLSig++){
dSigVSum += pdVoltBuffer[iLSig];lSigSum += piBuffer[iLSig];
if (piBuffer[iLSig] > iMax){
iMax = piBuffer[iLSig];}}
dSigSum = (double) lSigSum / dSignalLength;dSigVSum = dSigVSum/dSignalLength;
dBase2VSum= 0;
dBase2Sum = 0;lBase2Sum = 0;
if (lB2Length > 0){for (iLBase2=lB2Start; iLBase2<=(lB2Start+lB2Length); iLBase2++){dBase2VSum += pdVoltBuffer[iLBase2];lBase2Sum += piBuffer[iLBase2];}dBase2Sum = (double) lBase2Sum / dBase2Length;
dBase2VSum = dBase2VSum/dBase2Length;}
dSumVInt = dSumVInt + dSigVSum - (dBase1VSum+dBase2VSum)/2; // Value in VoltsdSumInt = dSumInt + dSigSum - (dBase1Sum+dBase2Sum)/2; // Value in ADU// MaxMin1D (piBuffer, 2000, &dmax, &imax, &dmin, &imin);
SetCtrlVal (panel1, PANEL_1_NUMERICTHERM_A2D, iMax);if (iMax > iADmax){
iADmax = iMax;
SetCtrlVal (panel1, PANEL_1_NUMERIC_ADmax, iADmax);
if (iMax > 2040) SetCtrlVal (panel1, PANEL_1_LED_A2D, 1);}/* Read inputs on 6025 board (Etalon and IR power) *//* We read each board four times to eliminate cross-talk between channels

*/

//
//
//
//

iStatus = AI_Read (iPCI6025, 0, 1, &sEtalon); /* Etalon - CH 0 */iStatus = AI_Read (2, 0, 1, &sVoltTrash); /* Etalon - CH 0 */iStatus = AI_Read (2, 0, 1, &sVoltTrash); /* Etalon - CH 0 */iStatus = AI_Read (2, 0, 1, &sTempVoltIn1); /* Etalon - CH 0 *///dSumVoltIn1 = dSumVoltIn1 + sTempVoltIn1;

//
//
//
//

iStatus = AI_Read (iPCI6025, 2, 1, &sTempVoltIn3); /* IR Power - CH 2 */iStatus = AI_Read (2, 2, 1, &sVoltTrash); /* IR Power - CH 2 */iStatus = AI_Read (2, 2, 1, &sVoltTrash); /* IR Power - CH 2 */iStatus = AI_Read (2, 2, 1, &sTempVoltIn3); /* IR Power - CH 2 *///dSumVoltIn3 = dSumVoltIn3 + sTempVoltIn3;/* Read the Signal Detector DC Voltage */// iStatus = AI_VRead (iPCI6110, 0, 1, &dDCSig);}// Close Loop for Pulse Averaging/* Pulse Average and Invert */dIntVPlot=dSumVInt/uPulseAve; // Value in VoltsdIntPlot=dSumInt/uPulseAve;// Value in ADU/* Output the Value of the datapoint to the Analog Out - to AutoScan *//* For debugging purposes . . .
if (dVolt == 1.0){
dVolt = 2.0;}
else{
dVolt = 1.0;}

226
iStatus = AO_VWrite (2, 0, dVolt);*/// Currently scaled and offset. Need to think about what this really is . . .
// Autoscan is 0-10V with 12bit resolution// dASVout = 2.5 + iASgain * dIntVPlot;// if (dASVout > 10.0 ) dASVout = 10.0;// if (dASVout < 0.0 ) dASVout = 0.0;// iStatus = AO_VWrite (iPCI6025, 0, dASVout);/* Output Voltage Saw */// dVSaw = (double) (icounter % TACres) * dVTACstep;// iStatus = AO_VWrite (iPCI6025, 1, dVSaw);/*
Read inputs on 6025 board - using 6110 Board b/c 6025 is broken*//* We read each board four times to eliminate cross-talk between channels/* The gain is set at 1 for a range of -10V - +10V */*//* Read the Ti:Sapph Fringes from the 250 MHz Marker Cavity */iStatus = AI_VRead (iPCI6025, 2, -1, &dFr250);/* Read the Signal Detector DC Voltage */iStatus = AI_VRead (iPCI6025, 0, 1, &dDCSig);// dDCSig = 0;/* Read the Reference Cell Detector DC Voltage */iStatus = AI_VRead (iPCI6025, 1, 10, &dDCRef);/* Read the Ti:Sapph Fringes from the 1500 MHz Marker Cavity */iStatus = AI_VRead (iPCI6025, 3, -1, &dFr1500);/* Plot all points except the first point */if (icounter!=0){
SetCtrlVal (panel1, PANEL_1_NUMBER_OF_POINTS, icounter);ulRun2=clock();
SetCtrlVal (panel1, PANEL_1_SCAN_TIME, (double)(ulRun2-ulRun1)/CLOCKS_PER_SEC);/* Plot the Signal */// Changed to voltage instead of ADU - TAB
PlotLine (panel1, PANEL_1_GRAPH_signal, icounter-1, dLastVPlot,
icounter,dIntVPlot, VAL_BLACK);dLastVPlot = dIntVPlot;
PlotLine (panel1, PANEL_1_GRAPH_signal, icounter-1, dLastDCSig+dOffsetDCSig,
icounter,dDCSig+dOffsetDCSig, VAL_GREEN);
dLastDCSig = dDCSig;
PlotLine (panel1, PANEL_1_GRAPH_signal, icounter-1, dLastDCRef+dOffsetDCRef,
icounter,dDCRef+dOffsetDCRef, VAL_RED);dLastDCRef = dDCRef;
PlotLine (panel1, PANEL_1_GRAPH_signal, icounter-1, dLastFr250+dOffsetFr250,
icounter,dFr250+dOffsetFr250, VAL_BLUE);
dLastFr250 = dFr250;
PlotLine (panel1, PANEL_1_GRAPH_signal, icounter-1, dLastFr1500+dOffsetFr1500,
icounter,dFr1500+dOffsetFr1500, VAL_MAGENTA);
dLastFr1500 = dFr1500;}

dLastVPlot = dIntVPlot;dLastDCSig = dDCSig;
dLastDCRef = dDCRef;
dLastFr250 = dFr250;
dLastFr1500 = dFr1500;/* Tell AutoScan it can read the data point */DIG_Out_Line(iPCI6025,0,iDIODataIn,1);
Delay(0.001);
DIG_Out_Line(iPCI6025,0,iDIODataIn,0);/* Save data in adScan */adScan[icounter+ulDataPoints]= dIntVPlot;adScan[icounter+2*ulDataPoints] = dFr250;
adScan[icounter+3*ulDataPoints] = dDCRef;
adScan[icounter+4*ulDataPoints] = dDCSig;
adScan[icounter+5*ulDataPoints] = dFr1500;} /*End of istopflag != 1
*/
else
{
/* istopflag = 1 --> Scan was interupted */GetUserEvent (0, &ipanelloc, &iEventLoc);
if (iEventLoc!=-1)
ProcessSystemEvents ();227
ulRun2=clock();
SetCtrlVal (panel1, PANEL_1_SCAN_TIME, (double)(ulRun2-ulRun1)/CLOCKS_PER_SEC);/* Reset DIGital outs */DIG_Out_Line(iPCI6025,0,iDIOSegIn,0);
DIG_Out_Line(iPCI6025,0,iDIODataIn,0);
SetCtrlVal (panel1, PANEL_1_LED_A2D, 0);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Return, ATTR_DIMMED, 0);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Save,
ATTR_DIMMED, 0);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Stop,
ATTR_DIMMED, 1);
return 0;}
DIG_In_Line(iPCI6025,0,iDIOSegOut,&iSegOut);icounter = icounter + 1;
iCountSeg++;}/* End of While (iSegOut == 1) loop */if (iCountSeg != ulPointsPerSeg){
strcpy(message,"");
strcat(message,"Missed or Extra Datapoints\n Found :");
Fmt(sCount,"%s<%i[w5p0]",iCountSeg);
strcat(message, sCount);
strcat(message,"
Expected : ");Fmt(sCount,"%s<%i[w5p0]",ulPointsPerSeg);
strcat(message,sCount);
strcat(message,"\n Do you wish to continue scan?");iAnswer = ConfirmPopup ("Segment Datapoint Error", message);if (iAnswer == 0) // Stop Scan{
break; // Break out of For over segments Loop}}
ProcessSystemEvents ();} /* Close For over segments Loop*/if (istopflag) // Need to reset user interface in case of crash{ /* Reset DIGital outs */DIG_Out_Line(iPCI6025,0,iDIOSegIn,0);
DIG_Out_Line(iPCI6025,0,iDIODataIn,0);
SetCtrlVal (panel1, PANEL_1_LED_A2D, 0);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Return, ATTR_DIMMED, 0);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Save,
ATTR_DIMMED, 0);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Stop,
ATTR_DIMMED, 1);}

