Energy Partitioning in Polyatomic Chemical Reactions:
Quantum State Resolved Studies of Highly Exothermic Atom
Abstraction Reactions from Molecules in the Gas Phase and at theGas-Liquid Interface
byAlexander M. Zolot

B.A., Colorado College, 2001

A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillmentof the requirements for the degree ofDoctor of Philosophy
Chemical Physics
2009This thesis entitled:
Energy Partitioning in Polyatomic Chemical Reactions:
Quantum State Resolved Studies of Highly Exothermic Atom Abstraction Reactions from
Molecules in the Gas Phase and at the Gas-Liquid Interface
Written by Alexander M. Zolot
has been approved for the Chemical Physics program by___________________________David J. Nesbitt___________________________
J. Mathias Weber

Date: ______________

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

iii
Zolot, Alexander M. (Ph.D. Chemical Physics)
Energy Partitioning in Polyatomic Chemical Reactions:
Quantum State Resolved Studies of Highly Exothermic Atom Abstraction Reactions from
Molecules in the Gas Phase and at the Gas-Liquid Interface
Thesis directed by Professor David J. Nesbitt

This thesis recounts a series of experiments that interrogate the dynamics ofelementary chemical reactions using quantum state resolved measurements of gas-phaseproducts. The gas-phase reactions F + HCl → HF + Cl and F + H2O → HF + OH are studied
using crossed supersonic jets under single collision conditions. Infrared (IR) laser absorption
probes HF product with near shot-noise limited sensitivity and high resolution, capable ofresolving rovibrational states and Doppler lineshapes. Both reactions yield inverted
vibrational populations. For the HCl reaction, strongly bimodal rotational distributions areobserved, suggesting microscopic branching of the reaction mechanism. Alternatively, such
structure may result from a quantum-resonance mediated reaction similar to those found in
the well-characterized F + HD system. For the H2O reaction, a small, but significant,branching into v = 2 is particularly remarkable because this manifold is accessible only via
the additional center of mass collision energy in the crossed jets. Rotationally hyperthermal
HF is also observed. Ab initio calculations of the transition state geometry suggest
mechanisms for both rotational and vibrational excitation.
Exothermic chemical reaction dynamics at the gas-liquid interface have been
investigated by colliding a supersonic jet of F atoms with liquid squalane (C30H62), a low
vapor pressure hydrocarbon compatible with the high vacuum environment. IR spectroscopy
provides absolute HF(v,J) product densities and Doppler resolved velocity component
distributions perpendicular to the surface normal. Compared to analogous gas-phase F +hydrocarbon reactions, the liquid surface is a more effective “heat sink,” yet vibrationallyiv
excited populations reveal incomplete thermal accommodation with the surface. NonBoltzmann J-state populations and hot Doppler lineshapes that broaden with HF excitation
indicate two competing scattering mechanisms: i) a direct reactive scattering channel,
whereby newly formed molecules leave the surface without equilibrating, and ii) a partially
accommodated fraction that shares vibrational, rotational, and translational energy with theliquid surface before returning to the gas phase.
Finally, a velocity map ion imaging apparatus has been implemented to investigate
reaction dynamics in crossed molecular beams. Resonantly enhanced multiphoton ionization(REMPI) results in rotational, vibrational, and electronic state selectivity. Velocity map
imaging measurements provide differential cross sections and information about the internalenergy distribution of the undetected collision partner.

For my wife, Sabina, and my mom, Laurel. I have been inspired by your hard work, and I am
eternally grateful for your boundless love, support, and patience.

vi
Acknowledgements
A process as long and arduous as obtaining Ph.D. is impossible to complete without
the help of an army of people who help along the way. This is my feeble attempt to recognize
all those people explicitly, but I will no doubt leave many out, and to them I apologize.
I am particularly indebted to my advisor, David Nesbitt, whose depth ofunderstanding and laser sharp intellect have made my graduate education a challenging andrewarding process. I have also had the opportunity to learn from visiting JILA fellow andJohns Hopkins Professor Paul Dagdigian, who gave the ion imaging experiment a shot in thearm and also seemed to finish another gas-liquid scattering model at home every night.
Thanks to the Nesbitt group members, past and present, for being there in a variety ofways. My lab partner, Danny Bell, who helped clean out a diffusion pump on multiple
occasions, and helped me (or let me help him) build the ion imaging apparatus v.2.0. I’ve
worked particularly closely with Brad Perkins, “the source” of all practical liquid scatteringknowledge, Mike Ziemkiewicz, whose science and non-science insights have taught memuch, and Mike Deskevich, whose tips on Unix scripting revolutionized my computer world.
I’ve also enjoyed learning with and from Nesbitt group members Tom Baker, Julie Fiore,
Melanie Roberts, Erin Sharp, Rob Roscioli, Larry Fiegland, Mike Wojcik, Oliver Monti,
Christian Pluetzer, Jose Hodak, Richard Walters, Chandra Savage, Erin Whitney, Feng Dong,
Vasiliy Fomenko, Thomas Haeber, and Warren Harper.
Outside the Nesbitt group, I have benefited greatly from the assistance of Mathias
Weber, Anne McCoy, and Carl Lineberger. A special thanks for the technical advice at
cookie time with JILA comrades Lenny Sheps, Elisa Miller, Django Andrews, Jeff Rathbone,and numerous other members of the Lineberger, Weber, and Ye groups. Nothing in my lab
would work without the constant input from the JILA mechanical, electronic, and computer
staff; a big thanks to Blaine Horner, Hans Green, Tom Foote, Tracy Buxkemper, Terry

vii
Brown, James Fung-A-Fat, Paul Beckingham, Peter Ruprecht, and many others, whom I havenot pestered as persistently as these poor souls.
Also, to my wonderful family, for their support and patience, and for providing
much-needed distractions, thanks: Matt, Liza, Rachel, Isaac, Alayna, Gabe, Heidi, Mom,
Jeanette, Lloyd, Doug, Sharon, Josh and Zach. I continued to be inspired by the memory of
my Father, Herbert Zolot, who taught me to love learning.
I especially need to thank my beautiful wife Sabina, the only public relations /development expert who knows what it means to fill a Dewar. My love for you is boundless.

viii
Contents

Chapter I Introduction ............................................................................................................................1
References for Chapter I ....................................................................................................................10
Chapter II Experiment..........................................................................................................................18
2.1 Introduction ..................................................................................................................................18
2.2 Infrared Laser Spectrometer.........................................................................................................19
2.3 Crossed Jet Apparatus ..................................................................................................................43
2.4 Data Analysis and Experimental Modeling..................................................................................51
References for Chapter II ...................................................................................................................64
Chapter III Reaction dynamics of F + HCl → HF(v,J) + Cl: experimental measurements and quasiclassical trajectory calculations ..............................................................................................................67
3.1 Introduction ..................................................................................................................................67
3.2 Experiment ...................................................................................................................................72
3.3 Results..........................................................................................................................................83
3.4 Analysis........................................................................................................................................91
3.5 Discussion ....................................................................................................................................93
3.6 Summary and Conclusion ............................................................................................................99
References for Chapter III................................................................................................................101
Chapter IV F + H2O → HF(v,J) + OH: HF(v,J) nascent product state distributions formed in crossed
molecular jets .......................................................................................................................................108
4.1 Introduction ................................................................................................................................108
4.2 Experiment .................................................................................................................................112
4.3 Results and Analysis ..................................................................................................................117
4.4 Discussion ..................................................................................................................................122
4.5 Conclusions ................................................................................................................................130
References for Chapter IV................................................................................................................131

ix
Chapter V Reactive scattering dynamics at the gas-liquid interface: Studies of F + squalane (C30H62)(liquid) via high-resolution infrared absorption of product HF(v,J).....................................................134
5.1 Introduction ................................................................................................................................134
5.2 Static Liquid Experiment ...........................................................................................................139
5.3 Continuously Refreshed Surface Experiment ............................................................................145
5.4 Comparing Results .....................................................................................................................152
5.5 Analysis of Results.....................................................................................................................156
5.6 Discussion ..................................................................................................................................169
5.7 Conclusions ................................................................................................................................174
References for Chapter V.................................................................................................................176
Bibliography.........................................................................................................................................179
Appendices...........................................................................................................................................192
Appendix A: F Center Laser Realignment .......................................................................................192
Appendix B: Ion Imaging Apparatus ...............................................................................................200
Appendix C: F + HCl Quasi-classical Trajectory Simulations.........................................................211
Appendix D: Surprisal Analysis of HF State Distributions Produced By F + H2O..........................219
Appendix E: Estimated State Resolved Branching Ratios ...............................................................222
References for Appendices A–E ......................................................................................................232

x
TABLES
3.1: HF densities and branching ratios following F + HCl → HF(v,J) + Cl

86

4.1: HF densities following F + H2O → HF(v,J) + OH

120

4.2: HF product branching ratios following F + H2O → HF(v,J) + OH

120

5.1: Summary of bond strengths in squalane and approximate reaction energies
for hydrogen abstraction by fluorine atoms

137

5.2: Normalized HF densities produced by reaction of F at the gas-squalaneinterface153

5.3: Energy partitioning following reaction of F with various hydrocarbons

173

A.1: Velocity map ion imaging electrode geometry204

A.2: HF state resolved residence times following F + HCl → HF(v,J) + Cl

224

A.3: HF state resolved residence times following F + H2O → HF(v,J) + OH

227

xi
FIGURES
2.1: Optical elements of the infrared spectrometer21

2.2: The F center laser

24

2.3: FCL tracer beam positioning on intracavity iris26

2.4: The laser wavelength meter28

2.5: The scanning Fabry-Perot interferometer30

2.6: Illustration of the elliptical laser spot positions on the Herriot cell mirrors

37

2.7: Gaussian optics predictions for the IR spot size in the Herriot cell39

2.8: The laser frequency servo loop

42

2.9: Illustration of the reaction vessel

44

2.10: Drawing of the radical jet source

47

2.11: Boltzmann plot of the HF background in the F atom source

49

2.12: Network of accessible infrared HF transitions

53

2.13: Illustration of the Monte Carlo simulation volume

58

2.14: Relative detection sensitivity to HF in the jet intersection region

61

3.1: Reaction coordinate for reaction F(2P) + HCl → HF(v,J) + Cl(2P)70

3.2: Illustration of the experimental apparatus

73

3.3: Sample HF infrared absorption data following the reaction
F + HCl → HF + Cl

77

3.4: Observed HF Doppler distributions

79

3.5: Ratios of HF(J) density at various total gas density

82

3.6: HF density distribution following the reaction F + HCl → HF + Cl85

3.7: HF vibrational branching and comparison to previous studies of F + HCl

87

3.8: HF rotational distributions in v = 2 and v = 1 and comparison to earlier
studies90

3.9: QCT calculations of HF state distribution

95

xii
3.10: Comparison of HF(v = 2,J) following the reactions F + HCl and F + HD

98

4.1: Reaction coordinate for the reaction F + H2O → HF + OH

110

4.2: Schematic of the F + H2O crossed jet apparatus

113

4.3: H2O jet curve of growth

113

4.4: Sample Doppler measurements following reaction F + H2O → HF + OH

115

4.5: HF v = 1 integral absorbance measurements as a function of gas density

118

4.6: Observed and fitted HF infrared stick spectra

118

4.7: HF density distribution following the reaction F + H2O → HF + OH

121

4.8: Comparison of HF vibrational branching in the present and previous studies

123

4.9: Boltzmann analysis of HF rotational populations

128

5.1: Illustration of squalane and possible gas-liquid interface encounters

137

5.2: Energy level diagram for HF and exoergicity for reaction with squalane

138

5.3: Schematic of the static liquid apparatus

140

5.4: Transient HF infrared absorption measurement following reaction at
a static squalane interface

140

5.5: Representative HF Doppler measurements following reaction of F at aliquid squalane surface

142

5.6: Jet density dependence of the observed HF absorption intensities andDoppler measurements

144

5.7: HF density distribution following reaction at the squalane interface

146

5.8: Schematic of the refreshed liquid apparatus

147

5.9: Transient HF infrared absorption measurement following reaction at
a refreshed squalane interface

149

5.10: Sample 3D profile of HF absorption versus frequency and time149

5.11: Sample HF Doppler measurements following reactive scattering aliquid squalane surface

151

5.12: Stick spectrum of HF reactively formed at the squalane interface

151

xiii
5.13: Comparison of HF densities observed following reaction at a static andrefreshed squalane surface with various acquisition time delays

154

5.14: HF transient absorption profiles from various vibrational manifolds

155

5.15: Vibrational distribution of HF product at various delay times

157

5.16: HF vibrational branching comparison following F + hydrocarbon reactions in
the gas phase and at the gas-liquid interface

160

5.17: Boltzmann plots of the HF rotational state distributions

161

5.18: Fit HF Doppler profiles

165

5.19: Trends in HF Doppler fits167

5.20: Comparison of energy partitioning following F + hydrocarbon reactionin the gas phase and at the liquid interface

171

A.1: Essential elements of the FCL laser cavity

194

A.2: Schematic of the ion imaging apparatus

201

A.3: Simulated ion trajectories and equipotential lines in the velocity map
ion imaging apparatus

204

A.4: Background ion spectrum of the HCl jet

210

A.5: Scaling of energy conservation versus QCT step size

212

A.6: Scaling computer time versus QCT step size

212

A.7: F + HCl reaction cross section from QCT calculations

214

A.8: HF state distribution for full QCT trajectories

214

A.9: HF state distributions for trajectories started in the transition state region

216

A.10: HF state distributions for QCT studies of the exit well

218

A.11: Surprisal analysis of HF vibrational partitioning

220

A.12: Surprisal plots of the vHF = 1 rotational distribution

221

A.13: Trends in the calculated HF residence times from Monte Carlo simulation

223

A.14: HF state resolved flux following the reaction F + HCl → HF + Cl

225

A.15: HF flux distribution following F + H2O → HF + OH

228

xiv
A.16: Normalized HF densities and inferred fluxes following F + squalane reaction230

1________________
Chapter I Introduction________________
The field of chemical reaction dynamics, as distinct from kinetics, originated with theadvent of quantum mechanics in the 1920’s. This revolution in physics established the laws
governing the motion of electrons and atoms, enabling the building blocks of matter to beunderstood for the first time and theoretical chemistry to become a topic for exploration from firstprinciples. The first steps toward comprehending elementary chemical reactions were taken by
London,1 who developed the idea of an electronically adiabatic potential energy surface (PES) for
the simplest chemical reaction, H + H2. Eyring, Polanyi, and Sato made further refinements,2,3
leading to methods for constructing semi-empirical surfaces.4 Significant computational hurdles
prevented calculation of PESs from ab initio considerations until electronic computers madelarge-scale numerical calculations possible. At this early juncture, the only experimental
measurements available for comparison were reaction rates, which shed little insight into thefundamental reaction process because of their highly thermally averaged nature.
Experimental methods capable of probing the nature of elementary reaction events began
to be explored in the second half of the twentieth century. Taylor and Datz5 initiated the use ofcrossed beams in their landmark study of the reaction K + HBr → KBr + H, and advances in thistechnique lead to the so-called “alkali era” of reaction dynamics.6 By the late 1960’s, highlysophisticated angular scattering experiments arose, notably in Lee and Herschbach’s “universal
detection” crossed beam apparatus, which detected products with a rotatable electron-impact
mass spectrometer.7 Around the same time, product state distributions began to be probed,
notably by Polanyi using chemiluminescence spectroscopy8 and chemical laser studies byPimentel and others.9,10

