HIGH-RESOLUTION INFRARED SPECTROSCOPY:
JET-COOLED HALOGENATED METHYL RADICALS AND
REACTIVE SCATTERING DYNAMICS
IN AN ATOM + POLYATOM SYSTEMbyERIN SUE WHITNEY
B.A., Williams College, 1996

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirement for the degree ofDoctor of Philosophy
Department of Chemistry and Biochemistry2006

UMI Number: 3207681

Copyright 2006 by
Whitney, Erin Sue
All rights reserved.

UMI Microform 3207681
Copyright 2006 by ProQuest Information and Learning Company.
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unauthorized copying under Title 17, United States Code.

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This thesis for the Doctor of Philosophy degree
entitled:

High resolution infrared spectroscopy: Jet cooled halogenated methyl radicals andreactive scattering dynamics in an atom + polyatom system

written by Erin Sue Whitney
has been approved for the Department of Chemistry and BiochemistrybyDavid J. Nesbitt

Veronica M. Bierbaum

Date

ii

Whitney, Erin S. (Ph.D., Chemistry)High-Resolution Infrared Spectroscopy: Jet-cooled halogenated methyl radicals andreactive scattering dynamics in an atom + polyatomic system
Thesis directed by Professor David J. Nesbitt.

This thesis describes a series of projects whose common theme comprises the
structure and internal energy distribution of gas-phase radicals. In the first two
projects, shot noise-limited direct absorption spectroscopy is combined with long
path-length slit supersonic discharges to obtain first high-resolution infrared spectra
for jet-cooled CH2F and CH2Cl in the symmetric and antisymmetric CH2 stretchingmodes. Drawing motivation from the question of the equilibrium structures of
halogen-substituted methyl radicals, spectral assignment yields refined lower andupper state rotational constants, as well as fine-structure parameters from least-square
fits to the sub-Doppler lineshapes for individual transitions. High-level CCSD(T)calculations extrapolated to the complete basis set (CBS) limit confirm the existenceof a non-planar (θ =29E) CH2F equilibrium structure with a 132 cm-1 barrier toplanarity and a vibrational bend frequency of 276 cm-1. Similar calculations forCH2Cl predict a slightly nonplanar equilibrium structure (θ =11E) with a vibrationallyadiabatic one-dimensional treatment of the bend coordinate yielding a fundamental
anharmonic frequency (393 cm-1). Both sets of calculations are in excellent
agreement with previous studies.
More interesting, however, are the unexpected intensity ratios of thesymmetric vs. antisymmetric bands for CH2F and the absence of an antisymmetriciii

band for CH2Cl. While a simple bond-dipole picture predicts a ratio of 1:3 for thesymmetric vs. antisymmetric intensities, the experimentally observed value for CH2F
is ~2:1. This ratio is confirmed by DFT [B3LYP/aug-cc-pVTZ] calculations in anovel albeit indirect probe of the effective non-planarity for CH2F. For CH2Cl,
similar DFT calculations predict a 30-fold decrease between the intensity of thesymmetric and antisymmetric CH2 stretches, leading to the postulation of a nearly
perfect cancellation of antisymmetric stretch intensity transition moment withchlorination.
These two projects are followed by an investigation utilizing a wellcharacterized radical source, F, in a reaction with ethane to form HF and ethyl radical.
The non-radical HF product is detected directly through similar high-resolution
infrared absorption methods as described above, and its analysis is used to makeinferences about the internal energy redistribution of the other radical fragment,
ethyl. State-to-state reaction dynamics under single collision conditions areinterpreted in the context of a simple impulsive model based on conservation of
linear/angular momentum yields predictions in good agreement with experiment.
Deviations from the model indicate only minor excitation of the ethyl vibrations, incontrast with a picture of extensive intramolecular vibrational energy flow but
consistent with Franck-Condon excitation of the methylene CH2 bending mode. The
results suggest a relatively simple dynamical picture for exothermic atom +polyatomic scattering, i.e., that of early barrier dynamics in atom + diatom systems
but modified by impulsive recoil coupling at the transition state between
translational/rotational degrees of freedom.

iv

DEDICATION

To women in sciencev

ACKNOWLEDGMENTS

Graduate school has been a long and twisting path for me, and one full of
personal and professional challenges. I am grateful to my advisor, David Nesbitt, forfacilitating a graduate experience which has taught me scientific discipline and innerfortitude. My fellow group members and the amazing JILA support staff haveprovided invaluable camaraderie and help. Special thanks go to Brad Perkins and
Tom Baker for their comic relief and encouragement, as well as to the fearless andamazing women of our research group for their personal examples. Margaret
Murnane, Veronica Vaida, Carl Lineberger, Veronica Bierbaum, and especially Anne
McCoy have cheered me on and offered invaluable expertise.
Outside the academic setting, I owe more than I can express to Julie
Emmerman, truly an earthbound angel, for helping me to more fully understand, love,and believe in myself and others. I have laughed, cried, and been immeasurably
sustained by wonderful girlfriends – Stacey Quesada, Dianne Ahmann, Cornelia
Alden, Elizabeth Pike, Deb Casher, and others too numerous to list. So many people
and experiences have inspired and shaped my journey here in Boulder.
I thank my family for their unconditional support over the years, especiallyduring these last months. My precocious malamute, Kenai, has continually kept me
grounded and sane by reminding me of simple joys such as dawn walks in the
Canyon and long trail runs in the mountains. And finally, to Frank Witmer, my bestfriend and partner in life’s adventures, thank you for your unwavering support,
patience, love, and enthusiasm.

vi

CONTENTS

CHAPTERPAGE

1. INTRODUCTION

1

References for Chapter 1

8

2. JET-COOLED INFRARED SPECTROSCOPY IN SLITSUPERSONIC DISCHARGES: SYMMETRIC AND
ANTISYMMETRIC CH2 STRETCHING MODES OF
FLUOROMETHYHL (CH2F) RADICAL

10

2.1 Introduction

10

2.2 Experiment16

2.3 Results and Analysis

18

2.3.1 Symmetric CH2 stretch line center assignments

18

2.3.2 Antisymmetric CH2 stretch line center assignments

23

2.3.3 Fine and hyperfine structure and analysis

26

2.4 Discussion30

2.4.1 Boltzmann intensity analysis

31

2.4.2 Complete Basis Set (CBS) inversion potential for CH2F

36

2.4.3 Intensity-based vidence for a nonplanar equilibriumgeometry40

2.5 Summary and Conclusion

43

References for Chapter 2

46

vii

3. HIGH-RESOLUTION INFRARED STUDIES IN SLIT-JET
DISCHARGES: SYMMETRIC CH2 STRETCH EXCITATIONOF JET-COOLED CH2Cl RADICAL
49
3.1 Introduction49

3.2 Experiment54

3.3 Results and Analysis

56

3.3.1 Symmetric CH2 stretch line center assignments

56

3.3.2 Fine and hyperfine structure and analysis

64

3.4 Discussion

67

3.4.1 CCSD(T) Complete Basis Set (CBS) bending potential

67

3.4.2 Vibrational band intensities

71

3.5 Summary and Conclusion

79

References for Chapter 3

82

4. REACTIVE SCATTERING DYNAMICS IN ATOM +85

POLYATOM SYSTEMS: F + C2H6 Æ HF(v,J) + C2H5
4.1 Introduction

85

4.2 Experiment90

4.3 Results and Analysis

92

4.3.1 Data collection

92

4.3.2 Nascent column-integrated densities

94

4.3.3 High-resolution infrared dopplerimetry

97

viii

4.4 Discussion

101

4.4.1 Impulsive model (rotation/translation)

101

4.4.2 Density-to-flux transformation

104

4.4.3 Nascent HF (v,J) populations

105

4.4.4 Dynamic Franck-Condon impulsive model

110

4.5 Summary and Conclusion

113

References for Chapter 4

115

BIBLIOGRAPHY

119

APPENDIX

127

A. PROCESSING AND CONCATENATION PROGRAMS

128

A.1 Introduction

128

A.2 Pre-processing of data

129

A.3 Fringe counting and spreadsheet tabulations

131

A.4 Concatenation with Fortran programs

135

A.5 Concatenation with Origin scripts

136

B. SPECTRAL PREDICTION AND LEAST-SQUARES FITTINGPROGRAMS141

B.1 Predictions

141

B.2 Least-squares fitting programs

143

B.3 Gaussian convolutions of predictions using Origin
programs

144

C. LEAST-SQUARES FITTING PROGRAM FOR LINESHAPES

ix

147

TABLESCHAPTER 2
2.1

Observed fine/hyperfine free line centers and (obs-calc) values
from Watson asymmetric top Hamiltonian least-squares fit to
the symmetric stretch (ν1) band of CH2F.

2.2

22

Observed fine/hyperfine free line centers and (obs-calc) values
from Watson asymmetric top Hamiltonian least squares fit to theantisymmetric stretch (ν5) band of CH2F.

2.3

24

Simultaneous least-squares fit results for CH2 symmetric andantisymmetric stretch rotational constants (in cm-1), with 1σ26

uncertainties in parentheses.
2.4

Least-squares results for spin rotation fine-structure constants
obtained from simultaneous fit to symmetric and antisymmetricCH2 stretch line contours, with 1σ uncertainties in parentheses.
Ground state fine/hyperfine constants, as well as excited-state
hyperfine constants are held fixed at values from microwave
30

studies.{Endo, 1983}

CHAPTER 3
3.1

Transition frequencies and least-squares fit for the CH235Cl
symmetric stretch

3.2

61

Transition frequencies and least-squares fit for the CH237Cl
symmetric stretch

63

x

3.3

Least-squares fitting results for the symmetric CH2 stretch line
centers in CH235Cl and CH237Cl. The uncertainties in parenthesis
represent one standard deviation from the least-squares fit to the
Watson asymmetric top Hamiltonian.

3.4

64

Least-squares fitting results for the CH2 symmetric stretch finestructure constants. The uncertainties in parentheses represent
one standard deviation from the least-squares fit to the effective
Hamiltonian detailed in the text.

67

CHAPTER 4
4.1

Ab initio results for H-C-C bond angle θ, moment of inertia I,
and distance to center-of-mass λ at transition state geometry.

xi

112

FIGURES
CHAPTER 2
2.1

One-dimensional potential energy function, illustrating
inversion of CH2F over a symmetric barrier and orientation ofmolecular axes.

15

2.2

Schematic of the slit-jet discharge spectrometer apparatus.

17

2.3

Sample CH2F data in the CH2 symmetric stretch region,
comparing experimental (top) to simulated (bottom) spectra
predicted from the least-squares fits.

2.4

20

Sample Q branch CH2F data for CH2 antisymmetric stretch,comparing experimental (top) to simulated (bottom) spectra
predicted from the least-squares fits and illustrating fully
resolved fine structure.

2.5

23

Sample data and contour predictions for the 211←202 transition,systematically including fine and hyperfine terms in the
Hamiltonian. a) Asymmetric top only. b) Asymmetric top plus
spin rotation. c) Asymmetric top, spin rotation and hyperfine
29

terms. d) Experimental data.
2.6

Boltzmann plot for ground state rotational populations
monitored in symmetric and antisymmetric CH2 stretch modes,
verifying jet-cooled conditions [Trot = 20.8(8) K] in the slit
discharge and demonstrating a 1.8(2):1 ratio between the twobands.

33

xii

2.7

Cartoon illustrating the competition between “bond dipole” and“charge sloshing” contributions to symmetric and antisymmetricCH stretch intensities in CH2F.

2.8

35

One-dimensional potential energy curve (solid line) obtained
from CCSD(T) complete basis set (CBS) calculations (see text
for details), with zero-point energies in all remaining
coordinates included adiabatically (dashed line). Ground andexcited state eigenvalues (dotted line) and eigenfunctions (solidline) from a multidimensional Rush-Wiberg analysis are also
indicated, which predict the ν4=1←0 anharmonic bending
frequency to be 276 cm-1.

2.9

38

Calculated intensity ratios for symmetric and antisymmetric CH2
stretches in CH2F, highlighting a remarkably strong dependence
on inversion angle. Note the essentially constant ratio predicted
for CH2D. Though large amplitude averaging is clearly
important, the experimental intensity ratio of 1.8(2):1 for CH2F
is qualitatively consistent with the potential surface equilibrium
angle of θ = 29o.

43

CHAPTER 3
3.1

Sample spectral data (a) for selected P-branch transitions in theCH2 symmetric stretch band of CH2Cl, compared with acalculated spectrum from the full least squares fit.

xiii

58

3.2

Comparison between high resolution predictions (a-c) andexperiment (d) for a sample symmetric stretch rovibrationaltransition (313 ← 212) of CH2Cl. The simulations begin with apure asymmetric top transition (i.e. S = ICl = IH = 0) (a),successively including fine (b) and hyperfine (c) interaction
66

terms in the Hamiltonian.
3.3

One dimensional potential energy curve fromCCSD(T)/AVnZ/CBS calculations, adiabatically corrected forzero point energy in all remaining non-bend coordinates. Also
shown are ground and first excited vibrational state (v4)eigenfunctions and eigenenergies, calculated via methods ofRush and Wiberg and explicitly including G matrix element
dependence on the bend angle (see text for details).

3.4

70

Comparison of one dimensional potential energy curves fromCCSD(T)/AVnZ/CBS calculations, for CH3, CH2Cl, and CH2F.
Note the clear progression toward a non-planar equilibriumgeometry, due to increasing sp3 vs sp2 hybridization of the
carbon atom with increasing electronegativity of the halogen
substituent.

3.5

72

Boltzmann temperature analysis of the CH235Cl symmetricstretch band verifying rotational equilibration to Trot ≈ 15 K in74

the slit jet.

xiv

3.6

Predicted band intensities of CH2 symmetric and antisymmetricstretch vibrations for CH2Cl, CH2F, and CH2D as a function of
inversion angle.

3.7

75

Comparison of symmetric (Isym) and asymmetric (Iasym) stretch
band intensities for CH2D, CH2Br, CH2Cl, and CH2F. Note thedramatic minimum in Iasym for CH2Cl due to near cancellation ofbond-dipole and “charge-sloshing” contributions, whichbecomes nonzero for either greater (CH2F) or weaker (CH2Br)
electron withdrawing nature of the halogen substituent.

79

CHAPTER 4
4.1

Energetics for the F + C2H6 reaction. The sum of reaction
exothermicity (∆H≈37.8) and center-of-mass collision energy(Ecom≈3.2) yields 41(1) kcal/mol, allowing energetic access to
product states as high as HF(ν=3,J≈13).

4.2

93

Nascent column-integrated densities for formation of HF(ν,J) in
specific rovibrational states from single collision F + C2H6
reactive events at Ecom = 3.2(6) kcal/mol. Note the extraction ofabsolute densities that are feasible in direct IR laser studies due
to measurement of absolute absorbances.

4.3

Sample high resolution profiles of HF(ν,J) nascent productstates from the F + C2H6 reaction, indicating strongly competing
Doppler structures due to (i) stimulated absorption [HF(ν = 4 ←xv

963),R(0)], (ii) competition between stimulated emission andstimulated absorption [HF(ν = 3 ← 2),R(2)], and (iii) stimulated
emission [HF(ν = 2 ←1),R(1)]. Solid lines are least-squares fits
to Gaussian line-shape functions, revealing velocity-dependent
population-inversion effects dependent on upper- and lower98

state translational energies.
4.4

Recoil energy plots from high-resolution Dopplerimetry of
single HF(ν,J) quantum states. The data indicate a clear linear
dependence between (i) <EHF(trans)> ≈ 3<Ez> and (ii) Eavail =Etot – EHF(ν,J), i.e., the remaining energy available for both
HF/ethyl translation and vibration/rotation/translational
excitation of the ethyl radical. Note the excellent qualitative
agreement with simple impulsive model predictions.

4.5

100

Cartoon depiction of the rotation/translation impulsive model,
based purely on the conservation of linear and angularmomentum. The angle (θ) and moment arm (λ) for delivering
torque are calculated from CCSD(T) ab initio calculations of thetransition state (see Table 4.1).
102

4.6

Nascent product-state fluxes (in relative units) based on Monte
Carlo modeling of the density-to-flux transformation. Note themodest sensitivity of these fluxes to modeling of the differential
cross sections.

106

xvi

4.7

Comparison of current HF(ν = 2,J) nascent fluxes with previous
vibrational “arrested relaxation” studies of Bogan and Setser.
Agreement is generally quite good, though evidence for partial
rotational relaxation is present. However, the nascent vibrational
populations from these previous studies, summed over final
rotational states, are in excellent agreement with the current
109

collision-free results.

APPENDIX
A.1

A sample “scanlist” file.

132

xvii

CHAPTER 1

INTRODUCTION

The name "free radicals" may suggest a quirky group of political intellectuals,
a similarity to a common local bumper sticker advocating freedom for a particular
Himalayan country, or even a reference to a backcountry ski technique that is also
known to “free the mind.” But, in fact, free radicals comprise a group of chemical
species that is highly reactive, short-lived, and characterized by one or more unpaired
electrons. Often used interchangeably with the term “transient species,” the idea of
an intermediate, short-lived chemical species first surfaced as a way to explain
chemical reaction mechanisms. As such, their existences were at first only
hypothetical.1 It is now known that free radicals, in particular, last only for the lengthof time it takes for their constituent atoms to rearrange themselves with othermolecules into new molecules – a few millionths of a second – making it extremely
difficult to obtain a spectrum of such fleeting entities. To be fair, the classification of“free radicals” does also include several stable species such as the ground states of
O2, NO, and NO2. But, in general, the term is not associated with stability.2
The first recorded measurement of a radical species was in the emission
spectrum of a Bunsen flame by Wollaston in 1802 and then again by Swan in 1857.2
However, the more general study of radicals did not gain prominence until the adventof significant advances in the understanding of molecular spectroscopy in the earlypart of the 20th century.3-5 The chemical detection and, more importantly,
identification of molecular free radicals in the gas phase was first demonstrated in theclassic thermal decomposition experiments of lead tetramethyl by Paneth and
Hofeditz in 1929,6 validating the incorporation of radicals into the mechanism ofchemical reactions.7 Subsequently, their study gained particular prominence throughthe work of Nobel Prize winner Gerhard Herzberg,8 among others, with his
pioneering investigations of methyl and methylene radical – well known from organic
chemistry. His work, in turn, helped stimulate a resurgence of investigations into thechemical reactions of gases, most notably by Polanyi,9 and followed by numerous
others.
Today, radicals are recognized as important species in numerous chemical
processes in both the laboratory as well as industry. Reactions involving radicals
span the range from fundamental gas reactions to condensed phase processes andoccur in flames, propellant systems, atmospheric pollution, chemical vapor
deposition, and plasma processing.10,11 These chemical processes consist of acomplex sequence of interrelated reactions in which molecular fragments play crucial

2

roles, often significantly influencing product distribution and yield even when present
in only very small concentrations.
Along these lines, the central theme of the work in this thesis is that oftransient phenomena, and specifically polyatomic gas-phase radicals. In our studies,
they are studied both directly and indirectly using high-resolution infrared
spectroscopic methods. This thesis begins with the two most recent studies, utilizing
direct absorption high-resolution infrared spectroscopy of CH2F and CH2Cl radicals.
Following that, the final project presents a nice parallel to the historical resurgence ofgas-phase dynamics investigations after pioneering free radical studies. Thisparticular project follows the reaction of a well-characterized fluorine radical sourcewith ethane, and focuses on the detection of the non-radical product HF to makeinferences about the internal energy redistribution in the other product radical
fragment, ethyl.
The first project, described in Chapter 2, uses a combination of shot noise
limited direct absorption spectroscopy with long path length slit supersonicdischarges to obtain the first high resolution infrared spectra for jet cooled CH2F
radicals in the symmetric (ν1) and antisymmetric (ν5) CH2 stretching modes. This
work builds directly on Herzberg’s and others’ investigations of the methyl radical.1216

In ESR experiments by Fessenden and Schuler, methyl radical was determined tohave an effectively planar structure, at least vibrationally averaged over the groundstate wave function.17 However, other spectroscopic efforts demonstrated that the
fully-fluorinated methyl radical, i.e. CF3, has a pyramidal structure in its groundelectronic state.14,18-23 Stated simply, such changes in equilibrium geometry reflect a3competition between sp2 (planar) and sp3 (pyramidal) hybridization of the C atom as afunction of electron-donating (or withdrawing) group substitution.
As such, our experiments with CH2F probe the effect of mono-halogen
substitution in the methyl radical. Spectral assignment has yielded refined lower andupper state rotational constants, as well as fine-structure parameters, from leastsquares fits to the sub-Doppler line shapes for individual transitions. Indeed, therotational constants provide indications of large amplitude vibrational averaging overa low barrier double minimum inversion bending potential. This is further confirmedby high level CCSD(T) calculations, extrapolated to the complete basis set (CBS)limit, which predict a non-planar equilibrium structure (θ ≈ 29o, where θ is defined as
180 o minus the angle between the C-X bond and the CH2 plane) ) with a 132 cm-1
barrier to planarity, and a vibrational bend frequency (νbend ≈ 276 cm-1) in excellent
agreement with previous microwave studies by Hirota and coworkers (νbend = 300(20)cm-1).24-26 The nearly 2:1 ratio of absorption intensities for the symmetric vs.
antisymmetric bands is in good agreement with DFT calculations, but in 6-foldcontrast with simple local mode CH2 bond dipole predictions of 1:3. This arises froma surprisingly strong dependence of the symmetric stretch intensity on the inversion
bend angle and provides further experimental support for a non-planar equilibrium
structure.
The anomalous ratio between the symmetric and antisymmetric stretch
intensities in CH2F provides motivation for the next project, described in Chapter 3.
In this second study, the effect of the halogen atom identity is probed, moving fromfluorine-substituted methyl radical to chlorine-substituted methyl radical, and first4

high-resolution infrared spectra are presented for jet-cooled CH235Cl and CH237Cl
radicals in the symmetric (ν1) CH2 stretching mode. A detailed spectral assignment
yields refined lower- and upper- state rotational constants, as well as fine-structure
spin rotation parameters from least-squares fits to the sub-Doppler line shapes forindividual transitions. The rotational constants are consistent with a nearly planar
structure, but do not exclude substantial large-amplitude-bending motion over a small
barrier to planarity accessible with zero-point excitation. High level coupled cluster(singles/doubles/triples) calculations, extrapolated to the complete basis set (CBS)limit, predict a slightly nonplanar equilibrium structure (θ ~11 degrees), with a 1-D
vibrationally adiabatic treatment of the bend coordinate yielding a v =1←0anharmonic frequency (393 cm-1) in excellent agreement with matrix studies (νbend ~400 cm-1). The antisymmetric CH2 stretch vibration is not observed despite highsensitivity detection (S/N > 20:1) in the symmetric stretch band. This is consistent
with density functional theory (DFT) intensity calculations indicating a > 35-foldsmaller antisymmetric stretch transition moment for CH2Cl, and yet contrasts
dramatically with high-resolution infrared studies of CH2F radical, for which both
symmetric and antisymmetric CH2 stretches are observed in a nearly 2:1 intensity
ratio. A simple physical analysis is presented based on a competition between bonddipole and “charge sloshing” contributions to the transition moment, which nicely
explains the trends in CH2X symmetric vs asymmetric stretch intensities as a functionof electron withdrawing group (X=D, Br, Cl, F).
Although conducted earlier in chronology than the first two projects, the final
project, described in Chapter 4, is a natural extension of the first two projects. The

5

investigation uses a well-characterized fluorine radical source to react with ethane
rather than as the object of the study itself. The non-radical HF product is thendirectly detected through similar high-resolution infrared absorption methods andused to make inferences about the internal energy redistribution of the other radical
fragment, ethyl. State-to-state scattering dynamics of F + C2H6 → HF(v,J) + C2H5
have been investigated at Ecom = 3.2(6) kcal/mol under single collision conditions, via
detection of nascent rovibrationally resolved HF(v,J) product states with highresolution infrared laser absorption methods. State-resolved Doppler absorption
profiles are recorded for multiple HF(v,J) transitions originating in the v=0, 1, 2, 3
manifold, analyzed to yield absolute column-integrated densities via known HF
transition moments, and converted into nascent probabilities via density-to-flux
analysis.
The spectral resolution of the probe laser also permits Doppler study oftranslational energy release into quantum-state-resolved HF fragments, which reveals
a remarkable linear correlation between (i) HF(v,J) translational recoil and (ii) theremaining energy available, Eavail = Etot – EHF(v,J). The dynamics are interpreted in thecontext of a simple impulsive model based on conservation of linear/angularmomentum that yields predictions in good agreement with experiment. Deviations
from the model indicate only minor excitation of ethyl vibrations, in contrast with apicture of extensive intramolecular vibrational energy flow but consistent withFranck-Condon excitation of the methylene CH2 bending mode. The results suggest a
relatively simple dynamical picture for exothermic atom + polyatomic scattering, i.e.,that of early barrier dynamics in atom + diatom systems but modified by impulsive

6

recoil coupling at the transition state between translational/rotational degrees of
freedom.

7

References for Chapter 1
1

E. Hirota, Chem. Rev. 92, 141 (1992).

2

J. C. Whitehead, Rep. Prog. Phys. 59, 993 (1996).

3

R. S. Mulliken, Phys. Rev. 30, 785 (1927).

4

W. E. Pretty, Proc. Phys. Soc. 40, 71 (1928).

5

F. Hund, 36, 657 (1926).

6

F. Paneth and W. Hofeditz, Ber. Chem. Ges. 62, 1335 (1929).

7

F. O. Rice, J. Am. Chem. Soc. 53, 1959 (1931).

8

G. Herzberg, The Spectra and Structure of Simple Free Radicals. (Cornell
University Press, Ithaca, NY, 1971).

9J. C. Polanyi, Accts Chem. Rsrch. 5, 161 (1972).