SetCtrlAttribute (panel1, PANEL_1_LED_SegOut, ATTR_CTRL_VAL, 0);/* Replot Full Scanned Data */DeleteGraphPlot (panel1, PANEL_1_GRAPH_signal, -1, VAL_IMMEDIATE_DRAW);
SetAxisScalingMode (panel1, PANEL_1_GRAPH_signal, VAL_XAXIS, VAL_MANUAL,
0.0, icounter);
PlotWaveform (panel1, PANEL_1_GRAPH_signal, adScan, icounter, VAL_DOUBLE,
1., 0., 0., 1.0, VAL_THIN_LINE, VAL_NO_POINT, VAL_SOLID, 1, VAL_BLACK);
PlotWaveform (panel1, PANEL_1_GRAPH_signal, adScan+ulDataPoints, icounter, VAL_DOUBLE,
1.0, dOffsetDCSig, 0, 1, VAL_THIN_LINE, VAL_NO_POINT, VAL_SOLID, 1, VAL_GREEN);
PlotWaveform (panel1, PANEL_1_GRAPH_signal, adScan+2*ulDataPoints, icounter, VAL_DOUBLE,
1.0, dOffsetDCRef, 0, 1, VAL_THIN_LINE, VAL_NO_POINT, VAL_SOLID, 1, VAL_RED);
PlotWaveform (panel1, PANEL_1_GRAPH_signal, adScan+3*ulDataPoints, icounter, VAL_DOUBLE,
1.0, dOffsetVSaw, 0, 1, VAL_THIN_LINE, VAL_NO_POINT, VAL_SOLID, 1, VAL_BLUE);
ulRun2=clock();
SetCtrlVal (panel1, PANEL_1_SCAN_TIME, (double)(ulRun2-ulRun1)/CLOCKS_PER_SEC);
DIG_Out_Line(iPCI6025,0,iDIOSegIn,0);
DIG_Out_Line(iPCI6025,0,iDIODataIn,0);
SetCtrlVal (panel1, PANEL_1_LED_A2D, 0);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Return, ATTR_DIMMED, 0);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Save,
ATTR_DIMMED, 0);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Stop,
ATTR_DIMMED, 1);
SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_GetXY, ATTR_DIMMED, 0);
break;}
return 0;
}

228
/*
********************************************************************** *//* ** This subroutine displays the signal waveform and shows where** *//*** three integration gates are located. ** *//*********************************************************************** */int CVICALLBACK Wave_Form (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
int iStatus=0, iRetVal, iIgnoreWarning=0, iYieldON;
const int iDevice = 1;/*
This is the PCI-6110*/
short sTimeBase=1, iDAQstopped=0;
unsigned int ulGpctr0 = ND_COUNTER_0;
unsigned int ulGpctr1 = ND_COUNTER_1;
unsigned int ulLOWcnt1, ulHIGHcnt1;
unsigned int ulLOWcnt2, ulHIGHcnt2;
unsigned int ulRun1, ulRun2, ulPulseRate;unsigned short uSampInt=0;
unsigned long ulRetrieved;
const unsigned long ulCount=2000; /* This is the number of data points in waveform
double dVoltage, dVoltout, dcounter, dTimeDelay;
const double dSampleRate=1000000.0; /* This is the sample rate in Hz */int iBase1, iBase2, iSig;
long lBase1Sum=0, lBase2Sum=0, lSigSum=0;
double dBase1Sum, dBase2Sum, dSigSum, dSig;
double dVolt = 1.0;
double dtmin, dtmax, dYmin, dYmax;
int iADgain;// double dTimeDelay;
time_t now;
struct tm *tp;long StoreDate;
int ic;long fheader[11];istopflag=0;
ibreakflag=0;
iexit = 0;
switch (event){case EVENT_COMMIT:
if (!isPulsing){MessagePopup ("Smooth Move Exlax", "Pulse Valve Not Running");
return 0;}/* Read the Delay between pulse valve trigger and trigger to DAQ
GetCtrlVal (panel0, PANEL_0_NUMERIC_time_delay, &dTimeDelay);*/

SetPanelAttribute (panel2, ATTR_VISIBLE, 1);/* Read the Baseline1 start and length AND transfer to waveform panel */GetCtrlVal (panel0, PANEL_0_NUMERIC_B1_GATE, &lB1Start);
GetCtrlVal (panel0, PANEL_0_NUMERIC_B1_LENGTH, &lB1Length);
SetCtrlVal (panel2, PANEL_2_NUMERIC_B1_GATE, lB1Start);
SetCtrlVal (panel2, PANEL_2_NUMERIC_B1_LENGTH, lB1Length);/* Read the Baseline2 start and length AND transfer to waveform panel */GetCtrlVal (panel0, PANEL_0_NUMERIC_B2_GATE, &lB2Start);
GetCtrlVal (panel0, PANEL_0_NUMERIC_B2_LENGTH, &lB2Length);
SetCtrlVal (panel2, PANEL_2_NUMERIC_B2_GATE, lB2Start);
SetCtrlVal (panel2, PANEL_2_NUMERIC_B2_LENGTH, lB2Length);/* Read the Signal start and length AND transfer to waveform panel */GetCtrlVal (panel0, PANEL_0_NUMERIC_S_GATE, &lSigStart);
GetCtrlVal (panel0, PANEL_0_NUMERIC_S_LENGTH, &lSigLength);
SetCtrlVal (panel2, PANEL_2_NUMERIC_S_GATE, lSigStart);
SetCtrlVal (panel2, PANEL_2_NUMERIC_S_LENGTH, lSigLength);/* Read the Gain AND transfer to waveform panel */GetCtrlVal (panel0, PANEL_0_RING_ADgain, &iADgain);
SetCtrlVal (panel2, PANEL_2_RINGSLIDE_Gain, iADgain);dYmax = 10. / (double) iADgain;
dYmin = -10. / (double) iADgain;/* Set up fast data acquisition for external startand use of internal clock for cycle of other conversions*/
iStatus = DAQ_Config (iDevice, 1, 0);
iRetVal = NIDAQErrorHandler(iStatus, "DAQ_Config", iIgnoreWarning);/* Set trigger source for AI initiation - Triggers on falling edge on PFI6 */iStatus = Select_Signal (iDevice, ND_IN_START_TRIGGER, ND_PFI_6, ND_HIGH_TO_LOW);

*/

229
iStatus = DAQ_Rate (dSampleRate, 0, &sTimeBase, &uSampInt);/* Setup Plots */SetAxisScalingMode (panel2, PANEL_2_GRAPH_WF, VAL_LEFT_YAXIS, VAL_MANUAL,-10./ (double) iADgain, 10./ (double)iADgain);
SetCtrlAttribute (panel2, PANEL_2_GRAPH_WF, ATTR_PLOT_BGCOLOR, VAL_WHITE);/* Loops until the button at bottom of screen is clicked
while (ibreakflag!=1){
ProcessSystemEvents ();*/if (iChangeWFGates){/* Read the Baseline1 start and length AND transfer to original panel */GetCtrlVal (panel2, PANEL_2_NUMERIC_B1_GATE, &lB1Start);
GetCtrlVal (panel2, PANEL_2_NUMERIC_B1_LENGTH, &lB1Length);
SetCtrlVal (panel0, PANEL_0_NUMERIC_B1_GATE, lB1Start);
SetCtrlVal (panel0, PANEL_0_NUMERIC_B1_LENGTH, lB1Length);/* Read the Baseline2 start and length AND transfer to original panel */GetCtrlVal (panel2, PANEL_2_NUMERIC_B2_GATE, &lB2Start);
GetCtrlVal (panel2, PANEL_2_NUMERIC_B2_LENGTH, &lB2Length);
SetCtrlVal (panel0, PANEL_0_NUMERIC_B2_GATE, lB2Start);
SetCtrlVal (panel0, PANEL_0_NUMERIC_B2_LENGTH, lB2Length);/* Read the Signal start and length
AND transfer to original panel */GetCtrlVal (panel2, PANEL_2_NUMERIC_S_GATE, &lSigStart);
GetCtrlVal (panel2, PANEL_2_NUMERIC_S_LENGTH, &lSigLength);
SetCtrlVal (panel0, PANEL_0_NUMERIC_S_GATE, lSigStart);
SetCtrlVal (panel0, PANEL_0_NUMERIC_S_LENGTH, lSigLength);/* Read the times to display */GetCtrlVal (panel2, PANEL_2_NUMERIC_tmin,&dtmin);
GetCtrlVal (panel2, PANEL_2_NUMERIC_tmax,&dtmax);
SetAxisScalingMode (panel2, PANEL_2_GRAPH_WF, VAL_BOTTOM_XAXIS, VAL_MANUAL,
dtmin, dtmax);iChangeWFGates = 0;}
if (iChangeWFGain){
GetCtrlVal (panel2, PANEL_2_RINGSLIDE_Gain, &iADgain);dYmax = 10. / (double) iADgain;
dYmin = -10. / (double) iADgain;
SetAxisScalingMode (panel2, PANEL_2_GRAPH_WF, VAL_LEFT_YAXIS, VAL_MANUAL,
dYmin, dYmax);
SetCtrlAttribute (panel2, PANEL_2_GRAPH_WF, ATTR_PLOT_BGCOLOR, VAL_WHITE);
SetCtrlVal(panel0, PANEL_0_RING_ADgain,iADgain);iChangeWFGain = 0;}/* Obtain ulCount data points on CH0 of fast card */iStatus = DAQ_Start (iDevice, 0, iADgain, piBuffer, ulCount, sTimeBase, uSampInt);
iStatus = DAQ_Check(iDevice, &iDAQstopped, &ulRetrieved);
while ( (iDAQstopped != 1) || (iStatus != 0)){/* Loop until all acquisition is complete. HINT: You can bedoing other foreground tasks during this time. */iStatus = DAQ_Check(1, &iDAQstopped, &ulRetrieved);}
iStatus = DAQ_VScale (iDevice, 0, iADgain, 1, 0, 2000, piBuffer, pdVoltBuffer);
DeleteGraphPlot (panel2, PANEL_2_GRAPH_WF, -1,VAL_IMMEDIATE_DRAW);
PlotY (panel2, PANEL_2_GRAPH_WF, pdVoltBuffer, ulCount,
VAL_DOUBLE, VAL_THIN_LINE, VAL_NO_POINT, VAL_SOLID,1, VAL_BLUE);/* Plot a line for the first baseline gate */PlotLine (panel2, PANEL_2_GRAPH_WF, lB1Start, 0,
lB1Start+lB1Length,0, VAL_BLACK);
PlotLine (panel2, PANEL_2_GRAPH_WF, lB1Start+lB1Length, dYmin,lB1Start+lB1Length,dYmax, VAL_BLACK);
PlotLine (panel2, PANEL_2_GRAPH_WF, lB1Start, dYmin,lB1Start,dYmax, VAL_BLACK);
PlotText (panel2, PANEL_2_GRAPH_WF, lB1Start+lB1Length/2-60, dYmin, "Base1",
VAL_APP_META_FONT, VAL_BLACK, VAL_WHITE);