2This experimental revolution was soon joined by a new era in theoretical studies, during
which the first semi-empirical, and then purely ab initio, PESs were developed with the help ofelectronic computers in the 1970’s. However, the tools needed to accurately predict the details of
any arbitrary chemical reaction remain out of reach to this day. The fundamental difficulty intheoretical chemistry is obtaining sufficiently accurate solutions to many body problems inquantum mechanics, which are not analytically solvable. In contrast, two body problems arereadily solved, as revealed by the analytical solutions to the hydrogen atom and harmonic
oscillator, to name two chemically relevant examples. However, approximate numerical methodsof solving many body problems arose by the 1930’s, such as Hartree’s treatment of atoms larger
than hydrogen via the self consistent field method.11,12
Numerical solutions to the Schrödinger equation for reactive chemical systems awaitedthe development of electronic computers. These large systems are significantly morecomputationally demanding for many following reasons. First, the cost of ab initio calculations
scales very quickly with the number of atoms and electrons in the system being modeled, suchthat high computational speed is absolutely crucial to obtain results. Secondly, meaningful resultson chemically relevant systems require calculations accurate to less than about 1 kcal/mol,
necessitating high-level theoretical methods13-15 and better and more sophisticated electronic basis
sets.16 Such accuracy is particularly remarkable, as it represents only a small portion of the total
system energy, which is 5–15 eV for loosely held electrons (i.e., 13.6 eV for a free H atom) to
several thousand eV for core electrons in third row elements (almost 4,000 eV for a Cl 1s
electron). Thirdly, accurate, and thus expensive, methods must be repeated at a large number of
atomic coordinates to span the 3N-6 dimensions describing a system with N atoms and construct
the multidimensional PES. Fourthly, after a PES has been constructed, modeling the dynamical
motion of the atoms adds computational expense, particularly when light hydrogen atoms
necessitate sophisticated quantum wave packet methods.17-19 Finally, single-surface methods fail3
due to non- Born-Oppenheimer dynamics, requiring calculations of multiple electronic surfaces,
the coupling elements between them, and multisurface dynamical methods.
Despite these challenges, advances in computer technology over the past two decades
have enabled high-level ab initio PESs in 3N-6 dimensions with chemical accuracy to be
produced for a handful of benchmark three-atom systems, including H + H2,20 O + H2,21 F +H2,22,23 Cl + H2,24 and F + HCl25 reactions. This milestone achievement has already produced
remarkable agreement with experiment, but significant challenges remain. In particular, as moreadvanced calculations are performed, one hopes to find the minimum level of sophisticationneeded to yield accurate predictions, necessitating close collaboration between experiment andtheory. Additionally, because of the increasing computer costs associated with larger chemicalsystems, approximate theoretical methods will be needed for reactions with more atoms than thecurrent state of the art, which can handle N = 4 atom systems in nearly full dimensionality.26-28 In
the foreseeable future, the vast majority of chemical reactions will not be accessible from firstprinciples considerations. Such theoretical hurdles strongly motivate the continued experimental
study of chemical reaction dynamics to provide detailed information on a large number ofchemical reactions with which to rigorously test approximate and limited dimensional theoreticalstudies of larger systems.
Experimental studies of chemical reaction dynamics aim to measure as many observables
as possible, to compare to detailed theoretical results. Using a quasi-classical description of thereaction event, the fundamental results may be expressed as an opacity function O(b,E,N), whichis the probability of reaction occurring with impact parameter b, collision energy E, and the set ofreactant quantum states denoted by the vector N. Kinetic rate constants hide many of these details
by averaging over the thermal distribution of b, E, and N, to provide the rate constant k, which
depends only on temperature. Ideally, dynamical studies specify as many reactant parameters as
possible, while measuring properties of the product, such as the product states N’, and angulardeflection Ω, defined with respect to the reactants’ relative velocity. Since b cannot usually be4experimentally controlled, it is generally integrated over to provide the ideal experimental result:state-to-state differential cross section, σ(E,N,N’,Ω). Thus, a perfect experiment would utilize
reactants with known E and N, and measure the product state distribution P(N’) and differential
cross section dσ/dΩ into each solid angle Ω,. Such detailed measurements would reveal generalfeatures of the reaction dynamics and enable various theoretical methods to be criticallyevaluated.
Practical applications for understanding chemical reactivity from first principles abound.
The physical insight gained from such studies may guide thinking about the nature of chemical
processes, assisting in the emerging field of coherent control, which aims to manipulate chemical
reactions using precisely constructed laser fields.29 In spite of the apparent simplicity ofelementary reactions, they have practical consequences in a number of regimes, including
atmospheric chemistry, combustion processes, the design and use of chemical lasers, and thechemistry of the interstellar medium.30-37
Whether the goal is to increase understanding of fundamental physics that governs
chemistry, or applying this to atomic level engineering, the field of chemical reaction dynamics
depends critically on close interaction between theory and experiment. Thus, the study ofchemical reaction dynamics has evolved into a highly complex field. Specialized experiments
depend upon high-level theory for interpretation, and leading edge theoretical techniques use
experimental results to vindicate novel methods.
Over the past few decades, the tools of experimental chemical reaction dynamics haveprogressed significantly. Skimmed supersonic beams provide cold, localized reactants withnarrow velocity distributions, while pseudo-random chopping of such jets facilitates
measurements of product speed distributions. For “universal” detection, products are ionized byelectron impact, and such detectors have also utilized spectroscopic ionization techniques toprovide state selectivity.38 Concurrent developments in laser technology have enabled novel

5
methods of state resolved characterization of products, including laser induced fluorescence(LIF),39 coherent anti-stokes Raman spectroscopy (CARS),40 Rydberg time of flight detection of
H atoms,41 and resonantly enhanced multiphoton ionization (REMPI). REMPI detection has
recently blossomed in conjunction with velocity map ion imaging (VMII) methods,42-49 whichenable sensitive velocity measurements to be made in conjunction with spectroscopicallyselective ionization. Each of these techniques presents unique advantages and problems withrespect to sensitivity, resolution, and applicability to a given molecular system.
In the Nesbitt group, we have developed high-resolution, high-sensitivity direct detectionof infrared (IR) laser absorption as a method for probing chemical reaction dynamics. IR
measurements result in unambiguous chemical assignments and rovibrational quantum-state
resolution. High-resolution measurements provide Doppler measurements of the producttranslational distributions projected onto the laser axis. High-sensitivity detection enables studies
under low-density conditions, which preserve the nascent distributions formed in the reactive
collision. Additionally, since all molecules other than homonuclear diatomics exhibit transition
intensity in the IR, this detection method can, in principle, be used to detect almost any molecularspecies. Indeed, recent advances in high-power, high-resolution lasers, such as continuous wave
optical parametric oscillators and quantum cascade sources, may lead to broader adoption of IR
absorption techniques. Ch. II includes a detailed description of the ultra-high sensitivity IR
spectrometer used for these dynamical studies.
Additional work has gone into constructing a VMII apparatus, as described in detail in
Appendix B. This new capability builds on remarkable developments over past decade, whichhave enabled vastly improved velocity resolution.50,51 Now, detailed velocity measurements canbe made quickly, without a bulky and expensive rotatable detection apparatus. REMPI
spectroscopy produces state selective generation of ions. Coupling this ion generation techniquewith VMII methods enables the parent ion’s velocity vector to be measured, coming tantalizingly
close to the perfect state resolved differential scattering cross section mentioned above.

6
Both IR spectroscopy and VMII techniques may be used to probe chemical reactions at ahighly detailed level. To fully appreciate the contributions made with these techniques, anunderstanding of the past half-century of reaction dynamics and the current state of the art isneeded. Three-atom systems provide some of the most rigorous tests to theory currently available,
since existing methods enable the PES to be developed in full 3N-6 = 3 dimensionality.25,52,53
Reactions such as H + H2,54-57 O + H2,21,58-60 F + H2,17,61-71 and Cl + H2,24,72-75 have received
particular attention because having only a single “heavy” (i.e. nonhydrogenic) atom makes thenparticularly approachable to high-level theoretical methods. More complicated three-atomsystems have also been treated with high-level theory, such as the reaction of F with HCl, whichis the subject of Ch. III.25
As one particularly well-studied example, the strongly exothermic reaction F + H2 and its
isotopic variants have proven to be an intensely productive focus of investigation from boththeoretical and experimental perspectives. Extensive crossed-beam studies have revealed detailsof reactive scattering, including the differential and integral cross section as a function ofcollision energy,66 as well as complete HF rovibrational quantum state distributions.70 On thetheoretical side, full-dimensional ab initio surfaces have been generated with global accuracy
approaching a few tenths of a kcal/mol.22,23 For three-atom system, rigorous quantum dynamical
calculations of the reaction on one or more electronic surfaces are computationally accessible.19
Indeed, the first definitive examples of elusive transition state resonance dynamics wereidentified experimentally in the isotopic variant reaction F + HD → HF + D68,76 and thenconfirmed in the F + H2 reaction.77 Calculation of non-adiabatic interactions between multiple
spin-orbit surfaces has also become feasible, and such benchmark calculations on the F(2P3/2,
2

P1/2) + H2 system have demonstrated the importance of including non-adiabatic processes.19,78

These theoretical achievements are remarkable for the nearly quantitative agreement withexperiment that has been obtained, and for demonstrating the importance of both i) nonadiabatic
dynamics on multiple surfaces and ii) quantum resonances in the reaction dynamics using

7
wavepacket methods. Indeed, the ability to generate a PES from first principles and obtain resultsfrom numerically exact dynamical calculations that can be rigorously tested against experiment
represents an important milestone achievement by the chemical physics community.
Advances in computational speed also enable existing methods to be tested on more
complex systems. One such step is hydrogen exchange between two “heavy” atoms such as thereaction F + HCl → HF + Cl, which has been studied using the IR spectroscopy to probe thereaction dynamics, discussed in detail in Ch. III. While roughly analogous to the wellcharacterized F + H2 reaction, this system poses significant challenges because it contains nearly
three times as many electrons, which increase the cost of calculating the PES. Also, this system
has low lying spin-orbit excited electronic states in both the entrance and exit channels, which
necessitate high-level dynamically weighted multireference techniques to simulate.25
Although three-atom reaction systems continue to provide key challenges, entirely new
phenomena arise in four-atom and larger systems, such as mode-specific chemistry79-91 andenergy transfer into “spectator” degrees of freedom.92,93 However, as system size increases, sodoes the number of open channels, necessitating considerably more detailed experimental
observations to characterize adequately the reaction channel and correlated product state
distributions. Furthermore, theoretical studies become significantly more challenging as
additional degrees of freedom dramatically increase the computational cost of i) exploring 3N-6
molecular dimensions when generating the PES, and ii) dynamically simulating atomic motion on
one or more electronic surfaces.
In spite of these challenges, the dynamics of polyatomic (i.e. N ≥ 4) reactions have begun
to be computationally feasible. In particular, remarkable advances have been made in developing
an accurate ab initio PES and performing exact quantum reactive scattering calculations for thebenchmark four-atom reaction system H + H2O ↔ H2 + OH.26-28,92 The rate of recent progress inthis dynamically rich reaction suggests that full-dimensional ab initio studies of four-atom

8systems with more than one heavy (i.e., non-hydrogenic) atom will be feasible in the near future.
Recent work by Bowman and coworkers94 on the F + CH4 system has demonstrated that chemical
reactions with N > 4 are also beginning to be accessible, and accurate simulation of increasingly
large systems is becoming attainable.
Of course, there are alternative methods to simulating chemical reactions that do notnecessitate the exploration of the full PES. For instance, direct dynamics techniques enableclassical trajectory simulations to be performed in arbitrary dimensions by calculating the PES
energy and its derivatives “on the fly,” at the nuclear coordinates traversed by a given
trajectory.95-98 However, computational costs in large systems restrict such calculations torelatively low levels of ab initio treatment. Furthermore, this method relies intrinsically onclassical dynamics, making inherently quantum phenomena, such as zero point energy99 andreactions promoted by tunneling through barriers,68 difficult to model.
The current intractability of full dimensional studies for all but the simplest four-atomsystem emphasizes the need for further experimental efforts at the state-to-state level. Such work
provides a crucial opportunity for benchmark testing of approximate theoretical methods against
detailed experimental measurements and stimulates the development of progressively more
rigorous multidimensional quantum computational techniques. Indeed, polyatomic reaction
dynamics remain an active area of investigation. Notable examples include rotationally resolved
studies of F + NH3, F + CH4,100,101 and F + C2H6102 performed by the Nesbitt group, and VMII
studies of F + CH4,45-48 and Cl reacting with oxygenated44 or halogenated43 hydrocarbons.
Theoretical investigations of F + CH4 have been published, and this reaction is emerging as thebenchmark atom plus penta-atom system.94,103 Indeed, this six-atom system appears to be a
fruitful testing ground for reduced dimensional studies, in part due to the large body ofexperimental measurements. Alternatively, the detailed experimental studies of F + H2O
presented in Ch. IV provide stimulus for comparison to more tractable lower dimensional
systems, as reduced dimensional methods continue to be developed.

9Moving further from the realm of full dimensionality and exact ab initio methods, thereaction of F atoms at the surface of a saturated liquid hydrocarbon (squalane, C30H62) ispresented in Ch. V. Although bulk liquids may never be studied in full dimensions using ab initio
treatments, methods for simulating self assembled monolayer surfaces (SAM) and bulk liquids
using molecular mechanics (MM) methods have been developed by Hase and coworkers.104-107
The MM technique enables hundreds of large molecules to be simulated by fitting interatomic
forces to analytical two-body expressions. Meanwhile, Schatz and coworkers108,109 have studied
the scattering of open shell species with quantum mechanical (QM)110 algorithms capable ofdescribing reactive events, as an extension of the MM approach. This computational method has
recently been extended to the study of bulk liquid interfaces, providing direct theoreticalcomparison to liquid scattering results.108,109
The development of theoretical tools capable of modeling such large chemical systems
represents a significant step toward the goal of understanding all chemistry from first principles.
Although simple three- and four-atom gas-phase reactions remain the only systems for which thefull dimensional PES can be computed, the lessons learned on these systems are alreadyproviding insight into reactions at the interface of macroscopic systems. Nevertheless, these earlymodels are likely to miss key elements of the true reaction dynamics, necessitating continued
dialogue between experiment and theory to develop appropriate physical insight and theoretical
tools that can accurately predict chemistry at the atomic level in a wide range of circumstances.

10

References for Chapter I
1

F. London, Z. Elektrochem. Angew. Phys. Chem. 35, 552 (1929).

2

S. Sato, J. Chem. Phys. 23, 2465 (1955).

3

H. Eyring and M. Polanyi, Z. Phys. Chem. B-Chem. Elem. Aufbau. Mater. 12, 279(1931).

4

S. Sato, J. Chem. Phys. 23, 592 (1955).

5

E. H. Taylor and S. Datz, J. Chem. Phys. 23, 1711 (1955).

6

K. R. Wilson, G. H. Kwei, D. R. Herschbach, J. A. Norris, J. H. Birely, and R. R. Herm,
J. Chem. Phys. 41, 1154 (1964).

7

Y. T. Lee, J. D. McDonald, P. R. Lebreton, and D. R. Herschbach, Rev. Sci. Instrum. 40,
1402 (1969).

8

J. C. Polanyi and D. C. Tardy, J. Chem. Phys. 51, 5717 (1969).

9J. H. Parker and G. C. Pimentel, J. Chem. Phys. 51, 91 (1969).

10

K. L. Kompa and G. C. Pimentel, J. Chem. Phys. 47, 857 (1967).

11

D. R. Hartree, Proc. Camb. Philol. Soc. 24, 111 (1928).

12

D. R. Hartree, Proc. Camb. Philol. Soc. 24, 89 (1928).

13

H. J. Werner and P. J. Knowles, J. Chem. Phys. 89, 5803 (1988).

14

R. J. Bartlett and G. D. Purvis, Phys. Scr. 21, 255 (1980).

15

S. R. Langhoff and E. R. Davidson, Int. J. Quantum Chem. 8, 61 (1974).

16

T. H. Dunning, J. Chem. Phys. 90, 1007 (1989).

11
17

S. C. Althorpe, Chem. Phys. Lett. 370, 443 (2003).

18

S. C. Althorpe and D. C. Clary, Annu. Rev. Phys. Chem. 54, 493 (2003).

19

F. Lique, M. H. Alexander, G. L. Li, H. J. Werner, S. A. Nizkorodov, W. W. Harper, and
D. J. Nesbitt, J. Chem. Phys. 128, (2008).

20

Y. S. M. Wu, A. Kuppermann, and J. B. Anderson, Phys. Chem. Chem. Phys. 1, 929(1999).

21

S. Rogers, D. S. Wang, A. Kuppermann, and S. Walch, J. Phys. Chem. A 104, 2308
(2000).

22

K. Stark and H. J. Werner, J. Chem. Phys. 104, 6515 (1996).

23

C. X. Xu, D. Q. Xie, and D. H. Zhang, Chin. J. Chem. Phys. 19, 96 (2006).

24

N. Balucani, D. Skouteris, G. Capozza, E. Segoloni, P. Casavecchia, M. H. Alexander, G.
Capecchi, and H. J. Werner, Phys. Chem. Chem. Phys. 6, 5007 (2004).

25

M. P. Deskevich, M. Y. Hayes, K. Takahashi, R. T. Skodje, and D. J. Nesbitt, J. Chem.
Phys. 124, 224303 (2006).

26

D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 99, 5615 (1993).

27

D. H. Zhang, J. Chem. Phys. 125, 133102 (2006).

28

R. P. A. Bettens, M. A. Collins, M. J. T. Jordan, and D. H. Zhang, J. Chem. Phys. 112,10162 (2000).

29

E. B. W. Lerch, X. C. Dai, S. Gilb, E. A. Torres, and S. R. Leone, J. Chem. Phys. 124,
(2006).

30

R. A. Sultanov and N. Balakrishnan, Astrophys. J. 629, 305 (2005).

31

S. Javoy, V. Naudet, S. Abid, and C. E. Paillard, Exp. Therm. Fluid Sci. 27, 371 (2003).

12
32

D. Gerlich, E. Herbst, and E. Roueff, Planet Space Sci. 50, 1275 (2002).

33

O. D. Krogh, D. K. Stone, and G. C. Pimentel, J. Chem. Phys. 66, 368 (1977).

34

M. J. Berry, J. Chem. Phys. 59, 6229 (1973).

35

C. Zhu, R. Krems, A. Dalgarno, and N. Balakrishnan, Astrophys. J. 577, 795 (2002).

36

D. A. Neufeld, J. Zmuidzinas, P. Schilke, and T. G. Phillips, Astrophys. J. 488, L141
(1997).

37

R. von Glasow and P. J. Crutzen, in Treatise on Geochemistry, edited by R. F. Keeling,
H. D. Holland, and K. K. Turekian (Elsevier Pergamon, Amsterdam, 2003), Vol. 4, pp.
347.