10

M. E. Jacox, J. Phys. Chem. Ref. Data 32, 1 (2003).

11

J. G. Anderson, Ann. Rev. Phys. Chem. 38, 489 (1987).

12

G. Herzberg, Molecular Spectra and Molecular Structure III. Electronic
Spectra and Electronic Structure of Polyatomic Molecules. (Van Nostrand,
New York, 1966).

13

S. Davis, Ph.D. Thesis, University of Colorado (1999).

14

K. Morokuma, L. Pedersen, and M. Karplus, J. Chem. Phys. 48, 4801 (1968).

15

D. M. Schrader and M. Karplus, J. Chem. Phys. 40, 1593 (1964).

16

C. Yamada, E. Hirota, and K. Kawaguchi, J. Chem. Phys. 75, 5256 (1981).

17

R. W. Fessenden and R. H. Schuler, J. Chem. Phys. 39, 2147 (1963).

18

G. A. Carlson and G. C. Pimentel, J. Chem. Phys. 44, 4053 (1966).

19

F. Bernardi, W. Cherry, S. Shaik, and N. D. Epiotis, J. Am. Chem. Soc. 100,
1352 (1978).

20

Y. Endo, C. Yamada, S. Saito, and E. Hirota, J. Chem. Phys. 77, 3376 (1982).

21

R. W. Fessenden and R. H. Schuler, J. Chem. Phys. 43, 2704 (1965).

8

22J. Nolte and H. G. Wagner, Ber. Bunsenges. Phys. Chem. 101, 1421 (1997).

23

C. Yamada and E. Hirota, J. Chem. Phys. 78, 1703 (1983).

24

J. W. Hudgens, C. S. Dulcey, G. R. Long, and D. J. Bogan, J. Chem. Phys. 87,4546 (1987).

25

Y. Endo, C. Hamada, S. Saito, and E. Hirota, J. Chem. Phys. 79, 1605 (1983).

26

S. V. Levchenko and A. I. Krylov, J. Phys. Chem. A 106, 5169 (2002).

27

L. Andrews and D. W. Smith, J. Chem. Phys. 53, 2956 (1970).

28

Y. Endo, S. Saito, and E. Hirota, Can. J. Phys. 62, 1347 (1984).

29

M. E. Jacox and D. E. Milligan, J. Chem. Phys. 53, 2688 (1970).

30

J. P. Michaut and J. Roncin, Chem. Phys. Lett. 12, 95 (1971).

9

CHAPTER 2

JET-COOLED INFRARED SPECTROSCOPY IN
SLIT SUPERSONIC DISCHARGES:SYMMETRIC AND ANTISYMMETRIC CH2 STRETCHING MODES OF
FLUOROMETHYHL (CH2F) RADICAL

2.1 Introduction
Free radicals, with their characteristic unpaired electron spin and resulting
enhanced reactivity, play essential roles as transient intermediates in a wide range ofchemical reactions. These reactions encompass both fundamental gas and condensed
phase processes in the realms of atmospheric chemistry and pollution, molecularbiology, combustion, propellant systems, and chemical vapor deposition.1,2 Indeed,radical intermediates were first proposed as hypothetical species to explain reaction
mechanisms, spurring a half-century of development and refinement of numerous
sophisticated experimental methods to confirm their transient existence and precisely
measure them.3 Spectroscopic probes of the vibrational, rotational, and even spin

angular momentum degrees of freedom provide a particularly detailed view into themechanical and electronic structure of these ubiquitous, albeit elusive, species.
One of the early developments along these lines was flash photolysis,4 whichin combination with electronic spectroscopy, enabled the production of radical
species in sufficient concentrations for spectral observation and lifetime
determination.5 Subsequent introduction of matrix isolation techniques6 allowed thestudy of gaseous radicals deposited on a cold surface with a buffer gas or generated
directly in an inert gas matrix. Such methods for trapped and low temperature radical
species have proven an exceptionally productive source for probing with visible,
infrared, and electron spin resonance (ESR) or electronic paramagnetic resonance(EPR) spectroscopy.7
With enhancements in detection sensitivity, infrared spectroscopy of gas
phase radical species became possible, with further high-resolution extension of
microwave methods into the millimeter- and submillimeter-wave regions.3 The use of
fixed-frequency lasers also increased sensitivity and was combined with electric-fieldor magnetic-field tuning of molecular transitions in laser magnetic resonance(LMR).8,9 Spectral ranges were increased with the development of tunable infrared
sources, such as diode and color-center lasers, as well as nonlinear difference
frequency generation methods.3 In addition to experimental efforts, recently improved
computational strategies have also informed the interaction between gas-phase andmatrix isolation spectroscopists. Specifically, ab initio and density functional
methods have achieved better estimations of structures and ground-state vibrationalfrequencies of small radical molecules, as surveyed by Byrd and co-workers in11

2001.10 Still, significant discrepancies exist between the most reliable computational
methods and existing experimental data.
Of particular interest in the current study is the fluoromethyl radical, CH2F.
As a benchmark intermediate in the photodecomposition and oxidation of partiallyhydrogenated chlorofluorocarbons, it is one of a number of important sources of
halogen atoms in the atmosphere.11,12 Photodissociation of the fluoromethyl radical
itself, as well as similar halomethyl radicals, may also compete with
nonphotochemical decomposition pathways such as bimolecular reactions with otherspecies.13 Halomethyl radicals are products of radical attack (reaction with H or OH)
on halomethanes, which are part of a family of halocarbons widely used as fire
suppressants, solvents, and refrigerants.14,15 The unreactive parent halocarbons canaccumulate in the urban atmosphere and may be relevant to atmospheric ozone
depletion and high global warming potentials.16 Models of incomplete combustion
processes, such as flame inhibition and waste incineration, or atmospheric chemistry
involving halocarbons require accurate values of the thermodynamics and kinetics
parameters of these molecules and their decomposition products.14,17-20
Experimental and theoretical investigations of the fluoromethyl radical havenaturally emerged from the study of methyl radical and its family of halogensubstituted derivatives. Methyl radical was first identified by Fessenden and
Schuler21 using ESR and determined to have an effectively planar structure, at least
vibrationally averaged over the ground-state wave function.22 However, otherspectroscopic efforts demonstrated that the fully fluorinated methyl radical, CF3, hasa pyramidal structure in its ground electronic state.23-25 Stated simply, such changes

12in equilibrium geometry reflect a competition between sp2 (planar) and sp3(pyrimidal) hybridization of the C atom as a function of electron-donating (orwithdrawing) group substitution. Indeed, this competition is clearly present even in
the nominally “planar” (sp2-hybridized) methyl radical. The sp3 hybridization adds ina small double minimum contribution, which when summed with the more harmonicsp2 contribution centered around planarity, results in an unusually flat inversion
potential and therefore an anomalous progression of levels shifting strongly to thehigher frequencies (i.e., negatively anharmonic) with increasing vibrational quantum
number.26 In fact, it is still somewhat controversial whether the equilibrium geometryof CH3 is actually planar,2 though the size of any putative barrier must be quite small
with respect to the zero point energy. On the other hand, the stronger propensity forsp3 hybridization in CF3 results in a clear double minimum potential which, in
combination with the much larger reduced mass, leads to significant localization of
the wave function in a nonplanar geometry.
This qualitative difference in potential surface topology and vibrationallyaveraged geometry for “planar” CH3 versus “pyramidal” CF3 radical naturally raises
interesting questions about the structure of partially substituted species such as CH2F
radical, which serves as a main focus of the current study. The history of the detection
and analysis of the monofluoromethyl (CH2F) radical is summarized nicely by
Nolte.27 Briefly, CH2F was first detected in krypton and xenon matrices, again by
Fessenden and Schuler.24 Shortly thereafter, Jacox and others28,29 identified the C-F
stretching band in an argon matrix, and Raymond described the CH2 scissors mode.28
Mucha and co-workers made the first gas-phase detection of CH2F radicals using far-13

infrared laser magnetic resonance (FIR-LMR) spectroscopy and also hypothesized anear-prolate ground vibronic state.30 Microwave spectroscopy studies identified Atype transitions out of the ground vibronic state as well as satellite transitions
assigned as arising from a thermally excited inversion vibrational mode (ν4) ≈300(30) cm-1.31,32 The ground state hyperfine structure was consistent with B1electronic symmetry, implying odd parity with respect to reflection through a planar
geometry (as expected for a p-type unpaired radical center on the C atom). Hudgens
and co-workers followed these efforts with the REMPI measurements of the out-ofplane vibrational frequency for ground-state CH2F and CD2F radicals andrecommended a value of 260(30) cm-1 for CH2F and 170(30) cm-1 for CD2F.33
Infrared diode laser spectra of CH2F were also obtained by the Hirota group by
exciting the CF-stretching mode (v3) and yielding A-type rovibrational transitions
with resolved spin-rotation fine structure.31,32 Only ∆Ka = 0 transitions could beobserved in these two studies because of dipole and dipole-derivative transition
moments along the C-F bond. This precluded least-squares determination of theground state A rotational constant, though sufficient asymmetric top JKa, Kc lines wereobserved to provide good first estimates for structural purposes. No C-type transitions
were reported in either study, consistent with a planar-averaged structure withvanishing dipole moment along the C-axis. These observations were all interpreted tobe consistent with a vibrationally averaged planar CH2F geometry, though thepresence of a small barrier at the planar configuration could not be ruled out.
Interestingly, although spectroscopic experiments to date yield data consistent
with planar geometries, ab initio theoretical efforts clearly predict a nonplanar

14equilibrium structure.26 Levchenko and Krylov reconcile these differences as theresult of zero-point vibrational averaging over a shallow double minimum potential,
which would also result in a large negative anharmonicity in the out-of-planevibrational mode.26 Additional information can be obtained in the CH2 stretch
vibrational spectral region, which represents the specific focus of this chapter. Here,transition dipole moment derivatives yield oscillator strength for both A-type(symmetric CH2 stretch) and B-type (antisymmetric CH2 stretch) bands (see Figure2.1), which provides opportunity for direct spectroscopic determination of all threeground-state rotational constants, as well as fine structure spectral splittings resulting
from the coupling of unpaired electron spin angular momentum and the end-over-end
tumbling angular momenta.

Figure 2.1 One-dimensional potential energy function, illustrating inversion of CH2F
over a symmetric barrier and orientation of molecular axes.

15

In this study, we utilize high-resolution infrared absorption spectroscopy
coupled with slit-jet expansion methods to provide the first vibrational and rotational
structure of both the symmetric (ν1) and antisymmetric (ν5) CH2-stretchingvibrational modes of the CH2F radical. The organization of this chapter is as follows.
Section 2.2 summarizes relevant experimental details of the slit-jet-cooled CH2F
discharge generation and concentration modulation laser spectroscopy. In Section 2.3,
least-squares fittings of the spectra to a Watson asymmetric top Hamiltonian arepresented which, under sub-Doppler conditions, also yields fully resolved fine andpartially resolved hyperfine structure. Section 2.4 tackles a number of topics
comprising a comparison of density-functional theory (DFT) calculations withexperimental determinations of vibrational band intensities, the development of aone-dimensional (1D) CBS potential energy curve and associated wave functions, andthe extraction of structural information. Section 2.5 summarizes and concludes thechapter.

2.2 Experiment
The slit-discharge laser spectrometer techniques have been discussed inprevious papers;34-37 the following description contains a brief summary relevant tothe current study. Figure 2.2 shows a simplified diagram of the experimental
apparatus. CH2F radicals are produced by adiabatically expanding an optimal mixtureof 0.5% CH2F2 in 70%/30% neon/helium buffer gas through a pulsed slit-jet (19 Hz,
500 µs pulse duration). The radicals are formed by electron dissociative attachmentfrom neutral CH2F2 precursor by a 50 kHz square-wave-modulated discharge (500 V,

16

0.8 A) localized upstream of the expansion orifice. Radicals are probed by directabsorption of transmitted infrared laser light (tunable from 2500-5000 cm-1) with a
combination of time-domain gating and 50 kHz lock-in detection to eliminate lowfrequency amplitude noise. At 600 Torr backing pressures and 4 cm x 300 µm slit
orifice dimensions, one routinely obtains as many as 1013-1014 radicals/cm3 in thelaser probe region ≈1 cm downstream.

Figure 2.2 Schematic of the slit-jet discharge spectrometer apparatus.

The laser probe is produced via nonlinear difference-frequency generation of
fixed-frequency single-mode argon ion laser light (514.5 nm) and tunable singlemode ring-dye laser light (R6G) in a temperature-controlled and heated periodicallypoled LiNbO3 (PPLN) crystal.38 The resulting infrared light frequency is stabilized toa few MHz by servo-loop locking of the argon ion laser to a confocal Fabry-Perot
etalon, which, in turn, is locked onto a polarization-stabilized He-Ne laser. Relative17

frequencies are determined to 0.0001 cm-1 precision by monitoring dye lasertransmission fringes on the same Fabry Perot etalon, with absolute frequencies
determined by referencing to the R(0) methane absorption line39 at 3028.7528 cm-1.
The infrared light is split into reference and signal beams of roughly the same
intensity, and the signal beam is multipassed in a Herriot cell 16 times through thelong axis of the slit-jet expansion region. Both the exiting signal beam and thereference beam are focused onto matched InSb photovoltaic detectors. Detection
sensitivities of 5 x 10-7/Hz1/2 are achieved through elimination of common-mode
infrared noise by subtracting signal and reference beams under servo-loop control.
Peak absorbances in the CH2F spectra observed under these expansion conditions areon the order of 0.3%, and peak signal-to-noise ratios are approximately 100:1.

2.3 Results and Analysis
2.3.1 Symmetric CH2 stretch line center assignments
The choice of CH2 stretch regions for high-resolution investigation requires
some theoretical input. The spectral search area is initially guided by DFT
calculations [B3LYP/G-311**6(3df,3pd)], where the harmonic predictions are scaledby vexp/vpredict = 0.9637. This factor has been empirically benchmarked from a leastsquares fit to CH and OH stretch band origins for ≈10 jet-cooled radical andmolecular ion species.40 Such methods predict symmetric and antisymmetric stretch
band centers to be approximately 3044 cm-1 and 3209 cm-1, respectively, with anestimated uncertainty of 10 cm-1. Additional DFT calculations [B3LYP/AUG-ccpVTZ] also predict the ratio of symmetric to antisymetric band intensities to be18

Isym/Iantisym = 2.1. For later discussion, it is worth noting that this ratio differs
substantially from the usual CH2 bond dipole expectations, which predict a 6-foldsmaller value of Isym/Iantisym ≈ 1/3. Based on these surprising intensity predictions, asearch for the stronger symmetric stretch was attempted first to optimize gas mixture
concentration before tackling the antisymmetric stretch.
Trial scans for the symmetric stretch quickly revealed strong progressions of
jet-cooled CH2F absorption lines centered around the 3045 cm-1 region, in close
agreement with the DFT-scaled predictions above. After optimizing gas mixture andscanning conditions, continuous single mode spectra ranging from 3027 cm-1 to 3071
cm-1 were then pursued, yielding extensive R and P branches with a much weaker Q
structure near the band origin. Sample data in the R-branch region are presented in
Figure 2.3, illustrating a clear A-type band progression of Ka=0←0, 1←1, and 2←2transitions spaced by B + C ≈ 1.96 cm-1. Note the roughly 3:1 intensity ratio between
the Ka=0 and Ka=1 lines; this ratio is consistent with ortho/para nuclear spin statisticalpredictions for the equivalent H atoms (i.e., IH(eff) = 0,1) and provides further
confirmation of the ground state B1 electronic symmetry of CH2F. There is also aclear sequential shift to lower frequency for Ka=0←0, 1←1, and 2←2 transitions,which indicates a decrease in the A constant with vibrational excitation. At higher
resolution, each line is split into fully resolved fine and partially resolved hyperfine
structure components, as will be discussed later.
After extraction of a vibrational band origin estimate from the strongest
transitions confirmed by approximate ground-state combination differences, theassignment proceeds rapidly by comparing experimental data with rigid asymmetric19

Figure 2.3 Sample CH2F data in the CH2 symmetric stretch region, comparing
experimental (top) to simulated (bottom) spectra predicted from the least-squares fits.

top spectra predicted from the microwave constants. However, attempts to further
confirm these assignments with more precise four-line (and ground state two-line)
combination differences are complicated by the extensive fine and hyperfine structure
superimposed on each NKa,Kc ← NKa,Kc transition. This structure results in
shifts/splittings up to a few GHz; i.e., greatly in excess of our experimental precision20

(< 10 MHz) and yet quite small on the ≈1000 GHz scale of the infrared spectrum. We
therefore developed a more sophisticated simulation program which includes thestandard asymmetric top Hamiltonian, plus all fine (spin rotation) and hyperfine(Fermi contact, dipole-dipole and electric quadrupole) coupling terms utilized in the
microwave analysis for a spin 1/2 electron and two nuclei (i.e. IH(eff) and IF) with
nonzero spin. This complete effective Hamiltonian is used for the final least-squares
analysis of the line profiles, as will be discussed in more detail later in this section.
For the moment, however, we focus exclusively on the rovibrational
information by predicting fine/hyperfine line intensities for a given NKa,Kc ← NKa,Kc
transition (estimated from Hirota’s ground-state constants) and convoluted over a≈ 60 MHz sub-Doppler linewidth in the slit jet. By simply shifting these predictions
with respect to the high-resolution data, the pure asymmetric top (i.e., fine/hyperfinefree) transition frequencies can be determined to an estimated precision of < 0.0001
cm-1; i.e., less than our experimental uncertainty. In this fashion, 40 fine/hyperfinefree line centers (see Table 2.1) have been identified in the symmetric stretch,comprising transitions from states up to N=8 and 6 in the R and P branch,respectively. By way of initial analysis, these fine/hyperfine-free transition
frequencies are least-squares fit to a Watson asymmetric top Hamiltonian for the
ground and symmetric stretch-excited state.41 However, the results reported in Table
2.3 reflect a more complete contour fit to both symmetric and antisymmetric stretch
bands, as described below.

21

Table 2.1: Observed fine/hyperfine free line centers and (obs-calc) values from
Watson asymmetric top Hamiltonian least-squares fit to the symmetric stretch (ν1)
band of CH2F.
J’

Ka ’

Kc’

J”

Ka ”

Kc”

Obs. (cm-1)

Obs. – calc. (10-4 cm-1)

9
8
8
7
7
6
6
6
5
5
5
5
5
4
4
4
4
4
3
3
3
2
2
2
1
1
2
0
1
1
1
2
2
2
3
3
4
4
5
5

0
0
1
0
1
1
0
1
1
0
1
2
2
1
0
1
2
2
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0

9
8
8
7
7
5
6
6
4
5
5
3
4
3
4
4
2
3
2
3
3
2
1
2
1
1
2
0
1
0
1
2
2
1
3
3
4
4
5
5

8
7
7
6
6
5
5
5
4
4
4
4
4
3
3
3
3
3
2
2
2
1
1
1
0
1
2
1
2
2
2
3
3
3
4
4
5
5
6
6

0
0
1
0
1
1
0
1
1
0
1
2
2
1
0
1
2
2
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0

8
7
7
6
6
4
5
5
3
4
4
2
3
2
3
3
1
2
1
2
2
1
0
1
0
0
1
1
2
1
2
3
3
2
4
4
5
5
6
6

3061.71113
3059.82793
3059.30971
3057.93083
3057.44685
3056.25346
3056.02127
3055.57726
3054.26141
3054.10114
3053.70186
3053.59370
3053.56964
3052.26520
3052.17164
3051.82056
3051.64177
3051.63043
3050.26515
3050.23363
3049.93449
3048.28887
3048.26293
3048.04361
3046.33860
3044.13825
3043.91543
3042.42706
3040.46804
3040.22320
3040.43635
3038.52536
3038.50852
3038.20898
3036.61337
3036.54900
3034.69938
3034.59081
3032.78429
3032.63456

-1.4
3.4
-9.9
3.6
-4.8
0.2
1.2
-2.4
-1.3
2.2
-1.7
3.9
-0.1
-2.2
4.4
-2.6
-3.7
0.0
-4.0
2.7
0.8
1.1
5.9
4.7
-1.1
17.
8.9
-2.3
-2.5
-4.6
-7.6
-12.
-5.7
-7.5
-1.1
-1.9
16.
-2.
46.
-6.1

22

2.3.2 Antisymmetric CH2 stretch line center assignments
The results from least-squares fits of the symmetric stretch line centersgenerate an improved rotational prediction for the B-type antisymmetric stretch band
which, from DFT calculations, should have an origin near 3209 cm-1. Single modescans have therefore been performed from 3167 cm-1 to 3234 cm-1, revealing a clear
R, P branch progression but also a strong Q branch feature characteristic of a B-typevibrational transition (see Figure 2.4 for an enlarged view of partially resolved
fine/hyperfine structure in the Q branch).

Figure 2.4 Sample Q branch CH2F data for CH2 antisymmetric stretch, comparing
experimental (top) to simulated (bottom) spectra predicted from the least-squares fits
and illustrating fully resolved fine structure.

23

Table 2.2 Observed fine/hyperfine free line centers and (obs-calc) values from
Watson asymmetric top Hamiltonian least squares fit to the antisymmetric stretch (ν5)
band of CH2F.
J’

Ka ’

Kc’

J”

Ka ”

Kc”

Obs. (cm-1)

Obs. – calc. (10-4 cm-1)

3
2
1
0
4
3
2
1
5
3
3
4
2
1
1
2
3
5
6
1
2
4
3
2
2
3
3

0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2

3
2
1
0
4
3
2
1
5
3
3
4
2
1
0
1
2
4
5
1
2
4
1
1
0
2
1

4
3
2
1
4
3
2
1
6
2
4
3
3
2
1
2
3
5
6
0
1
3
3
1
1
2
2

1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1

4
3
2
1
3
2
1
0
6
2
4
3
3
2
1
2
3
5
6
0
1
3
2
0
1
1
2

3168.68289
3170.43244
3172.23208
3174.08329
3175.42105
3175.65076
3175.82016
3175.93124
3179.09192
3182.00361
3183.44996
3184.10389
3185.56290
3187.62633
3191.64644
3191.75168
3191.9111
3192.40397
3192.74437
3193.49639
3195.34283
3198.87162
3206.60779
3210.78900
3210.89776
3212.63329
3212.95985

1.5
3.6
3.4
1.7
-1.7
-0.7
1.4
-2.3
2.1
-0.6
-0.5
-6.4
1.5
1.6
-2.9
-0.1
-0.3
0.6
1.0
-2.0
-1.0
-0.1
4.4
-3.2
2.5
2.8
-3.9

In contrast to the symmetric stretch, the antisymmetric stretch spectrum shows
very little congestion due to precursor species. A similar procedure of 2-line
combination differences with fine/hyperfine structure removed is then used for
assigning and verifying the transitions, as described for the symmetric stretch band. In
total, 27 transitions (see Table 2.2) are identified, with rotational levels sampling up

24

to N=6. Most notably, the peak antisymmetric stretch absorption strengths are foundto be nearly two times less intense than those of the symmetric stretch, despite
expectations of a threefold increase from bond dipole predictions discussed further in
Section 2.4. As a result, transitions from both nuclear spin ground states (i.e. Ka=0
and 1) are readily identified (see Figure 2.4), but no transitions out of any thermally
excited Ka states (Ka>1) are observed.
The analysis proceeds with both the symmetric and antisymmetric band line
centers simultaneously least-squares fit with a common ground state, yielding a
residual standard deviation of 15.6 MHz. This procedure allows further least-squares
adjustment of rotational constants (see Table 2.3) and identification of symmetric andantisymmetric stretch band centers of 3044.3850(2) cm-1 and 3183.8560(2) cm-1,
respectively. Of particular importance to this study is that the additional inclusion ofantisymmetric B-type stretch transitions (∆Ka = +/-1, ∆Kc = +/-1) allows
determination of all three rotational constants for both the ground state as well as both
symmetric and antisymmetric vibrationally excited states. This is particularly relevant
to a discussion of CH2F radical vibrationally averaged versus equilibrium geometry,based on previous difficulties in least-squares fitting the ground state A rotational
constant from microwave/near IR A-type bands. Unconstrained asymmetric rotor fits
to the combined near IR data yield ground-state B, C and centrifugal distortion
constants in agreement with the microwave studies to within experimental
uncertainty. However, the combined fits now yield independent information on the
ground state A constant, as well as rotational and partial centrifugal distortion
constants for both symmetric and antisymmetric stretch excited manifolds. The

25

results are summarized in Table 2.3, where the quoted values reflect fits to the fullline contours, as described below.

Table 2.3: Simultaneous least-squares fit results for CH2 symmetric andantisymmetric stretch rotational constants (in cm-1), with 1σ uncertainties inparentheses.
Constants (cm-1)

Ground state

Symmetric Stretch

AB
C

8.8488(3)1.03228(3)0.92492(2)8.78098(3)1.03159(3)0.92264(3)8.7179(2)1.03152(2)0.92405(3)∆N (10-5)∆NK (10-5)∆K (10-5)

0.26a
3.78a
64.79 a0.27(2)5.0(8)
78(6)0.27(25.0(8)
78(6)3044.3650(2)3183.8560(2)ν0aAntisymmetricStretchParameters previously determined by Hirota et al.