230/* Plot a line for the second baseline gate */PlotLine (panel2, PANEL_2_GRAPH_WF, lB2Start, 0,
lB2Start+lB2Length,0, VAL_GREEN);
PlotLine (panel2, PANEL_2_GRAPH_WF, lB2Start+lB2Length, dYmin,lB2Start+lB2Length,dYmax, VAL_GREEN);
PlotLine (panel2, PANEL_2_GRAPH_WF, lB2Start, dYmin,lB2Start,dYmax, VAL_GREEN);
PlotText (panel2, PANEL_2_GRAPH_WF, lB2Start+lB2Length/2-60, dYmin, "Base2",
VAL_APP_META_FONT, VAL_GREEN, VAL_WHITE);/* plot a line for the signal gate*/
PlotLine (panel2, PANEL_2_GRAPH_WF, lSigStart, 0,
lSigStart+lSigLength, 0, VAL_DK_RED);
PlotLine (panel2, PANEL_2_GRAPH_WF, lSigStart+lSigLength, dYmin,lSigStart+lSigLength, dYmax, VAL_DK_RED);
PlotLine (panel2, PANEL_2_GRAPH_WF, lSigStart, dYmin,lSigStart, dYmax, VAL_DK_RED);
PlotText (panel2, PANEL_2_GRAPH_WF, lSigStart+lSigLength/2-60, dYmin, "Signal",
VAL_APP_META_FONT, VAL_DK_RED, VAL_WHITE);/*
Calculate the integral of baselines and signal and subtractdBase1Sum=0;
if (lB1Length > 0){for (iBase1=lB1Start; iBase1<=(lB1Start+lB1Length); iBase1++)dBase1Sum += pdVoltBuffer[iBase1];dBase1Sum = dBase1Sum / (double) lB1Length;}*/

dSigSum=0;
for (iSig=lSigStart; iSig<=(lSigStart+lSigLength); iSig++)
dSigSum += pdVoltBuffer[iSig];
dSigSum= dSigSum / (double) lSigLength;
dBase2Sum=0;
if (lB2Length > 0){for (iBase2=lB2Start; iBase2<=(lB2Start+lB2Length); iBase2++)dBase2Sum += pdVoltBuffer[iBase2];dBase2Sum= dBase2Sum / (double) lB2Length;}dSig=dSigSum-(dBase1Sum+dBase2Sum)/2;
SetCtrlVal(panel2, PANEL_2_NUMERIC_Signal,dSig);
if (iSaveWaveform){
now=time(NULL);
tp=localtime(&now);
StoreDate=(tp->tm_year+1900)*10000+(tp->tm_mon+1)*100+tp->tm_mday;for (ic=0; ic <= 10; ic++) {fheader[ic] = 0;};fheader[0]=StoreDate; /* The date of the acquisition */fheader[1]=iADgain+1; /* ADgain setting (+1 to deal with 20V) */fheader[2]=(int) dTimeDelay * 1000; /* Time Delay for Acquisition */fheader[3]=lB1Start;/* start of first baseline gate*/
fheader[4]=lB1Length;/* length of first baseline gate*/
fheader[5]=lSigStart;/* start of signal gate*/
fheader[6]=lSigLength;/* length of signal gate*/
fheader[7]=lB2Start;/* start of second baseline gate*/
fheader[8]=lB2Length; /* length of second baseline gate*/// fheader[9]=ulPulseRate; /* repetition rate for pulsed valve *//* Popup window for saving data */// iStatus = FileSelectPopup ("c:\\Documents and Settings\\richard\\Desktop", "*.wfm", "*.wfm", "Waveform File Save",//
VAL_SAVE_BUTTON, 0, 1, 1, 1, save_file);
iStatus = FileSelectPopup (sDirDefDate, "*.wfm", "*.wfm","Waveform File Save", VAL_SAVE_BUTTON, 0, 1, 1, 1, save_file);
if (iStatus > 0){/* Saves header material as defined above as integers.
*/
iStatus = ArrayToFile (save_file, fheader, VAL_INTEGER, 10, 1, VAL_GROUPS_TOGETHER,VAL_GROUPS_AS_ROWS, VAL_SEP_BY_TAB, 10, VAL_ASCII, VAL_TRUNCATE);/* Saves the data traces/waves*/
iStatus = ArrayToFile (save_file, pdVoltBuffer, VAL_DOUBLE, 2000, 1, VAL_GROUPS_TOGETHER,VAL_GROUPS_AS_COLUMNS, VAL_CONST_WIDTH, 12, VAL_ASCII, VAL_APPEND);} /* if iStatus */231
iSaveWaveform = 0;
} // Close Save Waveform} // ibreakflag != 1
SetPanelAttribute (panel2, ATTR_VISIBLE, 0);
SetPanelAttribute (panel0, ATTR_VISIBLE, 1);
break;}
return 0;}/*******************************************************************/*** This subroutine saves the data in binary format ** *//*** It also saves header material that is used in some of the**/*** array of fortran programs used to plot and analyze data**/*******************************************************************
int CVICALLBACK Save_Data (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2)
{

*/
*/
*/
*/

int iStatus, isave, itrace, iStatus2;
double dfraction, dtrash, dLamAr, dLamDye, dLamIR, dStdIR;
double dwavelength;char dwavelengthr[40];double dReadWavelength;
long fheader[39], now, StoreDate;float fstepsize;
const short spacer[0]={3};char ch, ndate, c;
int ic, addloc;
struct tm *tp;
int iADgain;
char AutoscanFileName[20];char datafile[20], datafileout[20];switch (event){case EVENT_COMMIT:
now=time(NULL);
tp=localtime(&now);
StoreDate=(tp->tm_year+1900)*10000+(tp->tm_mon+1)*100+tp->tm_mday;
GetCtrlVal (panel0, PANEL_0_NUMERIC_Wavelength, &dwavelength);
GetCtrlVal (panel0, PANEL_0_CONSTANT_kvalue, &dwavelengthr[0]);dReadWavelength = atof(dwavelengthr);
GetCtrlVal (panel0, PANEL_0_RING_ADgain, &iADgain);for (ic=0; ic <= 38; ic++) {fheader[ic] = 0;};adScan[0]=(long) floor(dwavelength*10000);
adScan[1]=NTraces; /* Number of types of data stored for plotting (abs, ET, TAC, IR power)
adScan[2]=(long) uPulseAve;
adScan[3]=lB1Start;/* start of first baseline gate*/
adScan[4]=lB1Length;/* length of first baseline gate*/
adScan[5]=lSigStart;/* start of signal gate*/
adScan[6]=lSigLength;/* length of signal gate*/
adScan[7]=lB2Start;/* start of second baseline gate*/
adScan[8]=lB2Length; /* length of second baseline gate*/
adScan[9]=ulPulseRate; /* repetition rate for pulsed valve */adScan[10]=icounter; /* Number of data points taken*/
adScan[11]=dReadWavelength;
adScan[15]=StoreDate; /* The date of data acquisition */adScan[25]=ulNumSeg; /* # of Segments */adScan[26]=10200 / iStepSize; /* # Points per Segment */adScan[27]=ulDataPoints; /* Total Number of Points */adScan[30]=iADgain+1; /* ADgain setting (+1 to deal with 20V */adScan[31]=iStepSize; /* AS Step Size in MHz */adScan[38]=7; /* Version Info */// GetCtrlVal (panel0, PANEL_0_RING_Step_Size, &FreqStepSize);// fheader[36] = (long) FreqStepSize*icounter;/* approximate length of scan in MHz/* Popup window for saving data */iStatus=FileSelectPopup (sDirDefDate, "*.scn", "*.scn", "File Save",
VAL_SAVE_BUTTON, 0, 0, 1, 1,save_file);
if (iStatus > 0){/* In the data saving routine below, we only save the data acquired so file size

*/

*/

232
will be dependent on the number of data points.

*//* Saves header material as defined above as integers.
*/// iStatus = ArrayToFile (save_file, fheader, VAL_INTEGER, 39, 1, VAL_GROUPS_TOGETHER,// VAL_GROUPS_AS_ROWS, VAL_SEP_BY_TAB, 10, VAL_ASCII, VAL_TRUNCATE);/* Saves the data traces/waves*//* itrace = 0: Gated Signal Detector
itrace = 1: DC Signal Detector
itrace = 2: DC Reference Detector
itrace = 3: Unused */iStatus = ArrayToFile (save_file, adScan, VAL_DOUBLE, (NTraces+1)*ulDataPoints, (NTraces+1),
VAL_GROUPS_TOGETHER, VAL_GROUPS_AS_COLUMNS, VAL_CONST_WIDTH, 15, VAL_ASCII, VAL_APPEND);/* Dim Button because Data is Saved */SetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Save,}; /* if iStatus */ATTR_DIMMED, 1);/* Now tell Autoscan to save the x-axis data */// iStatus2 = PromptPopup("Save Autoscan Data","Enter name of file to save Autoscan data (8 digit max)",// AutoscanFileName,8);// strcpy(datafile,"WRITE ");// strcat(datafile,AutoscanFileName);// SendAutoscan(datafile,datafileout ,4);}
return 0;}/* ************************************************************ *//* ********************************************************** */int CVICALLBACK Signal_Up (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
isigoffset=isigoffset+100;
SetCtrlVal (panel1, PANEL_1_NUMERIC_Sig_Offset, isigoffset);
break;}
return 0;}/* ********************************************************** *//* ********************************************************** */int CVICALLBACK Signal_Down (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
isigoffset=isigoffset-100;
SetCtrlVal (panel1, PANEL_1_NUMERIC_Sig_Offset, isigoffset);
break;}
return 0;}/* **********************************************************/* **********************************************************
int CVICALLBACK Etalon_Up (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:*/*/

ietoffset=ietoffset+100;
SetCtrlVal (panel1, PANEL_1_NUMERIC_Et_Offset, ietoffset);
break;}
return 0;}/* ********************************************************** *//* ********************************************************** */int CVICALLBACK Etalon_Down (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:

233
ietoffset=ietoffset-100;
SetCtrlVal (panel1, PANEL_1_NUMERIC_Et_Offset, ietoffset);
break;}
return 0;}/* ********************************************************** *//* ********************************************************** */int CVICALLBACK Signal_Amplify (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
isigamp=isigamp*2;
SetCtrlVal (panel1, PANEL_1_NUMERIC_Sig_Amp, isigamp);
break;}
return 0;}/* ********************************************************** *//* ********************************************************** */int CVICALLBACK Signal_Attenuate (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
isigamp=isigamp/2;
if (isigamp<1)
isigamp=1;
SetCtrlVal (panel1, PANEL_1_NUMERIC_Sig_Amp, isigamp);
break;}
return 0;}/* ********************************************************** *//* ********************************************************** */int CVICALLBACK Etalon_Amplify (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
ietamp=ietamp*2;
SetCtrlVal (panel1, PANEL_1_NUMERIC_Et_Amp, ietamp);
break;}
return 0;}/* ********************************************************** *//* ********************************************************** */int CVICALLBACK Etalon_Attenuate (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:

ietamp=ietamp/2;
if (ietamp<1)
ietamp=1;
SetCtrlVal (panel1, PANEL_1_NUMERIC_Et_Amp, ietamp);
break;}
return 0;}/* **********************************************************/* ** Starts a new scan, resets control variables**/* **********************************************************
int CVICALLBACK New_Scan (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
int iStatus;
switch (event){case EVENT_COMMIT:// icounter=0;// iautocount=15;

*/
*/
*/

234
// iloopcount=15;
iStatus=AO_VWrite (1, 0, 0);
iStatus=AO_VWrite (2, 0, 0);/* If sending out a ramp of 10V --> 0V, replace the previous statement with:/* iStatus = AO_VWrite (1, 0, 10.); */SetPanelAttribute (panel0, ATTR_VISIBLE, 1);
SetPanelAttribute (panel1, ATTR_VISIBLE, 0);
SetPanelAttribute (panel2, ATTR_VISIBLE, 0);
SetPanelAttribute (panel3, ATTR_VISIBLE, 0);
SetPanelAttribute (panel4, ATTR_VISIBLE, 0);
SetPanelAttribute (panel5, ATTR_VISIBLE, 0);
SetPanelAttribute (panel6, ATTR_VISIBLE, 0);ibreakflag = 1;
break;}
return 0;}/* **********************************************************/* ** sets istopflag=1 which is used to quit current scan **/* **********************************************************
int CVICALLBACK Scan_Stop (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:

*/
*/
*/

istopflag=1;
SetCtrlAttribute(panel1, PANEL_1_COMMANDBUTTON_Save, ATTR_DIMMED, 0);
SetCtrlAttribute(panel1, PANEL_1_COMMANDBUTTON_Return, ATTR_DIMMED, 0);
SetCtrlAttribute(panel1, PANEL_1_COMMANDBUTTON_Stop, ATTR_DIMMED, 1);
SetCtrlVal(panel1, PANEL_1_LED_Scanning, 0);
break;}
return 0;}/* ********************************************************** *//* **Returns to current scan** *//* ********************************************************** */int CVICALLBACK Return_Scan (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
istopflag=0;
iexit=1;
SetPanelAttribute (panel0, ATTR_VISIBLE, 0);
SetPanelAttribute (panel2, ATTR_VISIBLE, 0);
SetPanelAttribute (panel1, ATTR_VISIBLE, 1);
break;}
return 0;}
int CVICALLBACK Scan_Jump (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
iexit=1;
SetPanelAttribute (panel3, ATTR_VISIBLE, 0);
SetPanelAttribute (panel2, ATTR_VISIBLE, 0);

break;}
return 0;}
int CVICALLBACK SetLPMax (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
double dMin, dMax;
switch (event){case EVENT_COMMIT:
GetCtrlVal (panel6, PANEL_6_N_LP_MIN, &dMin);
GetCtrlVal (panel6, PANEL_6_N_LP_MAX, &dMax);

*/

235
if (dMax <= dMin){
dMax=dMin+0.1;
SetCtrlVal (panel6, PANEL_6_N_LP_MAX, dMax);}
SetAxisScalingMode (panel6, PANEL_6_GRAPH_LP, VAL_LEFT_YAXIS,
VAL_MANUAL, dMin, dMax);
break;}
return 0;}
int CVICALLBACK SetLPMin (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
double dMin, dMax;
switch (event){case EVENT_COMMIT:
GetCtrlVal (panel6, PANEL_6_N_LP_MIN, &dMin);
GetCtrlVal (panel6, PANEL_6_N_LP_MAX, &dMax);if (dMin >= dMax){
dMin=dMax-0.1;
SetCtrlVal (panel6, PANEL_6_N_LP_MIN, dMin);}
SetAxisScalingMode (panel6, PANEL_6_GRAPH_LP, VAL_LEFT_YAXIS,
VAL_MANUAL, dMin, dMax);
break;}
return 0;}
int CVICALLBACK SetLPPMax (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
double dMin, dMax;
switch (event){case EVENT_COMMIT:
GetCtrlVal (panel6, PANEL_6_N_LPPULSE_MIN, &dMin);
GetCtrlVal (panel6, PANEL_6_N_LPPULSE_MAX, &dMax);if (dMax <= dMin){
dMax=dMin+0.1;
SetCtrlVal (panel6, PANEL_6_N_LPPULSE_MAX, dMax);}
SetAxisScalingMode (panel6, PANEL_6_GRAPH_LPPULSE, VAL_LEFT_YAXIS,
VAL_MANUAL, dMin, dMax);
break;}
return 0;}
int CVICALLBACK SetLPPMin (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
double dMin, dMax;
switch (event){case EVENT_COMMIT:
GetCtrlVal (panel6, PANEL_6_N_LPPULSE_MIN, &dMin);
GetCtrlVal (panel6, PANEL_6_N_LPPULSE_MAX, &dMax);if (dMin >= dMax){
dMin=dMax-0.1;
SetCtrlVal (panel6, PANEL_6_N_LPPULSE_MIN, dMin);}
SetAxisScalingMode (panel6, PANEL_6_GRAPH_LPPULSE, VAL_LEFT_YAXIS,
VAL_MANUAL, dMin, dMax);
break;}
return 0;}

int CVICALLBACK RefreshGraphLP (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
DeleteGraphPlot (panel6, PANEL_6_GRAPH_LP, -1, VAL_IMMEDIATE_DRAW);
break;}
return 0;}
int CVICALLBACK AD_Amplify (int panel, int control, int event,236
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
if (iADamp>=20)/* DEFAULT Gain changed from 20 to 2 on 06/25/06 by FD */iADamp=50;
if (iADamp==10)iADamp=20;
if (iADamp==5)iADamp=10;
if (iADamp==2)
iADamp=5;
if (iADamp==1)
iADamp=2;
LSB0=(double) (2.*10./iADamp/uMaxPoints*1000);
SetCtrlVal (panel1, PANEL_1_NUMERIC_AD_Amp, iADamp);
SetCtrlVal (panel1, PANEL_1_NUMERIC_LSB, LSB0);
break;}
return 0;}
int CVICALLBACK AD_Attenuate (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
iADamp=iADamp;
if (iADamp<=2)/* DEFAULT Gain changed from 20 to 2 on 06/25/06 by FD */iADamp=1;
if (iADamp==5)iADamp=2;
if (iADamp==10)iADamp=5;
if (iADamp==20)
iADamp=10;
if (iADamp>=50)
iADamp=20;
LSB0=(double) (2.*10./iADamp/uMaxPoints*1000);
SetCtrlVal (panel1, PANEL_1_NUMERIC_AD_Amp, iADamp);
SetCtrlVal (panel1, PANEL_1_NUMERIC_LSB, LSB0);
break;}
return 0;}/* Remove the pulse valve setup to its own section */int CVICALLBACK SetupPV (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
int iIgnoreWarning = 0, iStatus, iRetVal;
int iPulseRate, iPulseAve;
double dTimeDelay;
unsigned int ulGpctr0 = ND_COUNTER_0;
unsigned int ulHIGHcnt1, ulLOWcnt1;
switch (event){case EVENT_COMMIT:/*

Read Values off the Setup Control Panel*//* Read the Pulse Valve Trigger Rate*/
GetCtrlVal (panel0, PANEL_0_NUMERIC_pulse_rate, &iPulseRate);/* Read the Number of points to average*/
GetCtrlVal (panel0, PANEL_0_NUMERIC_Average, &iPulseAve);/* Read the Delay between pulse valve trigger and trigger to DAQ
GetCtrlVal (panel0, PANEL_0_NUMERIC_time_delay, &dTimeDelay);*//* Set up the counter, at the frequency read above to drive the pulse valve. */iStatus = GPCTR_Control(iPCI6110, ulGpctr0, ND_RESET);
iRetVal = NIDAQErrorHandler(iStatus, "GPCTR_Control/RESET",iIgnoreWarning);
iStatus = GPCTR_Set_Application(iPCI6110, ulGpctr0,ND_PULSE_TRAIN_GNR);
iRetVal = NIDAQErrorHandler(iStatus, "GPCTR_Set_Application",iIgnoreWarning);
iStatus = GPCTR_Change_Parameter(iPCI6110, ulGpctr0, ND_SOURCE,ND_INTERNAL_100_KHZ);
iRetVal = NIDAQErrorHandler(iStatus,"GPCTR_Change_Parameter/SOURCE", iIgnoreWarning);
ulHIGHcnt1 = 100*dTimeDelay;ulLOWcnt1 = 100000/iPulseRate-ulHIGHcnt1;