38

P. Casavecchia, Rep. Prog. Phys. 63, 355 (2000).

39

H. W. Cruse, P. J. Dagdigian, and R. N. Zare, Faraday Discuss. 55, 277 (1973).

40

P. M. Aker, G. J. Germann, and J. J. Valentini, J. Chem. Phys. 96, 2756 (1992).

41

X. M. Yang and D. H. Zhang, Accounts Chem. Res. 41, 981 (2008).

42

J. K. Pearce, B. Retail, S. J. Greaves, R. A. Rose, and A. J. Orr-Ewing, J. Phys. Chem. A
111, 13296 (2007).

43

R. L. Toomes, A. J. van den Brom, T. N. Kitsopoulos, C. Murray, and A. J. Orr-Ewing, J.
Phys. Chem. A 108, 7909 (2004).

44

C. Murray, A. J. Orr-Ewing, R. L. Toomes, and T. N. Kitsopoulos, J. Chem. Phys. 120,2230 (2004).

45

K. P. Liu, Phys. Chem. Chem. Phys. 9, 17 (2007).

46

J. J. M. Lin, J. G. Zhou, W. C. Shiu, and K. P. Liu, Chin. J. Chem. Phys. 17, 346 (2004).

47

J. G. Zhou, J. J. Lin, and K. P. Liu, J. Chem. Phys. 121, 813 (2004).

13
48

W. Shiu, J. J. Lin, K. P. Liu, M. Wu, and D. H. Parker, J. Chem. Phys. 120, 117 (2004).

49

J. G. Zhou, J. J. Lin, W. C. Shiu, S. C. Pu, and K. P. Liu, J. Chem. Phys. 119, 2538
(2003).

50

D. W. Chandler and P. L. Houston, J. Chem. Phys. 87, 1445 (1987).

51

A. Eppink and D. H. Parker, Rev. Sci. Instrum. 68, 3477 (1997).

52

G. Capecehi and H. J. Werner, Phys. Chem. Chem. Phys. 6, 4975 (2004).

53

J. F. Castillo, B. Hartke, H. J. Werner, F. J. Aoiz, L. Banares, and B. Martinez-Haya, J.
Chem. Phys. 109, 7224 (1998).

54

D. G. Truhlar and Kupperma.A, J. Chem. Phys. 56, 2232 (1972).

55

R. D. Levine and S. F. Wu, Chem. Phys. Lett. 11, 557 (1971).

56

S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N.
Zare, and E. Wrede, Nature 416, 67 (2002).

57

R. E. Continetti, B. A. Balko, and Y. T. Lee, J. Chem. Phys. 93, 5719 (1990).

58

P. F. Weck and N. Balakrishnan, J. Chem. Phys. 123, 144308 (2005).

59

D. J. Garton, T. K. Minton, B. Maiti, D. Troya, and G. C. Schatz, J. Chem. Phys. 118,
1585 (2003).

60

D. J. Garton, A. L. Brunsvold, T. K. Minton, D. Troya, B. Maiti, and G. C. Schatz, J.
Phys. Chem. A 110, 1327 (2006).

61

M. H. Alexander, D. E. Manolopoulos, and H. J. Werner, J. Chem. Phys. 113, 11084(2000).

62

M. Baer, M. Faubel, B. Martinez-Haya, L. Y. Rusin, U. Tappe, and J. P. Toennies, J.
Chem. Phys. 108, 9694 (1998).

14
63

M. Faubel, B. Martinez-Haya, L. Y. Rusin, U. Tappe, J. P. Toennies, F. J. Aoiz, and L.
Banares, J. Phys. Chem. A 102, 8695 (1998).

64

D. M. Neumark, A. M. Wodtke, G. N. Robinson, C. C. Hayden, and Y. T. Lee, J. Chem.
Phys. 82, 3045 (1985).

65

L. Y. Rusin and J. P. Toennies, Phys. Chem. Chem. Phys. 2, 501 (2000).

66

F. Dong, S. H. Lee, and K. Liu, J. Chem. Phys. 113, 3633 (2000).

67

Y. T. Lee, Science 236, 793 (1987).

68

R. T. Skodje, D. Skouteris, D. E. Manolopoulos, S. H. Lee, F. Dong, and K. Liu, J.
Chem. Phys. 112, 4536 (2000).

69

W. B. Chapman, B. W. Blackmon, and D. J. Nesbitt, J. Chem. Phys. 107, 8193 (1997).

70

W. B. Chapman, B. W. Blackmon, S. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 109,
9306 (1998).

71

W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 116, 5622 (2002).

72

B. F. Parsons and D. W. Chandler, J. Chem. Phys. 122, 174306 (2005).

73

M. H. Alexander, G. Capecchi, and H. J. Werner, Faraday Discuss. 127, 59 (2004).

74

F. Dong, S. H. Lee, and K. Liu, J. Chem. Phys. 115, 1197 (2001).

75

D. Skouteris, H. J. Werner, F. J. Aoiz, L. Banares, J. F. Castillo, M. Menendez, N.
Balucani, L. Cartechini, and P. Casavecchia, J. Chem. Phys. 114, 10662 (2001).

76

R. T. Skodje, D. Skouteris, D. E. Manolopoulos, S. H. Lee, F. Dong, and K. P. Liu, Phys.
Rev. Lett. 85, 1206 (2000).

77

M. H. Qiu, Z. F. Ren, L. Che, D. X. Dai, S. A. Harich, X. Y. Wang, X. M. Yang, C. X.
Xu, D. Q. Xie, M. Gustafsson, R. T. Skodje, Z. G. Sun, and D. H. Zhang, Science 311,
1440 (2006).

15
78

Y. R. Tzeng and M. H. Alexander, J. Chem. Phys. 121, 5183 (2004).

79

R. B. Metz, J. D. Thoemke, J. M. Pfeiffer, and F. F. Crim, J. Chem. Phys. 99, 1744
(1993).

80

M. Brouard, I. Burak, S. Marinakis, L. R. Lago, P. Tampkins, and C. Vallance, J. Chem.
Phys. 121, 10426 (2004).

81

A. Sinha, M. C. Hsiao, and F. F. Crim, J. Chem. Phys. 92, 6333 (1990).

82

A. Sinha, M. C. Hsiao, and F. F. Crim, J. Chem. Phys. 94, 4928 (1991).

83

S. Yan, Y. T. Wu, and K. P. Liu, Phys. Chem. Chem. Phys. 9, 250 (2007).

84

J. B. Liu, B. Van Devener, and S. L. Anderson, J. Chem. Phys. 119, 200 (2003).

85

J. R. Fair, D. Schaefer, R. Kosloff, and D. J. Nesbitt, J. Chem. Phys. 116, 1406 (2002).

86

B. R. Strazisar, C. Lin, and H. F. Davis, Science 290, 958 (2000).

87

C. Kreher, J. L. Rinnenthal, and K. H. Gericke, J. Chem. Phys. 108, 3154 (1998).

88

K. Kudla and G. C. Schatz, Chem. Phys. 175, 71 (1993).

89

M. J. Bronikowski, W. R. Simpson, B. Girard, and R. N. Zare, J. Chem. Phys. 95, 8647
(1991).

90

J. M. Pfeiffer, R. B. Metz, J. D. Thoemke, E. Woods, and F. F. Crim, J. Chem. Phys. 104,
4490 (1996).

91

J. D. Thoemke, J. M. Pfeiffer, R. B. Metz, and F. F. Crim, J. Phys. Chem. 99, 13748(1995).

92

D. H. Zhang, M. H. Yang, and S. Y. Lee, Phys. Rev. Lett. 89, 283203 (2002).

93

M. C. Hsiao, A. Sinha, and F. F. Crim, J. Phys. Chem. 95, 8263 (1991).

16
94

G. Czako, B. C. Shepler, J. B. Braams, and J. M. Bowman, J. Phys. Chem. A(in press)(2009).

95

K. Bolton, W. L. Hase, and G. H. Peslherbe, in Modern Methods for Multidimensional
Dynamics Computations in Chemistry, edited by D. L. Thompson (World Scientific,
River Edge, NJ, 1998), pp. 143.

96

W. Chen, W. L. Hase, and H. B. Schlegel, Chem. Phys. Lett. 228, 436 (1994).

97

S. Rudic, C. Murray, J. N. Harvey, and A. J. Orr-Ewing, J. Chem. Phys. 120, 186 (2004).

98

E. Uggerud and T. Helgaker, J. Am. Chem. Soc. 114, 4265 (1992).

99

G. H. Peslherbe and W. L. Hase, J. Chem. Phys. 100, 1179 (1994).

100

W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 113, 3670 (2000).

101

W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, Chem. Phys. Lett. 335, 381 (2001).

102

E. S. Whitney, A. M. Zolot, A. B. McCoy, J. S. Francisco, and D. J. Nesbitt, J. Chem.
Phys. 122, 124310 (2005).

103

D. Troya, J. Chem. Phys. 123, 214305 (2005).

104

S. A. Vazquez, J. R. Morris, A. Rahaman, O. A. Mazyar, G. Vayner, S. V. Addepalli, W.
L. Hase, and E. Martinez-Nunez, J. Phys. Chem. A 111, 12785 (2007).

105

T. Y. Yan and W. L. Hase, Phys. Chem. Chem. Phys. 2, 901 (2000).

106

T. Y. Yan, W. L. Hase, and J. R. Barker, Chem. Phys. Lett. 329, 84 (2000).

107

T. Y. Yan, N. Isa, K. D. Gibson, S. J. Sibener, and W. L. Hase, J. Phys. Chem. A 107,
10600 (2003).

108

D. Kim and G. C. Schatz, J. Phys. Chem. A 111, 5019 (2007).

109

B. K. Radak, S. Yockel, D. Kim, and G. C. Schatz, J. Phys. Chem. A (in press) (2009).

17
110

G. Li, S. B. M. Bosio, and W. L. Hase, J. Mol. Struct. 556, 43 (2000).

18________________
Chapter II Experiment________________
2.1 Introduction
In the late 1960’s, experimental advances in molecular jets, vacuum apparatus, andmolecular detection via ionization and spectroscopy made measurements of molecular scattering
dynamics possible, revolutionizing the field of chemical physics. Rapid growth in chemical
reaction dynamics lead the Nobel Prize committee, in 1986, to honor Polanyi, Herschbach andLee “for their contributions concerning the dynamics of chemical elementary processes.”1 On theexperimental front, these luminaries instigated the study of chemical reaction dynamics using twocomplimentary techniques. Polanyi’s infrared chemiluminescence method revealed internal state
distributions of molecules immediately following chemical reaction.2 Meanwhile, Herschbach
and Lee obtained detailed angular scattering measurements using a crossed jet apparatus coupledwith a rotatable mass analyzer.3
In the decades following these landmark achievements, the study of chemical reaction
dynamics has progressed into a mature field, and extensive efforts have focused on revealing thedetails of molecular scattering with increasing resolution and sensitivity. Many techniques havebeen developed to measure one or more characteristics of the nascent products, though the “Holy
Grail” of state-correlated differential cross sections remains elusive. However, recent
developments in molecular beam and laser detection methods have come tantalizingly close tothis ideal, with quantum-state resolution and highly detailed velocity distribution measurements.
Two such methods have been utilized in my Ph.D. research, and will be described in this chapter.
Consider a bimolecular reaction of the form,
A + B → C + D,

(2.1)

19
with known collision energy and quantum states of A and B. The quantum state resolved velocity
measurements of one fragment (C) enable the internal excitation of the unseen fragment (D) to beinferred from conservation of energy. One method capable of such state resolved velocity
measurements is high-resolution IR laser spectroscopy, due to its inherent rovibrational
selectivity, and the potential for Doppler resolution. Another method is velocity map ion imaging(VMII), which is considered in more detail in Appendix B. Briefly, VMII provides detailed
measurements of ions’ velocity vector distributions, while state selectivity results from resonantly
enhanced multiphoton ionization (REMPI).

2.2 Infrared Laser Spectrometer
Infrared detection of nascent product molecules provides several unique capabilities. In
addition to spectroscopic quantum-state resolution, IR absorption exhibits very narrow (≈ 1 MHz)
homogeneous linewidths under low-density conditions, typically limited by residence timebroadening in the continuous wave (CW) laser field. Thus, heterogeneous (Doppler) structure canelucidate product velocity distributions. Additionally, since most molecules are IR active, thistechnique can potentially be applied to detect almost any chemical species. Indeed, few otheroptical techniques can detect the HF molecule, the focus of the following work, because of thelack of a suitable fluorescent electronic state for LIF and particularly high energy electronic
states, which complicate ionization spectroscopy.4 Thus, IR detection provides a means of
expanding the number of chemical species whose dynamics can be measured beyond those withsuitable multiphoton transitions.
Key to the IR absorption method is the narrow bandwidth (Δν ≈ 3 MHz) tunable lightsource. The F center laser, also commonly called the FCL or color center laser, used in thepresent work has been discussed elsewhere.5,6 A detailed description of the Burleigh FCL-20 and20detailed realignment procedures comprises Appendix A. In practice, any narrow linewidth,
continuous wave, tunable IR laser could be used to construct such a spectrometer. This section
describes the IR source, the electro-optical diagnostic tools, and the components used to obtainabsorption sensitivity near the fundamental “shot-noise” limit for counting photons.
The optical elements of the apparatus are illustrated in Fig. 2.1 and consist of the tunable
IR source, a polarization stabilized HeNe reference laser (also used as a visible “tracer” beam), a
wavelength measurement device (λ meter), scanning Fabry-Perot cavity, a reference gas
absorption cell, the Herriot multipass cell, a pair of InSb detectors for high sensitivity differential
absorption detection, and a number of other power-monitoring and noise-reducing opticalelements. The following sections describe the electro-optical control of the laser frequency andintensity.

A. The F Center Laser:
The fundamental functioning of the FCL closely parallels that of a common CW dye
laser. A short wavelength pump source, in this case the 647 nm light from a krypton ion laser,
generates a population inversion which fluoresces at longer wavelength, i.e., the infrared. The
gain medium is a salt crystal with Farbe center defects, commonly called color centers or F
centers, which are lattice positions missing a monovalent anion, occupied instead by a single
electron. The pumped transition is “vertical,” i.e., an electronic excitation that occurs while
nearby atoms remain in their ground state equilibrium positions. Following excitation, the atoms
rapidly relax to a new equilibrium position for the excited state. IR fluorescence and stimulated
emission occur via another vertical transition at large Stokes shift, forming a four state laser. The
phonon broadening in the crystal results in a broad, homogeneous fluorescence and therefore alarge tuning range for a narrow pump frequency.

21

Figure 2.1

Optical elements of the infrared spectrometer. A 647 nm krypton ion laser
optically pumps the F center laser through an electro-optical modulator (EOM).
A polarization-stabilized helium neon laser (HeNe) overlaps with the IR laser
beam. The infrared diagnostics include a wavelength (λ) meter, an absorption gas
cell, a chopped-beam photovoltaic power meter, and scanning Fabry-Perot
Interferometer (FPI). Optical feedback from the latter can be isolated with a
Faraday Isolator (FI). Low density HF product is detected with increased path
length in a Herriot multipass cell. Paired InSb detectors detect differentialchanges in probe power with sensitivity near the shot noise limit.