2.3.3 Fine and hyperfine structure and analysis
As is clear from the Q branch transitions in Figure 2.4, the experimental
spectra show evidence of fine and hyperfine splittings resulting from different
couplings of molecular rotation, electron spin, and nuclear spin angular momentum.
To reproduce this structure and also to identify line centers for the least-squares fit
described above, considerable effort was invested into developing a program tosimulate and simultaneously least-squares fit actual line shapes of both the symmetricand antisymmetric bands. This program works for doublet asymmetric top radicals(S=1/2) with two different nonzero nuclear spin atoms [IF = 1/2 and IH = 0(para) and26

1(ortho)], as well as includes spin rotation, Fermi contact, and dipole-dipole andelectric quadrupole interactions. Exhaustive benchmark tests have been performed,
including numerical comparisons with similar program code developed by the Browngroup at Oxford, achieving agreement out to machine precision. For further program
development in other laboratories, sample eigenvalue output for a given set of
effective Hamiltonian parameters will be made available upon request.
Following the microwave analysis of Hirota, the effective Hamiltonian used
for simulation and fitting of the current near IR fine and hyperfine structure is givenby
H = H ROT + H SR + H F + H DD + H eQ ,(2.1)

where H ROT is the traditional Watson Hamiltonian for an asymmetric rotor and H SR ,H F , H DD , and H eQ represent the fine (electron spin) and hyperfine (nuclear spin)
coupling terms. The largest splittings in the CH2F rovibrational spectra are dominatedby rotational coupling between electron spin S and asymmetric top molecular rotation
N. The spin rotation fine structure coupling interaction, H SR , is expressed as

H SR = (1 / 2) ∑ ε αβ ( N α S β + S β N α ) , where εαβ is the spin rotation tensor and α, β
α ,βare labels for the a, b, c principal axes. For a species of orthorhombic symmetry (suchas CH2F), only the diagonal matrix elements (εaa, εbb,, εcc,) are nonzero and need to beconsidered. The dominant hyperfine terms are the isotropic Fermi contact
interaction, H F = a F I ⋅ S , the dipole-dipole interaction, H DD = S ⋅ Tdd ⋅ I , and thenuclear electric quadrupole interaction, H eQ = S ⋅ TeQ ⋅ I , where Tdd and TeQ eachdenote a second-rank traceless tensor with five independent components.

27

The total Hamiltonian is expanded in a Hund’s case(b)βJ basis set,
|N,K,S,J,I1,F1,I2,F,MF>, where the angular momenta are coupled via J = N + S, F1 = J+ I1, F = F1 + I2. I1 and I2 represent the F and H atom nuclear spins, respectively,
where I2=0 (or 1) for para (or ortho) coupling of the two identical H atoms. The
explicit matrix element expressions are obtained from Hirota,42 exploiting theextended expressions for hyperfine interactions caused by more than one nucleus. The
Hamiltonian matrices for a given upper and lower NKaKc state are diagonalized togenerate eigenvalues, with care taken to ensure the basis set includes all possible F
values to completely converge the fine and hyperfine patterns. Electric dipole
transition strengths between all allowed transitions (∆F = 0, +/-1) are then calculated
from eigenvector sums over Stark matrix elements, convolved over a Doppler width(assumed constant for all transitions), and compared with experimentally observed
line profiles via a least-squares fitting routine.
By way of example, sample fine and hyperfine data for the 211←202 transition(IH=1, ortho) in the asymmetric stretch band of CH2F are shown sequentially in
Figure 2.5. The top panel (a) illustrates the single ≈ 60 MHz Doppler line profile
anticipated in the absence of any electron or nuclear spin interactions, with the resultsin panels below illustrating the additional splittings and broadenings that result fromsuccessive inclusion of fine structure (b) and hyperfine structure (c). Finally, theobserved experimental line profile for this transition is given in panel (d), which is ingood agreement with the least-squares fitted fine/hyperfine predictions. It isparticularly noteworthy that both fine and hyperfine structure contribute to wellresolvable peaks in the predicted spectrum, although much of the structure is below

28

Figure 2.5 Sample data and contour predictions for the 211←202 transition,systematically including fine and hyperfine terms in the Hamiltonian. a) Asymmetric
top only. b) Asymmetric top plus spin rotation. c) Asymmetric top, spin rotation andhyperfine terms. d) Experimental data.

29

the sub-Doppler resolution limit. Analysis of fine/hyperfine information is more
typically confined to studies in the millimeter or microwave regime; experimental
access to this information in the near infrared is the result of sub-Doppler resolution
due to transverse velocity collimation in the slit jet expansion. To minimize numberof parameters in the least-squares fits, the ground state is fixed at previously
determined restrict the fit to the spin-rotation constants (εaa, εbb, εcc) in the excited
symmetric and antisymmetric stretch states, keeping the rotational, fine and hyperfine
parameters fixed at ground state values.31 A summary of the fitted fine structure
results is summarized in Table 2.4, which indicates modest but statistically significant
changes in all three spin rotation constants upon vibrational excitation.

Table 2.4: Least-squares results for spin rotation fine-structure constants obtained
from simultaneous fit to symmetric and antisymmetric CH2 stretch line contours, with
1σ uncertainties in parentheses. Ground state fine/hyperfine constants, as well as
excited-state hyperfine constants are held fixed at values from microwave
studies.{Endo, 1983}
Constants (cm-1)

Ground state

Symmetric Stretch

AntisymmetricStretchεaa (10-4)
εbb (10-4)
εcc (10-4)-358.902a-61.966 a-0.471 a-346(2)-60.0(3)-1.7(3)-352(1)-61.4(3)-0.6(3)aParameters previously determined by Hirota et al.

2.4 Discussion
One of the key unresolved issues about CH2F concerns its equilibriumgeometric structure, which fundamentally reflects the competition between sp2 versus

30sp3 hybridization of the central carbon atom as a function of electrophilic substitution.
Theory predicts CH2F to have a bent equilibrium structure with a shallow barrier tointerconversion, suggesting a quasiplanar geometry with extensive large amplitude
quantum sampling of nonplanar structures.26 Previous microwave studies yielded
rotational constants consistent with a near planar structure but could not rule out thepresence of large amplitude vibrational sampling over this inversion coordinate.31,32
Furthermore, these studies revealed no indication of tunneling structure, confirming
any barrier at planarity to be smaller than the zero point energy in the inversion
coordinate. More quantitatively, microwave satellite peaks due to transitions out of athermally accessible state were ascribed to v4=1 of the inversion mode, with atemperature dependence that suggested a bend vibrational frequency of 300(30) cm1 31. This is two-fold smaller than the 600 cm-1 bend frequency experimentallymeasured for methyl radical,43 despite simple harmonic expectations from a Wilson G
matrix analysis of only a ≈ 3.4 % decrease due to a ≈ 6.9% increase in bending
moment of inertia upon fluorination. At the very least, this suggests an even more
highly nonharmonic bending potential than observed in methyl radical, with thelikelihood of an appreciable barrier to planarity.

2.4.1 Boltzmann intensity analysis
The current high-resolution IR data for CH2F provides several important clues
to the issue of equilibrium structure, the first of which is the anomalous intensity ratio
for the symmetric and antisymmetric CH2 stretches. Boltzmann analysis of the line
intensities yields both a rotational temperature for the radicals as well as the relative31

intensities of the two bands. The experimental integrated line absorbances for a given
rovibrational transition (j← i) are given by

S exp = ∫ A(v)dv = N i ⋅ l ⋅ S 0ji ,

(2.2)
ji

where l is the absorption length (64 cm) and S 0 is the line strength per MJ state. The
number density of molecules in the lower state, Ni, can be expressed as

N i = N 0vib ⋅g NS ⋅ g J −( E − E ) / kT
⋅e
,
NS
QROT
i

NS
0

(2.3)

ROT

vib

where N 0 is the population in the specific vibrational state vib, g NS is the nuclear
NS

spin weight, g J is the rotational degeneracy, E0

is the lowest energy level withinNS

the same nuclear spin symmetry, and QROT is the rotational partition function of aparticular nuclear spin symmetry.
Data for both symmetric and antisymmetric band transitions for ∆J=1 andground-state Ka=0 are shown in Figure 2.6. The integrated line absorbances, Sexp, arescaled by calculated line strengths and nuclear spin weights and are plottedsemilogarithmically against the ground-state rotational energy. Least-squares fits ofthese data to a single slope yield a common rotational temperature of 20.8(8) K. Morerelevant to the present discussion, these data also permit the relative symmetricstretch and antisymmetric stretch band intensities to be estimated by band strength
integration for the two stretch manifolds, which for a single rotational temperature isdetermined by the difference in the Boltzmann plot intercepts. This procedure yields
an intensity ratio of 1.8(2) between the symmetric and antisymmetric CH2 stretches,
respectively. This is substantially larger than would be expected from a simple bond-32

dipole model for localized symmetric and antisymmetric stretch motion in an isolated
HCH group, which for a 120E HCH bond angle would predict a sixfold smaller ratioof 1:3.

Figure 2.6 Boltzmann plot for ground state rotational populations monitored insymmetric and antisymmetric CH2 stretch modes, verifying jet-cooled conditions [Trot= 20.8(8) K] in the slit discharge and demonstrating a 1.8(2):1 ratio between the twobands.

To further explore this anomaly, we have pursued moderately high-level
theoretical calculations utilizing density functional theory (B3LYP) with an aug-ccpVTZ basis, first optimizing the geometry and then calculating vibrational

33

frequencies and intensities using a Gaussian 03 software package.44 The DFT results
confirm the observed behavior with a predicted ratio of Isym/Iasym ≈ 2.1; i.e., inessentially quantitative agreement with the experimental value of 1.8(2).
Interestingly, however, the predicted infrared intensities for both bands (11.9 km/mol
and 5.60 km/mol for symmetric and antisymmetric stretches, respectively) are bothsignificantly larger than what would be expected for a simple bond dipole model of
the CH2 group. This prediction can be explicitly tested by performing similar DFT(B3LYP-aug-cc-PVTZ) frequency calculations for CH2D radical, whereby monodeutero substitution breaks the local mode degeneracy in CH3, thereby localizing theCH2 vibrations into symmetric and antisymmetric motions. The CH2D results indicate
symmetric and antisymmetric stretch intensities of 1.61 km/mol and 3.84 km/mol;i.e., both much lower than predicted for CH2F and indeed more nearly consistent witha simple bond dipole CH intensity ratio of Isym/Iasym ≈1:3. This behavior indicates thatfluorine substitution leads to a breakdown of the bond dipole model in describing CH
stretch intensities in CH2X radical.
Close inspection of the ab initio results reveals that this breakdown arises
from larger (and in fact opposing) dipole derivatives due to flow of atomic charge
densities under normal mode CH2 stretch displacements. Based on a simple Mullikan
charge description, the calculations (figuratively shown in Figure 2.7) indicate
significant decrease (-δqH) in H atom positive charge densities upon symmetricextension of the C-H bond. This decrease is accompanied by a corresponding

increase (+δqC and +δqF) in both carbon and fluorine charge densities (i.e., to lessnegative values). This “charge-sloshing” results in net flow of positive charge away34

from the C-H bond displacement, yielding transition dipole moment contributions in
the opposite direction from bond-dipole expectations. Indeed, detailed estimates for
the CH2 symmetric stretch in CH2F shows that the magnitude of this “chargesloshing” moment to be in excess of the conventional bond-dipole contribution, thus
actually reversing the direction of the overall transition dipole.

Figure 2.7 Cartoon illustrating the competition between “bond dipole” and “charge
sloshing” contributions to symmetric and antisymmetric CH stretch intensities in
CH2F.
Similarly for the antisymmetric CH2 stretch, the hydrogen atom charge
densities decrease (-δqH) and increase (+δqH) upon extension and compression of theC-H bonds, respectively (see Figure 2.7). Both carbon and fluorine atom charge
densities increase (+δqC and +δqF) with antisymmetric CH extension, though themagnitudes of δqC and δqF are far smaller since the H atom charge redistributions areof opposing sign. Once again, the “charge-sloshing” component of the transition
moment more than cancels that of the bond-dipole contribution and indeed reverses
the sign of the overall transition dipole. Interestingly, since the net CH stretch

35

transition moment reflects a competition between these two contributions, one might
anticipate a strong dependence of these vibrational band strengths on the nature of the
halogen substitution. This picture is supported by parallel high-resolution IR studies
of CH2Cl, for which the antisymmetric CH2 stretch band intensity is experimentallyfound to be more than 20-fold weaker than symmetric stretch excitation, as will be
discussed elsewhere.45 Stated simply, CH stretch vibrational intensity in these
halomethyl radicals is influenced not only by motion of localized charges on theatoms, but in fact by charge flow throughout the entire molecule. Such dramatic
failure of a bond dipole analysis clearly highlights the significant (and evenpredominant) contribution that a nominally “spectator” carbon-halogen bond canmake to IR intensities in the CH stretch region of the spectrum. There appears to be
steadily growing evidence for such “charge sloshing” intensity effects in other open
shell and ionic systems as well. One system is cis-perp HOONO from the Lester
group, for which the a-type overtone OH stretch dipole moment is dominated bycharge flow along the OONO framework and is therefore nearly perpendicular to the≈ c-type OH stretching motion. A second example is that of Cl-(H2O), for which theovertone of the HOH bending mode is much stronger than the fundamental due to avibrationally induced modulated polarization of the Cl- anion along the a-axis.

2.4.2 Complete Basis Set (CBS) inversion potential for CH2F
The DFT (B3LYP/aug-cc-pVTZ) calculations described above for CH2F
suggest (i) a significantly nonplanar equilibrium geometry (θ ≈ 25-30 degrees) as
well as (ii) a strong intensity dependence for both modes on the displacement from36

planarity. This provides sufficient motivation to pursue a higher ab initio treatment of
the inversion-bending potential at the CCSD(T) level, exploiting highly efficientquantum chemistry routines available from MOLPRO.46 To eliminate residual errors
resulting from finite basis set size, the optimized geometry and frequency calculations
have also been performed for a series of Dunning basis sets (AVnZ) and extrapolated
to the CBS limit.47 Specifically, geometries for CH2F are optimized at the CCSD(T)level as a function of the bending inversion angle θ (defined as the complement of the
CF angle with respect to the bisector of the CH2 plane) for an AVnZ basis set with n= 2, 3, and 4. Following the work of Peterson,47 these angle-dependent energies as afunction of n are extrapolated to the CBS limit by fitting toE (n) = ECBS + Be − ( n −1) + Ce − ( n −1)

2

(2.3)

and solving for ECBS. The level of convergence with respect to basis set size is quite
good, with the final EAVQZ-ECBS energy shifts reduced by more than five-fold from thecorresponding EAVDZ-EAVTZ differences.
To account for relatively minor vibrational energy corrections to the inversion
potential due to adiabatic zero point excitation in the remaining 3N-7=5 vibrational
coordinates, CCSD(T) frequency predictions have also been performed. In the current
version of MOLPRO, these more computationally demanding calculations require
numerical Hessians and therefore have only been performed at each inversion angle
for the AVDZ basis set. However, single point frequency calculations for planar andequilibrium geometries have been obtained at the AVTZ and AVQZ level, whichindicate a better than 99% level of convergence in zero point energies. The resulting
sum of zero-point energy (ZPE) over all high frequency vibrations is found to be37

nearly constant as a function of bend angle, and thus has a relatively minor qualitative
impact on the potential curve topology.
The resulting CBS inversion-bending potential for CH2F is shown in Figure
2.8 and indicates a clearly bent equilibrium geometry of θ ≈ 29E with a transitionstate barrier (Ebarrier ≈ 132 cm-1) to inversion at planarity. This equilibrium bend angle
is essentially identical for the CBS potential (θ ≈ 25E), though ZPE correction
deepens the well by an additional ≈46 cm-1 (from 86 cm-1) primarily because of aslight stiffening of the CH and CF stretching modes near the planar configuration.

Figure 2.8 One-dimensional potential energy curve (solid line) obtained fromCCSD(T) complete basis set (CBS) calculations (see text for details), with zero-point
energies in all remaining coordinates included adiabatically (dashed line). Groundand excited state eigenvalues (dotted line) and eigenfunctions (solid line) from amultidimensional Rush-Wiberg analysis are also indicated, which predict the ν4=1←0anharmonic bending frequency to be 276 cm-1.

38

This is also consistent with a geometry-dependent partial sp3 hybridization for thecentral C atom, which becomes purely sp2 (and therefore stiffer) at planarity. It is
worth noting that the ZPE uncorrected predictions of Ebarrier ≈ 86 cm-1 and θ ≈ 25E are
in reasonable agreement with earlier studies by Krylov and co-workers, who obtained
Ebarrier ≈ 109.9 cm-1 and θ ≈ 27E using CCSD(T) methods but without extrapolation to
the CBS limit.26
The spectroscopic impact of this 132 cm-1 barrier depends largely on its
relative position with respect to the ground-state energy. Vibrational eigenstates andeigenenergies have therefore been obtained for this potential, exploiting thepolyatomic 1D Schroedinger equation methods outlined by Rush and Wiberg.48 Thesemethods explicitly include coordinate-dependent changes in both the moments ofinertia [µ(θ)] and the vibration-rotation G matrix of Laane [G(θ)] which, for large
amplitude bending motion in CH2F, can represent a significant contribution. Quickly
summarized, the inverse G-1(θ) matrix is obtained at each bend angle coordinate bydifferentiation and numerically inverted to yield µ(θ) and the determinant |G(θ)|. The
relevant 1D Schroedinger equation for large amplitude polyatomic motion is obtained
from the rigid bender studies of Hougen, Bunker, and Johns,49 which yield a
Hamiltonian for J=0 expressed as∂ 2/∂ θ2 φ(θ) = {f(θ) +2µ(θ)/hbar2[V(θ)-E]}φ(θ),(2.4)

where the 1D vibrational wavefunction isΨ(θ) = µ(θ)1/2 φ(θ),(2.5)

f(θ) = |G(θ)|1/4 µ(θ)1/2{∂2/∂ θ2[|G(θ)|-1/4 µ(θ)-1/2]},

(2.6)

and

39

The angle-dependent quantities V(θ), µ(θ) and |G(θ)|-1/4 µ(θ)-1/2 are each fit to a high(n=12) order polynomial in θ, which then allows the energy eigenvalues and 1D
eigenfunctions to be obtained via standard Numerov-Cooley methods. The resulting
ground (E0 = 174 cm-1) and first excited state (E1 = 450 cm-1) energies and vibrational
wave functions for CH2F, calculated for the zero-point-corrected potential energy
curve, are displayed in Figure 2.8. The ground-state energy lies substantially above
the barrier to planarity, but the effect of such a highly nonharmonic well on the wave
function is clearly evident. The 1←0 vibrational spacing can therefore be predicted tobe E1←0 = 276 cm-1, which is in good agreement with both previous experimental
estimates of both Hudgens et al. (260 ± 30 cm-1) and Endo et al. (300 ± 30 cm-1). In
the interest of facilitating direct spectroscopic observation of this inversion mode, wehave also calculated higher vibrational states on this surface to be E2 = 948 cm-1, E3 =1510 cm-1, and E4 = 2134 cm-1, yielding frequency differences of E2←1 = 498 cm-1,
E3←2 = 562 cm-1, and E4←3 = 624 cm-1. Note the strong blue shifting (i.e., negative
anharmonicity) of this vibrational progression, characteristic of a more square wellpotential with a “flattened” or even “inverted” bottom due to a barrier at planarity.

2.4.3 Intensity-based evidence for a nonplanar equilibrium geometry
The traditional high resolution source of evidence for a planar versus
nonplanar equilibrium structure comes from analysis of the rotational constants,
which for a rigid planar geometry should yield a vanishing inertial defect (∆ = Ic-IbIa).50 In the presence of large out-of-plane amplitude motion, this inertial defectaverages in nonplanar contributions which make ∆ < 0,50 though for CH2F this40

naturally occurs in competition with large amplitude in-plane vibrational motion,
which tends to make ∆ > 0. Experimentally, the inertial defect derived from therotational constants is negative (∆ = -0.0096 amu A2) but, in fact, considerably
smaller than predicted for a rigid structure at the equilibrium geometry (∆ = -0.174
amu A2). This experimental result would be more consistent with the CH2F radical
sampling both wells of the potential function, resulting in a nearly zero inertial defect,
but still bent on average. A more dramatic piece of structural evidence arises from acloser investigation of the anomalous ratio for the symmetric and antisymmetric CH2
stretch band intensities. In particular, both the symmetric and antisymmetric stretch
intensities depend on the inversion bend angle, but with the antisymmetric stretch
intensity increasing considerably more rapidly with deviation from planarity. This canbe explicitly reproduced by density functional theory (B3LYP) calculations in an augcc-pVTZ basis set for CH2F frequencies and intensities, in which we freeze theinversion bend angle and optimize it with respect to all other coordinates. At theplanar C2v configuration, the symmetric and antisymmetric CH2 stretch intensities are
9.1 and 2.1 km/mol, respectively, which translate into a ratio of ≈ 4.3:1; i.e.,
considerably larger than the experimentally observed value of 1.8(2). At thetheoretically predicted equilibrium geometry of θ ≈ 29E, however, these intensities
increase to 11.8 and 5.5 km/mol, yielding a ≈ 2.1 ratio, now in much better agreementwith experiment. This strong dependence of the intensity ratio can therefore inprinciple be utilized as an novel, albeit indirect, probe of the effective nonplanarity of
CH2F.

41

A plot of the symmetric to antisymmetric stretch intensity ratio, calculated at
the B3LYP/aug-cc-pVTZ level, is shown in Figure 2.9 as a function of the inversion
bend angle for CH2F radical. This ratio varies by nearly 250% over the range ofplanar to equilibrium geometries. For comparison, results for CH2D are also provided,
which demonstrate the more “typical” intensity ratio of ≈ 0.4 with essentiallynegligible dependence on bending angle. Also indicated in the plot is theexperimentally observed intensity ratio and its implication in this simple model for aneffective non-planar bend angle (θ ≈ 29E). The consistency between the experimental
intensity ratio and the theoretically predicted equilibrium geometry is noteworthy,
though clearly from the large amplitude 1D wave-bending functions shown in Figure
2.8, the experimental data quantum mechanically samples over a continuum ofgeometries between θ ≈ ±50E. This large amplitude motion can be taken into accountby averaging the ab initio values of Isym and Iasym over the quantum probability as afunction of the bend angle, |Ψ(θ)|2. This 1-D integration yields <Isym> ≈ 11.5 km/mol,<Iasym> ≈ 5.7 km/mol, and a predicted intensity ratio of Isym/ Iasym ≈ 2.0. Given thesimplicity of this model, this is in remarkably good agreement with the experimental
result of Isym/ Iasym =1.8(2) and provides independent support for the ab initio
inversion potential in Fig 8. Of equal importance, the juxtaposition of this agreementwith a nearly 2-fold discrepancy from planar intensity predictions provides strong andrather novel confirmation of a nonplanar CH2F equilibrium geometry, based purely
on infrared CH stretch intensities.

42

Figure 2.9 Calculated intensity ratios for symmetric and antisymmetric CH2 stretches
in CH2F, highlighting a remarkably strong dependence on inversion angle. Note theessentially constant ratio predicted for CH2D. Though large amplitude averaging isclearly important, the experimental intensity ratio of 1.8(2):1 for CH2F is qualitatively
consistent with the potential surface equilibrium angle of θ = 29o.

2.5 Summary and Conclusion
First high-resolution infrared spectra for jet-cooled CH2F radicals have beenobtained for the symmetric and antisymmetric CH2 stretching modes. Subsequent
spectral assignment has enabled the determination of refined lower- and upper-state
rotational constants and fine-structure parameters from least-squares fits to the subDoppler line shapes for individual transitions. Band centers have been assigned forthe symmetric and antisymmetric stretches at 3044.3850(2) cm-1 and 3183.8560(2)cm-1, respectively. The symmetric stretch shows characteristically strong R and P
branches with a weaker Q branch, along with a clear A-type band progression of Ka=

430←0, 1←1, and 2←2 transitions spaced by B + C = 1.96 cm-1. In contrast, theantisymmetric stretch shows a strong Q branch characteristic of a B-type transition
and with fully resolved fine and largely unresolved hyperfine structure.
Analysis of these data lends insight into the question of the CH2F equilibriumgeometric structure. These rotational constants, as well as experimental andtheoretical findings by previous researchers, indicate the possibility of large
amplitude vibrational averaging over a low-barrier double minimum inversionbending potential, reflecting the competition between sp2 and sp3 hybridization of thecenter carbon atom as a function of electrophilic substitution. High-level CCSD(T)calculations extrapolated to the CBS limit confirm the existence of a nonplanar (θ =29E) equilibrium structure, predicting a 120 cm-1 barrier to planarity and a vibrational
bend frequency of 276 cm-1. This bend frequency prediction is in excellent agreementwith previous microwave studies of thermally excited hot bands by Hirota et al.
(300(30) cm-1) as well as REMPI measurements by Hudgens et al. (260(30) cm-1).
The ground state energy lies above the barrier to planarity, for which the delocalizing
effect of such a highly nonharmonic well on the wave function is clearly evident.
Higher vibrational energy levels (E2, E3, and E4) have been predicted to help
stimulate further experimental confirmation of this bend potential.
Particularly noteworthy is the ≈ 1.8(2):1 experimentally observed ratio ofsymmetric to antisymmetric CH2 stretch intensities for CH2F radical. This is muchlarger than simple geometric bond dipole predictions (≈ 1:3) and yet is much smaller
than ab initio calculations for a planar configuration (≈ 4.3:1) Indeed, such ab initio
calculations predict a surprisingly strong dependence of this intensity ratio on

44

bending angle, which has been exploited as a indirect source of evidence for a
nonplanar equilibrium CH2F geometry. Furthermore, analysis of these intensity
calculations suggest the CH2 symmetric and antisymmetric stretch band strengths to
be dominated by vibrationally induced “charge sloshing” between the H, C and F
atoms rather than the traditional “bond dipole” displacement of the charge centers.
Indeed, these charge flow effects are sufficiently strong in halomethyl radicals toreverse the sign of the dipole transition moment from simple bond dipole predictions
for both symmetric and asymmetric CH stretch modes. This novel opposition of
intensity contributions, in conjunction with the strong dependence of atomic charges
on electronegativity of the substituent, suggests interesting anomalies, such as near
perfect cancellation of IR intensities for symmetric or antisymmetric modes, may be
anticipated in other halomethyl radical systems. By way of support, high resolution
IR laser spectra of chloromethyl radical reveal a > 30:1 ratio of symmetric toantisymmetric CH stretch band intensities. However, additional experimental andtheoretical work will clearly be required to test this model further.