237
iStatus = GPCTR_Change_Parameter(iPCI6110, ulGpctr0, ND_COUNT_1,ulLOWcnt1);
iRetVal = NIDAQErrorHandler(iStatus,"GPCTR_Change_Parameter/COUNT1", iIgnoreWarning);
iStatus = GPCTR_Change_Parameter(iPCI6110, ulGpctr0, ND_COUNT_2,ulHIGHcnt1);
iRetVal = NIDAQErrorHandler(iStatus,"GPCTR_Change_Parameter/COUNT2", iIgnoreWarning);/* To output a counter pulse, you must call Select_Signal. */iStatus = Select_Signal(iPCI6110, ND_GPCTR0_OUTPUT,ND_GPCTR0_OUTPUT, ND_LOW_TO_HIGH);
iRetVal = NIDAQErrorHandler(iStatus,"Select_Signal/GPCTR0_OUTPUT-Enable", iIgnoreWarning);
iStatus = GPCTR_Control(iPCI6110, ulGpctr0, ND_PROGRAM);
iRetVal = NIDAQErrorHandler(iStatus, "GPCTR_Control/PROGRAM",iIgnoreWarning);
SetCtrlVal (panel0, PANEL_0_LED_PulseValve, 1);
isPulsing = 1;
break;}
return 0;}
int CVICALLBACK RescaleY (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
double dVmin, dVmax;
switch (event){case EVENT_COMMIT:
GetCtrlVal (panel1, PANEL_1_NUMERIC_Vmin, &dVmin);
GetCtrlVal (panel1, PANEL_1_NUMERIC_Vmax, &dVmax);
SetAxisScalingMode (panel1, PANEL_1_GRAPH_signal, VAL_LEFT_YAXIS,
VAL_MANUAL, dVmin, dVmax);
GetCtrlVal (panel1, PANEL_1_NUMERIC_offsetDCSig, &dOffsetDCSig);
GetCtrlVal (panel1, PANEL_1_NUMERIC_offsetDCRef, &dOffsetDCRef);
GetCtrlVal (panel1, PANEL_1_NUMERIC_offsetVSaw, &dOffsetVSaw);
PlotWaveform (panel1, PANEL_1_GRAPH_signal, adScan, icounter, VAL_DOUBLE,
1., 0., 0., 1.0, VAL_THIN_LINE, VAL_NO_POINT, VAL_SOLID, 1, VAL_BLACK);
PlotWaveform (panel1, PANEL_1_GRAPH_signal, adScan+ulDataPoints, icounter, VAL_DOUBLE,
1.0, dOffsetDCSig, 0, 1, VAL_THIN_LINE, VAL_NO_POINT, VAL_SOLID, 1, VAL_GREEN);
PlotWaveform (panel1, PANEL_1_GRAPH_signal, adScan+2*ulDataPoints, icounter, VAL_DOUBLE,
1.0, dOffsetDCRef, 0, 1, VAL_THIN_LINE, VAL_NO_POINT, VAL_SOLID, 1, VAL_RED);
PlotWaveform (panel1, PANEL_1_GRAPH_signal, adScan+3*ulDataPoints, icounter, VAL_DOUBLE,
1.0, dOffsetVSaw, 0, 1, VAL_THIN_LINE, VAL_NO_POINT, VAL_SOLID, 1, VAL_BLUE);

break;}
return 0;}
int CVICALLBACK Scan_Return_Setup (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
int isSaved, iContinue;
switch (event){case EVENT_COMMIT:
GetCtrlAttribute (panel1, PANEL_1_COMMANDBUTTON_Save, ATTR_DIMMED, &isSaved);
if (! isSaved) // File Not Saved{
iContinue = ConfirmPopup ("Warning!", "File Not Saved.\n
Do you wish to discard scan?");if (iContinue)// Discarding Scan{
SetPanelAttribute (panel0, ATTR_VISIBLE, 1);// SetCtrlVal(panel0,PANEL_0_NUMERIC_Wavelength,0.0);
return 0;
}
}
else
{
SetPanelAttribute (panel0, ATTR_VISIBLE, 1);// SetCtrlVal(panel0,PANEL_0_NUMERIC_Wavelength,0.0);}
break;}
return 0;}
int CVICALLBACK Wform_Return_Setup (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){

238
switch (event){case EVENT_COMMIT:
ibreakflag = 1;
break;}
return 0;}
int CVICALLBACK Change_Gates (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
iChangeWFGates = 1;
break;}
return 0;}
int CVICALLBACK Save_Waveform (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
iSaveWaveform = 1;
break;}
return 0;}

int CVICALLBACK Waveform_Gain (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
switch (event){case EVENT_COMMIT:
iChangeWFGain = 1;
break;}
return 0;}
char *Newdir(char *currdir,char *append_this ,int *Ierror){/*CREATES a new directory, and returns a pointer to an array ofcharacters containing the new directory. Use that name to construct
the path for saving or openning files. Use inside of strcpy to pass
the name of the new directory.
For error checking:0 : No error-8 : DIsk is full
-9 : DIrectory already exists*/
int oldBreakState;
int error;
char dir[MAX_PATHNAME_LEN]="";
strcpy (dir,currdir);
strcat(dir,"\\");
strcat(dir,append_this);oldBreakState = SetBreakOnLibraryErrors (0);*Ierror=MakeDir (dir);
SetBreakOnLibraryErrors (oldBreakState);
error=*Ierror;
currdir=dir;
return currdir;}
int CVICALLBACK GetXY (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
double dX, dY;
int iIndex;
switch (event){case EVENT_COMMIT:
GetGraphCursor (panel1, PANEL_1_GRAPH_signal, 1, &dX, &dY);
iIndex = floor (dX);
if (iIndex > 0 && iIndex < ulDataPoints)

239{
SetCtrlVal(panel1,PANEL_1_NUMERIC_Xval,iIndex);
SetCtrlVal(panel1,PANEL_1_NUMERIC_ACSig,adScan[iIndex]);
SetCtrlVal(panel1,PANEL_1_NUMERIC_DCSig,adScan[iIndex+ulDataPoints]);
SetCtrlVal(panel1,PANEL_1_NUMERIC_DCRef,adScan[iIndex+2*ulDataPoints]);
SetGraphCursor (panel1, PANEL_1_GRAPH_signal, 1, dX, adScan[iIndex]);}break;}
return 0;}
int CVICALLBACK stopPV (int panel, int control, int event,
void *callbackData, int eventData1, int eventData2){
int iIgnoreWarning = 0, iStatus, iRetVal;
unsigned int ulGpctr0 = ND_COUNTER_0;

switch (event){case EVENT_COMMIT:
iStatus = GPCTR_Control(iPCI6110, ulGpctr0, ND_DISARM);
iRetVal = NIDAQErrorHandler(iStatus, "GPCTR_Control/PROGRAM",iIgnoreWarning);
SetCtrlVal (panel0, PANEL_0_LED_PulseValve, 0);
isPulsing = 0;
break;}
return 0;}

Appendix C
Data Processing Scripts and Procedures

C.1

General Description
The raw data comes in the form of a block of voltages as recorded from each input

onto the A/D card. It is a bit of work to turn that into a spectra with an absolute, accurate,
and precise x-axis and % Absorbance on the y-axis. To do this, I wrote a series of scripts in
LabTalk (and some in C) to do this process automatically with places to check the process
along the way. The ﬁrst step is to open the main program in Origin’s script window. The
main program is set up to have an easy way to set up the ﬁle parameters, like ﬁle name andlocation, specifying frequency ranges for peak ﬁnding, etc. The main program then calls
each subroutine, passing along the pertinent information.
C.2

Origin Code/////////////////////// MAIN_ET.OGS (help.txt)////////////////////;//// INITIALIZATION FOR THE DATA ANALYSIS - PATH AND FILENAME PREFIX (from .001 to .999)////;%k=nov2111; %t=J:\4marobert\hd2op\nov2111; %n=C:\Users\Melanie\Documents\NewTable\Scripts_new;
if (exist(scanlist)!=2) {run.file(%n\EastScanList.ogs);};//// IMPORT RAW ASCII DATA////for (FN=11;FN<=12;FN++){// FN=03; ;gain=316; autoscan=0; segover=0; run.file(%n\EastOpenFile2.ogs);//// Ti:Sapph Laser Etalon Fringes Smoothing and Counting ////// FN=06;
smooth=0; FWHM=20; NWindow=10; FWHMPOS=3; Err=5.0; MinY=.2;
run.file(%n\EastLEtalon.ogs);};//enter missed/extra number of Large Etalon Fringes////;//then create interpolated large etalon axis and find Small etalon peaks///;for (FN=11;FN<=12;FN++){//FN=01;
LFSR=1.50462922013;
run.file(%n\RelFreqL.ogs);