22
Despite this apparent simplicity, color center lasers are notorious for their fickle gain
medium conditions. The salt crystals (primarily KCl or RbCl) are highly hygroscopic, such that
prolonged exposure to moist air is likely to damage their surface polish. Additionally, crystal
coloring occurs by exposing the crystals to a gas of alkali metal, resulting in the needed nonstoichiometric metal cation/chloride ratio and making the crystal reactive to adsorbed water.
Thus, surface roughening results in reaction with water and the formation of OH-, which absorbs
in the IR and seriously degrades crystal performance.
Moisture problems are further complicated by crystal temperature and light constraints.
The laser transition utilizes type II F centers, Cl- vacancies with a neighboring Li atom dopant,which minimize the excited color centers’ non-radiative rate. However, the F center–Li
association is only one of many that may form, and it is somewhat less strongly bound thanaggregates of two or more F centers, whose formation leads to the degradation of laser
performance. Additionally, electronically excited F centers migrate more readily through the
crystal, so aggregate F center formation must be prevented by never exposing the crystal to lightwhen the crystal is warmer than -20 °C, below which temperature the migration of excited type II
centers becomes adequately slow.
The combined constraints of cold and non-condensing conditions necessitate highvacuum as part of the laser apparatus. The crystals are mounted on a cold finger in a vacuum
Dewar, such that they cryogenically cooled while being optically pumped. The crystal chamber
has a built-in sorption pump and is also attached to an ion pump, such that a sufficiently
outgassed chamber has a pressure of about 0.5–2×10-10 Torr. Moving crystals in and out of thecrystal chamber raises the largest hazard. The crystal chamber may only be vented to atmosphere
after completely warming it to room temperature, a process that must be done with acryogenically trapped mechanical pump to remove the sorption-pumped CO2 and H2O as thewarming proceeds. The warmed crystals can only be handled in a darkened room with red

23safelight illumination, preferably with less than 50% relative humidity. Following removal,
crystals must be immediately transferred to a hermetically sealed container, surrounded bydesiccant, and placed in a freezer for storage. Likewise, reinstalling the crystals involves thawing
them before exposure to air and following the other precautions outlined in the Burleigh manual
when preparing the crystal chamber for the gain media.
Two separate color center crystals span the 2.5–3.3 μm region, both conveniently
pumped by the same 647 nm krypton ion wavelength. Crystal 3 (Li doped RbCl) covers the low
energy portion of the spectrum (2.7–3.3 μm) but is used less frequently because monolayers of
ice form on the crystal surface about 1–2 months after thermal cycling, absorbing at longer
wavelengths and reducing the useable tuning range accessed without regular maintenance. Crystal
2, (Li doped KCl) has a tuning range of 2.5–2.8 μm, and is used on a more routine basis while
searching for signal, aligning optics, or other wavelength independent tasks because it does not
suffer as drastically from water absorption, has a higher peak power output, lower lasing
threshold, and can be pumped with greater total power.
Alignment of the FCL must be performed regularly to attain optimal “single frequency”
oscillation on a lone longitudinal mode of the laser cavity. The high gain crystals enable thecavity to support oscillation on several modes simultaneously, necessitating precise aligning of
optical elements, illustrated in Fig. 2.2. This multi-line propensity is particularly significant on
the spatial hole burning mode (SHBM), which originates as follows. The desired longitudinalmode attains the highest gain in the vicinity of its maximum electric field intensity, and thelowest gain at its nodes. Since the cavity modes are standing waves, the positions of the nodes are
fixed in space. Thus, a mode with slightly different frequency (the SHBM) can receive high gain
if its frequency shift is such that its nodes overlap the main mode’s maxima, and vice versa. A
short focal length cavity end mirror separates these two modes by the largest possible frequency,
so the Burleigh design incorporates an f = 0.71 cm end mirror, resulting in an SHB displacement

24

Kr+ Pump Laser

Turning Mirror

Galvonometer
PlatesFolding Mirror

CavityEnd
MirrorDichroic
Beam
Splitter

Output Coupling
MirrorCornerReflector

Intracavity
EtalonGrating Output Coupler
Tuning Arm Chamber

Crystal Chamber

Figure 2.2

The F center laser (FCL), consisting of two independent vacuum regions. The
crystal chamber is always under vacuum when the crystal is present and cooledwith liquid nitrogen. The laser will operate without evacuating the tuning arm,
though operation will be impeded in the vicinity of water lines.

25
of 0.18 cm-1. For single-mode operation, a tunable “intracavity etalon” with a free spectral range(FSR) of 0.6 cm-1 is placed in the tuning arm. This FSR is about three times the frequency
displacement of the SHBM, so it highly attenuates that component of the laser oscillation. To
obtain single mode operation, the cavity end mirror must be carefully adjusted, helping eliminate
the SHBM, and the intracavity iris should be partially closed, to selectively add the loss ontransverse cavity modes other than the desired TEM0,0 mode. Both of these adjustments are madealong with the pump beam (via the input steering mirror) and grating vertical tilt to optimize thesingle mode laser power.
Particular difficulties may be encountered when scanning the laser continuously near theextreme red end of the RbCl crystal bandwidth, below about 3200 cm-1. It was empirically foundthat mode-hopping instabilities in this region mimic those observed when the intracavity etalon
has been tilted in its mount, away from optimal alignment. Specifically, the Burleigh manual
describes tilting the intracavity etalon such that the remnant of the 647 nm beam in the tuning arm(used as a tracer) is reflected from the first etalon surface and positioned on the left edge of thetuning arm iris. This positioning, as viewed from within the tuning arm, is illustrated as point A in
Fig. 2.3. For scanning the FCL below 3200 cm-1, this rotation should be exaggerated by rotating
the etalon further counterclockwise, placing the tracer reflection further to the left on the irismount, point B in Fig. 2.3.

B. Infrared Diagnostics
Two diagnostic devices are used to monitor the IR frequency. The first is a traveling
Michaelson interferometer, or λ meter, based on the design of Hall and Lee,7 which enables
absolute frequency calibration to within about 0.0005 cm-1. A home-built Fabry-Perot
Interferometer (FPI) provides an additional relative frequency calibration and real-time frequency

26

Figure 2.3

Position of the tracer beam reflected from the FCL etalon onto the intracavity
iris, as viewed from the tuning arm. Location A indicates the recommended
position according to the Burleigh manual, and location B is the position found to
facilitate continuous tuning at the extreme red tuning range of the FCL.

27
stability measurement via piezoelectric scanning of its free spectral range. The details of thesedevices are described next.
The λ meter works by counting interference fringes from the unknown (IR) and areference (polarization stabilized HeNe) lasers. Functionally, the IR laser and tracer HeNe are
directed onto a beam splitter and the two resulting laser beams reflect from a moving corner cube
cart, as illustrated in Fig. 2.4. The cart continuously translates on an air bearing, using solenoid“cart kickers” to counteract friction and maintain its back and forth motion without any user
influence. The two beams recombine on the beam splitter and interfere on two photovoltaic
devices, one for the IR and one for the visible beam.
The interference measurements relate to frequency as follows. A laser beam at frequency

ν picks up a Doppler shift Δν after reflecting off the corner cube with speed vcart, according to,Δν = ν vcart/c,(2.2)

where c is the speed of light. Because they reflect off the same cart, one laser channel picks up a
blue shift of ν + Δν, while the other is red shifted to ν - Δν. These beams recombine on the beam
splitter and interfere on a photodetector, producing a beat note (νb) at the difference between
these two frequencies, i.e. 2Δν. An equally valid analysis of this measurement is that when the
cart moves by λ/4 (λ = c/ν is the laser wavelength) then the difference in path length between thetwo interferometer arms changes by λ/2, and the interference cycles 180°, i.e. from constructive
to destructive interference. This cycle occurs every time the cart moves this distance, such thatthe photodetector signal oscillates at νb = 2vcart /λ = 2ν vcart/c, which is the same frequency
predicted under the Doppler picture, above.
The need to know vcart is removed by simultaneously measuring fringes generated by the
unknown IR laser (νIR) and a reference laser beam (νref) on separate detectors. The tracer HeNebeam provides a convenient reference, with precision better than the 1.5 GHz gain bandwidth8 of28

Figure 2.4

Schematic of the laser wavelength meter. A 50% beam splitter divides theincoming beam, containing both λref (HeNe) and λIR (IR), in two. Each beamreflects from a traveling cart, recombines, and lands on two separate
photodetectors. Interference fringes are detected and turned into square waves in
the phase locked loop / discriminator / frequency multiplier. The resulting squarewave is counted on the commercial waveform counter.

29
an unstabilized HeNe. Eq. 2.2 holds for the relation of each beat frequency and the corresponding
laser frequency, such that the ratio of two such equations can be used to find

νIR = νrefνb_IR/νb_ref,(2.3)

where νb_IR and νb_ref are the measured beat frequencies of the IR and reference channels,
respectively.
The λ meter signal analysis electronics also appear in Fig. 2.4. The signal from eachphotodiode is AC coupled and sent though a discriminator, turning the interference waveform
into a TTL pulse train. This square wave is used as the input to a phase lock loop, which servos tothe input frequency, providing a square wave with frequency F = Xνb, where X is a knobselectable frequency multiplier from 1–100. The output of the phase lock loop goes to a Hewlett
Packard “universal counter,” which counts the input square waves, and takes the ratio of the twochannels’ values. This value is multiplied by a calibration constant of 1579.807, corresponding to
the frequency of the reference laser in cm-1, divided by XIR/Xref = 10 for the relative discriminator
multiplier constants, such that the counter displays the IR frequency in cm-1. A typical cart speedof 7 cm/s and phase locked loop multiplication factors of 100 and 10 result in 2.8 and 1.1 million
cycles for the IR and reference channels, respectively, in typical integration time of 0.5 s. Thus,
the fractional frequency uncertainty is less than a part in a million, and the IR frequency can bemeasured with a precision of about 0.0005 cm-1. The accuracy of this measurement varies acrossthe FCL spectrum, but always suffices to locate 0.011 cm-1 Doppler broadened IR transitions.
This absolute wavelength measurement readily enables manual tuning of the FCL to any
desired HF transition, and the second frequency measurement device, a scanning Fabry-Perot
interferometer (FPI) schematically represented in Fig. 2.5, provides precise (1–2 MHz) relative
frequency calibration over short continuous scans. The confocal optical arrangement provides a“bowtie” optical path, and a free spectral range (FSR, in cm-1) given by
FSR = 1/(4L),

(2.4)

30

Figure 2.5

Schematic illustration of the scanning Fabry-Perot interferometer. A HV saw
tooth wave, applied to the PZT on one end-mirror, results in a series oftransmission fringes, which are monitored on a photodiode. The time delay
between the beginning of the saw tooth wave and the arrival of the firsttransmission fringe is recorded on a time to amplitude converter, producing
another saw tooth wave that can be used to calibrate the relative laser frequency.

31
where L is the distance between the cavity end mirrors. An L of 50 cm results in FSR of 0.005
cm-1. The exact value of FSR can be calibrated to better than 1×10-5 cm-1 by monitoring the FPI
output over short scans to get a good estimate of the FSR based on the λ meter reading. Following
small scans, the FCL can be tuned in progressively larger steps, which enable this calibration to
be extended over a very large frequency range and thereby increase the number of significant
digits in the calibration.
For typical diagnostic use, the FPI cavity modulates with a ≈ 500 V saw tooth wave,
applied to the cylindrical piezoelectric transducer (PZT) holding one of the cavity’s opticalelements. This voltage results in a mirror translation of about 2.5 μm, sufficient to make the FPI
resonant with the IR frequency 2–3 times. The scanning cavity has a finesse of approximately 20,
which is often sufficient to diagnose if the FCL is oscillating at one, or more than one, frequency
at a time. However, the 0.005 cm-1 FPI FSR roughly corresponds to twice the FCL longitudinalmode spacing of about 0.01 cm-1, so lasing on adjacent modes can be hard to identify using only
the FPI. Fortunately, such multi-mode oscillation can also be identified by the modulation of thefringe envelope on the λ meter, caused by interference between laser modes. Thus, single
frequency oscillation can be ascertained using the output of these two devices.
After recording short, continuous laser scans (0.3–10 GHz) the scanning FPI is used tocalibrate the frequency axis as follows. As the laser frequency changes, a time to amplitude
converter (TAC) measures the time from the start of the PZT translation to when the first fringe
exceeds a certain threshold voltage on the photodiode, as illustrated in Fig. 2.5. With increasing
laser frequency, the fringes are delayed and the TAC output increases. Thus, the rising edge ofthe saw tooth wave corresponds to an IR fringe moving with respect to the PZT driver pulse,
followed by a very rapid falling edge as the next etalon fringe is detected. Advantages of thismethod are that laser instabilities (particularly “hopping” between longitudinal modes, as occurs
with a poorly aligned FCL) are readily detected as discontinuities in the sloping side of the saw

32
tooth wave, and the abrupt “falling” edges of the TAC output provide markers for calibrating the
Doppler scan with the < 1×10-5 cm-1 precision of the FPI FSR measurement.

C. Intensity Stabilization and High Sensitivity Detection
In order to measure nascent HF product distributions with sufficiently low density tomaintain single collision conditions, absorption sensitivity close to the fundamental shot noise
limit, i.e., the limit determined by the counting of discrete photons, must be attained. In practice,reaching this limit involves i) stabilizing the broad-band laser intensity fluctuations, ii)
subtracting the remaining technical noise from the “signal” detector using a paired “reference”
detector, and iii) carefully aligning optics such that non-common mode noise sources (such as
clipping of the beam in the Herriot cell) are below the shot noise level in the detection bandwidth.
This subsection describes how these three goals are attained.
The first bit of noise reduction results from stabilizing the laser output intensity.
Instabilities in both the krypton ion pump laser and the FCL both contribute to the IR root meansquare (RMS) noise of about 4% of the DC value without active stabilization. A commerciallyavailable “laser noise eater” [ConOptics electro-optic modulator (EOM)], positioned as illustrated
in Fig. 2.1, reduces fluctuations on the 647 nm pump beam, reducing noise at acoustic
frequencies (about 10 kHz and slower) to be unobservable, with most of the remaining (≈ 0.2%
RMS) noise at 50 kHz and higher frequencies. However, since the EOM stabilizes the visible
laser light passing through it, 2-3% RMS noise remains on the IR light. Thus, a custom electronic
device, built by Terry Brown in the JILA electronics shop, has been inserted into the EOM servo
loop, which allows the feedback signal to be toggled between the 647 nm intensity and the FCL
IR power, as measured on the reference InSb detector. This servo operates synchronously with anumber of other electro-optical loops, as described in more detail in Sect. 2.2(D). The complexityof the feedback loop necessitates a highly sophisticated circuit, containing proportional, integral,

33
differential (or PID) filtering. Adjustable frequency response for the feedback filters enablesnoise cancellation in the maximum possible bandwidth and finely adjustable servo gain, tomaximize noise cancellation while maintaining servo loop stability. With this stabilization
implemented, acoustic noise on the IR laser is unobservably small and approximately 0.3% noise
remains, presumably caused by the servo loop because of its high frequency (100–500 kHz)approaching the ≈ 500 kHz EOM frequency response.
To obtain absorption sensitivity close to the shot noise limit, the remaining laser noise issubtracted from real “signal” fluctuations using a matched pair of low noise, liquid nitrogencooled, InSb detectors. Small (0.25 mm2) detectors result in fast (≈ 1 MHz) bandwidth, and very
quiet detector electronics result in a 0.9 pA/√Hz noise floor. This contribution is dwarfed by shotnoise on the detector’s photocurrent (ISN), given by

I SN = 2eI PC BW(2.5)

where e is the fundamental electron charge, IPC is the total photocurrent, and BW is the bandwidthof the measurement. For an IR power of 50 μW at 2.8 μm, IPC = 100 μA, and ISN/√BW = 5.9
pA/√Hz. Thus, the shot noise swamps technical noise by a factor of more than six. After
subtraction of the common mode noise between the two detectors, the ultimate detection
sensitivity is √2 times larger than IPC/ISN, about 7.6×10-8 Abs/√Hz.
The preceding argument suggests that increasing IR laser intensity I(ν) by a factor X
should increase the signal to noise by √X. In practice, increasing laser intensity leads to saturationof the optical transition. Such saturation is quantified9,10 by relating the number density (N1 andN2) in lower state 1 to upper state 2, via
N2g1/N1g2 = S/(1 + S).

(2.6)

Here, gx is the degeneracy of state x, and the saturation parameter S is the ratio of the excitation
rate to the relaxation rate when subjected to intensity I(ν). In the collision-free, transit timebroadened conditions in the crossed jets, this ratio becomes

34
S = I(ν)S0/(Δν)2,(2.7)

where S0 = 4.5×10-7 cm2Hz11 is the HF integral cross section and Δν is the transit time limited
homogeneous linewidth. For an HF velocity of approximately 1000 m/s, and a beam diameter of
1 mm, Δν = 1 MHz. Setting S = 1 provides the characteristic saturating intensity Isat(ν),
Isat(ν) = Δν2/S0 = 2.2×1016 photons/cm2s = 1.8 mW/mm2.