Acknowledgement
This work has been supported by funds from the National Science Foundationand the Air Force Office of Scientific Research. We would like to thank Prof. John
Brown (Oxford) for his gracious help in benchmarking computer programs developedin each of our groups for doublet electron spin states in asymmetric tops with two
non-zero nuclear spins.

45

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H.-J. Werner, P. J. Knowles, M. Schutz, R. Lindh, P. Celani, T. Korona, G.
Rauhut, F. R. Manby, R. D. Amos, A. Bernhardsson, A. Berning, D. L.
Cooper, M. J. O. Deegan, A. J. Dobbyn, F. Eckert, C. Hampel, G. Hetzer, A.
W. Lloyd, S. J. McNicholas, W. Meyer, M. E. Mura, A. Nicklab, P. Palmieri,
R. Pitzer, U. Schumann, H. Stoll, A. J. Stone, R. Tarroni, and T.
Thorsteinsoon, MOLPRO: a package of ab initio programs (2003).

47

K. A. Peterson, D. E. Woon, and T. H. Dunning, Jr., J. Chem. Phys. 100, 7410
(1994).

48

D. J. Rush and K. B. Wiberg, J. Phys. Chem. A 101, 3143 (1997).

49

J. T. Hougen, P. R. Bunker, and J. W. C. Johns, J. Mol. Spec. 34, 136 (1970).

50

T. Oka, J. Mol. Struct. 352/353, 225 (1995).

48

CHAPTER 3
HIGH-RESOLUTION INFRARED STUDIES IN
SLIT-JET DISCHARGES: SYMMETRIC CH2 STRETCH EXCITATION OF
JET-COOLED CH2Cl RADICAL

3.1 Introduction
Over the last several decades, partially halogenated chlorofluorocarbons(HCFCs) have been used to replace their fully halogenated analogs (CFCs) as theprincipal components of refrigerants, fire suppressants, ground-based pesticides, andchemical vapor deposition processes, among others.1-4 As a result, HCFCs currently
represent one of the important sources of halogen atoms in the atmosphere.5,6 The key
motivation for use of HCFCs is the extreme stability of CFCs with respect totropospheric oxidation and photolysis processes, which permit transport of theperhalogenated species into the stratosphere.7 At stratospheric altitudes, halocarbon
bonds in the CFCs can be photolyzed by solar UV radiation, yielding free halogen
radicals that aggressively participate in catalytic depletion of the ozone layer.8

By way of comparison, HCFCs are much more kinetically susceptible toattack by tropospheric oxidants such as OH and HO2, forming short-lived
hydrohalocarbon radicals that can be further photolytically degraded by the longer
solar wavelengths that reach into the troposphere.5,6 This increased reactivity has
naturally led to heightened interest in both the kinetic and spectroscopic properties ofsuch open-shell hydrohalocarbon species in order to facilitate better monitoring andmore accurate prediction of their long term impacts on the atmosphere. However, thetransient nature of these radicals also presents significant experimental challenges,
limiting ability to characterize structures, vibrational frequencies, and intramolecularpotentials for such chemically reactive species. Nevertheless, recent years havewitnessed substantial progress in laboratory detection and spectroscopic study ofsmall polyatomic radicals, further complemented by high level ab initio
computational efforts.3,4,9-17
Building upon these advances, this chapter presents the first high-resolution
infrared spectra for jet-cooled CH2Cl radicals in the symmetric (ν1) CH2 stretchingmode. This open shell species is part of an atmospheric series of halosubstituted
methyl derivatives, emerging from the early studies of the CH3 radical itself. First
identified by Fessenden and Schuler using Electron Spin Resonance (ESR), methyl
radical is thought to have an effectively planar structure,18 with later infrared
spectroscopic studies in the inversion bend coordinate indicating a negatively
anharmonic progression of vibrational levels. By way of a simple chemical picture,
this anomalous vibrational anharmonicity arises from a competition between sp3(pyramidal) and sp2 (planar) contributions to the C atom hybridization. These50

competing structural influences result in an unusually “flat” potential for out-of-planebending and therefore a more quadratic (i.e. “particle-in-a box” like) increase invibrational eigenenergies. Indeed, the methyl radical is still a subject of controversy;
the true equilibrium structure is probably nonplanar, though zero point energies above
the barrier result in a vibrationally averaged planar geometry. The presence of large
amplitude bending dynamics in CH3 has stimulated considerable interest in thedependence of the bend potential and vibrationally averaged geometries upon halogen
substitution, which can in principle be elucidated via high-resolution spectroscopic
methods.
Early spectroscopic investigations of chloromethyl using low-temperaturematrix isolation methods19-22 enabled characterization of the symmetric C-Cl stretch(~ 830 cm-1), the symmetric H-C-H bend (~ 1400 cm-1), and the out-of-planehydrogen bend (~ 400 cm-1) at low resolution. Michaut et al. also recorded ESR
spectra of the CH2Cl radical in a low-temperature single crystal of CH3Cl, deriving
the magnetic hyperfine coupling constant for the Cl nucleus.23 An important step into
the gas phase was made by Hirota and co-workers, who recorded the first purerotational spectrum of chloromethyl radical using microwave absorption methods, inwhich A-type transitions were observed with nearly fully resolved fine and hyperfine
components for both the 35Cl and 37Cl isotopic species in the ground vibrational
state.24 More recently, Reisler and co-workers have probed the photodissociation
dynamics of the gas-phase chloromethyl radical using ion imaging techniques, 25-27
with accompanying theoretical studies by Levchenko and Krylov.27 Self-association
rate constants for CH2Cl + CH2Cl have been established,28 and combined51

experimental/theoretical investigations have probed the radical-radical reaction
dynamics for O(3P) + CH2Cl.29-31
In their microwave studies of chloromethyl radical, Hirota and co-workers
calculated a small positive inertial defect, ∆0 = 0.0333 amu A2, from the rotational
constants. This value suggests that chloromethyl radical is effectively planar (at leastin a vibrationally averaged sense), which would also be consistent with a π radical
2

B1 ground electronic state. High-resolution studies of bromomethyl radical yield asimilarly small and positive inertial defect, ∆0 = 0.0320 amu A2, again suggesting anearly planar structure.32 This determination contrasts with the small but negativeinertial defect calculated for the fluoromethyl radicalby Hirota,33 ∆0 = -0.0090 amu
A2, also confirmed in recent studies from our group using high-resolution infraredabsorption methods.9 One suggestion has been that the less electronegative Cl and Br
atoms, relative to F, contribute to a more planar geometry by limiting electron
withdrawal from the central carbon atom toward the halogen substituent.24
The influence of halogen substituent on the inversion potential also has major
impact on experimentally observed bending frequencies. For example, the ~ 400 cm-1
out-of-plane bending mode for CH2Cl estimated from early matrix studies19,20 ishigher than the ~300 cm-1 vibrational frequency inferred from temperature-dependent
microwave satellite bands for CH2F radical,9,24 despite the opposite trend anticipatedfrom simple reduced mass considerations. Furthermore, theoretical attempts toreplicate these frequencies, along with experimentally determined structures of these
halogenated methyl radicals, have yielded significant discrepancies at the harmoniclevel. Specifically, the calculated harmonic out-of-plane bending frequency in CH2Cl,

52

using both CCSD(T) and DFT methods, is 2-fold smaller than observed
experimentally,19,20 whereas the calculated harmonic frequency for the same mode in
CH2F is 2-fold larger than the experimental value.33,34 Levchenko and Krylov havenicely reconciled these differences as the result of zero-point vibrational averaging
over a shallow double minimum potential, which would also rationalize the large
negative anharmonicity in the out-of-plane vibrational mode.35
In light of such a strong influence of halogenation on the bending potential,
high-resolution infrared studies of these halomethyl radical species represent a
particularly interesting target for investigation. The focus of the current study is on
infrared spectroscopy in the CH2 stretch manifold in chloromethyl radical,
characterizing both ground and excited vibrational-state rotational constants, as wellas fine structure parameters. The simple but quite versatile approach exploits
dissociative attachment formation of the radical species in a high pressure pulsed slit
discharge, followed by downstream direct infrared laser absorption in the resulting
supersonic jet expansion. This allows these species to supersonically cool andtherefore concentrate into their lowest accessible rotational levels, resulting in higher
density per quantum state, dramatic simplification of the spectroscopic assignment
process, and sub-Doppler spectral resolution due to velocity collimation in the slit jet.
The net result is a powerfully general method for high-resolution IR spectroscopic
study of reactive polyatomic radicals at low temperatures.
The organization of this chapter is as follows. The experimental setup andapproach for infrared detection of CH2Cl radicals is briefly summarized in Section
3.2. This is followed in Section 3.3 by spectroscopic results and analysis of the CH253

symmetric stretch at rovibrational resolution and least-squares fits of the spectra to a
Watson asymmetric top Hamiltonian. By virtue of sub-Doppler resolution in the slitjet expansion, the results of the spin-rotation and hyperfine interactions are alsopresented and analyzed. Finally, Section 3.4 tackles a number of topics, comprising
the development of a one-dimensional (1D) complete basis set (CBS) potential
energy curve and associated wave functions by Numerov-Cooley methods, theextraction of vibrationally averaged structural information, and a comparison of the
DFT calculation with experimentally observed vibrational band intensities. Section
3.5 summarizes and concludes the chapter.

3.2 Experiment
The experimental methods describing the slit supersonic discharge expansion
have been outlined in detail elsewhere.9,36-39 Briefly, the output of a tunable cw-ring
dye laser is combined with the output of a single frequency argon ion laser inside aperiodically poled lithium niobate (PPLN) crystal to generate tunable infrared light.40
After exiting the PPLN crystal, the infrared light is split into two beams, one of which
travels to a reference detector, while the other portion enters the vacuum chamber inwhich the radicals are produced. Once inside the chamber, the signal beam ismultipassed 16 times through a Herriot cell, which is centered underneath the slit
supersonic discharge expansion. The slit, 4 cm long and 300 microns wide, isarranged so that the long axis lies along the path of the signal beam. The pulsed valve
is operated at a repetition rate of 19 Hz and a duty cycle of 50, generating gas pulsesof ≈ 1ms. The electric discharge is achieved by applying – 0.6 kV to both sides of the54

jaws and grounding the body of the pulsed valve so electrons flow from the jaws of
the discharge upwards. In this manner, radicals are generated within the body of thepulsed valve and then allowed to supersonically cool. Common mode noise iseliminated by servo loop-controlled electronic subtraction between signal andreference InSb detectors.
Concentration modulation and phase sensitive detection at 50 kHz is
additionally used to reduce the appearance of precursor absorptions. Generation oforganic radicals is typically achieved by homolytic cleavage of a C-X bond (X = I,
Br, Cl, F) to form a radical and a halogen atom. For chloromethyl radical, typicalprecursor mixtures of 0.11% bromochloromethane in Neon-70 were exposed todischarge currents of 0.6-0.9 A to generate radicals. Under these conditions,absorptions of 0.15-0.30% are observed, giving peak signal-to-noise ratios of ≈ 20:1.
Stabilization of the argon ion laser to ≤ 1-2 MHz is achieved by stabilization on a 30
cm Fabry-Perot marker cavity, which in turn is actively locked over multiple days toa polarization-stabilized HeNe laser. The dye laser is locked onto a stabilized FabryPerot etalon and typically scanned in 6.5 MHz steps, which proves adequate to fully
resolve fine structure due to spin-rotation interactions, with residual linewidths due tohyperfine structure and suppressed Doppler broadening. Relative frequency
differences (< 10 MHz day-to-day reproducibility) are obtained by recording dyelaser fringes on the marker cavity, with absolute infrared frequencies referenced toR(3), R(2), and R(1) lines of methane.41

55

3.3 Results and Analysis
3.3.1 Symmetric CH2 stretch line center assignments
Since this study reflects the first infrared detection and spectral assignment forchloromethyl radical, high quality vibrational predictions prove extremely useful tominimize the search region to be scanned at high resolution. In previous work, DFT
calculations [B3LYP/6-311++G (3df, 3dp)] have been used to predict harmonic
hydride stretching vibrational frequencies (CH, OH, NH) in multiple radicals andmolecular ions, and to benchmark these against spectroscopic band centers observed
experimentally.42 This analysis revealed a high correlation between theory andexperiment, suggesting that hydride stretching vibrations in unknown radicals can bepredicted to within a sufficiently small window of ± 5-10 cm-1. Based on such
frequency correlations, the symmetric and antisymmetric CH2 stretch vibrations inchloromethyl are predicted at approximately 3055 cm-1 and 3201 cm-1, respectively.
Furthermore, these DFT frequency calculations also predict the ν1 symmetric stretch
band intensity to be relatively strong (6.15 km/mol), whereas the antisymmetricstretch intensity is quite anomalously weak (0.14 km/mol). This unusual ratio of band
intensities (Isym/Iasym nearly 45:1) is inconsistent with the more typical intensity
behavior (Isym/Iasym = 0.5) for the CH2 group, as can be seen by comparing with thecorresponding symmetric (1.61 km/mol) and antisymmetric stretch (3.84 km/mol)
vibrations in CH2D. Interestingly, these predictions indicate that chloro-substitution
in methyl radical results in a substantial increase in symmetric stretch intensity, and56

yet virtual elimination of the antisymmetric stretch mode intensity. We will return tothis point in the discussion section.
Trial scans for the symmetric stretch quickly reveal strong progressions of jetcooled CH235Cl and CH237Cl absorption lines between 3050 and 3060 cm-1, in close
agreement with the scaled DFT predictions above. After optimization of the precursor
gas mixture and scanning conditions, continuous single-mode spectra from 3040 to3070 cm-1 are then obtained for chloromethyl radical, yielding strong P and R branch
progressions characteristic of an A-type band (consistent with expectations for thesymmetric stretch) and with what appears to be relatively weak Q-branch structure in
the vicinity of 3055 cm-1. Due to the presence of 35Cl and 37Cl, the two isotopomer
rotational progressions are strongly overlapped, requiring closer examination tounambiguously confirm assignment of the respective band origins.
A sample region of the P-branch rotational progression in the symmetricstretch vibration of chloromethyl radical is shown in Figure 3.1, highlighting
contributions from both CH235Cl and CH237Cl. A-type transitions from the Ka = 0 and
Ka = 1 manifolds are observed for both isotopes of chlorine, with clear evidence ofpartially resolved structure on each peak due to intramolecular fine (electron spinrotation) and hyperfine (nuclear dipole-dipole, quadrupole and fermi contact)interactions. Furthermore, an approximately ≈ 3:1 intensity ratio is observed between
transitions out of the two Ka = 0 : Ka = 1 manifolds, which is consistent with apartially filled “π-radical” center on the central carbon atom and cooling down into
the lowest (3:1 for ortho:para) nuclear spin statistics for the two identical H atoms.

57

Figure 3.1 Sample spectral data (a) for selected P-branch transitions in the CH2
symmetric stretch band of CH2Cl, compared with a calculated spectrum from the full
least squares fit.

As expected from the previous microwave work of Hirota and co-workers,24 a~ 2B ≈ 1.02 cm-1 separation between P-branch transitions for each of the isotopomer
bands is observed, but with strong interleaving between the two isotopomers due to avibrational band shift accidentally commensurate with 2B. Specifically, the band
center of the CH237Cl symmetric stretch is shifted ≈1.10 cm-1 (i.e., also ≈ 2B) to thered of the CH235Cl band, due to increased reduced mass for the 37Cl isotopomer. Thiscan be readily rationalized by G matrix analysis, which for a simple model of a rigid
CCl bond would yield an effective symmetric stretch mass ofµeff = (1/µH-CCl + cos(θHCH)/2MCl)-1,

58

(3.1)

For a 120° HCH bond angle, this translates in the perturbative limit into a fractionalchange in vibrational frequencies of∆ν/ν ≈ 3/8[MH/mC35Cl - MH/mC37Cl],(3.2)

This expression predicts a roughly 0.99 cm-1 isotopic shift for a 3055 cm-1 symmetricstretch vibration, which, given the simplicity of the model, is in good agreement withthe 1.10 cm-1 value observed experimentally.
Identification of the isotopomer vibrational band origins can be readily madefrom ground-state combination difference estimates based on the strongest P, R
branch transitions, with further assignment proceeding rapidly by comparing
experimental data with rigid asymmetric top spectra predicted from microwave
constants. Quantitative confirmation of these assignments with four-line (and groundstate two-line) combination differences are complicated by the extensive fine andhyperfine structure superimposed on each NKaKc ← NKaKc transition. This structure
results in asymmetric contour shift and splittings of up to several GHz, i.e., greatly inexcess of the putative experimental precision (< 10 MHz). As discussed elsewhere, amore sophisticated simulation program has been developed that includes the standard
Watson asymmetric top Hamiltonian, plus all fine (spin rotation) and hyperfine(Fermi contact, dipole-dipole and electric quadrupole) coupling terms utilized in the
microwave analysis for a spin ½ electron and two nuclei with non-zero spin. This
complete Hamiltonian is used for a full least-squares analysis of all line profiles, as
discussed later in this section.
For initial assignments, however, we focus exclusively on the rovibrational
information by predicting fine/hyperfine line profiles for a given NKaKc ← NKaKc

59

transition (estimated from Hirota’s ground-state constants) and convoluted over the ~60 MHz sub-Doppler linewidth in the slit jet. By shifting these predicted profiles withrespect to the high-resolution data, the pure asymmetric top (i.e., “fine and hyperfine
free”) transition frequencies can be determined to much less than the reported
uncertainty. In this fashion, 41 fine/hyperfine free line centers have been identified in
the CH235Cl symmetric stretch and 26 for CH237Cl. These line centers comprisetransitions from states up to N = 8 and 9 in the CH235Cl R and P branches (see Table3.1), respectively, and up to N = 8 and 7 in the CH237Cl R and P branches (see Table3.2), respectively. By way of initial analysis, these fine/hyperfine-free transition
frequencies are least-squares fit to a Watson asymmetric top Hamiltonian for the
ground and symmetric stretch excited states. Within experimental uncertainty, thefitted ground-state rotational constants are completely consistent with previous resultsof Hirota and co-workers, yielding standard residuals of 9 MHz and 11 MHz for the35

Cl and 37Cl isotopomers, respectively. The upper state rotational constants extracted

from the fit are summarized in Table 3.3.

60

Table 3.1: Transition frequencies and least-squares fit for the CH235Cl symmetricstretch

J’

Ka ’

Kc ’

J”

Ka ”

Kc ”

Obs. (cm-1)

Obs. – calc. (10-4 cm-1)

9
8
7
7
6
6
6
5
5
5
4
4
4
3
3
3
2
2
2
1
1
1
0
1
1
1
2
2
2
3
3

0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1

9
8
7
7
6
5
6
5
4
5
4
3
4
3
2
3
2
1
2
1
0
1
0
1
1
0
2
2
1
3
3

8
7
6
6
5
5
5
4
4
4
3
3
3
2
2
2
1
1
1
0
1
1
1
2
2
2
3
3
3
4
4

0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1

8
7
6
6
5
4
5
4
3
4
3
2
3
2
1
2
1
0
1
0
1
0
1
2
2
1
3
3
2
4
4

3064.17536
3063.18267
3062.18573
3061.96625
3061.18363
3061.16849
3060.98041
3060.17729
3060.14554
3059.98951
3059.16687
3059.11869
3058.99515
3058.15108
3058.08722
3057.99539
3057.13074
3057.05171
3056.99123
3056.10592
3054.99189
3054.93168
3054.04157
3053.00279
3052.92237
3052.86383
3051.95964
3051.89377
3051.80602
3050.91258
3050.86007

-0.6
1.9
-12.
1.4
0.9
3.6
2.1
0.1
2.8
-3.0
4.7
4.8
3.5
2.5
3.2
3.6
1.8
5.2
8.1
3.2
1.7
-2.1
-2.0
-2.6
-5.3
-1.9
-3.2
-0.7
-2.2
-0.6
0.1

61

Table 3.1 (continued): Transition frequencies and least-squares fit for the CH235Cl
symmetric stretch

J’

Ka ’

Kc ’

J”

Ka ”

Kc ”

Obs. (cm-1)

Obs. – calc. (10-4 cm-1)

3
4
4
4
5
5
5
6
7
8

1
0
1
1
0
1
1
0
0
0

2
4
4
3
5
5
4
6
7
8

4
5
5
5
6
6
6
7
8
9

1
0
1
1
0
1
1
0
0
0

3
5
5
4
6
6
5
7
8
9

3050.74390
3049.86107
3049.82131
3049.67771
3048.80589
3048.77842
3048.60714
3047.74721
3046.68486
3045.61979

-3.3
-2.2
-3.9
-3.9
-2.2
-4.8
-9.0
-1.1
-3.4
-2.5

62

Table 3.2: Transition frequencies and least-squares fit for the CH237Cl symmetricstretch

J’

Ka ’

Kc ’

J”

Ka ”

Kc ”

Obs. (cm-1)

Obs. – calc. (10-4 cm-1)

9
8
7
6
5
5
5
4
4
4
3
3
3
2
2
1
1
0
1
2
3
3
4
5
5
6

0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0

9
8
7
6
5
4
5
4
3
4
3
2
3
2
1
1
1
0
1
2
3
2
4
5
4
6

8
7
6
5
4
4
4
3
3
3
2
2
2
1
1
0
1
1
2
3
4
4
5
6
6
7

0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0

8
7
6
5
4
3
4
3
2
3
2
1
2
1
0
0
0
1
2
3
4
3
5
6
5
7

3063.05405
3062.05490
3061.05324
3060.04933
3059.04312
3058.98241
3058.83301
3058.03430
3057.95777
3057.83908
3057.02346
3056.93170
3056.84360
3056.01035
3055.90351
3054.99506
3053.81074
3052.95915
3051.93858
3050.91574
3049.89208
3049.69873
3048.86658
3047.83953
3047.61799
3046.81140

0.2
0.4
0.3
1.8
3.9
2.2
-1.2
2.6
0.3
-0.9
3.2
2.1
5.4
2.2
0.5
-0.1
-5.0
-0.2
0.7
-4.2
1.3
-4.5
-1.9
-4.0
-3.3
-4.0

63

Table 3.3: Least-squares fitting results for the symmetric CH2 stretch line centers in
CH235Cl and CH237Cl. The uncertainties in parenthesis represent one standard
deviation from the least-squares fit to the Watson asymmetric top Hamiltonian.
Constants(cm-1)

CH235Cl
Excited StateCH237Cl
Excited State

A
B
C

9.04055(20)0.52991(1)0.49971(1)9.01341(25)0.52310(1)0.49391(1)∆N (x 10-5)∆NK (x 10-5)∆K (x 10-5)-0.06(1)6.3(8)
76.a

0.05(1)
2.(1)
76.a

υ0

3055.0760(2)3053.9781(1)aParameters previously determined by Hirota et al. Ground-state parameters werealso set to Hirota’s values.

3.3.2

Fine and hyperfine structure and analysis
As mentioned above, the experimental spectra show clear fine structure

splittings, resulting predominantly from coupling of electron spin angular momentum(S) with overall molecular rotation (N).9,43 There is also additional line broadening
evident from extensive hyperfine interactions due to three nuclei with non-zero spins.
In the interest of completeness, analysis of these features in both the CH235Cl andCH237Cl manifolds is based on a full least-squares fit to the explicit actual absorption
line contours, utilizing the complete asymmetric top, fine, and hyperfine Hamiltonian.
This simulation program has been developed for spin rotation, Fermi contact, dipoledipole, and electric quadrupole terms in an asymmetric top with multiple non-zerospin nuclei, utilizing coupling matrix elements from Hirota44 and extensively tested incollaborative comparison with program development by the Brown group in Oxford.

64

By way of example, sample data scans over the 313 ← 212 transition (IH = 0,para) in the symmetric stretch band of CH235Cl are shown sequentially in Figure 3.2.
The top panel (a) illustrates the single ~60 MHz Doppler line profile anticipated in
the absence of any electron or nuclear spin interactions, with the results in panels
below illustrating the additional splittings and broadenings that result from successive
inclusion of (b) electron spin-rotation fine structure and (c) nuclear spin Fermi
contact, dipole-dipole, and electric quadrupole hyperfine structure. The observed
experimental line profile for this transition is given in panel (d) and is in qoodagreement with the least-squares fitted fine/hyperfine predictions. The electron spinfine structure clearly contributes to well-resolvable peaks in the predicted spectrum,
although the nuclear hyperfine contribution is below the resolution limit.
Experimental access to such high resolution information in the near infrared isnoteworthy, observable as a result of the sub-Doppler velocity collimation in the slitjet.
In final fits to the high resolution profiles, all ground-state constants are fixedat previously determined microwave values,24 floating the rotational and spin-rotation
constants in the vibrationally excited state. The absorption contours do exhibit partial
sensitivity to hyperfine constants, however, much less than observed previously in IR
studies of CH2F radical. To further minimize parameter correlation, the hyperfine
interaction is held fixed at ground-state values. A summary of the fitted results isreported in Table 3.4; the results indicate only modest (albeit statistically significant)changes in the three spin rotation constants upon vibrational excitation.

65

Figure 3.2 Comparison between high resolution predictions (a-c) and experiment (d)for a sample symmetric stretch rovibrational transition (313 ← 212) of CH2Cl. The
simulations begin with a pure asymmetric top transition (i.e. S = ICl = IH = 0) (a),successively including fine (b) and hyperfine (c) interaction terms in the Hamiltonian.

66

Table 3.4: Least-squares fitting results for the CH2 symmetric stretch fine-structure
constants. The uncertainties in parentheses represent one standard deviation from theleast-squares fit to the effective Hamiltonian detailed in the text.
Constants(MHz)

CH235Cl
Ground StateCH235Cl
Excited StateCH237Cl
Ground StateCH237Cl
Excited State

εaa
εbb
εcc

-3149.45(36)a-237.623(114)a
11.814(100)a-3047.(4)-236.3(8)10.6(8)-3149.58(24) a-234.080(118) a
11.699(100) a-3103.(28)-231.(4)10.(4)aParameters previously determined by Hirota et al.