241//FN=01;
NWindow=2; sreffile=08; offset=100000.0; MinY=0.8;
run.file(%n\EastSEtalon.ogs);};/////create small etalon axis//////////////;for (FN=11;FN<=11;FN++){//FN=01;
sreffile=08; SFSR=0.24984691172; soffset=100000;
run.file(%n\RelFreqS.ogs);};///use peakfinder on the small etalon axis get freq reference peak///;
FN=02;
NWindow=4; NIni=2663; NFinal=2665; MinY=0.2;
run.file(%n\refpeak.ogs);//// Stitch together segments////;//enter name for spreadsheet containing concatenated data//;//for now, list files in order of increasing freq//%t=%ktot2;
files={09,10,11};
pkGHz=24987.471865; //relative GHz of reference peak//;
refpk=2651.3865; //D2O v3 000 111 line//;run.file(%n\EastConcatenate.ogs);////// Peak Finding on concatenated data///;%t=%ktot;
Nwindow=7; Amin=.02;
FreqIni=2605; FreqFinal=2627; run.file(%n\EastSnyderPeakFinder.ogs);//// Peak finding on the reference line//////;%t=%k001N;
Nwindow=7; Amin=.02;
FreqIni=24984; FreqFinal=24992; run.file(%n\EastSnyderRefCell.ogs);//////////////////////////////END//////////////////////////;///////////////////////// OPENFILE.OGS////////////////////////////////////;//////////////////////////////////////////////////////////////////////////;/// ASCII DATA IMPORTED, AND TRANSFORMED TO THE FOUR COLUMN DATASHEET. //;/// PUT DATA INTO % ABSORBANCE FORM//;//////////////////////////////////////////////////////////////////////////;%q=scanlist;%p=%k$(FN); if (FN<100) %p=%k0$(FN); if (FN<10) %p=%k00$(FN);
if (exist(temp)==2){win -cd temp;};if (exist(%pN)==2){win -cd %pN;};
win -t data data1 temp;
open -w %t\%p.scn; @WD=1;
win -t data data1 %pN;//////////////////////////////////////////////////////////////////////////;//// Creating worksheet ////;

win -a %pN;
work -a 12;
work -n 1 Points;
work -t 1 2;
work -n 2 GHz;
work -t 2 4;
work -n 3 relFr;
work -t 3 1;
work -n 4 relGHz;
work -t 4 1;
work -n 5 Signal;
work -t 5 1;
work -n 6 LEtalon;
work -t 6 1;
work -n 7 SEtalon;
work -t 7 1;
work -n 8 RefCell;
work -t 8 1;
work -n 9 IRpower;
work -t 9 1;
work -n 10 LEtnew;
work -t 10 1;
work -n 11 SEtnew;
work -t 11 1;
work -n 12 Abs;
work -t 12 1;%pN!wks.col1.digitmode=1;%pN!wks.col2.digitmode=1;%pN!wks.col3.digitmode=1;%pN!wks.col4.digitmode=1;%pN!wks.col5.digitmode=1;%pN!wks.col6.digitmode=1;%pN!wks.col7.digitmode=1;%pN!wks.col8.digitmode=1;%pN!wks.col1.digits=0;%pN!wks.col2.digits=4;%pN!wks.col3.digits=4;%pN!wks.col4.digits=4;%pN!wks.col5.digits=4;%pN!wks.col6.digits=4;%pN!wks.col7.digits=4;%pN!wks.col8.digits=4;//////////////////////////////////////////////////////////////////////////;///////////Entering data into worksheet///////////////////////////////////;
win -a temp;
limit temp_d;
LN = limit.size; minv=limit.ymax;

242
win -a %pN;
for (i=1;i<=LN;i++){%pN_Points[i]=i;%pN_Signal[i]=temp_b[i];%pN_SEtalon[i]=temp_c[i];%pN_Refcell[i]=temp_d[i];%pN_IRpower[i]=temp_e[i];%pN_LEtalon[i]=temp_f[i];// %pN_VET1[i]=-temp_d[i]+minv;};//////////////////////////////////////////////////////////////////////////;//////////making % Absorbance column//////////////////////////////////////;
win -a %pN;
%pN_Abs=100*(%pN_signal/$(gain))/(-1*%pN_IRpower);//////////////////////////////////////////////////////////////////////////;/////////// putting scan info into scanlist worksheet ////////////////////;
win -a %q;wcol(1)[FN]$=%p;wcol(2)[FN]=$(FN);
if(temp_a[1]==0.0){
wcol(17)[FN]=temp_a[12];}else{wcol(17)[FN]=temp_a[1]/10000;}
if (segover==0){
wcol(5)[FN]=temp_a[26];wcol(6)[FN]=temp_a[28];wcol(8)[FN]=wcol(6)[FN]/wcol(5)[FN];}
else{wcol(5)[FN]=segover;wcol(8)[FN]=1021;
wcol(6)[FN]=wcol(8)[FN]*wcol(5)[fn];}wcol(7)[FN]=temp_a[32];wcol(9)[FN]=$(gain);//////////////////////////////////////////////////////////////////////////;/////// generate x-axis if there is no autoscan file /////////////////////;

startfreq=%q_TSStart[FN];
startghz=startfreq*29.9792458;
stepsize=%q_iStepSize[FN];seglength=%q_SegPts[FN];
numseg=%q_ulNumSeg[FN];
icount=1;
for (i=0;i<numseg;i++){for(j=0;j<(seglength);j++){%pN_GHz[icount]=startghz+j*(stepsize/1000)+i*10;
icount=icount+1;};};//////////////////////////////////////////////////////////////////////////;////////////////entering VET data from autoscan if desired //////////////;
if (autoscan==1){
win -t data data1 temp2;

open -w %t\%m0$(FN).sca;

win -a %pN;
for (i=1;i<=LN;i++){wcol(9)[i]=temp2_b[i];wcol(10)[i]=temp2_b[i+1+LN];};
work -t 1 2;
work -t 2 4;};

243///////////////// Draw the experiental plots (vs channels) ///////////////;
if (exist(%pfig1)==3) {win -c %pfig1;};
win -t graph %n\RawSignal %p.fig1;
layer -i %pN_RefCell; layer -i %pN_SEtalon; layer -i %pN_Signal;
set %pN_SEtalon -c 2;
rescale;layer -i %pN_VET1; layer -i %pN_LEtalon;
set %pN_VET1 -c 5;
set %pN_VET2 -c 17;
label -xb GHz;label -yl VOLTS;////////////////////////////////////////////////////////////////////////;
win -a %pN; win -h 1;
delete -v TN; delete -v %q; delete -v Nexist; win -cd temp; win -cd temp2;//////////////////////////////////// End. //////////////////////////////;//////////////////////////////////////////////////////////////////////////;// Subroutine for etalon fringes counting ////////////////////////////////////////////////////////////////////////////;
cm2GHz=29.97924580;//FWHM=5;//FWHMPOS=1;//NWindow=3;//MmiY=0.1;// Gauss smoothing of the etalon signal;// Gauss smoothing of the FPI position;// Snyder algorithm for finding etalon peak position (in fractional data points.
// Minimum intensity (in percentage of the maximum intensity) when determining a fringe.

/* Finding scanfile name (%p) relating to filenumber FN, if the data has been analyzed before.*/%p=%k$(FN); if (FN<100) %p=%k0$(FN); if (FN<10) %p=%k00$(FN);
win -a %pN;//////////////////////////////////////////////////////////////////////;////// Optional Gauss filter of the etalon signal ////////////////////;//FWHM=5;// Gauss smoothing of the etalon signal;

if (smooth!=0){
if (exist(et)==2) {win -cd et; };win -t data data1 et;
et_A=%pN_Letalon;
et_B=et_A;
limit et_B;
NIni =1;
NFinal=limit.size;
if(run.LoadOC("%n/Gaussfilter.c",1) != 0){
type -b "Error trying to load and compile Origin C file ’%n\Gaussfilter.c";break 1;};Gaussfilter(NIni,NFinal,FWHM,"et_A","et_B");// limit et_B;%pN_LETnew=et_B;%pN_LEtnew = -%pN_LEtnew;
limit %pN_Letnew;%pN_LEtnew = %pN_Letnew-limit.ymin;
delete -v FWHM;
win -cd et;
};
else
{
win -a %pN;
limit %pN_Points;
LN = limit.size;for (i=1;i<=LN;i++){%pN_LEtnew[i]=-%pN_LEtalon[i];};};///////////////////////////////////////////////////////////////////;//// create the worksheets needed to store the data ///////////////;// data point number is the x-axis here.
//Nwindow=3;// Snyder algorithm for finding etalon peak position (in fractional data points).

244//MmiY=0.1;// Minimum intensity (in percentage of the maximum intensity) when determining a fringe.

nseg=%q_ulNumSeg[FN];
npts=%q_SegPts[FN];
if (exist(%pP)==2){
win -cd %pP;};
newbook n:=%pP o:=1;
for(j=1;j<=nseg;j++){newsheet b:=%pP n:=segment_$(j) c:=6;
work -n 1 Points;
work -t 1 4;
work -n 2 LFringes;
work -t 2 1;
work -n 3 LEtalon;
work -t 3 1;
work -n 4 AsGHz;
work -t 4 1;
work -n 5 LAxis;
work -t 5 4;
work -n 6 SEtalon;
work -t 6 1;
work -n 7 SFringes; work -t 7 1;};
range ww=[%pP]Sheet1!;
ww.name$="summary";
ww.ncols=7;
ww.col1.name$=segment;
ww.col2.name$=SndLFr;
ww.col3.name$=SndSFr;
ww.col4.name$=LMissed;
ww.col5.name$=SMissed;
ww.col6.name$=LRelNo;
ww.col7.name$=SRelNo;for(j=1;j<=nseg;j++){%pP_segment[j]=j;};///////////////////////////////////////////////////////////////////////////////;///////////use the Snyder Peak Finder Algorithm to get the etalon peaks ///////;////the peaks in each segment go in a different worksheet in the P workbook////;

if(run.LoadOC("%n\snyder.c",1) != 0){
type -b "Error trying to load and compile Origin C file ’%n\snyder.c";break 1;};//win -a %pP;
for(k=1;k<=nseg;k++){NIni=(k-1)*npts+1;
NFinal=k*npts-1;
range ne=[%pP]segment_$(k)!LEtalon;
range np=[%pP]segment_$(k)!Points;
range nf=[%pP]segment_$(k)!LFringes;
range no=[%pP]segment_$(k)!AsGHz;
snyder(NWindow,NIni,NFinal,MinY,%pN_Points,%pN_LEtnew,ne,np,nf);// now change from points to autoscan x-axis/////////////////////;
range nf=[%pP]segment_$(k)!LFringes;
limit nf;
frnum=limit.ymax;
for(i=1;i<=frnum;i++){strt=int(np[i]);diffp=np[i]-strt;
slen=%pN_GHz[strt+1]-%pN_GHz[strt];
interp=slen*diffp;
no[i]=%pN_GHz[strt]+interp;};};
range ni=[%pP]summary!SndLFr;
for(k=1;k<=nseg;k++){range no=[%pP]segment_$(k)!AsGHz;
ni[k]=no[2];};///////////////// Cleanup //////////////////////////////////////////////;
delete -v MinY;
delete -v %q;
delete -v Nini; delete -v NFinal; delete -v NMax;
delete -v %s;