(2.8)

The probe beam is typically < 100 μW power in a 1 mm2 beam, such that laser intensity remains
more than a factor of ten below saturation. Significantly, the saturation parameter calculated via
Eq. 2.7 is independent of tightness of the laser focus under these transit time broadened
conditions, because I(ν) scales inversely with the square of the laser beam diameter, and so does(Δν)2. Thus, all measurements are in a non-saturating regime and directly correlate to absolute HF
densities in the laser path, as used to estimate absolute reaction cross sections in Sect. 2.3.
Next, common mode laser noise is removed from the measured IR signal by comparisonof the laser intensity on the reference and signal InSb detectors. Approximately 40% of the power
is diverted onto the reference detector, to measure the IR power and fluctuations. The remaining
60% passes through the Herriot cell, about half of which makes it onto the signal detector. A
custom built “laser noise subtractor” scales the reference detector response to the DC level of thesignal detector and subtracts common mode noise. The output of this device is amplified 10-fold,such that the IR shot noise swamps the electronic noise of subsequent electronic devices.
Experimentally realizable sensitivities of about twice the shot noise limit have beenobtained, resulting in absorbance noise of AS = 3×10-5 Abs in a 5 kHz bandwidth. The ultimate
HF detection limit comes from Beer’s law considerations of HF density and maximizing
absorption path length through the Herriot cell. With practically realizable configurations of 16
passes through 5 cm of absorbing HF (l = 80 cm), and σ = 1.4×10-15 cm2, (based on an integral
line strength of 1.5×10-17 cm/# and a 0.011 cm-1 Doppler width) Beer’s law produces a detection
limit (ρmin) of

35

ρmin = AN /σl,

(2.9)

and a detection threshold of 4×108 HF/cm3 per quantum state.
Additional sensitivity enhancement results from the redundant information obtained
scanning the high-resolution laser in ≈ 3 MHz steps through a ≈ 300–900 MHz HF Doppler
profile. At each frequency, an independent measurement of absorption is obtained to construct the
Doppler profile, discussed in detail in Sect. 2.3(C). This scanning redundancy produces a large
number of independent data points [N > 100–150 under a typical Doppler full width half
maximum (FWHM)], providing a √N ≈ 10- to 12-fold gain in sensitivity. This effect isconclusively demonstrated in Ch. III and IV, where F atoms reacting with either HCl or H2O
result in signal intensities on par with this limiting noise. Nevertheless, robust results have beenobtained via this Doppler averaging, as discussed in more detail in Ch. III. Statistics are further
improved by a regimen of signal averaging, during which each IR transition is probed repeatedly
over the course of the experiment. The 2.5–3.3 μm tunability of the IR source also enables many
HF(v,J) states to be probed on both the P (ΔJ = -1) and R (ΔJ = + 1) branch transitions, further
increasing the degree of data oversampling.
Finally, obtaining shot noise limited sensitivity also depends upon careful alignment of
the IR laser. Several optical components are likely to attribute to absorbance noise. The HeNe
tracer beam can weakly couple onto an InSb detector, but can be eliminated by placing an IRtransmitting germanium filter in the beam path. Also, transmission problems can occur whenretroreflected IR beams overlap with incident ones and create standing waves along the beampath, which effectively become low finesse etalons. Such interference is readily identified by thesinusoidal noise pattern obtained when tapping on optical components that form one end of theetalon. Such optics are most likely detector windows and nearby fast-focusing lenses, because of
their close proximity and weak sensitivity to lens alignment. This type of noise can be eliminatedusing irises and careful rotation of components to prevent back reflection.

36
Another likely culprit for laser noise is the FPI, which also readily produces opticalfeedback into the laser as it scans to modulate its transmission. However, this feedback is readily
identified because it oscillates with the FPI PZT translation, is synchronous with the HV driver,and mimics the shape of the cavity transmission curve. Spatially filtering the FPI from the laser
by closing an alignment aperture and/or by using a Faraday isolator (FI in Fig. 2.1) effectively
eliminates this effect.
Partial clipping on the edge of the InSb detectors is another likely source of alignment
noise. The fast InSb detectors are small (0.5 mm square), necessitating short (5 cm) focal length
lenses to tightly focus the IR beam. The focus must be carefully centered on the detectors with atranslation stage, such that small lens displacements or beam steering does not change themeasured intensity. Remaining sources of loss along the laser path can cause intensity noise, as
small motions result in differential changes between the detected reference and signal levels.
However, stable optical mounts suppress such motion, which also tends to be in 100 Hz andlower “acoustic” frequencies that are far removed from the faster signal bandwidth.
Finally, the Herriot cell12 is the most sensitive optical element to align for two reasons.
First, the long distance (60 cm) between the Herriot cell mirrors amplifies any mirror motion,such that clipping noise readily becomes detectible. Secondly, the spherical mirrors enable laser
divergence to be manipulated, but an understanding the laser propogation is needed to utilize thiseffect to prevent clipping on the laser beam on the edges of the mirrors. Specifically, the Herriot
cell consists of two spherical mirrors with 30 cm radius of curvature, positioned in a nearly
concentric fashion, i.e., they share an axis, but are somewhat less than d = 60 cm away from eachother. The laser beam produces an elliptical pattern on the Herriot cell mirrors, as illustrated inFig. 2.6. Careful choice of input spot position readily eliminates clipping on the entering beam,focused into the Herriot cell via a 50 cm lens. However, subsequent spots reflecting from themirror increase in size, as the concave mirrors alter the beam divergence. Gaussian optics

37

Figure 2.6

Illustration of the elliptical laser spot positions on the Herriot cell mirrors. The
beam divergence changes following each reflection from the curved optics. For
optimal mirror spacing, the output beam is highly collimated to prevent clipping
as it passes by the mirror and travels to the signal detector.

38
considerations13 reveal how laser spot size (ω, the 1/e electric field radius) changes as it passes
through the Herriot cell, as shown in Fig. 2.7. In this figure, the spot size is plotted as a functionof laser propagation distance. Reflections off the curved optics are readily identified as local
maxima in beam size, i.e., where the diverging beam becomes converging. The spot sizes on the
mirrors increase and then decrease for mirror spacing d less than twice the mirrors’ radius ofcurvature. For the 16 pass cell modeled in Fig. 2.7, the spacing in panel b) leads to the mostcollimated output spot, and therefore the least clipped beam. In practice, this alignment can beattained by measuring the outgoing laser’s spot size with a translatable iris near the chamber
output while “walking” the mirror spacing to minimize this beam diameter.
The importance of laser collimation and alignment cannot be overemphasized, since lightfluctuations of ten parts per million will quickly dominate the detection noise. Indeed, anattempted variation of the Herriot cell failed for this exact reason. Specifically, a triangularmultipass configuration was implemented in which the laser beam traveled from one curved
mirror to the other, off a flat mirror, and then returned to the first curved mirror. Thus, the jets
could be positioned such that the laser passed in only one direction through the intersection
region, parallel to the plane of the two jets’ axes. This arrangement was designed to produce
asymmetric Doppler shifts capable of distinguishing between forward and backward scattering of
the HF product. However, tilting of the curved mirrors into the triangular configuration
effectively changed the radius of curvature for one axis relative to the other, producing
astigmatism. Thus, the mirror spacing needed to collimate the output spot, as illustrated in Fig.
2.7 was different for the horizontal versus vertical beam dimensions and the outgoing spot
diverged on at least one axis, producing elliptical spots with different confocal beam parameters
on two perpendicular axes. In principle, this effect could be corrected using an astigmatic optic(e.g., a cylindrical lens) in the triangular beam path. However, this additional complication to the

39

1.2

d=58.5 cm

1.0

mirror reflections

0.8
0.6
0.4
0.2
0.0

spot size (cm)1.2

d=59.35 cm

Herriot cell exit
Output
Beam

1.0
0.8
0.6
0.4
0.2
0.0
1.2

d=59.6 cm

1.0
0.8
0.6
0.4
0.2
0.0
0

200

400

600

800

1000

propagation distance (cm)Figure 2.7

Gaussian optics predictions for the IR spot size in the Herriot cell. Mirror
reflections are located at the circles, where local maxima of beam diameter occur.
Minima are approximately at the squares, the locations of beam waists. After
exiting the Herriot cell, the laser beam can only propagate to its waist and thencontinue to diverge. For the top panel, the mirrors are too close and the
maximally collimated beam occurs prior to the outgoing pass. For the bottom
panel, they are too far apart and the outgoing pass also diverges rapidly The
middle panel, with mirror spacing d = 59.35 cm, produces a well-collimatedoutput beam.

40
vacuum alignment was not attempted, and all of the reported results utilize a traditional Herriot
cell.

D. Continuous and Automated Frequency Scanning
A pair of Brewster windows, mounted on a galvanometer (or galvo for short) as drawn in
Fig. 2.2, enables continuous tuning of the FCL, while maintaining single mode operation.
Functionally, these calcium fluoride windows displace the laser path by a small amount andchange the cavity’s free spectral range without changing the output path of the laser. Applying acurrent to the galvo tilts the plates in opposite directions, refractively displacing the laser beamand tuning the free spectral range of the cavity. To vary the IR frequency continuously, theintracavity etalon must track the moving longitudinal mode as the galvo plates scan. Thus, both
the galvo and etalon PZT stacks must be calibrated for frequency tuned per volt applied. The ratioof these values determines the relative feed forward voltage applied to these devices tocontinuously scan the FCL frequency.
The single mode FCL output is monitored on the scanning FPI cavity to calibrate the feed
forward calibration as follows. With the etalon unplugged and therefore static, scanning the galvo
plates continuously changes the laser frequency until an adjacent longitudinal mode of the cavity
experiences lower loss through the etalon and the IR frequency “hops” to oscillate on this mode
instead. A plot of galvo monitor voltage versus the number of hops reveals the displacement of
the original longitudinal mode in units of cavity FSR = 0.01 cm-1, resulting in a feed forward
value of 7.23 V/cm-1. Although FSR is technically changing with the galvo scan, it only does soin proportion to the number of observed hops out of the cavity mode number that is oscillating (n≈ 350,000), such that it can be treated as constant.
A similar process is used to calibrate the etalon PZT feed forward with the galvo plates
stationary, except that in this case the laser frequency remains constant until the etalontransmission shifts enough to transfer lasing to the adjacent longitudinal mode. Measuring these41
transitions as a function of etalon feed forward provides a similar calibration curve, and a value of–6.98 V/cm-1, as measured on the PZT HV driver output monitor. Unfortunately, the etalon PZT
responds nonlinearly to applied voltage over its 0–1000 V range, so this calibration is best
performed at about 500 V to obtain a median value of the tuning response.
To compensate for laser frequency drift and nonlinearities in the galvo and etalon feed
forward calibration, an servo loop prevents hopping between longitudinal modes as the cavity
scans. This servo loop, illustrated in Fig. 2.8, functions by continuously “dithering” the etalon
PZTs by applying a sinusoidal modulation voltage at frequency ω ≈ 2 kHz on top of the DC
voltage applied to maintain the proper intracavity etalon mode spacing. Thus, the etalon mirrors
oscillate at ω, but with low enough amplitude to avoid mode hops, resulting in a slight
modulation of the output IR intensity as the etalon transmission moves relative to the longitudinalmode on which the cavity is oscillating. If the etalon is perfectly centered on the longitudinalmode, the modulation frequency will be at 2ω, while any average frequency mismatch results insome intensity modulation at the dither frequency, ω. Thus, synchronous detection of the error
signal at ω provides feedback to the etalon servo.
The feedback signal comes from one of two places. If the krypton ion pump laser
intensity is constant, then the reference InSb detects the IR modulation directly, as illustrated by
the short dashed line in Fig. 2.8. Alternatively, under data acquisition conditions, the FCL poweris actively constrained to be constant by the laser intensity servo described in Sect. 2.2(C). In thiscase, the EOM transmits higher pump laser power to maintain the same IR power as the etalon
dithers. Thus, the EOM error signal contains the dither feedback information at frequency ω, andthe FCL servo loop is completed according to the long dashed line in Fig. 2.8.

42Figure 2.8

Schematic for the laser frequency servo loop. The FCL servo dithers theintracavity etalon voltage and monitors the error signal at the applied frequency.
In the first servo mode (short dashed line), the IR intensity varies and is directly
monitored. However, when the IR laser intensity servo is used, the EOM
modulates the pump laser power changes to maintain constant IR power. In thismode, the error signal from the laser intensity servo (long dashed line) contains
the information about the etalon dither.

43
2.3 Crossed Jet Apparatus
For the gas-phase reaction dynamics studies, reactants enter the ≈ 100 L diffusionpumped vacuum chamber via two supersonic molecular jets. The jet axes are oriented at 90°
angles and intersect 2.5–5.0 cm downstream from their orifices, as illustrated in Fig. 2.9. One jetemanates from a custom-built Proch-Trickl14 valve, which uses a PZT disc actuator to generate
200–500 μs gas pulses. This valve delivers about 8×1013 molecules/cm3 to the jet intersection
region at typical backing pressures of 200 Torr for a 500 μm pinhole orifice. The radical source,
described in detail below, uses a HV plasma (50–500 μs duration) to dissociate F2 into reactive F
atoms during an approximately 2 ms gas pulse. This valve has an approximately 0.03 by 0.3 cm
orifice and typically operates with a stagnation pressure of 70 Torr, resulting in an additional
1.0×1014 #/cm3 in the probe region. With the valves pulsing at 10.1 Hz, the average pressure in
the chamber rises to ≈ 1.0×10-4 Torr, corresponding to a mean free path of λ ≈ 50 cm between
molecular collisions, i.e., considerably greater than the distance to the chamber walls.
Low-density conditions ensure that the probability for secondary molecular collisions ison the order of 1 % prior to leaving the ≈ 0.5 cm detection volume. Most collisions are withhelium and other rare carrier gas atoms which have small cross sections for rovibrationallyinelastic scattering;15 hence, this represents an upper limit for redistribution of the HF(v,J)
population. Nevertheless, possible inelastic relaxation is a concern that has been explicitly tested
for each system, as discussed in subsequent chapters. In general, such single collision conditions
are readily satisfied, as only 0.04% of the approximately 1×1012 #/cm3 F atoms present in theprobe region need to react and form HF in a given (v,J) state to exceed the detection thresholdcomputed in Sect. 2.2(C). Thus, the IR detection technique has enabled the study of reaction
dynamics of systems with rate constants up to about ten times lower than the gas kinetic rate (i.e.,cross sections of about 1 Å2). The cross section for do-able experiments will scale with the44

Figure 2.9

Illustration of the reaction vessel. Unskimmed molecular jets intersect at a 90°
angle, centered on the IR multipass cell, whose axis is perpendicular to the plane
defined by the central axes of the jets.

45
reactant densities, the absorption path length probed by the IR laser, and the RMS absorbancenoise, while scaling inversely with the IR line strength and the number of populated productquantum states. Since the HF IR transition is a particularly strong one, and the present densities
have been pushed close to the limits of single collision conditions, probable areas for
improvement include lower noise (i.e., faster) data acquisition techniques, different probe
geometries (such as cavity ring down), and different jet sources, such as crossed slit jets or higher
efficiency radical sources.
In addition to providing a convenient source for directed, low density molecules, thesupersonic jets also cool the reactants, with rotational temperatures of ≈ 30 K observed for thehydrides considered here, and colder distributions likely for species with smaller rotational
constants. Jets also provide a means to vary translational energy via choice of carrier gas. These
effects narrow the number of states and make kinetic energy dependent studies possible. The jets
can be characterized a number of ways. First, the measured velocities closely match the predicted
terminal velocities anticipated by fluid dynamics,16 indicating efficient cooling of the expansion
gases. Additionally, direct IR observations of HCl and the naturally present H218O isotopologue(whose low atmospheric concentration makes it easy to probe in low rotational states) also
confirm efficient cooling.
A major new capability has also been developed for studying the nature of chemical
reaction events at the vacuum interface of bulk liquid surfaces. These gas-liquid scatteringexperiments utilize the same F atom source as the crossed jet studies, but otherwise introduce anumber of novel features. The use of bulk liquids in vacuum raises a number of interesting points.
First, low vapor pressure (≈ 10-7 Torr) liquids are used to prevent loss of reactant and maintainlong mean free paths. Secondly, the probability of a molecule incident upon the liquid colliding
with the surface is essentially unity, and reaction probabilities are similarly high. However,checks against jet shocks at the surface and other nonlinear effects are also necessary. Finally,

46
issues of surface cleanliness in vacuum must be confronted by continuously refreshing thesurface. These issues and further experimental details of the gas-liquid scattering studies can befound along with the experimental results in Ch. V.

A. Radical Source:
The F atom source is a standard solenoid fuel injector modified to generate radicals in anelectrical discharge at the throat of the supersonic expansion, as shown in Fig. 2.10. The F atoms
are produced as follows. The solenoid pulses 50–100 Torr of a 10% F2 / 90% rare gas excimer
pre-mix into a small (≈ 0.025 mL) volume defined by a slotted hole in a 0.5 mm inert(polychlorotrifluoroethylene) disk insulator, sandwiched between two metal electrodes. A
miniature slit (300 μm × 0.3 cm) in the downstream electrode forms the limiting orifice, fromwhich the gas expands past two slit-jet expansion-defining “jaws” and into the chamber. This
source utilizes a slit expansion geometry because it prolongs the time between routine cleaningand sanding of the electrodes, presumably because the elongated orifice provides more electrodesurface area for a given nozzle area, such that plasma wear is diluted over more electrodematerial. At the peak of the 2 ms gas pulse, a 500 μs HV pulse (≈ -1 kV) is applied to the lower
electrode, striking an electrical discharge through the gas mixture to the grounded upper electrodeon the valve body. Measuring HF densities produced in crossed jet studies of F + H2, with known
reaction cross section,17 enables F densities of approximately 2.6×1012 atoms/cm3 to be inferred.
Such densities correlate to ≈ 2×1016 F atoms/cm3 at the limiting orifice, or ≈ 10% of the F2
dissociating into F atoms in the plasma. These measurements have also been used to estimate thereaction cross section for several systems, as discussed in detail in the next subsection.
Very recently, a similar plasma source has been designed for use with a Proch-Trickl
pulsed valve, based on a design borrowed from the Ye group at JILA. For this valve, a pinhole
source replaces the slit, and either ceramic or plastic insulators may be used. Based on the advice

47

Figure 2.10

Drawing of the radical jet source. High voltage applied to the cathode strikes aplasma upstream of the limiting orifice, generating reactive F atoms.