3.4

Discussion

3.4.1

CCSD(T) Complete Basis Set (CBS) bending potential
As previously introduced in a companion high-resolution IR study of theCH2F radical, the planar versus bent equilibrium geometric structure of CH2Cl
remains an intriguing question, indirectly sampling the competition between sp2
versus sp3 hybridization of the central carbon atom. At the simplest level, one canconsider the inertial defect, ∆ = Ic-Ib-Ia, which for CH2Cl is quite small in the ground(∆ ≈ 0.033 amu A2) state. Purely from analysis of the rotational constants, both themicrowave and infrared data are consistent with a nearly planar equilibrium structure.
However, this is not sufficient to rule out large amplitude motion in the bending
coordinate which, if energetically above any barrier at planarity, can lead to
substantial delocalization of the wave function. Indeed, CH2F also exhibits inertial
defects close to zero in the ground (-0.0096 amu A2) state, despite the fact that theactual bending potential is decidedly nonplanar, with a minimum at θ ≈ 29E and anearly 132 cm-1 barrier to planarity. Inertial defects close to zero can also arise from67

dynamical competition between large amplitude in-plane and out-of-plane motions,which tend to raise or lower the inertial defect, respectively. Such large amplitude
averaging effects have made it difficult historically to establish the presence ofbarriers based on rotational constants alone. Indeed, CH3 is an example where thebarrier to planarity is thought to be quite small or possibly even zero and, in any
event, negligible with respect to the zero point energy. In light of the nearly zero andnon-zero barriers for CH3 and CH2F, respectively, the question of a barrier height inCH2Cl naturally occurs, or, alternatively stated, the degree of sp2 versus sp3
hybridization in methyl radical as a function of electronegative substitution is of greatinterest.
Krylov and co-workers have performed CCSD(T) calculations for CH2Cl
using a 6-311G++(3df,2pd) basis set, predicting a planar equilibrium structure with alarge negative anharmonic potential for the out-of-plane bending vibrational mode.45
From an approximate 1D analysis, the anharmonic frequency for this transition was
estimated to be 422 cm-1. As a measure of the nonharmonic nature of the potentials,
this value is more than twice the harmonic frequency of 168 cm-1, though still inreasonable agreement with the experimentally determined matrix values of 402 cm1 19,20.

Interestingly, this out of plane CH2Cl prediction is ~30% smaller than thecorresponding bend frequency for methyl radical of 600 cm-1, but nevertheless ~30%

larger than experimentally inferred for CH2F (~300 cm-1).33 This discrepancy isclearly not due to simple reduced mass G-matrix effects, which are dominated by thehydrogen atoms and in fact predict only a < 5 % decrease in bend frequencies forchlorine substitution.

68

This provides sufficient motivation to revisit this issue with a complete basis
set (CBS) ab initio treatment of the inversion bending potential. Calculational details
closely parallel that described elsewhere in our experimental high-resolution study ofCH2F radical; the essential features can be briefly summarized. CCSD(T) geometry
optimizations have been performed as a function of inversion bending angle, θ(defined as 180E minus the angle between the CCl bond and the CH2 plane) in an
AVnZ Dunning basis set, exploiting efficient quantum chemistry routines available
from MOLPRO.46 To correct for finite basis set effects, the CCSD(T) energies for n =2, 3, 4 are extrapolated to the CBS limit, using the methods of Dunning andPeterson.47 This 1D CBS bending potential is then corrected for zero point vibrationalenergy in the remaining 3N-7 = 5 coordinates, resulting in the adiabatic potential
curve for CH2Cl shown in Figure 3.3. In sharp contrast with the predictions for CH2F,
the equilibrium geometry of CH2Cl at the CBS limit is essentially planar, though thepotential is quite visibly flat rather than harmonic.
Calculation of adiabatic bending eigenenergies and wave functions on this 1D
potential is modeled on the work of Rush and Wiberg,48 which, in turn, is based on
the large-amplitude rigid-bender effective Hamiltonian analysis of Hougen, Bunker
and Johns.49 Note that these polyatomic methods explicitly take the angulardependence of the inertial moments into account, which is necessary to obtain true
anharmonic vibrational predictions correctly independent of the arbitrary choice of
1D bending coordinate. The resulting ground (E0 = 178 cm-1) and first excited state(E1 = 571 cm-1) energies and vibrational wave functions for CH2Cl, calculated for thezero-point corrected potential energy curve, are displayed in Figure 3.3.

69

Figure 3.3 One dimensional potential energy curve from CCSD(T)/AVnZ/CBS
calculations, adiabatically corrected for zero point energy in all remaining non-bendcoordinates. Also shown are ground and first excited vibrational state (v4)eigenfunctions and eigenenergies, calculated via methods of Rush and Wiberg andexplicitly including G matrix element dependence on the bend angle (see text for
details).
The predicted anharmonic 1←0 vibrational bend frequency on this CBS potential is
E1←0 = 393 cm-1, consistent with previous theoretical estimates and in agreement withexperimental matrix studies (400 cm-1). In the interest of facilitating direct
spectroscopic observation of this inversion mode, we also calculate higher vibrational
states on this surface to be E2 = 1083 cm-1, E3 = 1654 cm-1, and E4 = 2268 cm-1. Thispredicts a series of hot band origins with ∆E 2←1 = 512 cm-1, ∆E 3←2 = 571 cm-1, and∆E 4←3 = 614 cm-1, potentially observable with current diode laser technology in the ≈70

600 cm-1 region. Particularly noteworthy is the negatively anharmonic (i.e., blue
shifted) progression of adjacent level spacings, which converges toward more
harmonic behavior with increasing number of vibrational quanta. This is entirely
consistent with competing sp3 contributions to a nominally sp2 bending potential,
resulting in an anomalously flat topography near planarity.
The calculations and experimental data elucidate a striking qualitative
difference between chloro- and fluoro-substituted methyl radicals, suggesting a strong
dependence to the barrier contribution on the electronegativity of the substituent. To
complete this picture, we have also calculated a 1D CCSD(T) potential surface for the
methyl radical itself at the same level of CBS treatment. The result for all threepotentials in this CH2X (X = H, Cl, F) series is shown in Figure 3.4. This figure
illustrates the unambiguous progression from a relatively harmonic potential formethyl radical, to a much flatter potential for chloromethyl radical, and finally, to the
distinctly double-minimum potential for fluoromethyl. The difference between thestrongly bent equilibrium geometry for CH2F radical and the successively more
confined planar equilibrium structures of CH2Cl and CH3 is striking, and nicely
underscores an increasing propensity toward sp3 hybridization with greater electron
withdrawal from the central C atom.

3.4.2

Vibrational band intensities
Boltzmann analysis is used to compare the intensities of the CH235Cl andCH237Cl symmetric stretch bands. Boltzmann analysis yields both a rotationaltemperature of the radicals as well as the relative intensities of the two bands.

71

Figure 3.4 Comparison of one dimensional potential energy curves fromCCSD(T)/AVnZ/CBS calculations, for CH3, CH2Cl, and CH2F. Note the clear
progression toward a non-planar equilibrium geometry, due to increasing sp3 vs sp2
hybridization of the carbon atom with increasing electronegativity of the halogen
substituent.
Following calculations described previously,39 the experimentally measured
integrated line absorbance for a rotational transition from a lower state i to an upper
state j is expressed as

S exp = ∫ A(v)dv = N i ⋅ l ⋅ S 0ji ,(3.3)

where Ni is the number density of molecules in the lower state i, l is the absorptionjilength (64 cm), and S 0 is the line strength per MJ state. The number density ofmolecules in the lower state, Ni, can be expanded in the following expression,72

N i = N 0vib ⋅g NS ⋅ g J −( E − E ) / kT
⋅e
,
NS
QROT
i

NS
0

(3.4)

ROT

vib

where N 0 is the population in the specific vibrational state vib, g NS is the nuclear
NS

spin weight, g J is the rotational degeneracy, E0

is the lowest energy level withinNS

the same nuclear spin symmetry, and QROT is the rotational partition function of aparticular nuclear spin symmetry.
Data for CH235Cl symmetric band transitions for ∆J = 1 and ground-state Ka =0 are shown in Figure 3.5. For each transition, the integrated line absorbance, Sexp, isscaled by the calculated line strength factor, including nuclear spin statistics
weighting and is plotted semilogarithmically against the ground-state rotationalenergy. A linear least squares fit shows a corresponding temperature of 18.2(5) K.
Integration of band strengths for both CH235Cl and CH237Cl yield an intensity ratio of
2.6(2), which is also in rough agreement with the 3:1 ratio of their naturalabundances.
With the symmetric CH2 stretch band observed with high signal to noise (≈20:1), experimental conditions maximized for most efficient formation of CH2Cl, andhigh confidence in vibrational band origin predictions, a scan for the antisymmetricCH2 stretch has been attempted. No CH2Cl radical transitions are observed for either
isotopomer that, based on a ≈ 20:1 signal to noise in the corresponding symmetricstretch region, permits us to safely conclude that the band intensity is at least tenfold
weaker. This is consistent with the theoretical intensity predictions of a 45-folddifference between the symmetric and antisymmetric stretch band strengths.

73

Figure 3.5 Boltzmann temperature analysis of the CH235Cl symmetric stretch band
verifying rotational equilibration to Trot ≈ 15 K in the slit jet.
This experimental confirmation of such dramatic weakening of theantisymmetric CH2 stretch with chloro vs. fluoro substitution represents one of themore intriguing results of this study and deserves closer investigation. It is important
to note that both symmetric and antisymmetric stretch bands are experimentallyobserved for CH2F in a 1.8(2):1 ratio, in quantitative agreement with ab initio
theoretical predictions of 2.1:1. A simple bond-dipole model predicts an intensity
ratio of the symmetric vs. antisymmetric stretches of 1:3, where the antisymmetricstretch intensity is larger than that of the symmetric stretch. This is confirmed intheoretical calculations for CH2D, reaffirming confidence in the general paradigm for74

CH2 stretch intensities. However, this prediction is incorrect by approximately sixfold
for CH2F and at least by 60-fold for CH2Cl. Furthermore, from comparison with
CH2D, this is not simply due to a decrease in asymmetric stretch intensity, but rather
must also result in part from an increase in symmetric stretch intensity.

Figure 3.6 Predicted band intensities of CH2 symmetric and antisymmetric stretch
vibrations for CH2Cl, CH2F, and CH2D as a function of inversion angle. .

75

This trend is illustrated in Figure 3.6, which shows a comparison between thecalculated symmetric and antisymmetric CH2 stretch intensities for CH2F, CH2Cl, andCH2D as a function of out of plane bend angle. Clearly, halogen substitution of
methyl radical has a profound impact on the origin of vibrational intensities.
This dramatic variation in CH2 stretch intensities between CH2D, CH2F, andCH2Cl, warrants closer investigation. The significant increase in symmetric stretch
excitation with halogenation seems at first glance consistent with a simple bonddipole model, whereby a larger µCX results in a larger dipole moment derivative.
However, inspection of the normal mode displacements indicates these effects
contribute in the wrong direction – specifically the CX bond length decreases slightly
with symmetric extension of the CH bonds. Furthermore, the center of mass
displacement of halide atom for asymmetric stretch excitation is relatively small,whereas the dynamic range in intensity changes for this mode is by far the largest andmost puzzling to explain. Additional investigation into the source of these vibrational
intensities indicates that the conventional bond dipole picture is in fact overshadowedby surprisingly large changes in atomic charges upon symmetric and antisymmetricCH2 stretch motion.
Specifically, from a usual first order Taylor series expansion of <v’|µ(Q)|v”>,
the v’← v” vibrational transition moment associated with normal mode Q and dipole
moment operator µ(Q) = Σl ql rl can be readily shown to be<v’|(∂µ/ ∂Q)|v”> = <v’|Σl [ ql (∂rl/∂Q) + rl (∂ql/∂Q)]|v”>.

(3.5)

The first term in parenthesis represents normal mode vector displacement of charge
distributions on the atoms, i.e., the standard bond-dipole model. The second term

76

represents changes in the net molecular dipole due to vibrationally induced charge
flow in/out of each atom, which we refer to as “charge sloshing”. Gaussian
calculation results indicate that the hydrogen atom’s positive charge densities

decrease upon the characteristic extension of the C-H bond in the CH2 symmetricstretch. These decreases are accompanied by an increase in the carbon and halogen
atom’s positive charge densities, from more negative to less negative values. This
“charge-sloshing effect” results in net electron density flowing synchronously withthe extension of the C-H bonds, leading to a transition dipole moment in the opposite
direction from that of bond-dipole expectations. Indeed, for CH2Cl, the magnitude of
the transition dipole resulting from these “charge-sloshing” contributions is more than
twice that of the regular bond-dipole contribution, thereby canceling and actually

reversing the direction of the overall transition dipole.
For the antisymmetric CH2 stretch, the two hydrogen atom charge densities

decrease and /increase upon the C-H bond stretch and compression, respectively,
with the carbon and halogen atom’s charge densities following the same trends as
seen in the symmetric stretch. Once again, this “charge-sloshing” contribution iscommensurate to that of the bond-dipole contribution and reverses the expected signof the overall transition moment. However, whereas this reversal in CH2F leaves
sufficient intensity in the asymmetric stretch mode to permit observation in the slit
jet, the behavior for CH2Cl indicates a near perfect cancellation between bond dipoleand “charge-sloshing” contributions and therefore an experimental reduction inasymmetric stretch intensity by > 20 fold. The important role of this competition isfurther confirmed by the out of plane dependence of these ab initio intensities, which77

vanish identically in CH2Cl near θ ≈ 20 degrees, in clear contrast with the systematicand more nearly uniform increase with θ noted for symmetric stretches in CH2D and
CH2F. Interestingly, there are also indications of bond-dipole vs “charge sloshing”
competition in the CH2F asymmetric stretch mode, which from Figure 3.6 starts out
weak at the planar configuration, growing much more rapidly with bending angle
than any of the symmetric stretch bands as well as either symmetric or asymmetricstretch band of CH2D. Indeed, this strong dependence of asymmetric stretch intensity
on out of plane bend angle was used to confirm the existence of a non-planar
equilibrium geometry in CH2F, but with large amplitude bending motion and a zero
point energy above the isomerization barrier.
By way of final confirmation of these charge sloshing effects in CH2Cl andCH2F radicals we have also performed similar ab initio calculations for the CH2
symmetric and antisymmetric stretch intensity for bromomethyl radical, CH2Br.
These calculations are summarized in Figure 3.7 for CH2D, CH2Br, CH2Cl, andCH2F, i.e., in order of increase electron withdrawing nature of the substituent. As
expected, the results indicate a rapid monotonic increase in symmetric stretch
intensities with substituent electronegativity, but with a near vanishing of theasymmetric stretch intensities localized around CH2Cl. This clear non-monotonic
behavior provides additional support for a competition between bond-dipole andcharge-sloshing effects in this radical series, as well as strongly suggests a signchange in the CH2X asymmetric stretch vibrational transition moments between X =D, Br and X = F, with nearly perfect cancellation for X = Cl. While this physical78

picture is presented as a possible simple explanation for our results, further theoreticaland experimental work will clearly be needed to fully develop these concepts.

Figure 3.7 Comparison of symmetric (Isym) and asymmetric (Iasym) stretch band
intensities for CH2D, CH2Br, CH2Cl, and CH2F. Note the dramatic minimum in Iasym
for CH2Cl due to near cancellation of bond-dipole and “charge-sloshing”
contributions, which becomes nonzero for either greater (CH2F) or weaker (CH2Br)
electron withdrawing nature of the halogen substituent.

3.5 Summary and Conclusion
First high-resolution infrared spectra for jet-cooled CH235Cl and CH237Cl
radicals have been obtained for the symmetric CH2 stretching mode. Subsequent
spectral assignment has enabled the determination of refined lower and upper state
rotational constants, as well as fine structure parameters, from least-squares fits to the79sub-Doppler line shapes for individual transitions. Band centers for the CH235Cl andCH237Cl symmetric stretches are 3055.0760(2) and 3053.9781(1) cm-1, respectively.
The spectral progressions for both isotopomers show characteristically strong
R and P branches with a weaker Q branch, along with clear A-type band progressions
from the Ka = 0 and Ka = 1 manifolds. There is also evidence of partially resolved
structure on each peak due to intramolecular fine and hyperfine interactions.
Integration of the band strengths for both isotopomers yields an intensity ratio of
2.6(2) that is also in rough agreement with the 3:1 ratio of their natural abundances.
The rotational constants are consistent with a nearly planar structure but do not
exclude substantial large-amplitude bending motion over a small barrier to planarity
readily accessed with zero-point excitation. High level CCSD(T) calculations,
extrapolated to a CBS limit, predict a slightly nonplanar structure (θ ≈ 11E), with avibrationally adiabatic 1D treatment of the bend coordinate yielding a fundamental
anharmonic frequency (393 cm-1), in excellent agreement with previous matrix
studies (νbend ≈ 400 cm-1) as well as theoretical predictions. We have also calculated
higher vibrational energy levels (E2, E3, and E4) to help stimulate further experimental
confirmation of this bend potential.
The antisymmetric CH2 stretch band is not observed for either isotopomer ofCH2Cl, despite high signal to noise on the corresponding symmetric stretch band.
This concurs with theoretical calculations that indicate surprisingly weak intensities
for the CH2Cl antisymmetric stretch (S0 ≈ 0.14 km/mol) relative to the symmetricstretch (S0 ≈ 6.15 km/mol). These predictions contrast with predicted CH2F
symmetric and antisymmetric stretch intensities of S0 ≈12 km/mol and S0 ≈ 6 km/mol,

80

respectively, for which both bands were experimentally detected in previous studies.
Both sets of results are in fundamental disagreement with simple bond dipole
predictions of an Isym/Iasym ≈ 1:3 ratio for CH2D, suggesting a significant impact of
halogenation on the CH stretch intensity dynamics. These differences among
intensities for CH2Cl, CH2F, and CH2D suggest a simple physical model based on thecompeting and often dominant role of vibrationally mediated charge flow
(i.e.,“charge-sloshing”) between atoms. This analysis indicates that “charge-sloshing”
contributions in CH2F and CH2Cl halomethyl radicals actually reverse the sign of thesymmetric stretch transition moment away from conventional bond-dipole
predictions. Furthermore, this competition is responsible for the cancellation of theasymmetric CH2 stretch dipole moment in CH2Cl, in good agreement withexperiment. Finally, ab initio calculations for the series of CH2D, CH2Br, CH2Cl andCH2F radicals indicate an emerging and self consistent picture for “charge-sloshing”
vs bond dipole contributions to symmetric and asymmetric stretch intensities as afunction of substituent electronegativity.

Acknowledgment
This work has been supported by grants from the National Science
Foundation, as well as from the Air Force Office of Scientific Research. T.H. would
like to acknowledge postdoctoral support from the Alexander von Humboldt
Foundation. M.D.S expresses his appreciation for partial sabbatical support from the
National Science Foundation. We would also like to acknowledge many helpful
discussions with Prof. Anne B. McCoy about IR vibrational band intensities.

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84

CHAPTER 4

REACTIVE SCATTERING DYNAMICS IN
ATOM + POLYATOM SYSTEMS:
F + C2H6 Æ HF(v,J) + C2H5

4.1 Introduction
The fundamental dynamics of chemical transformation reflect simple bondbreaking and bond formation, the detailed understanding of which has been a longstanding, albeit elusive, target for the chemical physics community ever since
Arrhenius’ first development of a reaction-rate theory in 1889.1 However, from amore modern chemical physics perspective, the rate constant does not always provide
a sufficiently detailed molecular picture since it represents an average of microscopic
reactant to product rate coefficients over all possible encounters, characterized bydifferent relative velocities, orientations, vibrational and rotational quantum states,
and impact parameters. An ongoing dual challenge of fundamental reaction dynamics
has therefore been (i) to understand in detail how energy is distributed among nascentrotational, translational, and vibrational degrees of freedom in product molecules aswell as (ii) to provide simple physical pictures of the essential dynamics necessary to
predict these distributions successfully. This latter issue is particularly important as
the systems grow in complexity and degrees of freedom, from “atom + diatom”
reactions to polyatomic reaction dynamics.
There have been several pioneering experimental and theoretical efforts toaddress these needs. The development of Fourier transform infrared spectroscopy(FTIR) “arrested-relaxation” chemiluminescence methods by Polanyi and coworkers
proved ground breaking in providing first data on rovibrational excitation of products
for a number of prototypical “A + BC” exothermic chemical reactions.2-4 This work
resulted in valuable theoretical concepts such as early/late barriers, which, in
conjunction with detailed balance arguments, provided a relatively simple framework(i.e., “Polanyi rules”)5 for predicting nascent distributions as well as reagent
vibrational vs. translational promotion over a chemical reaction barrier. Over asimilar period, Herschbach,6 Lee,7 and coworkers evolved crossed-molecular beam
methods into an even more powerful tool for study of reaction dynamics underrigorous single-collision conditions.8 Although product fragment detection via timeof-flight energy loss9 provides more limited resolution of internal quantum states thanspectroscopic methods, the greater control of collision energy and access todifferential-scattering information have clearly facilitated the most comprehensive
tests of fundamental reaction dynamics.
This has been particularly true for elementary atom + diatom systems such as
H + H2,10-14 F + H2 ,9,15-21 Cl + H2,22-25 and O + H226-28 (and isotopic variants thereof),86which, augmented by sensitive laser-based laser-induced fluorescence (LIF),29
resonance enhanced multiphoton ionization (REMPI)30 or Rydberg detection of
products,26 have received an enormous amount of attention. The justification for a
focus on three-atom systems is absolutely clear: these systems represent reactions forwhich it is possible to develop accurate ab initio potential energy surfaces31 as well as
perform full quantum mechanical scattering calculations.32,33 In many cases, thecalculations can be done without any dynamical approximations and sometimes with
the inclusion of nonadiabatic dynamics on multiple electronic surfaces.34 Although
there are some outstanding questions yet to be resolved, particularly relating to issuesof nonadiabatic reaction dynamics,22,23 ,34 these synergistic experimental andtheoretical treatments of three-atom dynamics have been remarkably productive andrepresent a major intellectual achievement of the chemical physics community.
Similarly detailed levels of comparisons between experiment and theory inmore complicated systems such as atom + polyatom reactions have provenchallenging. Much of the difficulty arises from theory, both at the ab initio level (i.e.,reliable generation of potential energy surfaces) and dynamics level (i.e., converged
methods for quantum reactive scattering) in high dimensionality. Indeed, the only
numerically converged quantum-dynamics-scattering calculations for a system withmore than three particles has been OH + H2 by Zhang et al., a heroic achievement but
nevertheless still a system with only one heavy (nonhydrogenic) atom.35,36 Significant
challenges are also present for crossed beam studies, for which conventional time-offlight methods are typically unable to resolve internal state distributions of the
products. This has provided further incentive for atom + polyatom crossed beam87

studies with spectroscopic-based detection of products, as explored by Liu, Zare,
Suits, Valentini and others.37-41
Counterbalancing these challenges, however, is the substantially richer worldof reaction dynamics that opens up at the atom + polyatom level. Consider, forexample, a simple atom abstraction in a highly exothermic atom + polyatom system.
If the bond breaking event occurs on time scales comparable to intramolecularvibrational redistribution (IVR), one might anticipate substantial deposition of
exothermicity into the polyatomic fragment, with less energy available for the
diatomic product-state rovibrational distributions.42 On the other hand, if IVR wereslow compared to the reactive encounter, one might anticipate an essentially “sudden”
Franck-Condon like process, with relatively little influence due to the potentiallydense vibrational structure of the polyatomic fragment. Furthermore, kinetic energy
release at the transition state might result in dynamical constraints that linktranslational, rotational, and vibrational degrees of freedom. More generally stated,
one might therefore look for bimolecular reaction dynamics to reveal dynamicalcorrelations at the quantum-state-resolved level, analogous to what has been
elegantly demonstrated in the unimolecular photolysis literature.43
In this study, we use high-resolution infrared absorption spectroscopy to
examine state-to-state reaction dynamics of an atom + polyatom system, the F + C2H6

→ HF(v,J) + C2H5 reaction, under single collision conditions in a crossed jet
apparatus. This work builds upon previous crossed-beam–reactive-scattering studies
of F + CH4/CD4 by Liu, Harper and others,44-46 REMPI studies of Cl + alkanes ofZare, Orr-Ewing, Kitsopolous,38,39,47,48 as well as extensive studies of O(3P) +88

methane and nonmethane hydrocarbons by Suits, McKendrick and others.29,41,49,50
The work also builds on early FTIR studies of the F + C2H6 system by Setser andcoworkers, who report relative HF (v=1,2,3) vibrational energy distributions,51
although under incompletely “arrested” rotational relaxation conditions.
The advantage of a high-resolution single-mode infrared laser source forstudying reaction dynamics is twofold. First, the narrow (∆νlaser ≈ 0.0001 cm-1)
linewidths translate into HF(v,J) product state detection with full rovibrational
quantum state resolution, yet with peak sensitivities that permit operation at
sufficiently low densities to maintain single collision conditions. Second, HF productvelocity resolution is adequate to observe Doppler-broadened line shapes due totranslational energy of the HF(v,J) product and thereby elucidate correlations between
internal quantum state (i.e., rotation and vibration) and recoil away from the transition
state. Most importantly, the availability of such quantum-state-resolved
Dopplerimetry results hopefully provides the necessary stimulus for further ab initio
development of high-quality potentials as well as novel dynamical pictures for atom +polyatom reactive scattering.
The remainder of this chapter is organized as follows. In Section 4.2, theexperimental setup is briefly described. Section 4.3 describes the extraction ofcolumn integrated densities for nascent HF(v,J) distributions. Section 4.4 presents
Doppler analysis of the experimental HF(v,J) absorption profiles, which reveal astriking linear correlation between translational energy release and rovibrational
excitation of the ethyl radical fragment. This trend is interpreted in the context of asimple impulsive model, based on conservation of linear and angular momentum, that89

nearly quantitatively reproduces the observed behavior and permits nascent HF(v,J)
fluxes to be inferred via a simple model of the density-to-flux transformation.
Concluding comments are summarized in Section 4.5.