245/////////////////////plot////////////////////////////////////////////////;
if (exist(%p_fig)==3) {win -cd %p_fig; };//Create 2 panels
newpanel 2 1 name:=%p_fig optn:=1 result:=%p_fig;//add a new layer
layadd;layadd;//plot the data
k=1;
plotxy iy:=[%pN]Sheet1!Signal plot:=0 legend:=0 ogl:=[%p_fig]1;

plotxy iy:=[%pN]sheet1!RefCell plot:=0 legend:=0 ogl:=[%p_fig]2;//Set the properties of X axis in Layer3 and layer4
laysetscale igp:=[%p_fig] layer:=3 axis:=x from:=0 to:=900;
laysetscale igp:=[%p_fig] layer:=4 axis:=x from:=0 to:=900;
layer3.y.from=-20;
layer3.y.to=20;//copy the scale from layer3 to layer4
laycopyscale igl:=3 dest:=4 axis:=2;
plotxy iy:=[%pN]sheet1!SEtalon plot:=0 legend:=0 ogl:=[%p_fig]3;
set %pN_SEtalon -c 3;
plotxy iy:=[%pN]sheet1!LEtalon plot:=0 legend:=0 ogl:=[%p_fig]4;//Set the Width and height of each layer
layer1.width=90;
layer1.height=60;
layer2.width=90;
layer2.height=25;
layer3.width=90;
layer3.height=25;
layer4.width=90;
layer4.height=25;//Set the layer’s position
laysetpos igp:=[%p_fig] layer:=1 top:=35 unit:=page;
laysetpos igp:=[%p_fig] layer:=1 left:=5 unit:=page;
laysetpos igp:=[%p_fig] layer:=2 left:=5 unit:=page;
laysetpos igp:=[%p_fig] layer:=2 top:=35 unit:=page;
laysetpos igp:=[%p_fig] layer:=3 left:=5 unit:=page;
laysetpos igp:=[%p_fig] layer:=3 top:=10 unit:=page;
laysetpos igp:=[%p_fig] layer:=4 left:=5 unit:=page;
laysetpos igp:=[%p_fig] layer:=4 top:=10 unit:=page;//Link layers
laylink igp:=[%p_fig] igl:=1 destlayers:=2:4 XAxis:=1;/////////////// END. ////////////////////////////////////////////////////;/////////////////////////////////// RelFreqL.ogs //////////////////////////////////////////// Calculating relative frequencies based on marker cavity peak number and the FSR////////////////////////////////////////////////////////////////////////////////////////////////////// set constants and defaults. ////
cm2GHz=29.979245800;%q=scanlist;%p=%q_scanfile[FN]$;
nseg=%q_ulNumSeg[FN];
npts=%q_segPts[FN];
if (exist(%pS)==2) {win -cd %pS;};@wd=1; win -t data data1 %pS;
work -a 5*nseg+1;
work -n (5*nseg+1) datapt;
work -t (5*nseg+1) 4;/////////////////////////////////////////////////////////////////////////////////;//// for each segment, adjust the large fringe spacing to be the large FSR////;/////////////////////////////////////////////////////////////////////////////////;
for(i=1;i<=nseg;i++){246
sa=(i-1)*5+1;
work -n sa Linterp_$(i); work -t sa 1;
work -n (sa+1) Lrel_$(i);work -n (sa+2) SEt_$(i);work -n (sa+3) Sinterp_$(i);work -n (sa+4) Srel_$(i);start=(i-1)*npts+1;
end=i*npts;
count=0;
for(j=start;j<=end;j++){count=count+1;%pS_datapt[count]=j};range aa=[%pP]segment_$(i)!LFringes;
range bb=[%pS]Sheet1!datapt;%pS_Linterp$(i)=aa(bb);};///////////////////////////////////////////////////////////////////////////;///////////////////////////////////EastSEtalon.ogs //////////////////////////////////////////// Calculating relative frequencies based on marker cavity peak number and the FSR////////////////////////////////////////////////////////////////////////////////////////////////////// set constants and defaults. ////
%q=scanlist;
cm2GHz=29.979245800;%p=%q_scanfile[FN]$;
nseg=%q_ulNumSeg[FN];
npts=%q_segPts[FN];%r=%q_scanfile[sreffile]$;// calculate the relative fringe number for each segment based upon //////;// the first segment of the reference scan.///////////////////////////////;
range na=[%rP]summary!SndLFr;
range nb=[%pP]summary!LRelNo;
range nd=[%pP]summary!SndLFr;
reffreq=na[1];for(j=1;j<=nseg;j++){nb[j]=(nd[j]-reffreq)/LFSR+offset;};//now create the large etalon relative axis//////////////////////////////;
for(k=1;k<=nseg;k++){
str=round(nb[k],0);
range nc=[%pS]sheet1!Linterp$(k);for(i=1;i<=npts;i++){%pS_Lrel$(k)[i]=(nc[i]+str)*LFSR;};};/////////////////////////////////////////////////////////////////////////////////;//// use the interpolated large x-axis to find////;//// the peak positions of the small etalon////;/////////////////////////////////////////////////////////////////////////////////;//first bring in the small etalon data//;for(j=1;j<=nseg;j++){strtseg=(j-1)*npts+1;
for(i=1;i<=npts;i++){%pS_SEt$(j)[i]=-%pN_SEtalon[strtseg+i];};};//use peak finder to find the small etalon peak wrt the large etalon rel axis//;if(run.LoadOC("%n\snyder.c",1) != 0){
type -b "Error trying to load and compile Origin C file ’%n\snyder.c";break 1;};247
for(k=1;k<=nseg;k++){NIni=1;
NFinal=npts-1;
range ne=[%pP]segment_$(k)!SEtalon;
range np=[%pP]segment_$(k)!LAxis;
range nf=[%pP]segment_$(k)!SFringes;
snyder(NWindow,NIni,NFinal,MinY,%pS_LRel$(k),%pS_SEt$(k),ne,np,nf);};////take the 10th fringe and use that as the small etalon fringe////////;
range ni=[%pP]summary!SndSFr;
for(k=1;k<=nseg;k++){range no=[%pP]segment_$(k)!LAxis;ni[k]=no[10];};////////////////cleanup/////////////////////////////////////////////////;/////////////////////////////////// RelFreqS.ogs //////////////////////////////////////////// Calculating relative frequencies based on marker cavity peak number and the FSR////////////////////////////////////////////////////////////////////////////////////////////////////// set constants and defaults. ////
%q=scanlist;
cm2GHz=29.979245800;%p=%q_scanfile[FN]$;
nseg=%q_ulNumSeg[FN];
npts=%q_segPts[FN];////////////use the 10th fringe of each scan to create relative axis////;

range ni=[%pP]summary!SndSFr;%r=%q_scanfile[sreffile]$;range na=[%rP]summary!SndSFr;
range nb=[%pP]summary!SRelNo;sreffreq=na[1];for(j=1;j<=nseg;j++){nb[j]=(ni[j]-sreffreq)/SFSR+soffset;};////fill relative fringe of first segment into scanlist worksheet////////;%q_TSFringe[FN]=nb[1];/////////////////////////////////////////////////////////////////////////////////;//// for each segment, adjust the small fringe spacing to be the small FSR////;/////////////////////////////////////////////////////////////////////////////////;
work -a %pS;
for(i=1;i<=nseg;i++){// sa=(i-1)*4+1;// start=(i-1)*npts+1;// end=i*npts;// count=0;// for(j=start;j<=end;j++)// {// count=count+1;// %pS_datapt[count]=j// };range aa=[%pP]segment_$(i)!SFringes;
range bb=[%pS]Sheet1!Lrel$(i);range cc=[%pS]Sheet1!Sinterp$(i);cc=aa(bb);};/////////////////////////////////////////////////////////////////////////////;////turn the small etalon interpolated axis into a relative frequency axis///;// and copy it into the N spreadsheet////////////////////////////////////////;
icount=0;248
for(k=1;k<=nseg;k++){
str=round(nb[k],0);
range nc=[%pS]sheet1!Sinterp$(k);for(i=1;i<=npts;i++){%pS_Srel$(k)[i]=(nc[i]+str)*SFSR;
icount=(k-1)*npts+i;%pN_relGHz[icount]=%pS_Srel$(k)[i];};};/////////////////////////////////////END///////////////////////////////////;///////////////////////////////////////////////////////////////////////////;////subroutine for finding the peak to be used as the reference frequence//;///////////////////////////////////////////////////////////////////////////;%q=scanlist;%p=%q_scanfile[FN]$;
nseg=%q_ulNumSeg[FN];
npts=%q_segPts[FN];
if (exist(%prP)==2) {win -cd %prP;};@wd=1; win -t data data1 %prP;
work -a 1;
work -n 1 relGhz;
work -t 1 4;
work -n 2 Peak;work -n 3 Peaknum;///////////////////////////////////////////////////////////////////////////////;///////////use the Snyder Peak Finder Algorithm to get the etalon peaks ///////;