48of the Ye group, the electrodes were finely polished using a series of progressively finer sandpaper grits, a fine paste polish, and then electro polishing, to remove surface roughness andextend the stable lifetime of the electrodes between servicing. This valve has been briefly used in
the ion imaging apparatus described in Appendix B, and radical Cl production efficiency iscomparable to that found for F atoms, above.
Because of the harsh environment in the radical atom source, the high voltage electrodesurfaces physically and chemically degrade, leading to unstable plasma current and F atom
production efficiency. Erratic performance generally arises after about a week of regular
operation, but sanding and polishing the electrodes restores stability. This wear results in drift of
the F atom density on an inverse day time scale, necessitating normalization of the data set withrespect to F atom density. Thus, a strong reference transition is observed every 2–3 hours during
data acquisition, such that the entire data set can be normalized and data collected over manyweeks meaningfully compared and signal averaged.
The high sensitivity to HF product density also necessitates compensation for trace
amounts of background HF contamination. This background originates from the F source,
presumably via pre-reaction with impurities in the gas mixture at part per million concentrations.
Fortunately, efficient cooling in the supersonic jet (even with the discharge on) confines all suchbackground to HF v = 0, with a rotational temperature of ≈ 60 K, as shown in Fig. 2.11. Thisbackground is explicitly measured by re-scanning each transition originating in HF(v = 0) without
the second jet, such that the differential increase in integrated absorption can be attributed to the
HF reactive product channel. This procedure works well but often generates significant
uncertainties for the lowest [HF(v = 0,J < 6)] states arising from subtraction of weak and nearly
equivalent populations. Nevertheless, the plasma source and IR technique enable the HF
populations to be observed, and provide direct measurement of population in the groundvibrational state, inaccessible via IR chemiluminescence methods.2,18-29

49

ln[ P(J)/g(J) ]

v=0
3

2

56K

1

0
0

50

100

150

Erot/kB (K)
Figure 2.11

Boltzmann plot of the HF background produced in the F atom plasma source.
The density of HF background is much smaller than that reactively produced in
the crossed jets. Supersonic cooling confines the background to low J in the v = 0
manifold, as indicated by the ≈ 60 K fit to the rotational distribution.

50
B. Data acquisition
HF produced via reaction at the intersection of the pulsed jets results in a transient change
in the intensity of the IR probe when the frequency lies within the Doppler profile of a populated
HF(v,J) transition. A transient recorder (or, in a recent upgrade, a computer digital acquisitionboard) digitizes this transient absorption waveform, and it is analyzed in real time. Specifically,
the absorption pulse is numerically averaged under a 100–500 μs window, coinciding with thepeak absorption signal and resulting in a 2–10 kHz detection bandwidth. Additional time gates,
preceding and/or following the signal gate by several hundred microseconds, are also averaged inorder to correct for pulse-to-pulse changes in the absorption baseline and eliminate slow noise
fluctuations. The net absorption is plotted as a function of laser frequency to construct Doppler
profiles such as those presented in Fig. 3.3, 4.4, 5.5, and 5.10.
A digital to analog converter provides a voltage ramp used to automate the laser tuning as
described in Sect. 2.2(D). Typically, the laser tunes about 3 MHz between jet pulses, and theprocess is repeated ≈ 1000 times over a 3 GHz window, sufficient to resolve the entire Doppler
profile. However, it is also necessary to calibrate the frequency axis during the scan. For thispurpose, the TAC output is also recorded, providing a measure of the FPI output at each laser
step, as described in Sect. 2.2(B) and depicted in the top panel of Fig. 2.5. The TAC saw tooth
wave contains sharp falling edges, spaced by the FSR of the FPI, such that a simple edge finding
routine can be used to calibrate the frequency axis with the precision of the scanning etalon.
Additional DC data are acquired, including the signal InSb detector DC level, used to convert
measured waveforms into absorbance units, and the transmission of a reference gas cell, which
provides absolute frequency calibration.
When acquiring data, the Doppler profiles are typically scanned at least three times insuccession. This redundancy improves the statistical uncertainty of the measurements and also
helps reveal systematic changes (e.g., poor plasma reproducibility in the F atom source), which

51
can be missed during long average scans. Some degree of redundancy is warranted, as Doppler
measurements require only about one hundred seconds of acquisition time, and a similar amountof time goes into manually tuning the laser and preparing it when transitioning between spectral
lines. Repeat measurements also statistically decrease uncertainties, an important effect for low
signal experiments.

2.4 Data Analysis and Experimental Modeling

A. Spectral Analysis
Sample Doppler measurements are presented in each chapter for the reaction being
studied. Figs. 3.3 and 5.5 illustrate the types of signal to noise and spectral features obtained forthe various studies. Because chemical reaction readily produces vibrationally excited HF product,
the measured absorption profiles, A(ν), contain structure according to the density of HF absorbing
from the lower state j and emitting from the upper state i at each Doppler detuning ν−ν0according to the Beer-Lambert law, expressed as
Aij (ν-ν0) = ∫dx ∫dν’ [σi→j(ν-ν’)κi(x,ν’-ν0)- σi←j(ν-ν’)κj(x,ν’-ν0)].

(2.10)

Here κi/j(x,ν’-ν0) is the spectral density (i.e., molecules/cm3/cm-1) of absorbers in states i or j, at a
position x along the absorption path with Doppler shifted center frequency ν’-ν0. σj←i(ν-ν’) andσj→i(ν-ν’) are the homogeneously broadened absorption/emission cross sections between states iand j centered on ν’. Since the homogeneous lineshape is much narrower than the inhomogeneous
Doppler profile, it can be approximated as a delta function such that integrating over ν’ yields
Aji(ν-ν0) = Si→j ∫dx κi(x,ν-ν0) - Si←j ∫dx κj(x,ν-ν0).

(2.11)

Thus, the net absorption at ν−ν0 is related to the difference in HF column-integrated spectral
density ∫dx κi/j(x,ν-ν0), weighted by the appropriate line strengths (Si↔j).

52
To simplify the discussion of the quantum-state distributions, measured Doppler profiles
are numerically integrated, and more detailed analysis of the absorption lineshapes is postponed
until Sect. 2.4(C). Integrating Eq. 2.11 with respect to ν relates the integral absorbance to the total
HF column-integrated density ∫dx ρi/j(x) = ∫dx ∫dν κi/j(x,ν-ν0)∫A(ν-ν0) dν = Si→j ∫dx ρi(x) - Si←j ∫dx ρj(x).

(2.12)

Eq. 2.12 permits the difference in column-integrated densities (CIDs) for the lower and upperprobe states to be extracted using the absorption line strengths (Si↔j), well known from theanalysis of Arunan, Setser and Ogilvie.11
For the excited vibrational populations observed following reactive scattering, significant
HF density often forms in both upper, j, and lower, i, states, resulting in a competition between
stimulated emission and absorption signals. Such non-equilibrium conditions are readily
anticipated following chemical reaction, and form the basis of chemical lasers.30 The presence of
two unknown CIDs in Eq. 2.12 leads to correlation between upper and lower state populations ina least-squares fit to the spectral data. However, observation of lines originating from the highest
energetically accessible (vmax) manifold effectively breaks this correlation, since the population inthe (vmax + 1) upper state can be set to zero. Furthermore, the tunability of the IR laser permits
observation of both P and R branch transitions out of many HF(v,J) lower states, increasing thenumber of measurements probing each state.
The network of accessible HF transitions in Fig. 2.12 illustrates the redundancy of the IR
spectral measurements. This presentation emphasizes that more than one transition is measured
for a large number of HF(v,J) states, and that the population in a given state is linked to that inevery other. Fitting the entire spectrum simultaneously produces the set of HF(v,J) CIDs from themeasured spectrum without any ad hoc assumptions. States whose energy exceeds the available
energy can also be probed, and the absence of measurable population justifies fixing the density
in these states to zero in the least squares fit. However, since the HF density in each manifold

53

Figure 2.12

The network of accessible HF transitions in the 2.5–3.3 μm tuning range of the
IR laser. A large number of J states in the v = 0–3 manifolds are accessible, manyof them via both P and R branch transitions.

54
depends upon measurements in every higher populated manifold, illustrated in Fig. 2.12, thefitted uncertainties tend to increase in lower vibrational manifolds. This trend has been observedin every data set presented here. Nevertheless, robust measurements of HF density have generally
been obtained down to the ground vibrational manifold.

B. Density-to-flux Transformation and Monte Carlo Simulation of the Crossed MolecularJets
The measured IR spectrum yields HF state resolved column-integrated densities via leastsquares fitting of the spectrum described in the previous section. However, under crossed jet
conditions the flux of product molecules, not the density, is directly proportional to the state
resolved reaction cross section. Obtaining product fluxes requires consideration of the wellknown density-to-flux transformation,31-33 i.e. correctly taking into account the velocity-dependent
detection sensitivity intrinsic in any density-based measurement technique, such as IR
spectroscopy.
The single-collision conditions and excited Doppler measurements, discussed in moredetail in Sect. 2.4(D), emphasize the need for the density-to-flux transformation. Essentially, if
HF product is observed under single collision conditions it cannot be considered translationallyequilibrated, and by simple energy conservation, lower energy product states can be expected tohave higher recoil energies and spend less time in the detection volume. Conversely, translational
equilibration necessarily entails post-reaction collisions, which may also cause inelastic
redistribution of energy. Benchmark chemiluminescence studies2,18-22,24-27,29,34-38 were performed
under such translationally equilibrated conditions, further emphasizing the present interest inrevisiting these reactions under lower density.
The relationship between reaction cross section and product density can be found via
considerations based on those of Sonnenfroh and Liu.31 Fundamentally, the probability PF of an F

55
atom reacting following a displacement dl in the center of mass frame in the vicinity of a point r,
with density ρHX(r) of reactant HX is given by the Beer’s law-type expression,
PF = σjρHX(r)dl,(2.13)

where σj is the total reaction cross section for forming HF in state j, treated as a constant for thecurrent discussion. Shifting to the laboratory frame requires the substitution dl = (vrel/vF)dx,
where vrel = dl/dt is the relative velocity in the center of mass frame, and vF = dx/dt is thelaboratory-frame F velocity, defined to be along the x axis. Thus, PF becomes
PF = σjρHX(r)(vrel/vF)dx.

(2.14)

Thus, the rate of F loss RF(r) (in #/cm3/s) at r is given by -PF times the density of F at r, ρF(r),divided by the time spent at r, dt = dx/vF. The rate of formation of HF is RHF = -RF, such that
RHF(r) = PFρF(r)vF/dx = σjρF(r)ρHX(r)vrel,(2.15)

Note that the ρF(r) and ρHX(r) terms appear symmetrically in this expression, as they must, since italso could have been derived from identical considerations of the HX jet.
The local HF density ρHF(r) results from the HF formation rate at r and the flux of HF
passing through r, due to reaction elsewhere. Mathematically, the density ρHF and the laboratoryframe velocity vHF are related via the continuity equation of fluid dynamics,dρHF(r)/dt = RHF(r) - ∇⋅ρHF(r)v.

(2.16)

Integrating Eq. 2.16 over a finite volume V, ∫∫∫V dV, emphasizes the physical interpretation that therate of change of HF molecules in V [∫∫∫V dV dρHF(r)/dt] must be equal to the rate at which they
are formed [∫∫∫V dV RHF(r)] minus the net flux leaving V through its bounding surface A. This lastterm is made explicit by substituting ∫∫∫V ∇⋅ρHF(r)vHF = ∫∫Ac ρHF(r)vHF⋅dA, where ∫∫Ac denotes
integral over a closed area A bounding V, according to Gauss’ divergence theorem.
When ρHF(r) is probed for a short time after the reaction begins in the crossed jets, theexplicit time dependence of ρHF(r) must be taken into account according to Eq. 2.16 in a detailed
model of the experimental conditions. For the present experiment, the steady state limit is valid,

56
since the approximately 10–50 μs HF travel time from anywhere in the reaction region the probe
laser is much smaller than i) the > 200 μs signal gate for averaging IR absorption data and ii) theeven longer ( > 0.5 ms) pulsed jet durations. Thus, time-dependent models can be avoided andsetting the left hand side of Eq. 2.16 to zero results in∫∫∫V RHF(r)dV = ∫∫Ac ρHF(r)vHF⋅dA,(2.17)

which states that the HF flux away from r must be equal to the rate of HF production at r for
steady state conditions. Integrating over a sufficiently small region around r, the velocity vector
points normal to dA at all points. Denoting the small volume ΔV and surface area ΔA, dividing by

ΔA, and substituting in for RHF(r) using Eq. 2.15, one finds an expression for the localized flux
per unit area Φ,Φ(r) = σjρFρHXvrelΔV/ΔA = ρ(r)vHF.

(2.18)

Here, the explicit r dependence of ρF, ρHX, and vrel has been dropped because ΔV is assumed to besmall enough that they are nearly constant.
Eq. 2.18 is too simple to accurately represent the conditions in the crossed jet apparatus,
where a distribution of fluxes exist at each position, due to the generation of HF at every otherposition, and with a velocity distribution depending upon the HF point of origin and location of
the flux in question. However, the total flux is a superposition of various flux components(labeled with subscript i), each of which still obey

Φi = ρivi.

(2.19)The total flux, ΦTot = ΣiΦi, is still directly proportional to the state resolved cross section σj, in thelimit that any changes in collision energy are small and do not result in dramatically different
reaction cross section for portions of Φi originating from regions with significantly different mean
collision energies. The relationship between ΦTot and ρTot = Σiρi can be found by dividing bothsides of Eq. 2.19 by vi and summing over i,ρTot = ΣiΦi/vi.

(2.20)

57
Dividing this expression by ΦTot, one finds that the right hand side is 〈1/v〉 the flux-weighted
expectation value of the inverse speed, which rigorously connects ΦTot to ρTot according to,ρj_Tot/〈1/v〉j = Φj_Tot.

(2.21)For fixed probe geometry 〈1/v〉 is also directly proportional to 〈τ〉, which is used as the density toflux conversion factor in Ch. III and IV, and Appendix E, since the flux is subsequently
normalized to provide the relative magnetude of σj for various j. This substitution is also
intuitively appealing because 〈τ〉 weighting reveals an enhanced detection probability formolecules in states that recoil such that they spend more time in the probe region.
In principle, the sum represented in Eq. 2.20 could be converted to an integral andevaluated for the explicit experimental conditions. In practice, such integration is cumbersome
and is replaced by numerical Monte Carlo (MC) simulation instead. Specifically, the simulation
models the explicit HF formation and absorption events for each of the crossed jet systems inorder to directly approximate this sum. The details of the MC routine are as follows and areillustrated in Fig. 2.13. The program randomly samples “reaction locations” r within the cubic
simulation volume with side 2d, where d is the distance from the jet orifices to the probe axis.
The product center of mass (COM) recoil direction is also randomly sampled within user-choseni) differential scattering constraints and ii) change in kinetic energy corresponding to formation ofa given product state. The reactant velocities are also randomly sampled from within the known
speed distribution, while constraining the velocity vector to be parallel to the line connecting r to
the corresponding reactants’ nozzle orifice.
Thus, the MC routine simulates the distribution of speeds, densities, collision angles, andscattering angles present under the experimental conditions. The inputs to the model are as
follows: i) probe and jet geometries, ii) and product masses, iii) reaction exothermicity, iv) jet

58

Figure 2.13

Illustration of the Monte Carlo computational volume used to simulate the F +HCl reaction conditions. The jet sources define two edges of the cubic volume,
located d = 4.5 cm from their intersection point. The Herriot cell probe volume,
shaded red, is centered at this point and simulated by a 0.5 cm diameter cylinder,
perpendicular to the plane of the jets. The contours are the detection probability
for HF formed with ΔEtrans = 0.0 kcal/mol, also presented in Fig. 2.14.