4.2 Experiment
The infrared laser and crossed jet apparatus used for this experiment havebeen described previously.52,53 Thus only details relevant to the current study will bebriefly summarized. Single collision reaction dynamics are investigated in a 216 L
vacuum chamber (60 cm × 60 cm × 60 cm), at the intersection region 5 cm
downstream of two unskimmed, pulsed supersonic valves oriented at right angles.
The reagent pulsed jet delivers a 10% ethane gas mixture in He diluent through a 500µm pinhole orifice driven with a piezoelectric valve, with typical backing pressures of
200 Torr and 500 µs pulse duration. Fluorine radicals are efficiently formed from
dissociative electron attachment in a F2/He mixture though a modified solenoid valve
body with a 5 mm × 0.3 mm slit orifice, with a pulse duration of ≈ 2 ms. The F atoms
are formed in the F2/He stagnation region by a fast discharge (600 volts, 100 mA peakcurrent), timed to occur only at the center slice (500 µs) of the gas pulse. The
discharge is confined upstream of the expansion orifice via bias polarity and interacts
with the supersonic gas for ≈ 1 µs. The ethane and F atom jet speeds can be measured
directly (in real time) by translating a small microphone inside the chamber and arefound to be 1.38(6) × 105 cm/s and 5.49(37) × 104 cm/s, respectively. This is in good
agreement with supersonic jet predictions based on the relevant gas mixtures and heat
capacity ratios.54

90

The chamber is pumped with a 10-inch oil diffusion pump (5000 L/s) andbacked by a 300 L/s roots-blower/mechanical-pump combination. With both pulses
operating, the average pressure in the chamber is < 1 × 10-5 Torr, which translates
into mean free collision paths of 300 cm, i.e., greatly in excess of the chamber
dimensions. Peak densities in the intersection region are 1.0 × 1013 molecules/cm3,
corresponding to net reaction probabilities for F atom abstraction of < 1%, andsufficiently small to make the probability of rovibrationally inelastic collisions
negligible on the transit time scale through the reaction zone. By way of supporting
evidence, the nascent HF(v,J) populations are detected with superthermal velocity
distributions, despite the expectation of collision cross sections for translational
equilibration considerably larger than for rovibrational relaxation events. Indeed,high-resolution Doppler analysis of these nascent velocity distributions proves usefulin characterizing translational energy-release dynamics of the reaction event, as will
be discussed in Section 4.4.
The nascent HF(v,J) distributions are probed by direct absorption of a highresolution color-center infrared laser source, pumped by the 647 nm red line of anactively amplitude-stabilized krypton ion laser. The infrared laser output is attenuatedto <100 µW to avoid optical saturation of the nascent HF transitions and split into
probe and reference beams. The probe beam is then multipassed (16 times) throughthe jet intersection region in a Herriott cell configuration to increase absorption
sensitivity. Both probe and reference beams are focused onto matched InSb
photovoltaic detectors (0.5 mm × 0.5 mm) with 1MHz transimpedance amplifiers.
The resulting photocurrents monitored in dual beam subtraction mode with fast (1091MHz) active servo-loop electronics for reducing common-mode technical-amplitude
noise to near shot-noise levels. Typical rms absorbance noise is ~1 × 10-4 absorbanceunits in a 10 kHz bandwidth, corresponding to a detection limit of < 1.0 × 109 HF
molecules/cm3/quantum state.
These time-dependent nascent HF absorbance signals for a given absorption
frequency rovibrational transition are captured with a transient digitizer on a pulseby-pulse basis. Residual noncommon mode noise in the probe beam is further filteredby 100 µs gating and baseline subtraction before/after the pulse, yielding Dopplerresolved absorption signals as a function of laser frequency in ≈ 4 MHz increments.
Column-integrated populations are obtained by directly integrating over these
Doppler profiles and converting with known HF transition moments.53,55 Relative
frequency calibration is provided by simultaneously recording etalon transmission
fringes [free spectral range (FSR) ≈ 150 MHz]. Absolute IR frequencies are
determined with a traveling Michelson interferometer which facilitates tuning to a
specific HF transition.56

4.3 Results and Analysis
4.3.1

Data collection
The energetics of the F + ethane reaction are summarized in Fig. 4.1. The

reaction exothermicity is 37.8 (±1.0) kcal/mol,57,58 which, in addition to an
experimental collision energy of Ecom = 3.2(6) kcal/mol, translates into a total energy
release of 41(1) kcal/mol. The uncertainty in the collision energy is due primarily toangular divergence in the unskimmed jet geometry, but represents less than 2% of the92total energy release for such an exothermic reaction. Also indicated in Fig. 4.1 are theenergetically allowed HF rovibrational states, which range up to HF(v = 3,J = 8) for
stationery reactants and HF(v = 3,J≈12) for Ecom = 3.2(6). Note that the HF(v = 4, J =0) manifold is not accessible; thus any v = 4 ← 3 transitions must arise purely due toabsorption from the lower state.

Figure 4.1 Energetics for the F + C2H6 reaction. The sum of reaction exothermicity(∆H≈37.8) and center-of-mass collision energy (Ecom≈3.2) yields 41(1) kcal/mol,allowing energetic access to product states as high as HF(ν=3,J≈13).

93

High-resolution infrared-absorption Doppler profiles have been recorded forall product HF rovibrational transitions accessible within the 2.5 – 3.1 µm tuning
range of the color-center laser. Each profile is scanned over a ≈ 0.1 cm-1 (3000 MHz)frequency interval with 3 MHz step size, yielding ≈1000 data points per profile. This
scan range is 3–10 times larger than a typical HF product absorption at full-width
half-maximum (FWHM) of 0.01 – 0.03 cm-1. Data collection comprises
approximately 75 R and P transitions from HF in v = 0, 1, 2, and 3 manifolds. Eachtransition is scanned multiple times (typically ≈ 6 – 9 fold) to improve statistics.
Probing on both P and R branches provides a two-fold redundancy for transitions outof the same lower state, substantially overdetermining column-integrated populations
inferred from subsequent least-squares analysis. The massive size of this data set
requires acquisition over several months of experimentation; thus, all absorption
intensities are measured with respect to a reference transition [HF(v = 4 ← 3) R(3)] tocalibrate for long-term drift and day-to-day variations in the F-atom discharge
efficiency. Additionally, for transitions from the lowest HF(v = 0) vibrational
manifold, Doppler profiles are scanned with and without the ethane reagent pulse, tocorrect for trace background absorbance due to jet cooled HF (v = 0) impurities fromthe F atom source.

4.3.2

Nascent column-integrated densities
The data are treated in several ways. First of all, each Doppler profile isnumerically integrated over all frequency steps to obtain quantum-state-resolved–
column-integrated absorbances in absolute units, increasing typical signal-to-noise94

ratio (S/N) of the raw profiles by a factor of 10. These integrated absorbances are thenconverted to column-integrated densities by the following expression55

8π 3 v 0 m µ 2 ⎡ ∫ [ HF (v" , J " )]dl ∫ [ HF (v' , J ' )]dl ⎤∫ A(v)dv = 3hc ⎢⎢ (2 J "+1) − (2 J '+1) ⎥⎥ ,
⎣
⎦

(4.1)

where µ is the v’,J’ ← v,J transition dipole moment obtained from studies by Setser
and Swalley,55,59 m = -J, J + 1 for P and R branches, respectively, and v0 is the rest
transition frequency. As in any direct absorption measurement, these columnintegrated densities reflect the difference between upper and lower state
concentrations. Therefore, individual state populations are obtained by least-squares
fitting the data set, with populations in energetically inaccessible states HF(v = 4 andhigher) constrained to zero. This process involves sequential fitting of higher v states
to obtain populations in lower states; thus uncertainty in the fitted values increases
with decreasing v. Nevertheless, the high statistical quality of the data set permits
unambiguous determination of nascent populations even in v = 0, which would beunobservable in conventional IR fluorescence measurements. The results for nascentquantum-state-resolved populations are summarized in Fig. 4.2. We will return tothese populations later in Section 4.4 to correct for density to flux transformation andto interpret the resulting nascent fluxes.

95

Figure 4.2 Nascent column-integrated densities for formation of HF(ν,J) in specificrovibrational states from single collision F + C2H6 reactive events at Ecom = 3.2(6)kcal/mol. Note the extraction of absolute densities that are feasible in direct IR laser
studies due to measurement of absolute absorbances.

964.3.3High-resolution infrared dopplerimetry
The high-resolution Doppler profiles themselves contain important additional

information on the reaction dynamics. At a cursory level, inspection of the sample
Doppler profiles in Fig. 4.3 reveals transitions with both absorption/stimulated
emission character. All v = 4 ← 3 profiles reflect pure absorption signals, since the v= 4 vibrational manifold is energetically inaccessible. By way of contrast, all of the v= 2 ← 1 transitions are dominated by stimulated emission, reflecting a strongly
inverted population with increasing vibrational quantum states. However, what occurs
more often are mixed-stimulated-emission and “stimulated-absorption” Doppler
profiles, as exemplified by the HF(v = 3 ← 2) R(2) line in Fig. 4.3 and indicating avelocity-dependent population inversion. This inversion naturally arises fromconservation of energy and reflects the smaller range of translational recoil speeds
energetically accessible for the upper vs. lower probe states. It is worth noting thatwith the exception of the highest energy HF(v = 3,J) levels, all these Doppler profiles
are translationally “hot,” which under non-single collisions would be rapidly
thermalized by postreactive collision events. This observation provides additional
confirmation for single collision conditions in the intersection region.

97

Figure 4.3 Sample high resolution profiles of HF(ν,J) nascent product states fromthe F + C2H6 reaction, indicating strongly competing Doppler structures due to (i)stimulated absorption [HF(ν = 4 ← 3),R(0)], (ii) competition between stimulated
emission and stimulated absorption [HF(ν = 3 ← 2),R(2)], and (iii) stimulated
emission [HF(ν = 2 ←1),R(1)]. Solid lines are least-squares fits to Gaussian lineshape functions, revealing velocity-dependent population-inversion effects dependent
on upper- and lower-state translational energies.
Although the intrinsic probe laser resolution (∆ν ≈ 0.0001 cm-1) translates intoa velocity resolution along the laser axis of ≈10 m/s, detailed structure in this98

distribution is effectively averaged due to finite aperture effects in an unskimmed
beam. To extract average HF(v,J) product-recoil speeds and translational-energy
components along the laser axis, therefore, each absorption or emission Doppler
profile is fit to a Gaussian curve using nonlinear least-squares fitting methods.
Parameter correlation restricts the transitions that can be least-squares fitted to
predominantly pure absorption or emission profiles. Doppler widths from leastsquares fits to the pure absorption and/or stimulated emission profiles are converted
into expectation values of <Ez> = <pz2/2M> along the laser axis (i.e., perpendicular tothe plane of the reactant jets) via the standard Doppler expression4522⎛ ∆v c ⎞ M
pz< Ez > == ⎜⎜ D ⎟⎟,2M⎝ v0 ⎠ 16 ln 2

(4.2)

where ∆vD is the Doppler width, v0 is the transition frequency, c is the speed of light,
and M is the molecular mass. In essence, Eq. (4.2) represents the second moment of
the HF momentum distribution projected along the laser probe z-axis.
These Doppler-width data reveal a remarkable trend (see Fig. 4.4). The totalenergy available to both HF and ethyl product fragments is Etotal = Ecom + Erxn ≈ 41(1)kcal/mol. Since the internal rovibrational energy (EHFinternal) of a given HF quantum
state is known spectroscopically, the remaining energy available (Eavail) for either (i)translational recoil or (ii) rotation/vibration of the ethyl radical can be predicted from
Eavail = Etotal - EHFinternal. The energies associated with the experimentally measured HF
z-axis recoil distributions [i.e., Eq. (4.2)] are plotted in Fig. 4.4 as a function of Eavail.
Despite the large number of degrees of freedom and potential complexity in such areaction, the data reveal a surprisingly simple linear correlation between <Ez> =99

<pz2/2MHF> and the available energy, with a slope of m ≈ 0.12(1). Given the size of
this system, such an unambiguous correlation between HF internal and recoil energies
strongly suggests the presence of dynamical constraints guiding the reaction
dynamics. The origin of these constraints is further investigated in the context of asimple impulsive model described in the following section.

Figure 4.4 Recoil energy plots from high-resolution Dopplerimetry of single HF(ν,J)
quantum states. The data indicate a clear linear dependence between (i) <EHF(trans)>≈ 3<Ez> and (ii) Eavail = Etot – EHF(ν,J), i.e., the remaining energy available for both
HF/ethyl translation and vibration/rotation/translational excitation of the ethyl radical.
Note the excellent qualitative agreement with simple impulsive model predictions.

100

4.4 Discussion

4.4.1 Impulsive model (rotation/translation)
For any atom + diatom reaction system, energy flowing into the nascentdiatomic product comes at the expense of translational recoil (neglecting electronic
excitation of the atom). Thus, conservation of energy and momentum generates anatural anticorrelation between internal and recoil energy of the nascent diatomic
product. However, it is not clear how such dynamical behavior might be altered in
atom + polyatomic systems, specifically by additional rovibrational degrees of
freedom in the nascent polyatomic fragment. Indeed, there have been several
interesting models proposed for A + BC reactive scattering, with various forms ofenergy release and repulsive interaction between the recoiling fragments.4,60 Whatmakes the F + ethane case particularly intriguing is the presence of such a large leverarm in the ethyl fragment, which can significantly shift the dynamics of energy
release from atom + diatom treatments. This poses an interesting and open question,
toward which the linear correlation in Fig. 4.4 provides important initial clues.
As a limiting case, we consider a simple impulsive model for the energy
partitioning in the F + C2H6 reaction, based purely on conservation of angular/linear
momentum and total energy. In this model (illustrated in Fig. 4.5), the product ethyl
fragment is treated as a rigid object with moment of inertia, I, that is rotationallyexcited by momentum recoil from the departing HF product. The final HF(v,J) state iswell characterized by detection with the high-resolution IR laser. Thus, the total
amount of available energy, Eavail, for distribution into translation (of ethyl and HF)
and rovibration (of ethyl) is fixed by energy conservation:101

Eavail = Etrans(HF) + Etrans(ethyl) + Erot(ethyl) + Evib(ethyl) .

(4.3)

The fractional amount of energy that flows into ethyl vibrations is not immediately
obvious. For a long lived reaction intermediate, as in an IVR model, one might
anticipate a statistical sharing of the reaction exothermicity (∆H) among all degrees of
freedom. From a simple Franck-Condon picture, on the other hand, one would expect
relatively modest excitation of the methylene CH2 bending motion, with internal
vibrational energies much less than ∆H. As will become clear below, the data areconsistent with only relatively modest vibrational excitation of the polyatomic
fragment. We will return to this issue later, but for now, temporarily neglect internal
vibrational excitation of the ethyl radical, Evib(ethyl) ≈ 0.

Figure 4.5 Cartoon depiction of the rotation/translation impulsive model, based
purely on the conservation of linear and angular momentum. The angle (θ) andmoment arm (λ) for delivering torque are calculated from CCSD(T) ab initio
calculations of the transition state (see Table 4.1).

102

In the center-of-mass frame, the HF and ethyl recoil speeds are constrained byconservation of linear momentum, i.e.,
Etrans(HF)/Etrans(ethyl) = Methyl/MHF .

(4.4)

For a known transition state geometry (specifically the angle θ between the newly
breaking C-H bond and the principal A axis), we can therefore estimate the rotational
excitation of the ethyl fragment to beErot(ethyl) ≈ L2/2I ≈ Methyl λ2 sin2(θ)Etrans(ethyl)/I ,(4.5)

where λ is the distance from the methylenic C atom and the ethyl radical center ofmass. This provides a dynamical constraint between Erot (ethyl) and Etrans(ethyl),yielding
Eavail ≈ Etrans(HF) [1+MHF/Methyl + MHF λ2sin2(θ)/I] .

(4.6)

These Doppler profiles are recorded along the lab frame z-axis. However, theangular divergence in the crossed jet geometry already averages over a substantial
range of incident/recoil angles in the center-of-mass frame. If we make thesimplifying assumption that these momentum-recoil distributions are approximately
equivalent along each of the three axes, <Ex> ≈ <Ey> ≈ <Ez>, one obtains:<Ez> ≈ Eavail/{3(1+ MHF/Methyl + MHF λ2sin2(θ)/I)} .

(4.7)

Thus, the impulsive model predicts a simple linear correlation between <Ez> andEavail, as experimentally observed.
We can test this prediction further by calculating the H-C-C bond angle θ,
moment of inertia I, and distance to center of mass λ at the transition state geometry.
This has been performed at a series of ab initio levels up to CCSD(T)/6-31G*,61
yielding θ = 109.8, l = 0.825 Å, and I = 22.70 amu Å2. These results predict <Ez> as a103

function of Eavail in Eq. (4.7) to have a slope of m ≈ 0.15. Given the simplicity of themodel, this value is already respectably close to the experimental value of 0.12(1).
We will explore reasons for the residual differences in Section 4.5 but stress here thekey point that elementary conservation of linear and angular momentum (i) correctlypredicts a linear scaling of HF recoil energy with Eavail, and (ii) accounts for ≈ 80% of
the observed correlation. Given the potential for dynamical complexity that one might
anticipate in such atom + polyatom systems, this is a remarkably simple andencouraging result.

4.4.2 Density-to-flux transformation
The analysis in Section 4.3.2 yields column-integrated densities for productformation into a given nascent HF(v,J) quantum state, whereas cross sections aredefined in terms of product fluxes. To explicitly convert these densities into fluxes
requires information on product velocities to account for distribution of quantumstate-resolved residence times in the laser probe region. Indeed, this is true for any
nonflux-based detection method, e.g., direct absorption, LIF, REMPI, or IR
chemiluminescence. For the F + C2H6 system, no quantum-state-resolved differential
scattering information is available from previous work. Furthermore, although these
IR methods do provide complete resolution of HF(v,J) product quantum states, thevelocity distributions are sampled only along the laser multipass z-axis.
However, the preceding section indicates the presence of dynamical
constraints that may help simplify such a density-to-flux analysis, specifically, thelinear correlation between mean HF recoil in the lab frame and the available energy.

104

In the spirit of this impulsive model, therefore, we first make the simplest assumption
consistent with the data and use it with the best-fit line to experiment (Fig. 4.4) topredict lab frame recoil-velocity distributions as a function of HF quantum state. This
distribution is then used in conjunction with detailed Monte Carlo simulations of thecrossed jet intersection geometry to predict quantum-state-resolved-averaged
residence times, τres, and thus relative detection sensitivity S(v,J) ∝ <τres> for thisstate in the IR laser probe region.20 One can then repeat this process with different
assumed angular distributions and thereby explore the sensitivity of these results for aseries of possible angular distributions.

4.4.3 Nascent HF (v,J) populations
The results of the Monte Carlo simulations, residence times, and density-toflux transformation permit the conversion of experimental column-integrated
densities (Fig. 4.2) into nascent quantum state populations. The results, normalized tounity by summing over all states, are reported in Fig. 4.6. Comparison of the threedifferent scattering models (i.e., isotropic [I(θ) ∝ constant], forward-backward [I(θ)∝ sin2(θ)], and side scattering [I(θ) ∝ cos2(θ)]) shows only rather modest variations in
the inferred populations. This insensitivity to assumed cross section reflects the factthat the translational recoil speeds substantially exceed the initial lab frame velocity,
as well as additional blurring due to angular divergence in the crossed jet geometry.
Indeed, the only significant differences are observed to occur in v = 3, reflecting thesmall amount of recoil energy remaining for the HF product in the highest vibrational
manifold. This weak sensitivity to differential cross section suggests that the density-105

to-flux transformation is quantitatively reliable. However, we note that thefundamental experimental measurements are the column-integrated densities in Fig.
4.2, for which error bars are reported.

Figure 4.6 Nascent product-state fluxes (in relative units) based on Monte Carlomodeling of the density-to-flux transformation. Note the modest sensitivity of thesefluxes to modeling of the differential cross sections.

106

The data illustrate several interesting points. First, when summed over J states,
the relative vibrational populations are 0.28 to 0.43 to 0.12 to 0.16 for v = (3:2:1:0).
This indicates a strong predominance of population funneling into the highest
vibrational levels, consistent with the Polanyi rules5 for maximal deposition of energy
into the newly formed H-F bond. Interestingly, there also appears to be a small, but
substantial, nascent population in the v = 0 manifold, which would have previously
been invisible to IR chemiluminescence methods. Second, the rotational populations
in all vibrational manifolds extend to rather high values of J. This is qualitatively
consistent with a noncollinear transition-state geometry, as is indeed obtained fromCCSD(T) transition-state calculations used in the impulsive model. Third, thoughquite hot, the rotational populations are relatively thermal in nature. Indeed, the mostpopulated HF(v = 2) and HF(v = 3) manifolds are reasonably well fit to a Boltzmann
distribution, with rotational “temperatures” of Trot = 1307 K and 496 K, respectively.
This reflects a considerably cooler distribution for the more vibrationally populated
level, which is qualitatively consistent with less energy available for rotational
excitation. Of dynamical interest, however, these rotational distributions drop to zeroconsiderably below the energetically accessible limits in the v = 2 and v = 3
manifolds of HF. This differs qualitatively from previous studies of F + H2 and F +HD reaction dynamics and signals the presence of additional energy-loss pathways
into the polyatomic ethyl radical.20,53 This interpretation is consistent with thepresence of additional dynamical constraints in addition to conservation of energy,
specifically recoil rotational excitation of the ethyl fragment.

107

Previous work by Bogan and Setser on the F + C2H6 system employed“arrested relaxation” FTIR chemiluminescence measurements in a continuous flow
reactor with much higher densities and residence times in the detection region.51
Although this earlier work focused only on nascent vibrational populations assufficiently “arrested,” the basic trends in the rotational distributions are in fact
similar to what we find. This comparison is highlighted in Fig. 4.7 for the maximally
populated HF(v = 2) manifold; there is very good qualitative agreement with thecollision-free results, though clearly somewhat cooler due to partially unarrested
rotational relaxation prior to the detection event. Similar partial relaxation has also
been noted in comparisons between crossed-jet and arrested-relaxation studies of F +CH4, presumably also caused by collisional effects in the flow reactor.44,45,62 The
more appropriate comparison, however, is obtained by summing over these rotational
distributions to yield nascent vibrational-population ratios of 0.338(4) : 0.520(12) :0.142(1) for vHF = 3:2:1. These vibrational ratios are in excellent agreement with theBogan and Setser values of 0.33 : 0.53 : 0.14, confirming that vibrational relaxation
was indeed arrested in the early flow-reactor studies.

108

Figure 4.7 Comparison of current HF(ν = 2,J) nascent fluxes with previous
vibrational “arrested relaxation” studies of Bogan and Setser. Agreement is generally
quite good, though evidence for partial rotational relaxation is present. However, thenascent vibrational populations from these previous studies, summed over final
rotational states, are in excellent agreement with the current collision-free results.

An important advantage of direct absorption IR laser methods is that it permits
detection of all rovibrational levels, including the nonemitting HF(v=0) manifold. If
we include v=0 populations in the normalization, the nascent vibrational ratios
become 0.283(4) : 0.434(12) : 0.119(1) : 0.165(36). It is worth noting thesubstantially non-zero nascent population in the vHF = 0 manifold, indeed, appreciably
more (40%) than is formed in HF(v = 1). This is dynamically interesting, since
populations in the lowest HF(v = 0) manifolds have been inaccessible in thepioneering chemiluminescence studies of Polanyi, Sloan, Setser and others,51,63 but
were inferred to be nearly zero by surprisal-plot analysis and extrapolation from thehigher-vibrational manifolds. In fact, the present data on F + C2H6 indicate that this is109not always a valid assumption. Furthermore, the nonmonotonic behavior at low vHF
may suggest the presence of “bimodal” reaction dynamics. Specifically, the increaseof HF(v) product with low vibrational excitation may be signaling reactive events that
occur on time scales long enough to permit vibrational energy flow from the F-H-C
transition-state region into the “bath” manifold of vibrational levels supported by the
ethyl fragment. If so, this would indicate an intriguing duality of dynamical
processes, primarily dominated by (i) impulsive energy release localized in thetransition-state region, but nevertheless augmented by (ii) IVR energy flow out of thehighly energized F-H-C moiety and into the polyatomic fragment, on a time scale thatis slow with respect to the bond-breaking and bond-making events.