if(run.LoadOC("%n\snyder.c",1) != 0){
type -b "Error trying to load and compile Origin C file ’%n\snyder.c";break 1;};//the frequency range (Nini and Nfinal), nwindow, and minimun y-value should be//;// entered when calling the subroutine. The relative frequency axis from the//;// small (250 MHz etalon)//;
range ne=[%prP]sheet1!Peak;
range np=[%prP]sheet1!relGHz;
range nf=[%prP]sheet1!Peaknum;// snyder(NWindow,NIni,NFinal,MinY,%pN_relGHz,%pN_Abs,ne,np,nf);//////////////////END//////////////////////////////;
delete -v MinY;
delete -v %p;delete -v Nini; delete -v NFinal;delete -v NWindow;////////////////////////East Concatenate//////////////////////////////////;//////////////////////////////////////////////////////////////////////////;%q=scanlist;
cm2GHz=29.9792458;
if (exist(%t)==2) {win -cd %t;};@wd=1; win -t data data1 %t;
work -a 4;
work -n 1 frequency;
work -t 1 4;
work -n 2 percentAbs;
work -n 3 RefCell;
work -n 4 IRpower;
work -n 5 Letalon;
work -n 6 Setalon;
limit files;
num=limit.size;
icount=0;249
for (k=1;k<=num;k++){FN=files[k];%p=%q_scanfile[FN]$;
nseg=%q_ulNumSeg[FN];
npts=%q_segPts[FN];
ntot=nseg*npts;
icount=;ntot=;for (i=1;i<=ntot;i++){icount=icount+1;%t_frequency[icount]=((%pN_relGHz[i]-pkGHz)/cm2GHz)+refpk;%t_percentAbs[icount]=%pN_Abs[i];%t_RefCell[icount]=%pN_RefCell[i];%t_IRpower[icount]=%pN_IRpower[i];%t_Letalon[icount]=%pN_LEtalon[i];%t_Setalon[icount]=%pN_SEtalon[i];};};// Snyder peak finder subroutine ////Nwindow=1;//Amin=0.005;//FreqIni=-0.1;//FreqFinal=47;%r=%tP;if (exist(%r)!=2){win -t data data1 %r; work -a 1;
work -n 1 X; work -n 2 Y; work -n 3 Label; work -t 3 5;};else {win -a %r; clearworksheet %r;work -n 1 X; work -n 2 Y; work -n 3 Label; work -t 3 5;};%s=snyder;if (exist(%s)!=2){win -t data data1 %s;};
else {win -a %s; clearworksheet %s;};//if (IFGHz==1) {%s_a=%t_GHz;}; else {%s_a=%t_CM;};//if (IFGSSM==0) {%s_b=%t_Absorbance;}; else {%s_b=%t_GSSM;};%s_a=%t_frequency;%s_b=%t_percentAbs;
limit %s_b;
if (abs(FreqIni-FreqFinal)<0.0001){FreqIni=Limit.xmin;
FreqFinal=Limit.xmax;};
if (FreqIni<limit.xmin){FreqIni=Limit.xmin;};if (FreqFinal>limit.xmax){FreqFinal=Limit.xmax;};//FreqIni=; FreqFinal=;
Nini =xindex(FreqIni,%s_b);
NFinal=xindex(FreqFinal,%s_b);//Nini=;NFinal=;
Dif0=1.0;
Nmax=0;for (NI=Nwindow+Nini; NI<=NFinal-Nwindow;NI++){SumU=0.0;
SumL=0.0;
for (NJ=NI-Nwindow; NJ<=NI-1; NJ++){
SumL=SumL+%s_b[NJ];};for (NK=NI+1; NK<=NI+Nwindow; NK++){
SumU=SumU+%s_b[NK];};
Dif1=SumL-SumU;
Dif01=Dif0*Dif1;
If ((Dif01<=0.0)&&(%s_b[NI]>Amin)&&(dif0<0.0)){
NMax=NMax+1;
ymax0=Max(%s_b[NI-2],%s_b[NI-1],%s_b[NI],%s_b[NI+1],%s_b[NI+2]);%r_Y[NMax]=ymax0;
DifX=%s_a[NI]-%s_a[NI-1];%r_X[NMax]=%s_a[NI]-DifX*Dif1/(Dif1-Dif0);};
Dif0=Dif1;};%r_Label=int(%r_X*100000)/100000;
win -a %r; win -ch 1;
delete -v A*;
delete -v N*;
delete -v D*;
delete -v Freq*;
win -cd %s;250delete -v %s;
delete -v %r;/* End *//*------------------------------------------------------------------------------** File Name:** Creation: ** Purpose: OriginC Source C file ** Copyright (c) ABCD Corp. 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 ** All Rights Reserved ** ** Modification Log: made by Melanie 1/2010 **------------------------------------------------------------------------------*/////////////////////////////////////////////////////////////////////////////////////// Including the system header file Origin.h should be sufficient for most Origin// applications and is recommended. Origin.h includes many of the most common system// header files and is automatically pre-compiled when Origin runs the first time.
// Programs including Origin.h subsequently compile much more quickly as long as// the size and number of other included header files is minimized. All NAG header// files are now included in Origin.h and no longer need be separately included.
//// Right-click on the line below and select ’Open "Origin.h"’ to open the Origin.h// system header file.
#include <Origin.h>#include <math.h>#include <data.h>//////////////////////////////////////////////////////////////////////////////////////#pragma labtalk(0) // to disable OC functions for LT calling.
////////////////////////////////////////////////////////////////////////////////////// Include your own header files here.

////////////////////////////////////////////////////////////////////////////////////// Start your functions here.
// datax - x-axis of dataset// datay - y-axis of dataset// peaks - peak position y-axis// points - peak position x-axis
void snyder(int Nwindow, double Nini, double NFinal,
double MinY, string datax, string datay, string peaks, string points, string frnum){int NMax, NI, NJ, NK;double Dif0, Dif01, Dif1, DifX, Dstep, Dstep0, SumU, SumL, ymax0, xmax0;
vector<double> test(6);Dataset dsdX(datax);
Dataset dsdY(datay);
Dataset dspX(points);
Dataset dspY(peaks);
Dataset dspN(frnum);vector vdX, vdY, vpX, vpY, vpN;
vdX=dsdX;
vdY=dsdY;

Dif0=1.0;
NMax=0;for (NI=Nwindow+Nini; NI<=NFinal-Nwindow;NI++){SumU=0.0;
SumL=0.0;
for (NJ=NI-Nwindow; NJ<=NI-1; NJ++){
SumL=SumL+vdY[NJ];}
for (NK=NI+1; NK<=NI+Nwindow; NK++){
SumU=SumU+vdY[NK];}
Dif1=SumL-SumU;
Dif01=Dif0*Dif1;
if ( (Dif01<=0.0) && (vdY[NI]>MinY) && (Dif0<0.0) ){NMax=NMax+1;
test[1]=vdY[NI-2];
test[2]=vdY[NI-1];
test[3]=vdY[NI];test[4]=vdY[NI+1];
test[5]=vdY[NI+2];
ymax0=max(test);
DifX=vdX[NI]-vdX[NI-1];
xmax0=vdX[NI]-DifX*Dif1/(Dif1-Dif0);

251
vpX.Add(xmax0);
vpY.Add(ymax0);
vpN.Add(NMax);}
Dif0=Dif1;}
dspX=vpX;
dspY=vpY;
dspN=vpN;}/*------------------------------------------------------------------------------** File Name:** Creation: ** Purpose: OriginC Source C file ** Copyright (c) ABCD Corp. 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 ** All Rights Reserved ** ** Modification Log: **------------------------------------------------------------------------------*/////////////////////////////////////////////////////////////////////////////////////// Including the system header file Origin.h should be sufficient for most Origin// applications and is recommended. Origin.h includes many of the most common system// header files and is automatically pre-compiled when Origin runs the first time.
// Programs including Origin.h subsequently compile much more quickly as long as// the size and number of other included header files is minimized. All NAG header// files are now included in Origin.h and no longer need be separately included.
//// Right-click on the line below and select ’Open "Origin.h"’ to open the Origin.h// system header file.
#include <Origin.h>////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// Include your own header files here.

////////////////////////////////////////////////////////////////////////////////////// Start your functions here.
/* Raw - raw dataset needed to be gauss smoothed;gauss - New dataset after gauss smoothing
NMin, NMax - start and End point, datapoints in-between will be gauss-smoothed*/
void Gaussfilter(int NMin, int NMax, int FWHM, string raw, string gauss){
int i, j, j0, IMax, NPoints, MinMax;
double Cutoff, sumtotal, FWHMnorm, IMax0, ssum, ff, temp;
double vFA[1000];if (FWHM>0){
Cutoff=0.0001;
Dataset dsA(raw);
Dataset dsB(gauss);
vector vA, vB;
vA=dsA;vB=dsB;
NPoints=dsA.GetSize();/* rationalize start point NMin and End Point NMax*/
if (NMin>NMax) {MinMax=NMin; NMin=NMax; NMax=NMin;};if (NMin==NMax) {NMin=1; NMax=NPoints;};
if (NMin<1) NMin=1;
if (NMax>=NPoints) NMax=NPoints;
FWHMnorm=2.772588722/(FWHM*FWHM);//

IMax0=-ln(Cutoff)/FWHMnorm;
IMax=sqrt(IMax0);
sumtotal=0;
printf ("IMax= %d\n", IMax);for (i=0;i<=IMax;i++){vFA[i]=0.0;}

for (i=0;i<=IMax;i++){vFA[i]=exp(-i*i*FWHMnorm);sumtotal=sumtotal+vFA[i];};sumtotal=2*sumtotal-vFA[0];for (i=0;i<=IMax;i++){vFA[i]=vFA[i]/sumtotal;};

252
/*

for (i=1;i<=Nmin-1;i++){%r_B[i]=%r_A[i];}; */for (i=NMin;i<=NMin+IMax-1;i++){ssum=0;
ff=0;
for (j=-IMax;j<=IMax;j++){if ((i+j)>=1) {j0=abs(j);ssum=ssum+vFA[j0];ff=ff+vA[i+j]*vFA[j0];}; };vB[i]=ff/ssum; };for (i=NMin+IMax; i<=NMax-IMax-1;i++){
ff=vA[i]*vFA[0];for (j=1;j<=IMax;j++){ff=ff+(vA[i+j]+vA[i-j])*vFA[j];};vB[i]=ff;};
for (i=NMax-IMax;i<=NMax-1;i++){ssum=0;
ff=0;
for (j=-IMax;j<=IMax;j++){if ((i+j)<NPoints) {j0=abs(j);ssum=ssum+vFA[j0];ff=ff+vA[i+j]*vFA[j0];};};vB[i]=ff/ssum; };dsB=vB;}}/* End */