59
angular and speed distributions [measured experimentally via high-resolution Dopplerimetry on
IR chromophores doped in the incident beams in a separate experiment], and v) the adiabatic,
zero-point corrected transition-state barrier heights obtained from high-level ab initio
calculations,39,40 below which the reaction can not proceed classically. These parameters and arandom sampling of the recoil dynamics enable the laboratory-frame trajectory of the HF productto be computed. If a randomly generated trajectory intersects the detection volume V (a cylinder
with 0.5 cm radius, whose long axis is perpendicular to the plane of the jets), then such scattering
trajectories contribute to the detected signal. The relative importance of the detected trajectory isfound by histogramming the results according to the right hand side of Eq. 2.18, i.e., the productflux, numerically proportional to the product of ρF(r), ρHX(r), and vrel. The histogrammed results
provide information on the distribution of HF residence times in the probe region, the spatial
distribution of detected reactions, the Doppler projection of the HF product, and the collisionenergies. Sampling a million MC trajectories produces good convergence, and the process isrepeated for various differential scattering limits. A separate calculation is performed for eachvalue of recoil translational energy change, ΔEtrans, based on specific HF(v,J) states and assumed
coproduct (X radical from HX reacant) internal energy.
In general, the MC results are relatively insensitive to the assumed differential crosssection largely because spatial averaging within the unskimmed jets blurs the details of the recoil
dynamics. Nevertheless, different angular scattering limits are considered for each reaction
system, as discussed in more detail in Appendix E. The density-to-flux transformation results in amodest increase in product branching into low-energy HF(v,J) states, when compared to the raw
HF column-integrated densities. This effect arises from the higher average laboratory-frame
velocities resulting for HF formed in lower internally excited states. Indeed, this physical picture
predicts that the computed 〈τ〉 values should scale inversely with the recoil speed, i.e., with the

60average energy available to products to the negative one-half power, 〈Eavail〉-1/2, as observed forsufficiently large Eavail, regardless of assumed differential cross section, as shown in Fig. A.13(b).
Of course, the exact values of the calculated 〈τ〉 values are dependent on the chosen
detection volume shown in Fig. 2.13. However, only the ratios of the HF residence times
influence the final results, since the normalized HF populations are ultimately reported.
Additionally, small changes in the shape or position of the probe volume are unlikely to perturb
the ratios of the 〈τ〉 values. This conclusion is expected because an average time was used as aconveniently calculated value, versus the true 〈1/v〉 scaling factor derived from Eq. 2.20.
In addition to providing 〈τ〉 values, the MC model provides a number of other insights
into the experimental conditions. Specifically, the collision energy distribution is obtained fromthe computation, and found to be somewhat higher than expected for the jets intersecting at 90°.
This increase results from the spatial distribution of detected products presented in Fig. 2.14,
which reveals that “head on” collisions, i.e., those occurring closer to the line connecting the twojets, are somewhat likely to be detected, increasing the mean collision energy. This figure reveals
that in every recoil energy regime, the highest sensitivity is for products formed near the detection
volume, and collisions downstream with respect to the laboratory-frame center-of-mass velocity
have negligible detection probability. However, products formed closer to the valve orifices havea reasonable probability of passing through the detection volume because the laboratory-frame
velocity of the collision partners points that direction. The top left panel in Fig. 2.14 reveals thatparticularly endothermic processes that absorb kinetic energy (ΔEtrans < 0) preferentially sample
the region connecting the two jets. This effect occurs because this region corresponds to thehighest energy “head-on” collisions, and excessively energetic collisions are not likely elsewhere.
Thus, the Monte Carlo results match simple expectations based on and product flow.

61

Distance from F source

ΔE= =-7-7kcal/mol
ΔEKIN
kcal/moltrans

ΔE= 0 kcal/mol
ΔE
KIN
trans = 0 kcal/mol

ΔE= -3
kcal/mol
ΔE= -3
kcal/mol
trans
KIN

ΔE
= 11
kcal/mol
ΔE= 11kcal/mol
trans
KIN

2 cm

Distance from HCl source
Figure 2.14

The relative detection sensitivity to HF formed following the reaction F + HCl,integrated with respect to the coordinate perpendicular to the plane of the jets.
Representative results are shown for varying amounts of energy released into
kinetic energy (ΔEtrans) by the reaction event. The distance from the HCl and F
sources are the horizontal and vertical axes, respectively, as illustrated in Fig.
2.13. Contours are linearly spaced from 10% to 90% detection probability. The
red circle denotes the location of the detection region.

62
Additionally, the MC model predicts detailed HF Doppler distributions for a given
angular scattering distribution. However, the signal to noise ratio obtained in the F + H2O and F +HCl reactions described in Ch. III and IV is too low to enable detailed comparison to thepredictions. Geometric averaging of laboratory-frame COM and relative velocities under
unskimmed jet conditions tends to blur detailed information about HF product recoil in the COM
frame. Nevertheless, observed Doppler widths do directly report on the average energy released
into translational energy following the reactive event, as discussed in more detail Sect. 2.4(D).

C. Reactive Cross Section Estimates
The IR absorption technique also enables absolute measurement of HF density, fromwhich the reaction cross section σ can be estimated. Specifically, Eqs. 2.18 and 2.20 reveal that σscales with ρHF and inversely with ρF, ρHX, vrel, and 〈τ〉. Since ρHF varies with the discharge
conditions, it must be calibrated against a system with known reaction cross section. For thepresent studies, F + H2 serves as a convenient reference, well characterized by Dong’s17 measured
cross section of σrxn(F + H2) = 3.0 Å2 and Chapman’s41 HF quantum-state distribution at 2.3
kcal/mol collision energy. Since the total density of HF has been measured previously, it is only
necessary to measure a single quantum state, j, and relate the fractional population fj in that state
to the total density via ρHF = ρHF,j/fj.
Thus, the relative cross sections for two reactions (denoted 1 and 2) can be expressed
according to parameters known experimentally or via MC simulation

σ1
ρ HF 1 ρ HX 2 vrel 2τ 2≈.
σ 2 ρ HX 1vrel1τ 1
ρ HF 2(2.22)The values obtained in this way are somewhat approximate, since they depend critically upon themodeling of the reaction conditions that produce the average 〈τ〉 values, as discussed in section

63
2.4(B). Nevertheless, cross sections calculated in this way for F + HCl and F + H2O agree withthe approximate values obtained from temperature-dependent rate constant measurements.42,43

D. Doppler Analysis
Doppler measurements obtained from the IR spectrometer can be considered“orthogonal” information about the reaction dynamics when compared to the quantum-state
distributions. The observed Doppler profiles directly reveal laboratory-frame HF velocities,
projected along the probe axis, following the reaction event. However, as mentioned in theprevious section, the detailed information about the angular scattering dynamics of the F + H2O
and F + HCl systems is difficult to obtain with the signal to noise resulting from these relatively
low cross section reactions. Given the signal to noise shown in the sample Doppler measurements
in Fig. 3.3, and 4.4, we have been unable to disentangle velocity distributions for upper and lower
states (according to Eq. 2.11) from the experimental noise. Instead, we have fit a number of
selected states, whose upper state population have been found to be negligible, to a simple
Gaussian lineshape according toA(ν) = A0 exp(-4ln(2)[(ν−ν0)/Δν] 2),(2.23)

where A(ν) is the measured Doppler profile, and the fitted parameters are the overall amplitude
A0, the line center ν0, and the Gaussian FWHM Δν. The Δν values are presented in the following
chapters, and measured values exceed the room temperature HF Doppler width (Δνthermal = 330
MHz) and vary explicitly as a function of HF(v,J) rovibrational state. These observations strongly
indicate that HF distributions remain translationally excited following the reactive encounter,direct evidence for single collision conditions at the jet intersection region. Additional Doppler
analysis was possible for the large signals obtained following reaction at the gas-liquid interface.
More precise modeling was performed in this case, as described in detail in Ch. V.

64References for Chapter II
1

From, pp. http://nobelprize.org/nobel_prizes/chemistry/laureates/1986/.

2

J. C. Polanyi and D. C. Tardy, J. Chem. Phys. 51, 5717 (1969).

3

Y. T. Lee, J. D. McDonald, P. R. Lebreton, and D. R. Herschbach, Rev. Sci. Instrum. 40,
1402 (1969).

4L. M. Tashiro, W. Ubachs, and R. N. Zare, J. Mol. Spectrosc. 138, 89 (1989).

5

W. Gellermann, J. Phys. Chem. Solids 52, 249 (1991).

6

J. V. V. Kasper, C. R. Pollock, R. F. Curl, and F. K. Tittel, Appl. Optics 21, 236 (1982).

7

J. L. Hall and S. A. Lee, Appl. Phys. Lett. 29, 367 (1976).

8

T. M. Niebauer, J. E. Faller, H. M. Godwin, J. L. Hall, and R. L. Barger, Appl. Optics 27,
1285 (1988).

9

J. T. Verdeyen, Laser Electronics, 3rd ed. (Prentice Hall, Upper Saddle River, NJ, 1995).

10

W. Demtroder, Laser Spectroscopy. (Springer, Berlin, 1996).

11

E. Arunan, D. W. Setser, and J. F. Ogilvie, J. Chem. Phys. 97, 1734 (1992).

12

D. Herriot, H. Kogelnik, and R. Kompfner, Appl. Optics 3, 523 (1964).

13

A. Yariv, Quantum electronics, 3rd ed. (Wiley, New York, 1989).

14

D. Proch and T. Trickl, Rev. Sci. Instrum. 60, 713 (1989).

15

W. B. Chapman, M. J. Weida, and D. J. Nesbitt, J. Chem. Phys. 106, 2248 (1997).

16

D. R. Miller, in Atomic and molecular beam methods, edited by G. Scoles (Oxford
University Press, New York, 1988), pp. 14.

65
17

F. Dong, S. H. Lee, and K. Liu, J. Chem. Phys. 113, 3633 (2000).

18

D. Brandt and J. C. Polanyi, Chem. Phys. 35, 23 (1978).

19

D. Brandt and J. C. Polanyi, Chem. Phys. 45, 65 (1980).

20

A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi, and J. L. Schreiber, Faraday
Discuss. 55, 252 (1973).

21

L. J. Kirsch and J. C. Polanyi, J. Chem. Phys. 57, 4498 (1972).

22

J. C. Polanyi and K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).

23

P. Beadle, M. R. Dunn, N. B. H. Jonathan, J. P. Liddy, and J. C. Naylor, J. Chem. Soc.,
Faraday Trans. II 74, 2170 (1978).

24

P. Beadle, M. R. Dunn, N. B. H. Jonathan, J. P. Liddy, J. C. Naylor, and S. Okuda, J.
Chem. Soc., Faraday Trans. II 74, 2158 (1978).

25

D. Bogan and D. W. Setser, in Fluorine-containing free radicals: kinetics and dynamics
of reactions: based on a symposium sponsored by the Division of Physical Chemistry at
the 169th meeting of the American Chemical Society, Philadelphia, Pennsylvania, April
7-11, 1975, edited by J. W. Root (American Chemical Society, Washington, 1978), pp.
237.

26

D. J. Bogan and D. W. Setser, J. Chem. Phys. 64, 586 (1976).

27

N. Jonathan, Melliars.Cm, D. Timlin, and D. H. Slater, Appl. Optics 10, 1821 (1971).

28

N. Jonathan, Melliar-Smith Cm, S. Okuda, D. H. Slater, and D. Timlin, Mol. Phys. 22,561 (1971).

29

K. Tamagake, D. W. Setser, and J. P. Sung, J. Chem. Phys. 73, 2203 (1980).

30

K. L. Kompa and G. C. Pimentel, J. Chem. Phys. 47, 857 (1967).

31

D. M. Sonnenfroh and K. P. Liu, Chem. Phys. Lett. 176, 183 (1991).

66
32

H. W. Cruse, P. J. Dagdigian, and R. N. Zare, Faraday Discuss. 55, 277 (1973).

33

C. Naulin, M. Costes, A. Benseddik, and G. Dorthe, Laser Chem. 8, 283 (1988).

34

J. C. Polanyi, Accounts Chem. Res. 5, 161 (1972).

35

M. A. Wickramaaratchi, D. W. Setser, H. Hildebrandt, B. Korbitzer, and H. Heydtmann,
Chem. Phys. 94, 109 (1985).

36

W. H. Duewer and D. W. Setser, J. Chem. Phys. 58, 2310 (1973).

37

H. W. Chang, D. W. Setser, M. J. Perona, and R. L. Johnson, Chem. Phys. Lett. 9, 587(1971).

38

J. P. Sung and D. W. Setser, Chem. Phys. Lett. 48, 413 (1977).

39

M. P. Deskevich, D. J. Nesbitt, and H. J. Werner, J. Chem. Phys. 120, 7281 (2004).

40

M. P. Deskevich, M. Y. Hayes, K. Takahashi, R. T. Skodje, and D. J. Nesbitt, J. Chem.
Phys. 124, 224303 (2006).

41

W. B. Chapman, B. W. Blackmon, S. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 109,
9306 (1998).

42

E. Wurzberg and P. L. Houston, J. Chem. Phys. 72, 5915 (1980).

43

P. S. Stevens, W. H. Brune, and J. G. Anderson, J. Phys. Chem. 93, 4068 (1989).

67________________
Chapter III Reaction dynamics of F + HCl → HF(v,J) + Cl: experimental measurements
and quasi-classical trajectory calculations________________
3.1 Introduction
Elementary chemical reactions play a pivotal role in the foundations of chemical reaction
dynamics.1,2 Three-atom hydrogen exchange reactions in the form X + HY → HX + Y have been
particularly important because of the theoretical tractability of developing potential energy
surfaces (PES) in full 3N-6 = 3 dimensionality.3-5 Intense effort has been focused toward reactions
such as O + H2,6-9 Cl + H2,10-14 H + H2,15-18 and F + H2,19-28 due to the accessibility of high-level
theoretical methods to systems with only a single “heavy” (i.e. nonhydrogenic) atom. In spite of
the apparent simplicity of such systems, the dynamics of these three-atom reactions have provento be extremely rich, with important roles in fields such as atmospheric, combustion, chemicallaser, and interstellar chemistry.29-35
As one particularly well-studied example, the strongly exothermic reaction F + H2 and its
isotopic variants has proven to be an intensely productive focus of investigation from boththeoretical and experimental perspectives.19-28
Extensive crossed-beam studies have revealed details of reactive scattering, including thedifferential and integral cross section as a function of collision energy,22 as well as complete HF
rovibrational quantum state distributions.36 On the theoretical side, a full-dimensional ab initio
potential energy surface (PES) has been generated4,37 with global accuracy approaching a few
tenths of a kcal/mol. For such a three-atom system, rigorous quantum reaction dynamics on one
or more electronic surfaces are computationally accessible.38 Indeed, the first definitive examplesof elusive transition state resonance dynamics were identified experimentally in the isotopic

68
variant reaction F + HD → HF + D27 and then confirmed in the F + H2 reaction.39 Calculation of
non-adiabatic interactions between multiple spin-orbit surfaces has also become recently feasible,
with such benchmark calculations performed on the F(2P3/2, 2P1/2) + H2 system.40 These theoreticalachievements are remarkable for their nearly quantitative agreement with experiment. Indeed, theability to generate a PES from first principles and obtain results from numerically exact dynamics
calculations that can be rigorously tested against experiment represents an important milestoneachievement by the chemical physics community.
Advances in computational speed also enable existing methods to be tested on more
complex systems. One such step is hydrogen exchange between two “heavy” atoms such as thereaction F + HCl → HF + Cl, which forms the subject of this chapter. Although the Cl atom’s
added electrons (when compared to F + H2) significantly increases the cost of ab initio
calculations, the F + HCl reaction offers a number of desirable features. First, it involves the twolightest halogen atoms, each of which have already been studied through their respective
reactions with molecular hydrogen.10-14,20-23,25,26 Secondly, open shell halogen reactants andproducts necessarily result in multiple, low-lying spin orbit surfaces and the possibility of nonadiabatic dynamics. These surfaces can be explored in all 3N-6 reaction dimensions using
multireference ab initio techniques at achievable computational cost. Thirdly, from a purely
energetic perspective, the reaction can be viewed as a “substitution” for the spectator H atom in
the F + H2 system. Indeed, the nearly equal reaction exothermicity for these reactions [F + HCl→ HF + Cl ΔH0 = -33.059(14) kcal/mol,41,42 F + H2 → HF + Cl ΔH0 = -32.001(14) kcal/mol43]
provides an interesting opportunity for probing mass related changes in reaction dynamics
without significantly different energetics. Finally, dynamical studies of such surfaces can help
elucidate both classical and quantum dynamical contributions along the progression F + H2, F +HD, and F + HCl, a perspective which proves particularly useful in light of the large body ofwork on heavy-light-heavy (HLH) mass combinations in chemical reactions.44 Indeed, based on

69
the understanding of F + HD, such HLH systems may be expected to exhibit quantum transition
state resonance dynamics, roughly corresponding to rapid “chattering” motion of the light atom
between the two heavy atoms.28,45,46 The convergence of theoretical and experimental techniques
capable of identifying such phenomena15,16,18,28,39,45-47 further motivates renewed studies of the F +HCl system.
Further clarification of this broad analogy between F + H2 and F + HCl reaction systems
necessitates detailed comparison of their theoretical PES. Two F + HCl surfaces have been
recently reported, hereafter referred to as the SHHG PES48, and the DHSN PES.5 Both surfaces
exhibit strongly bent transition-state geometries with an F−H−Cl angle of 131.2° and 123.1° for
the SHHG and DHSN surfaces, respectively. This reaction geometry is surprisingly close to the≈119° F–H–H angle found using multireference calculations on F + H2.4,37 There is generalagreement between experiment and theory about the low F + H2 classical barrier height (≈ 2
kcal/mol). In contrast, single reference variational methods used to generate the SHHG PES
revealed a classical barrier of 4.01 kcal/mol. This value was empirically scaled to 1.12 kcal/molon the SHHG surface, in light of the ≈ 1 kcal/mol activation energies inferred from temperaturedependent kinetic studies.49-51 However, the larger value is in much better agreement with thatfound on the more recent DHSN surface (3.75 kcal/mol), developed using high level
multireference ab initio methods. By way of support, the present study requires high speed,
helium carrier gases in crossed molecular jets, with the HF product not detectable under lower
collision energy conditions. This qualitative observation lends credence to the appreciablebarriers predicted by theoretical treatment.
Other differences between F + HCl and F + H2 are readily evident, such as the ≈ 1–2
kcal/mol F–HCl and HF–Cl van der Waals wells visible in Fig. 3.1. These wells have been
experimentally characterized via spectroscopy in argon-matrices52 and helium nanodroplets,53

70

Figure 3.1

Reaction coordinate for the reaction F(2P) + HCl → HF(v,J) + Cl(2P), on the
ground 1A’ and excited surfaces, reported in Ref. 5. The dashed line represents
the total energy available in the center of mass frame, with the collision energy
distribution shown in inset.