4.4.4 Dynamic Franck-Condon impulsive model
As a final comment, we return to the impulsive model and offer somerefinements. Based on rigid translational/rotational excitation of ethyl radical, thismodel successfully accounts for the observed linear correlation between Etrans(HF)
and Eavail as well as most (≈ 80%), but not all, of the Doppler recoil energy. In
principle, the residual (≈ 20%) deviations could be due to strongly anisotropic
differential scattering of the HF product in the forward/backward direction, and thus asystematic undersampling of the lab frame recoil kinetic energies. However, based on
the range of collision angles sampled in the crossed jet geometry and the modest
dependence of detection sensitivity on scattering distributions (see Fig. 4.6), this does
not appear likely to account for all of the residual deviations. A simpler explanation110could be that they are due to vibrational excitation successfully imparted to the ethyl
radical, which was explicitly neglected in our zeroth order treatment.
A plausible correction to the impulsive model would be to assume that thebond-breaking event occurs much more rapidly than the methylene group canvibrationally relax to its equilibrium geometry. This would result in a Franck-Condon
excitation of the CH2 group and, from the simplest perspective, predict a constantenergy offset due to sequestering of this relaxation energy in the methylene moiety.
Indeed, such a model has been successfully invoked by Suits et al. in studies of O
atom abstraction of H atoms from hydrocarbons.41 An alternative picture would also
allow for additional excitation of the torsional modes of ethyl radical, though thiswould seem unlikely based on the Cs symmetry of the translational state geometry. In
any event, the relevant relaxation energy can be predicted from high level ab initio
calculations performed at the F--H--CH2CH3 transition state, abruptly removing the
HF to infinity and then using gradient-following methods to relax the ethyl radical toits global minimum. Ab initio results obtained at a series of method/basis set sizes are
summarized in Table 4.1, with CCSD(T)/6-31G* representing the highest level oftreatment. The calculations indicate an increasing trend in relaxation energies, withthe highest level predictions of ≈ 4.24 kcal/mol. This is appreciably larger thancomparable relaxation values (≈ 2.45 kcal/mol) obtained for the F-H-CH3 system,
presumably due to a softer CH2 bending coordinate in the resulting methyl vs. ethyl
radical.

111

Table 4.1. Ab initio results for H-C-C bond angle θ, moment of inertia I, anddistance to center-of-mass λ at transition state geometry.
MethodBasis Set

λ (Å)

CCD

6-31G*CCSD
CCSD(T)2θ (degrees)I (amu Å )E relax (kcal/mole)

0.8222

109.14223.931

3.815

6-31G*

0.8233109.501

23.935

4.086

6-31G*

0.8253109.827

23.997

4.242

The effect of Franck-Condon “sequestering” of energy in CH2 would be tolimit the energy available for vibration/rotation, and thereby shift simple impulsive
model predictions to a higher energy by ≈ 4.24 kcal/mol. Such an additional plot isshown with a dashed line in Fig. 4.4, which proves to be in reasonable agreementwith experiment, particularly at the higher values of Eavail. Larger discrepancies exist
for the lowest Eavail [i.e., highest HF(v,J) states], which could reflect the finite angularspread of lab frame collision velocities for the crossed jet configuration. However, thedescrepancies could also indicate a transition back to a less “sudden” picture of CH
bond breaking, with adiabatic relaxation of the CH2 group made possible in the limitof slow HF recoil. Further confirmation of this elementary treatment and the physicalorigin of excess population in the HF(v = 0) manifold would be extremely interesting
to explore with ab initio direct-dynamics calculations, which are currently
underway.64 In any event, the current state-resolved F + ethane data already provide
strong support for a simple “impulsive model” based on (i) recoil coupling ofrotation/translation fragment energies, suitably modified by (ii) Franck-Condon
vibrational excitation in the relaxing moiety.

112

4.6

Summary and Conclusion
State-to-state scattering dynamics of F + C2H6 → HF(v,J) + C2H5 under single

collision conditions have been studied via detection of nascent rovibrationallyresolved HF(v,J) product states with high-resolution IR laser-absorption methods.
Doppler absorption profiles have been observed for HF(v,J) transitions in allenergetically accessible vibrational manifolds and analyzed to yield nascent columnintegrated densities as a function of rovibrational quantum state. Corrected for thedensity-to-flux transformation, the trends in these data indicate a high-efficiency
vibrational excitation accompanied by relatively modest rotational excitation of the
newly formed bond. This is consistent with Polanyi rules5 for early-barrier dynamics
in atom + diatom systems and in good agreement with high-level ab initio
calculations of a slightly noncollinear F-H-C transition state. Vibrational51,65
populations summed over rotational levels are in excellent agreement with early FTIR
flow-cell reactor studies, though elimination of rotational relaxation is evident undersingle-collision conditions in the crossed jet. Additionally, the IR laser experiment
exploits the unique ability of direct absorption methods to determine nascentpopulations in the non-emitting HF(v = 0) manifold, which for the F + C2H6 system
prove to be substantially more populated than predicted from surprisal analysis trends
in the previously studied HF(v = 1,2,3) manifolds.44 Indeed, the significant populationof vibrationally cold HF (v = 0) might signal the presence of a (minor) parallel
dynamical pathway involving IVR energy flow from HF into the ethyl fragment on
the time scale of the chemical reaction. The prospects for such intermolecular113

dynamics might be further investigated with analytical models for IVR mode
coupling from a F-H-C transition state down along the alkane chain as well as fromab initio direct dynamics calculations.64
Of special dynamical interest, analysis of the high-resolution Doppler profiles
reveals a striking correlation between (i) HF recoil velocities and (ii) the remaining
energy for distribution into translation and rovibrational degrees of freedom for theethyl fragment. This correlation motivates analysis via a simple “impulsive model”
based on sudden energy release from a transition-state geometry and invoking
conservation of energy, linear momentum, and angular momentum. This model
successfully predicts the experimentally observed correlation between HF recoil andexcess energy, and accounts for the majority (≈ 80%) of the ethyl fragment excitationin the form of translational recoil and end-over-end tumbling perpendicular to the CC bond. The remaining ethyl internal energy predicted from this experimental
correlation is consistent with a Franck-Condon-like excitation of the CH2 moiety, due
to a ≈ 4.5 kcal/mol relaxation of the spectator methyl group into a sp2-hybridized
methylene radical center. More work, both experimental and theoretical, will clearlybe required to test if such a simple model will prove generally applicable in
exothermic atom + polyatom reaction systems. However, this would appear apromising zeroth order paradigm with which to approach the potential complexity ofreaction dynamics beyond A + BC.

114

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126

APPENDIX

This section documents the numerous computer programs used in JILA B212
for processing data files, concatenating scans, generating spectral predictions, andrunning least-squares fits on the data. Appendix A details the processing andconcatenation programs; it comprises programs which were written before my timebut, until now, have no documentation. Appendix B summarizes and directs the user
to appropriate programs for generating predicted spectra and running least-squares
fits on assigned line centers. Finally, Appendix C comprises my contribution to thedata analysis, in the form of an extensive least-squares program used for the fitting ofactual line shapes to fine and hyperfine structural parameters. Many thanks are owed
to David Nesbitt as well as John Brown’s group at Oxford for their assistance withexhaustive benchmark tests and comparisons with program predictions to yieldagreement to machine precision.
Chandra Savage and Thomas Haeber have provided helpful reviews of theseappendices, and Feng Dong deserves significant recognition for his authorship of theOrigin programs.

127

A. PROCESSING AND CONCATENATION PROGRAMS

A.1 Introduction
If there is one service I would like to leave my successors in JILA B212, it isdocumentation for the processing, linearization, and spectral concatenation programs
required to generate the spectral scrolls. To my knowledge, these procedures havebeen passed on by word-of-mouth only, and one of my biggest frustrations at the startof experiments in B212 was the lack of overlap with anyone who knew this process.
To prevent future such occurrences, this section explains the necessary programs. At
the start of my tenure with these experiments, this process used a series of Fortranprograms on the VMS system. However, by the time I finished doing experiments,
the graphing and visualization program Origin was used exclusively. Instructions forboth methods are provided, including hard copies and/or locations of relevant Fortranprograms and Origin scripts.

128

A.2 Pre-processing of data
Master copies of the Fortran 77 programs referenced here are stored in the[b212.source] directory on the JILA server. Ask anyone in B212 for login andpassword information. This guide is intended only to more quickly facilitate the useof these programs, and the user is advised to review the original code for a moredetailed understanding. Programs may not be modified in the [b212.source]
directory, but they may be copied to individual directories for use. If changes arenecessary, the following compilation, linking, and execution steps are necessary,for program.forlink program.obj,starg/l,nagg/lrun program
where “program” stands for the name of the program to change. Once recorded, theindividual scans must be converted with the “newbin” program into a readable fileformat used by the linearization, concatenation, and printing programs. Basically,“newbin” converts the frequencies and intensities into double precision floating point
numbers. Execution of the different programs simply requires typing the name of the
program (i.e., “newbin”). The output of the “newbin” program adds the prefix “f” toeach scan and is hereby referred to as an “fscan,” indicating that the file now has thecorrect binary format.
For most of the programs, there also exists a “multi” counterpart (e.g.,“multinewbin”) which allows the user to process multiple files by invoking the
program only once. The “multi” version will ask the user for the basename (the part
before the dot in the filename) of the files to change and the start and stop index of
the scan number, used as the file suffix.

129Once converted to a readable binary format, each “fscan” needs to beprocessed by the “et” program. This program analyzes the etalon fringes,
simultaneously recorded with the scanned data, and linearizes the frequency axis byusing the FSR of the etalon. Use the “setet” program to change program parameters,e.g., the FSR. The user is asked to input internal and overall fringe numbers; at thisstage, these inputs can be ignored since the purpose is simply to create a linearized
output from which the fringes can be counted. The output of the “et” program adds
the prefix “l” to each scan, indicating that it has been linearized, and is herebyreferred to as an “lscan”. Each “lscan” can be processed by the “smbl” program,which smoothes the baseline of the scan by averaging over a certain number of points
adjacent to each data point and subtracting this value from the intensity. Care must
be taken when the spectrum contains particularly intense peaks because the result canbe artificially negative regions of the “smoothed” baseline on either side of suchpeaks. The output of the “smbl” program adds the prefix “s” (e.g., smoothed) to eachscan and is hereby referred to as an “sscan”. To prepare the sscan for printing, use
the “uni” program. There are various parameters which can be changed in thisprogram to vary the graphical layout of the output. Even more options are available
with the “setuni” program. The “uni” program always generates a postscript filecalled “riedle.pst,” which is the last name of the famous author of many of these
programs. Printing from the “uni” program can only be done for parts of the full
spectrum for which a frequency range is specified. For final printing of the output
from “uni,” type “post riedle.pst/noflag.”130

Another useful processing program is “irnorm,” which normalizes themeasured signal to the overall infrared power. This program is useful in determining
the absolute absorbance of the signals and asks for a scale factor (default 650) whichshould prevent rounding errors when exporting scan data into ASCII files. Finally,
the “viewlin” program is used to convert binary files into ASCII outputs which canthen be imported into a spreadsheet program such as Excel, Origin, etc.

A.3 Fringe counting and spreadsheet tabulations
With these print-outs from the pre-processing steps, the fun begins. Startingfrom the low-frequency end of the scan and the first fully resolvable fringe, count the
number of etalon fringes across the length of the scan, ending with and including the
top of the fringe at the high-frequency start of the scan (scans are always performed
from higher to lower frequencies). There may be counting numbers printed justbelow the etalon fringes; while helpful, they do need to be verified in the event that a(low intensity) fringe may have been skipped. Also be sure to record the count of thehighest-frequency equally-spaced fringe, which will typically be a couple fringes lessthan the total number of fringes contained in the scan, and will be the fringe at which
the scan is linked to the next high-frequency scan. (This last point also underscores
the necessity of having sufficient fringe overlap between successive scans if one istrying to create a continuous spectrum over a certain region. However, it should also
be noted, and will be explained later, that non-overlapping scans can also be linked.)
After all fringes have been counted in all relevant scans, open or create an
Excel file, typically called “scanlist,” as shown in Figure A.1 (split into two panels)131for a sample chloromethyl scan. An understanding of this spreadsheet format isessential to understanding the Fortran programs which will be explained later. The
most important piece of information in this spreadsheet is the free spectral range(FSR) of the marker cavity (~250 kHz) specified in cell D7, which should be verified
daily and never taken off lock, if at all possible. This value calibrates the distance
between etalon fringes, which is critical for accurately determining the frequency. As
such, only scans with the same FSR can be concatenated.
A

B

C

D

E

F

G

H

4
5
6
IR

Dn/cm

Ar+
fringe#16215.7217

3214.1959

2.79740.06033337.0515

16216.9332

3212.9840

1.58550.01213191.0549

19429.9171

16218.5186

3211.3985

0.00000.00003000.0000

19429.9173

16219.8632

3210.0541-1.34440.02412837.9637

19429.9174

16220.7510

3209.1664-2.23210.03622730.9758

7
8
9
10
11
12
13

Scan

ref.
fringescan0513

FSR

8.298139E-03

0513.001#1d

19429.9176

0513.002#1d

19429.9172

0513.003#1d0513.004#1d0513.005#1d

4
5

offset

J

K

Ar+

R

L

I

dye

M

-1

dye
fringe #

1/cm

N

O

P

Q

R

drift

et
drift

join
freq.

MHz

MHz

GHz

0

0

S

3000
irregularities

6

IR

7
8
9
10
11
12
13

fringe ## offringes
found infile

ref. fringeinternal ref.
#
#

173

100

3337.1117

3337

3264

3264

3191.0669

3191

54

52

3189

3189

0

0

3000.0000

3000

175

172

2997

2997

0

0

2837.9878

2838

151

148

2835

2835

0

0

2731.0120

2731

169

166

2728

2728

0

0

at
GHz
(internal)

Figure A.1 A sample “scanlist” file for chloromethyl radical data collection. The
spreadsheet is split into two panels here for ease of display, and the bold numbers on
the left side of each panel show how they are linked.

132

Column A is the datafile label. Column B is optional and contains
information on which fringe was used for reference in conjunction with thewavemeter readout. Column C specifies which scan (labeled “R” in the figure)contains a known absolute reference line (methane, etc.) against which thefrequencies of the other scans in a set can be calibrated. Columns D, E, and F are theuser inputs for starting frequencies of the argon ion laser, dye laser, and wavemeterIR readings for the specified scan. It is critical here that each scan starts at the top ofan etalon fringe, and not to either side, so that an exact starting frequency can be
assigned and used in subsequent calculations.
Column G values are the frequency differences (cm-1) between the starting IR
frequency of each scan and that of the assigned reference scan (“R”). For scan
0513.001, for example, this quantity (G8) is expressed as (F8-$F$10). Column Hvalues are the number of argon ion laser fringes separating the start of the specified
scan and the start of the reference scan. For cell H8, in Figure 1, this is calculated as
the frequency difference divided by the FSR, or (D8-$D$10)/$D$7. Column I is
calculated similarly for the number of dye laser fringes, where the quantity is thensubtracted from an arbitrary offset (cell K3). This arbitrary offset is also assigned tobe the starting fringe number of the reference scan (cell I10). Subsequent scans arethen concatenated together based on the fringe number at which they start, relative tothat of the reference scan. (For ease of use, it is suggested that this offset be large
enough such that the starting fringe of the lowest-frequency scan is greater than zero.)
The number of dye laser fringes, as just described, is subtracted from this offset
because scans typically proceed towards higher frequencies. For example, in Figure133A.1, I8=-(E8-$E$10)/$D$7+$K$3. The number of IR fringes in column J are again
calculated similarly, but instead added to the same offset (K3) because the scans
typically proceed towards lower frequencies. Again, by way of example,
J8=G8/$D$7+$K$3.
The values in column J may also be used to check the stability of the FSR andthe quality of the data by the extent to which they differ from integer values. An
unstable FSR or sloppy wavemeter measurements of the reference fringe will yield IR
fringe numbers which are very different from integers. Generally, any deviation fromthe correct integral number by less than 5% is acceptable (less than or equal to 0.05).
Column K, then, is just the rounded value of the calculated IR fringe number incolumn J. For example, K8=ROUND(J8,0). Column L is the user input for the total
number of fringes in the scan, as detailed at the beginning of this section, where thelast fringe must be the one which is referenced by the wavemeter values in columns
D, E, and F. (This is quite important !!! because, at this point, the wavemeterreadouts are actually linked to the scans.) Also detailed at the beginning of thissection, Column M is the count of the highest-frequency equally-spaced fringe, which
will typically be a couple fringes less than the total number of fringes contained in thescan, and will be the fringe at which the scan is linked to the next high-frequency
scan. By not using the very last and often distorted fringe, a non-linearity (quite
typical) in the first stages of the scan is omitted. As such, Column N shifts the value
from column M relative to the arbitrary offset in cells K3 and K10. For example,
N8=K8-(L8-M8).

134

Columns P and Q refer to daily frequency drift which can be factored into the“et” programs. Although the marker cavity is quite stable, slightly differentalignments from day to day lead to small changes in the absolute frequency of thefringe for the same fringe number. If a part of a spectrum is measured on different
days, the same spectral region with distinctive bands needs to be measured on anotherday of scanning. Afterwards, the frequencies of these bands in both scans can becompared to determine the drift between days. (Ideally, this drift should be no morethan 5-10 MHz.)

A.4 Concatenation with Fortran programsOnce the fringes have been counted and the spreadsheet has been completed,the user must go back to the “et” program for each scan and assign “internalreference” and “overall” fringes (from columns N and L, respectively). This processassigns relative frequencies to the scans and prepares them for concatenation. In
other words, each scan is put on the same frequency scale by shifting the frequency
axis according to the overall fringe number. It is advisable to again create individual
print-outs with the “uni” program. Now check the overlap between adjacent scans,pick out a “joining” frequency for the two scans and note it in Column R of the
spreadsheet. Both scans will be concatenated at that frequency.
To join the scans, use the joining frequencies from the “scanlist” spreadsheet.
Use the “zus” program, starting with the lowest-frequency scan and concatenating thescans in the direction of increasing infrared frequency. (Note, the lowest-frequency
scan will typically be the highest-numbered scan after a day of scanning since the135scanning is done in the direction of decreasing frequency). The input for “zus” will
go something like this:Input file name: sno1003.010
Join frequency: (freq from spreadsheet)
Input file name: sno1003.009
Join frequency: (freq from spreadsheet)
At the end, save the newly concatenated file and print using the “uni” program.
Printing from the “uni” program can only be done for parts of the full spectrum forwhich a frequency range is specified.

A.5 Concatenation with Origin scripts
The necessary script for spectral concatenation in Origin is “main_et.ogs,”
which are available on the J network drive in the [4djn/B212 Origin] directory. This
script calls upon the following subroutines (available in the same directory) which
also must be accessed. While the “main_et.ogs” script can be renamed and copied to
any location, the subscripts must all be in the same directory and cannot be renamed.
scanlist.ogs
openfile.ogs
DAC.ogs
reverteddigitalfilter.ogs
Fringe2GHz.ogs
relativefreq.ogs
concatenate,ogs
con_plots.ogs
modehop.ogs
The concatenation process in Origin is based on the same principles used in the VMS
programs, and the only major challenge is learning the script syntax. Ths scripts are
written in Origin C, a language similar to C, but with program-specific commands.
Once again, this guide is meant to facilitate the concatenation process by highlighting136

the main steps and key variables. However, the user is strongly advised to refer to therelevant subroutines for a more detailed understanding, especially of variables that areoften not changed.
The key to using the “main_et.ogs” script is to run it in discrete parts andmonitor the outputs along the way. The entire script cannot be run at once! The
subroutine “Path and filename prefix” is run first by highlighting the text from the topof the script to just before the start of the next subroutine (“Import Raw Ascii Data”)
and hitting the carriage return. The filename prefix (%k) and path to the data files(%t) must be specified along with the FSR. Note that the data files must all be in thesame directory. In addition, verify that the subroutines are in fact located in the
directory specified by %n, as this is where Origin will look for them. This section
only needs to be run once for all scans with the same file name prefix and path. If it
doesn’t already exist, this section creates a “scanlist” worksheet, which contains thesame information as the Excel spreadsheet used for the VMS programs.
The next four subroutines can be run (i.e., highlight + carriage return)together, starting with “Import Raw Ascii Data” and ending just before “Calculating
Relative Fringes…”. This section may be run for each scan individually or in a loop.
To loop over multiple scans, modify the FN inputs in the line just below the “Import
Raw Ascii Data” header. In this statement, FN is the starting scan number, and “FN<= #” specifies the ending scan number (“#”). To run the loop, comment out(precede with one or more “/” characters) all lines beginning with “FN=” and uncomment (delete all the “/” characters) the line beginning with “for (FN=” as well as
the “};” on the line just before “Converting channels.”

137

The first section (beginning with “Import”) reads the raw ASCII data file, puts
the scan information into the scanlist, and plots the digitized data. It also creates%kN, %kP, and %kFL files which contain the processed data. The next section(beginning with “Data Baseline”) smoothes the baseline and converts the digitizedsignal into actual absorbance units. In order to accomplish this, the gain must be set.
Currently, its format is [Gain = a x b x c x d], where a is the signal gain on thesubtractor box (1.0 to 0.2), b is the overall gain on the subtractor box (0.045 to 450), c
is the output gain from the subtractor box (0.01 to 1.0), and d is the gain of the lock-in
amplifier, most recently measured at 290. “DACtrue” is a flag to indicate whether
analog-to-digital conversion was used and should be set to 1. The variable“SMFWHM” specifies the number of points on either side for adjacent averagesmoothing. For example, a value of 2 indicates 2 points on either side of each data
point for a total 5-point smoothing. “Nblsm” is the parameter used in the smoothing
procedure and is set to 100. The third section (beginning with “Dye Laser”) counts
the number of fringes from the beginning of the scan, using the parameters “MinY”(the minimum y-value for a point to be counted as a fringe), “err” (the error in thefringe spacing), and “Step” (the estimated step size). If the fringes are strong, set“MinY” to a large value (~ 400). If the program is not picking them up, decrease thevalue until they are all counted. Similarly, the error and step size can be changed if
fringes are missed. The fourth section linearizes the spectrum to obtain relative
frequencies and plots the graph. “GHzPerCM” sets the scale of the graph according
to how many GHz the user wants plotted on 1 cm of the page. “Abmin” and138

“Abmax” are the minimum and maximum y-values, respectively, for the plot. If thedefault values don’t fit all of the data on the page, change them and try again.
The next subroutine (“Calculating Relative Fringes”) can only be run after all
the raw data has been imported. In order for the fringe to be counted properly, theuser must enter the number of missed fringes at the beginning of each scan in the“Missed No” column in the scanlist worksheet. The variable “RefFN” is thereference scan number and is the same as specified in the FN column of the scanlist
worksheet. The variable “RefFringe” is also the same arbitrary offset as in the Excel
spreadsheet described earlier for the VMS programs. “OffRef” is the daily frequency
offset, in GHz, calculated from the reference peak.
At this point, the user should be sure to save the project before concatenating
the individual scans. The two sections dealing with concatenating the data should be
run separately. The first section does the actual concatenation, and the second plots
the data. In order to run this section, the user must enter the starting and ending
frequencies, for each scan to be joined together, in the “JointStart” and “JointEnd”
columns of the scanlist worksheet. This is the same as the join frequency from the“zus” Fortran program. The variable “TotalSN” must also be changed in the script to
the number of scans to be joined.
To concatenate the data and display its absolute frequency relative to a knownreference line, the variable “%f_CM” should be modified to reflect the chosenreference line. Both the literature frequency as well as the relative frequency of thereference line (in GHz) are needed. The syntax is: “%f_CM = [literature freq] +(%f_GHz – [relative freq])/29.9792458. Once the user has entered the values and run

139this section, Origin will copy the appropriate data from the individual scans and pastethem into a single worksheet name %kall. It will then delete the original data, so be
sure to save the concatenated file separately from the original.
Once the data are concatenated, there are several choices for plotting thespectrum. If the spectrum is to be plotted in GHz, set “ifGHz” to 1. For cm-1, set it to
0. “GHzPerCm” sets the horizontal scale, again in terms of how many GHz (or cm-1
if “ifGHz” = 1) per centimeter of the paper. “AbMin” and “AbMax” set the y-scale
as before. They can be the same values used previously or can be different. Finally,
if the user would like to have the peaks labeled on the spectrum, choose them firstusing Origin’s “Pick Peaks” tool, rename the resulting worksheet “Peaks” and set“LabelPeaks” = 1. Otherwise, set “LabelPeaks” to 0. This section of script will plot
the concatenated data on as many graphs as necessary, based on the value of“GHzPerCm”.
The final subroutine is a way of working on mode hopping. It creates the“%pTac” worksheet where one may enter the starting and ending values of the rangeof points that were hopped and then run the next part (“run %n\modehop.ogs”) inorder to cut out the specified range of data. This is a tricky procedure and can ruin
your concatenation if used carelessly. Ask someone who has used it if you are
unsure.

140

B. SPECTRAL PREDICTION AND LEAST-SQUARES FITTINGPROGRAMS

B.1 Predictions
This section outlines the necessary steps for creating spectral simulations thatcan be compared with experimental data, followed by an overview of the programused for least-squares fitting of spectral line centers. As with the programs outlinedin Appendix A, the master copies of these programs are also stored in the[b212.source] directory on JILA.
For simulations, there are currently three programs in circulation: “asy,”“asydjn,” and “asy2005.” Their input files are identical and are shown by thefollowing example . (The numbers preceding each line should not be included in theactual input file; they are only used here to link the respective line of input with its
descriptor at the end of the input file.)

(1)
(2)
(3)
(4)
(5)

input file (ch2f asym stretch) for asy2005
0, 20000
0.0000001, 01, 21021.0882

141

(6)

(7)

(8)
(9)
(10)
(11)
(12)
(13)
(1)
(2)
(3)
(4)

(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)

(13)

265.27136,30.946966,27.728436
0.00007801, 0.001133, 0.019424, 0.00000828, 0.0010260
0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000
261.33515,30.923790,27.701996
0.00007801, 0.001133, 0.019424, 0.00000828, 0.0010260
0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000
0., 292.999796, 292.999796, 0.
0, 20, 1
0,300021.0, 21.0, 21.0, 21.0
3.0, 1.0, 1.0, 3.02
nameiprint-brief(0) or full(1) output, # of points in frequency array
minimum intensity saved, data in cm-1(1) or GHz (0)(unit of all parameters should be the same, in GHz or cm-1)
selection rules (1-photon =1, 2-photon = 2);
for near prolate top band type (A = 1, B = 2, C = 3)
for near oblate top, band type (A = 2, B = 3, C = 1)band origin
lower state rotational constants (starting with A, B, C...)
upper state rotational constants (starting with A, B, C...)energies for lowest state of each nuclear spin symmetry(Ezo(i)=Ezo(1), if Ezo(i)=0, i=2,4)
Jmin, Jmax, Jstep(jmax will be determined automatically, if jmax is set to 0)
range of frequencies saved
Trot for each symmetry species (unit in K)(Trot(i)=Trot(1), if Trot(i)=0, i=2,4)
nuclear spin weight for each symmetry species:(sw(i)=sw(1), if sw(i)=0, i=2,4)
for near prolate top (ee,oo,oe,eo)
for near oblate top (ee,eo,oo,oe)
ipol
[EOB]

Starting with the earliest version of the asy programs, “asy” handles arbitrary
asymmetric tops but is not 100% reliable for all limits. Therefore, a more recent
program, “asydjn,” is recommended for use. The output of both “asy” and “asydjn”
is the binary file “theo.dat.” To convert this output to a readable ASCII format, the142program “asypr” must then be run, creating an unsorted list of predicted frequencies
and intensities known as “raus.lis.”At this point, if one is using the Fortran programs, the “theo.dat” output may
be printed as a simulation spectrum using the “uni” programs described in Appendix
A. No pre-processing is necessary, in contrast to the treatment of the “scan” files. To
obtain a sorted ascii version of “raus.lis,” type the command “sort raus.lis” and entera filename of the type “*.srt” for the output file.
“Asy2005” is different from both “asy” and “asydjn” in that it does not createa binary “theo.dat” output file. It handles oblate or prolate tops and also makes atemperature correction for the nuclear spins (which are handled incorrectly in asy andasydjn). The ascii output of “Asy2005” is, not surprisingly, called “asy2005.dat.”
There is no binary output from “asy2005,” and this program is recommended forprimary use especially if one is not using the Fortran processing programs on the
VMS system.

B.2 Least-squares fitting programs
To do a least-squares fitting analysis of line centers (not lineshapes, as will be
discussed in Appendix C), use the program “asybothdjn” which requires input files ofthe following format called “pinfile.dat.”'generating term values CH2F'
1 10 0 50 50 'A' 1
0265.200000030.948322
00027.727773
0000.00000828
0000.001026
0
0

1
1
1
0
0

265.2000
30.948322
27.727773
0.00000828
0.001026

143

1
1
1
0
0

0
0
0

0.d0
0.d0
0.d0

0
0
0

0
0
0

0
0
0

0.d0
0.d0
0.d0

0
0
0

0
0
0
0
0
0
0
9

0.00007801
0.0011334
0.019424
0.0d0
0.d0
0.d0
0.d0
1021.

2
1
0
0
2
1
0
0

0
1
2
0
1
2
3
0

0
0
0
0
0
0
0
1

0.00007801
0.0011334
0.019424
0.d0
0.d0
0.d0
0.d0
0.d0

0
0
0
0
0
0
0
0

0
0

1 1 0 1 0 1 1254.640
2 1 1 2 0 2 1257.7950

99 2 7 7 2 5 0.

1.
1.
0.

0
0

5

The user is referred to the “Asyboth.for Information” document prepared by Miles
Weida, Sept. 16, 1993 for thorough documentation of the input and programs.
Variations on this program also include “asycombfit,” developed by Feng Dong,
which allow two upper states to be held in common while floated.

B.3 Gaussian convolutions of predictions using Origin programs
To plot Gaussian convolutions of the “asy2005.dat” output, one can use an
Origin script called “GaussConvolution” which is available on the J network drive inthe [4djn/B212 Origin] directory. For this procedure, the use will need the main
“GaussConvolution.org” scripts, as well as the “GaussConvolutionCore.ogs” and“AsySrtImport.ogs” subroutine. All of the scripts should be in the same folder.
“Gaussconvolute” cannot handle the “theo.dat” output from “asy” or “asydjn,” but144can handle the “raus.lis” or “*.srt” outputs from these two programs. See thefollowing notes for an unsorted (i.e., “raus.lis”) vs. sorted (i.e., “*.srt”) output file.
As mentioned in Appendix A, Section 5, the key to using the Origin script is
to run it in discrete parts and monitor the outputs along the way. The entire script
cannot be run at once! The first subroutine (up to and including“run.file(%p\AsySrtImport.ogs)”) should be run on the output from the “asy2005” or“asydjn” program. The user must specify “%p” as the path to the script files, “%t” as
the path to the “*.srt” files, and “%k” as the file name. “Lsmin” is the minimum
calculated intensity that will be imported. Ths “AsySrtImport” script will sort thedata by frequency, so it can handle unsorted (raus.lis) as well as sorted (*.srt) files.
If the file is some other list of lines, import it into an Origin worksheet and run
the second subroutine. In this case, “%k” is the worksheet name, and the data should
be comprised of two columns, the first being frequency and the second being
intensity. The script will sort the data by frequency so that the user does not have tosort it before running the convolution. The final subroutine does the actual
convolution of the data and then outputs the convolution into another worksheet withthe prefix “c” added to the original worksheet name (whatever “%k” is assigned tobe). The important parameters are “FWHM,” the line width at half maximum, andthe step size for the stimulated spectrum. Both of these values must be entered inMHz. As with the concatenation scripts, setting “IFGHz” to 1 will produce an output
in GHz, and setting it to 0 yields wavenumbers.

145

C. LEAST-SQUARES FITTING PROGRAM FOR LINESHAPESThe program “erinhyperfit” is used for least-squares fits of actual CH2F andCH2Cl lineshapes. It is based on a core subroutine called “hyperspecatop” and iscapable of handling doublet asymmetric top radicals (S=1/2) with two different nonzero nuclear spin atoms and including spin rotation, Fermi contact, dipole-dipole, andelectric quadrupole interactions. As with all programs documented in theseappendices, they are archived in the [b212.source] directory on the JILA server. We
have performed exhaustive benchmark test on this program, including a collaborative
comparison with program predictions from John Brown’s group at Oxford, yielding
agreement to machine precision. In the following text, the format of the input file isdetailed for ease of use, and the user is referred to the program “erinhyperfit” formore a more detailed understanding of the calculations. A sample input file isattached at the end for reference.
This input file was used for CH2F to fit one set of ground state parameters andtwo sets of excited vibrational state parameters (for the CH2 symmetric andantisymmetric stretches, respectively). The opening character on line 1, assigned a146value of 0 of 1, denotes whether the program will make a line-shape prediction (1) for
one transition or do a least-squares fitting (0) of a group of transitions. The prediction
option will be discussed in more detail at the end of this section. For now, theremaining input parameters are detailed.
Lines 2-17 are ground state parameters, which are similarly repeated in lines
18-33 and 34-49 for the symmetric and antisymmetric stretch upper states,
respectively. All units are in MHz, unless otherwise noted. For the ground stateparameters, lines 2-9 are the rotational and centrifugal distortion constants (A, B, C,∆N, ∆NK, ∆K, δN, δK). These are followed by fine structure (spin-rotation) terms inline 10 (εxx, εyy, εzz where x = b, y = c, and z = a). For a species of orthorhombic
symmetry such as CH2F, only the diagonal matrix elements (εaa, εbb, εcc) are non-zeroand need to be considered. The spin-rotation centrifugal distortion terms follow inline 11 (∆sN, ∆sNK, ∆sK, δsN, δsK).
Lines 12-14 (15-17) are the hyperfine structure terms for nucleus #1 (#2), in
this case fluorine (hydrogen). The entry at line 12 (15) is the Fermi contact term, a,and the three entries in line 13 (16) are the dipole-dipole interaction tensor elements(Txx1, Tyy1, Tzz1). Line 14 (17) comprises the electric quadropole interaction tensor
terms (Xxx1, Xyy1, Xzz1). Lines 18-33 and 34-49 follow similarly for the two upper
states.
Line 50 specifies the spin of the electron (XS), the spin of nucleus 1 (XI1), andthe spin of nucleus 2 (XI2). The numbering of these two nuclear spins also
corresponds to the ordering of the hyperfine input parameters in each of the groundand two excited states. When “erinhyperfit” is run in prediction mode, the individual147

electron and nuclear spins can be set to zero or nonzero values to make predictions
for a non-perturbed line center, a line with only fine structure, or a line with fully
resolved hyperfine structure.
The next three groupings of input values (lines 51-54, 55-58, and 59-62)
correspond to the three previous sets of input parameters for the ground and two
excited vibrational states. Their values indicate whether to float “0” or fix “1” thecorresponding input parameters. In the example shown, the rotational constants (A,B, and C) are floated for each of the ground and two excited states.
Line 63 is the number of ascii data files (in a two-column format of frequency
and intensity with no headers), up to a maximum of 9, although this maximum
number can easily be modified if necessary. The files are then numbered and namedin the following lines (64-72). These files should be in the same directory as the
program.
The rest of the program comprises the snippets of spectral data whoselineshapes are to be fit. Line 73 is detailed below as it is annotated in the example,
for a sample transition N Ka Kc (upper) Å N Ka Kc (lower).
Nupper;Ka (upper);Nlower;Ka (lower) ;Spectrum number from which raw data originates;
Symmetry of band (A = 0, B = +1, C = -1);
Removes the K degeneracy (= 0 for all K, +1 for Kc (lower) = J, and -1 forKc (lower) = J-1);(h) M aximum K(upper) over which to do hyperfine calculation (= -1 for all K);(i) Maximum K(lower) over which to do hyperfine calculation (= -1 for all K);(j) Low frequency limit for data snippet from ascii file (as specified in (e));(k) High frequency limit for data snippet from ascii file (as specified in (e));(l) Number of points between (j) and (k) over which the “hyperspecatop”
interpolates the calculated spectrum;
(a)
(b)
(c)
(d)
(e)
(f)
(g)

148

(m) Minimum transition intensity included in the calculated spectrum;(n) experimental data offset(o) predicted spectrum offset(p) Band center frequency;(q) Indicates whether to fix (“1”) or float (“0”) the band center frequency (p);(r) Provides the ability to hold the band center in common among more than

one transition. The number entered here is the number of the transition towhich this transition should be linked. For example, the transition notatedin this example is the first transition, and it is hence not linked to anytransition (“0”). However, the third transition listed is linked to the firsttransition and is thus assigned a value of “1” for this parameter. Because
the transition are not numbered, it is suggested that the transition to which
others are linked be listed first so that it is easy to find and reference.
(s) Linewidth (GHz) used in convolution of calculated spectrum;(t) Indicates whether to fix (“1”) or float (“0”) the linewidth (s);(u) The same as (r) but for the linewidth (s) instead of the band center
frequency;(v) Vertical (intensity) scaling factor for the calculation. This number
stretches or shrinks the calculated line shape vertically to match theexperimental intensity.
(w) Indicates whether to fix (“1”) or float (“0”) the vertical scaling factor (v).
It is often useful to set the vertical scaling factor based on a preliminary(by eye) comparison of the calculated lineshape with the experimental
lineshape and then fix it in the least-squares fit of the lineshapes. This
process can often help the program “zero in” on a fit.
(x) Y-axis offset to adjust the baseline of the calculated lineshape to beconsistent with that of the experimental lineshape.
(y) Indicates whether to fix (“1”) or float (“0”) the y-axis offset (seediscussion for (w))(z) Flag indicating whether the entire experimental data snippet should be
included in the fit.

Sample input file for CH2F
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)

0
265320.67
30948.03
27730.46
0.078011.133419.4240.00828
1.026

(10)

-212.0310.97-1040.91

149

(11)

0.

0.0

0.0

0.

0.

(12)
(13)
(14)

184.103-212.310
0.
0.

467.5150.

-255.205

(15)
(16)
(17)

-60.734
24.2
0.0
0.0

1.4
0.0

-25.676

(18)
(19)
(20)
(21)
(22)
(23)
(24)
(25)

261160.34
30935.23
27655.81
0.078011.133419.4240.00828
1.026

(26)
(27)

-207.06
0.
0.0

10.14
0.0
0.

-1046.51
0.

(28)
(29)
(30)

184.103-212.310
0.
0.

467.5150.

-255.205

(31)
(32)
(33)

-60.734
24.2
0.0
0.0

1.4
0.0

-25.676

(34)
(35)
(36)
(37)
(38)
(39)
(40)
(41)

261230.71
30921.20
27698.98
0.078011.133419.4240.00828
1.026

(42)
(43)

-191.48
0.
0.0

-0.33
0.0
0.

-1072.96
0.

(44)
(45)
(46)

184.103-212.310
0.
0.

467.5150.

-255.205

150

(47)
(48)
(49)

-60.734
24.2
0.0
0.0

1.4
0.0

(50)

0.5

0.5

1.0

(51)
(52)
(53)
(54)

0
1
1
1

0
1
1
1

0
1
1
1

1
1
1
1

1
1
1
1

1
1
1
1

1
1
1

1
1
1

(55)
(56)
(57)
(58)

0
1
1
1

0
1
1
1

0
1
1
1

1
1
1
1

1
1
1
1

1
1
1
1

1
1
1

1
1
1

(59)
(60)
(61)
(62)

0
1
1
1

0
1
1
1

0
1
1
1

1
1
1
1

1
1
1
1

1
1
1
1

1
1
1

1
1
1

(63)
(64)
(65)
(66)
(67)
(68)
(69)
(70)
(71)
(72)

9
1 testascii011404.dat
2 test_ch2f_asym1_ascii.dat
3 test_ch2f_asym2_ascii.dat
4 test_ch2f_asym3_ascii.dat
5 test_sde0403shifted_all.dat
6 test_sde0403shifted_all2.dat
7 ascii0321shifted.all2
8 ascii_nscan0318.all
9 ascii_0317shifted.all-25.676(a) (b) (c) (d) (e) (f) (g) (h)

(73)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

2 0 1 0 5 0 1 -1 -1 1335.2 1336.2 2000 0.001 0.0 0.0
1218.6547 0 0 .0602 0 0 420.62 1 23.93 1
1(p)(q) (r)(s)(t) (u) (v)(w) (x)(y)(z)

2 1 2 0 3 1 1 -1 2 1257.0 1259.0 2000 0.001 0.0 0.0
1021.2168 0 0 .0641 1 1 192.93 1 -1.20 11
0 0 1 0 1 0 1 -1 -1 1159.5 1160.5 2000 0.001 0.0 0.0
1218.64 1 1 .074 1 1 78.70 1 -0.83 11
3 0 2 0 1 0 1 2 -1 1393.5 1394.5 2000 0.001 0.0 0.0
1218.54 1 1 .060 1 1 347.0 1 7.61 1
1

151

3 2 3 1 4 1 1 2 2 1919. 1920. 2000 0.001 1919.322 0.0
1021.22 1 2 .065 1 1 100. 0 0.0 01
2 1 2 2 2 1 -1 -1 -1 511. 512. 2000 0.001 511.582 0.0
1021.22 1 2 .065 1 1 100. 0 0.0 0
1
0 0 0 0 -999 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0

0For benchmark testing, we have run the “hyperspecatop” subroutine for the 312←211
transition in CH2F. The input parameters displayed above for the ground state andsymmetric stretch excited state of CH2F have been used, and the outputs for three
scenarios are shown below. The outputs are (1) S=0, I1=0, and I2=0; (2) S=1/2, I1=0,
and I2=0;; and (3) S=1/2, I1=1/2, and I2=0.

Output 1 (S=0, I1=0, and I2=0)transition NU,KaU - NL,KaL
3
1 --A-type band
NBASISU =4
KMAXU =
-1.00000000000000
A,B,C UPPER
261160.340000000
27655.8100000000
SPIN ROT U =-774.079583548531
AFERMI U =184.103000000000
DIP DIP U =-127.602500000000
EQUAD U =0.000000000000000E+000

230935.2300000000
0.000000000000000E+000-60.7340000000000-12.8000000000000
0.000000000000000E+000

upper state eigenvalues
for N =
3.00000000000000
S,I1,I2 =0.00000
0.00000
0.00000xnxk
xs
xj
xi1 xf1 xi2 xf
3.0 1.0 0.0 3.0 0.0 3.0 0.0 3.0
3.0 -1.0 0.0 3.0 0.0 3.0 0.0 3.0
3.0 3.0 0.0 3.0 0.0 3.0 0.0 3.0
3.0 -3.0 0.0 3.0 0.0 3.0 0.0 3.0
NBASISL =2
KMAXL =
-1.00000000000000
A,B,C LOWER
265320.670000000
27730.4600000000

1

eigv.
573506.89537
593183.18432
2436644.28175
2436644.51280

30948.0300000000

152

SPIN ROT L =-767.817054772815
AFERMI L =184.103000000000
DIP DIP U =-127.602500000000
EQUAD U =0.000000000000000E+000

0.000000000000000E+000-60.7340000000000-12.8000000000000
0.000000000000000E+000

lower state eigenvalues
for N =
2.00000000000000
S,I1,I2 =0.00000
0.00000
0.00000xnxk
xs
xj
xi1 xf1 xi2 xf
2.0 1.0 0.0 2.0 0.0 2.0 0.0 2.0
2.0 -1.0 0.0 2.0 0.0 2.0 0.0 2.0

A-type band
N upper =K upper =N lower =K lower =eigv.
407161.50724
416814.21724

3.00000000000000
1.00000000000000
2.00000000000000
1.00000000000000

transitions consistent with band type
and Nupper,Kupper --- Nlower, Klower
Eup
freq

Elo

Kup Klo

Jup Jlo F1up F1lo Fup Flo

inten

593183.18432 416814.21724-1.0-1.0 3.0 2.0 3.0 2.0 3.0 2.0
176.36897 0.88888# of non-zero transitions:1

Output 2 (S=1/2, I1=0, and I2=0)transition NU,KaU - NL,KaL
3
1 --A-type band
NBASISU =14
KMAXU =
-1.00000000000000
A,B,C UPPER
261160.340000000
27655.8100000000
SPIN ROT U =-774.079583548531
AFERMI U =184.103000000000
DIP DIP U =-127.602500000000
EQUAD U =0.000000000000000E+000

230935.2300000000
0.000000000000000E+000-60.7340000000000-12.8000000000000
0.000000000000000E+000

upper state eigenvalues
for N =
3.00000000000000
S,I1,I2 =0.50000
0.00000
0.00000xnxk
xs
xj
xi1 xf1 xi2 xf
3.0 1.0 0.5 3.5 0.0 3.5 0.0 3.5
3.0 1.0 0.5 2.5 0.0 2.5 0.0 2.5
3.0 -1.0 0.5 3.5 0.0 3.5 0.0 3.5
3.0 -1.0 0.5 2.5 0.0 2.5 0.0 2.5
3.0 3.0 0.5 3.5 0.0 3.5 0.0 3.5
3.0 -3.0 0.5 3.5 0.0 3.5 0.0 3.5
3.0 3.0 0.5 2.5 0.0 2.5 0.0 2.5

153

1

eigv.
573321.26302
573753.60908
592835.27628
593647.67765
2435425.95744
2435426.18307
2438263.74571

3.0 -3.0

0.5

2.5

0.0

2.5

0.0

NBASISL =10
KMAXL =
-1.00000000000000
A,B,C LOWER
265320.670000000
27730.4600000000
SPIN ROT L =-767.817054772815
AFERMI L =184.103000000000
DIP DIP U =-127.602500000000
EQUAD U =0.000000000000000E+000

2.52438263.98409

30948.0300000000
0.000000000000000E+000-60.7340000000000-12.8000000000000
0.000000000000000E+000

lower state eigenvalues
for N =
2.00000000000000
S,I1,I2 =0.50000
0.00000
0.00000xnxk
xs
xj
xi1 xf1 xi2 xf
2.0 1.0 0.5 2.5 0.0 2.5 0.0 2.5
2.0 1.0 0.5 1.5 0.0 1.5 0.0 1.5
2.0 -1.0 0.5 2.5 0.0 2.5 0.0 2.5
2.0 -1.0 0.5 1.5 0.0 1.5 0.0 1.5
A-type band
N upper =K upper =N lower =K lower =eigv.
406958.56428
407464.92725
416500.38129
417285.39840

3.00000000000000
1.00000000000000
2.00000000000000
1.00000000000000

transitions consistent with band type
and Nupper,Kupper --- Nlower, Klower
Eup
freq

Elo

Kup Klo

Jup Jlo F1up F1lo Fup Flo

inten

592835.27628 416500.38129-1.0-1.0 3.5 2.5 3.5 2.5 3.5 2.5
176.33489 1.01546
593647.67765 417285.39840-1.0-1.0 2.5 1.5 2.5 1.5 2.5 1.5
176.36228 0.71179
593647.67765 416500.38129-1.0-1.0 2.5 2.5 2.5 2.5 2.5 2.5
177.14730 0.05051# of non-zero transitions:3

Output 3 (S=1/2, I1=1/2, and I2=0)transition NU,KaU - NL,KaL
3
1 --A-type band
NBASISU =42
KMAXU =
-1.00000000000000
A,B,C UPPER
261160.340000000
27655.8100000000
SPIN ROT U =-774.079583548531
AFERMI U =184.103000000000
DIP DIP U =-127.602500000000
EQUAD U =0.000000000000000E+000

154

2

1

30935.2300000000
0.000000000000000E+000-60.7340000000000-12.8000000000000
0.000000000000000E+000

upper state eigenvalues
for N =
3.00000000000000
S,I1,I2 =0.50000
0.50000
0.00000xnxk
xs
xj
xi1 xf1 xi2 xf
3.0 1.0 0.5 3.5 0.5 3.0 0.0 3.0
3.0 1.0 0.5 3.5 0.5 4.0 0.0 4.0
3.0 1.0 0.5 2.5 0.5 3.0 0.0 3.0
3.0 1.0 0.5 2.5 0.5 2.0 0.0 2.0
3.0 -1.0 0.5 3.5 0.5 3.0 0.0 3.0
3.0 -1.0 0.5 3.5 0.5 4.0 0.0 4.0
3.0 -1.0 0.5 2.5 0.5 3.0 0.0 3.0
3.0 -1.0 0.5 2.5 0.5 2.0 0.0 2.0
3.0 3.0 0.5 3.5 0.5 3.0 0.0 3.0
3.0 -3.0 0.5 3.5 0.5 3.0 0.0 3.0
3.0 3.0 0.5 3.5 0.5 4.0 0.0 4.0
3.0 -3.0 0.5 3.5 0.5 4.0 0.0 4.0
3.0 3.0 0.5 2.5 0.5 2.0 0.0 2.0
3.0 -3.0 0.5 2.5 0.5 2.0 0.0 2.0
3.0 3.0 0.5 2.5 0.5 3.0 0.0 3.0
3.0 -3.0 0.5 2.5 0.5 3.0 0.0 3.0
NBASISL =30
KMAXL =
-1.00000000000000
A,B,C LOWER
265320.670000000
27730.4600000000
SPIN ROT L =-767.817054772815
AFERMI L =184.103000000000
DIP DIP U =-127.602500000000
EQUAD U =0.000000000000000E+000

30948.0300000000
0.000000000000000E+000-60.7340000000000-12.8000000000000
0.000000000000000E+000

lower state eigenvalues
for N =
2.00000000000000
S,I1,I2 =0.50000
0.50000
0.00000xnxk
xs
xj
xi1 xf1 xi2 xf
2.0 1.0 0.5 2.5 0.5 2.0 0.0 2.0
2.0 1.0 0.5 2.5 0.5 3.0 0.0 3.0
2.0 1.0 0.5 1.5 0.5 2.0 0.0 2.0
2.0 1.0 0.5 1.5 0.5 1.0 0.0 1.0
2.0 -1.0 0.5 2.5 0.5 2.0 0.0 2.0
2.0 -1.0 0.5 2.5 0.5 3.0 0.0 3.0
2.0 -1.0 0.5 1.5 0.5 1.0 0.0 1.0
2.0 -1.0 0.5 1.5 0.5 2.0 0.0 2.0

A-type band
N upper =K upper =N lower =K lower =3.00000000000000
1.00000000000000
2.00000000000000
1.00000000000000

transitions consistent with band type
and Nupper,Kupper --- Nlower, Klower

155

eigv.
573203.85090
573411.39967
573646.00464
573906.25852
592777.85391
592869.05920
593650.09171
593663.97581
2435395.58206
2435395.80996
2435444.91870
2435445.14239
2438245.67784
2438245.91145
2438282.60288
2438282.84491

eigv.
406845.69419
407037.60442
407369.26226
407627.79087
416441.19535
416531.23150
417277.84557
417306.06874

Eup
Elo
Kup Klo Jup Jlo F1up F1lo Fup Flo
freq
inten
592777.85391 416531.23150-1.0-1.0 3.5 2.5 3.0 3.0 3.0 3.0
176.24662 0.03027
592777.85391 416441.19535-1.0-1.0 3.5 2.5 3.0 2.0 3.0 2.0
176.33666 0.85816
592869.05920 416531.23150-1.0-1.0 3.5 2.5 4.0 3.0 4.0 3.0
176.33783 1.14238
593650.09171 417306.06874-1.0-1.0 2.5 1.5 3.0 2.0 3.0 2.0
176.34402 0.81775
593663.97581 417306.06874-1.0-1.0 2.5 1.5 2.0 2.0 2.0 2.0
176.35791 0.07204
593663.97581 417277.84557-1.0-1.0 2.5 1.5 2.0 1.0 2.0 1.0
176.38613 0.53368
593650.09171 416531.23150-1.0-1.0 2.5 2.5 3.0 3.0 3.0 3.0
177.11886 0.06804
593663.97581 416531.23150-1.0-1.0 2.5 2.5 2.0 3.0 2.0 3.0
177.13274 0.00282
593650.09171 416441.19535-1.0-1.0 2.5 2.5 3.0 2.0 3.0 2.0
177.20890 0.00355
593663.97581 416441.19535-1.0-1.0 2.5 2.5 2.0 2.0 2.0 2.0
177.22278 0.02670# of non-zero transitions:10156