71
and via molecular beam-scattering studies.54 A new exit-well PES has recently been reported andbound states of the Cl–HF complex characterized on this surface.55,56 Such strong attraction
between the HX permanent dipole moment and the polarizability/quadrupole of thecorresponding halogen atom create significant interaction that are not present on the F + H2
surface. Several studies have provided a theoretical framework for characterizing van der Waals
potentials in such open-shelled systems.57-59 However, the influence of these wells on highly
exothermic reactive dynamics has yet to be determined, further motivating the present work.
Previous studies of F + HCl → HF + Cl reveal a number of noteworthy features thatsuggest rich dynamic processes underlie this three-atom reaction. Temperature-dependent kinetic
studies by Houston and coworkers have revealed strongly non-Arrhenius behavior, which wasinterpreted as evidence of microscopic branching through direct versus complex-mediatedreaction mechanisms.49,50 Pioneering studies by Beadle, Polanyi, Setser and others60-65 exploited
fast flow arrested-relaxation conditions to measure highly inverted HF vibrational branchingratios consistent with early barrier dynamics.66 The influence of collisions in these studies on HF
state distribution was carefully monitored and not found to perturb vibrational populations;however, the measured rotational populations were significantly bimodal and thought to bepartially relaxed.60,61,67 As a result, the Boltzmann-looking low J state populations were attributed
to rotational thermalization prior to IR detection and hence neglected, with only the higher J
states considered truly nascent.
As will be described more fully herein, the present direct absorption experimental results
offer an alternative and intriguing analysis. Specifically, our results reveal a bimodal formation
pathway into both low J and high J states, even under reaction conditions with approximately a1000-fold reduction in relaxation probability (i.e., residence time × density) when compared toarrested relaxation studies.60,63,68-70 The observation of bimodal HF rotational distributions in
HF(v = 1, 2) therefore resurrects the possibility of microscopic branching, as first proposed to
explain non-Arrhenius kinetics. Interestingly, no indication of either microscopic branching or72bimodal HF rotational distributions has been found in previous theoretical studies of F + HCl,
including QCT calculations on a LEPS surface,71 and QCT66 and wave-packet72 studies on the
SHHG PES. Along with interest in both i) HLH resonance mediated and ii) nonadiabatic hopping
dynamics in chemical reactions, this has provided additional incentive for recent work5 indeveloping and fitting a new high level ab initio potential for F + HCl, along with thecorresponding nonadiabatic matrix elements coupling these surfaces.73 It is our hope that theavailability of such benchmark surfaces will further facilitate theoretical investigations necessary
for unraveling the reaction dynamics in this fundamental, albeit dynamically rich, bond-breaking
and bond-making event.

3.2 Experiment
A crossed molecular-beam apparatus has been used to resolve the nascent product state
distributions in the reaction F + HCl → HF + Cl under rigorous single collision conditions. An
illustration of the crossed-jet–direct-infrared-absorption apparatus appears in Fig. 3.2 (a). The
experimental details have been described in detail previously.74-76 Here we present a brief
overview of the experiment, emphasizing the specific apparatus modifications and operating
conditions used in the present work.
Reactants are introduced into a 100 L diffusion-pumped vacuum chamber via two
supersonic molecular jets. The jet expansion axes are oriented at 90° to each other and the laser
probe axis. The F atom source is a standard solenoid fuel injector modified to generate radicals in
an electrical discharge at the throat of the supersonic expansion, as illustrated in Fig. 3.2 (b). The
F atoms are produced as follows. A pulsed solenoid valve releases 65 Torr (133.3 Pa/Torr) of a
10% F2 / 90% He gas mixture into a small (≈ 0.025 mL) volume defined by a slotted hole in a 0.5
mm inert (polychlorotrifluoroethylene) disk insulator sandwiched

73

Figure 3.2(a) Diagram of the crossed molecular jet apparatus used to study the reaction
F(2P) + HCl → HF(v,J) + Cl(2P). HF product is detected via absorption of
infrared laser light multipassed orthogonal to the plane containing the jet axes.
Low jet densities enable the reaction to be studied under rigorously single
collision conditions. See text for details. (b) Schematic of the modified solenoid
valve, which generates F(2P) radicals in a plasma discharge between the limiting
orifice and the valve body.

74
between two flat nickel electrodes. A miniature slit (300 μm×0.3 cm) in the downstream
electrode forms the limiting orifice from which the gas expands past two slit-jet expansiondefining “jaws” and into the chamber. At the peak of the 2 ms gas pulse, a 500 μs HV pulse (≈ -1kV) is applied to the lower electrode, striking an electrical discharge through the gas mixture to
the grounded upper electrode on the valve body. A resulting radical density of approximately
2.6×1012 F atoms/cm3 in the probe region has been measured against other H abstraction systems
with known reaction cross sections (e.g., F + H2). Such densities correlate to ≈ 2×1016 F
atoms/cm3 at the limiting orifice, or ≈ 10% of the F2 dissociating into F atoms in the plasma. The
relative HF density produced in the reaction F + H2 can also be used to crudely estimate thereaction cross section (at Ecom ≈ 4.3(1.3) kcal/mol) for F + HCl. Based on Dong’s22 measured
cross sections [σrxn(F + H2) = 3.0 Å2] at the F + H2 collision energy of 2.3 kcal/mol and thequantum-state distribution reported by Chapman74, the relative density in HF(v = 3,J = 3) and the
F + HCl branching ratios reported herein is consistent with a total F + HCl reaction cross sectionof σrxn(F + HCl) ≈ 0.2–0.5 Å2 at our experimental collision energy. This value is slightly smallerthan, but in reasonable agreement with, the ≈ 1 Å2 value from temperature-dependent rate
constant measurements.49
The second jet is a 1:1 mixture of HCl:He emanating from a custom-built Proch-Trickl77
valve, which uses a PZT disc actuator to generate 500 μs pulses. 200 Torr of the gas mixture
expands from a 500 μm pinhole to yield ≈ 4×1013 HCl molecules/cm3 at the jet intersection
region. The unskimmed jets intersect at a 90° angle, 4.5 cm downstream from each of the nozzle
orifices. With the valves pulsing at 10.1 Hz, the average pressure in the chamber rises to≈ 1.0×10-4 Torr. This pressure corresponds to a mean free path of λ ≈ 50 cm between molecularcollisions, i.e., considerably greater than the distance to the chamber walls and well outside the 1
cm laser probe region.

75
To increase signal size, both jet expansions employ helium carrier gases, which results injet velocities of 1.3×105 cm/s (10% F2/He) and 9.2×104 cm/s (50% HCl/He), as directly measured
by translating a small hearing aid microphone along each expansion axis. The measured velocities
closely match the predicted terminal velocities anticipated by fluid dynamics,78 indicating
efficient cooling of the expansion gases. High collision energies are also necessary to surmountthe anticipated ≈ 4 kcal/mol barrier to reaction.5,48,79 Computational modeling of the experimental
conditions yields the collision energy distribution [P(Ecom)], inset in Fig. 3.1. The averagecollision energy is 4.3(1.3) kcal/mol, such that most F + HCl collisions are expected to exceed thebarrier. Modeling of the experimental conditions, discussed in more detail in Sect. 3.4, takes into
account the velocity and angular distributions of gas in the supersonic expansions, as measured
experimentally via high-resolution Dopplerimetry on IR chromophores doped in the incident
beams in a separate experiment. Such measurements reveal translational velocity distributions
with widths corresponding to a temperature of 30–50 K, caused by incomplete jet cooling andvelocity slip relative to He carrier gas. Nevertheless, the reactant speed distribution makes arelatively small contribution to the width of the experimental collision energy distribution whencompared to the wide range of lab-frame collision geometries available at the intersection of theunskimmed jets, which is primarily responsible for the broad collision energy distribution.
Product HF is detected via direct laser absorption on the Δv = + 1 fundamental (v = 1←0)and successive rovibrational “hot” bands (v = 2←1, v = 3←2, v = 4←3) in the near infrared. The
tunable IR source is a single mode (Δν ≈ 3 MHz) continuous wave (CW) F-center laser (FCL)
outfitted for continuous scanning by the addition of tunable galvo plates and a servo-loopcontrolled intracavity etalon. The product HF is probed with < 50 μW infrared power, kept
intentionally low to eliminate nonlinear effects due to optical saturation. Thus, high-sensitivity IR
intensity changes can be attributed to the interaction with HF product in a linear regime, such thatmeasurements can be directly correlated to absolute HF densities in the laser path length. The

76
absolute IR laser wavelength is measured with a traveling Michaelson interferometer80 referenced
to a polarization stabilized HeNe laser. This calibration is accurate to ≈ 15 MHz, more thansufficient to locate individual HF rovibrational transitions. The relative frequencies during each
Doppler resolved scan are measured to much higher (1–2 MHz) precision via transmission fringes
from a scanning Fabry-Perot cavity.81
A sample Doppler measurement for the HF product absorbing on the transition HF(v’ =4, J’ = 4) ← HF(v” = 3, J” = 3) is shown in Fig. 3.3(a). Typical HF(v,J) signal strengths
correspond to densities of about 5×107 HF molecules/cm3/quantum state in the intersection
region, which approaches the current detection sensitivity for the direct absorption technique.
Indeed, these absorption signals are comparable to the fundamental peak-to-peak noise limit of≈ 2×107 HF molecules/cm3/state [double-dashed lines in Fig. 3.3(a)] created by the IR “photon
counting” shot-noise.
A number of experimental improvements are therefore vital to attaining sensitivities
approaching the shot-noise floor. First, the signal is increased via long absorption path length bymultipassing the IR light through the reaction chamber 16 times using a modified Herriot cell.82,83
Second, IR intensity fluctuations are minimized and removed from signal with the use of several
custom electronic devices. Specifically, the CW IR intensity fluctuations are reduced via electro
optical modulation and servo feedback control of the FCL’s pump laser intensity. Remaining
intensity noise is eliminated by electronic subtraction of common-mode noise observed on two
liquid nitrogen-cooled InSb detectors. The resulting “difference signal” is obtained with sufficientsensitivity to reveal small (≈ 1 part in 105) intensity fluctuations on the signal detector caused by
the transient absorption of HF(v,J) product. On typical transitions, such methods yield a signal tonoise ratio (S/N) of ≈ 2:1 under conditions used in the current study.

Integrated Absorbance (kHz)

Absorbance (10-5)77

10vHF=3,JHF=3

a)Δν = 630 MHz
5
0
-5
20

b)

15
Integral
Signal

10
5
0
-1000

-500

0

500

1000

ν−ν0 (MHz)Figure 3.3

Sample infrared absorption data on the line HF(v’ = 4, J’ = 4) ← HF(v” = 3, J” =3). (a) Absorption as a function of laser frequency. Open circles: raw data at 3
MHz frequency resolution. Dashed lines: theoretical peak-to-peak quantum shotnoise limit. Solid line: Savitzky-Golay (55 point, 4th order) smoothed data.
Dotted line: Gaussian fit of the raw data, with indicated FWHM width of 630
MHz. (b) Integral of the raw data as a function of frequency, yielding thecolumn-integrated absorbance for the transition.

78
Additional sensitivity enhancement is obtained by scanning the high resolution laser in≈ 3 MHz steps through a ≈ 400–900 MHz HF Doppler profile. At each frequency, we obtain an
independent measure of absorption by digitally recording the signal wave form and numericallyintegrating over 330 μs. The step size, approximately equal to the laser bandwidth, results in alarge number of independent data points [N > 100 under a typical Doppler full width half
maximum (FWHM)], providing a √N ≈ 10- to 12- fold gain in sensitivity. The solid line in Fig.
3.3(a) presents the raw data smoothed by a 55-point, 4th-order Savitzky-Golay algorithm,84 which
better represents the uncertainty of the measurement. Indeed, profiles for significantly populated
states can even be least-squares fitted to a simple Gaussian lineshape. Such a fit to theunsmoothed data is shown as the dotted curve in Fig. 3.3(a). The Doppler width from this leastsquares fit yields approximate information on HF recoil velocities in the lab frame, which areclearly hotter than room temperature (Δνthermal = 330 MHz) and indeed vary explicitly as afunction of HF(v,J) rovibrational state.
By way of example, the inferred Doppler widths are plotted in Fig. 3.4 for severaltransitions originating in the v = 2 and v = 3 manifold. The plot abscissa is the enthalpy releasedin the reaction (-ΔH0) minus the internal energy of the HF product formed (EHF internal(v,J)), i.e., thetranslational energy release upon reaction (ΔEtrans(v,J)). These widths are ≥ 2-fold broader than that
expected for room temperature HF, shown in Fig. 3.4 as a dashed line. Indeed, the observed
Doppler widths increase systematically with ΔEtrans(v,J), as expected from conservation of energy.
Such excess translational Doppler excitation in the laboratory frame is consistent with exothermic
energy release into the HF(v,J) products and represents additional confirmation of nascent, single
collision conditions.

79

1.2

Δν/ν0 /10

5

1.0
0.8
0.6
0.4

Δν/ν0 (300 K)

0.2
0.0
-2

0

ΔE

Figure 3.4

2
trans

4

6

8

(v,J) (kcal/mol)

Observed HF Doppler width (FWHM) distributions projected along the laser axis
as a function translational energy released [ΔEtrans(v,J) = -ΔH0 - EHF internal(v,J)]. The
solid curve represents expected values based on a Monte Carlo simulation of theexperimental conditions. The horizontal dashed line is a 300 K HF Doppler
distribution.

80
Nascent column-integrated HF(v,J) product densities (reported in Sect. 3.3) are obtained
from the total area under the various Doppler profiles. A representative analysis is presented inFig. 3.3(b), where the integral of the raw data is plotted as a function of laser frequency. The
smoothness of the plot underscores that the integral absorption values also benefit from a √N
improvement over N independent Doppler-resolved absorption measurements. Statistics of theintegral absorption measurements are further improved by a regimen of signal averaging during
which each IR transition is probed in at least three independent sets of triplicate scans (i.e., ninetimes) during the course of the experiment. The 2.3–3.3 μm tunability of the IR source alsoenables many HF(v,J) states to be probed on both the P (ΔJ = -1) and R (ΔJ = + 1) branchtransitions, further increasing the degree of oversampling of the data set. Data are also collected
on a strong reference transition [i.e., HF(v’ = 4, J’ = 4) ← HF(v” = 3, J” = 3)] every 2–3 hours
during data acquisition. By normalizing the entire data set to concurrent reference line
observations, day-to-day fluctuations in the electrical discharge and F atom densities are
eliminated from the analysis, so data acquired over multiple weeks can be meaningful compared.
Background HF(v = 0, J) in the ground vibrational state is present at trace levels, due topre-reaction with impurities in the fluorine source at the parts per million level. Fortunately,
efficient cooling in the supersonic jet confines all such background to HF v = 0, low J levels. To
take this into account, each transition out of the HF(v = 0,J) manifold is scanned with and without
the HCl reactant jet; the differential increase in integrated absorption is attributed to the HF
reactive product channel. This procedure works well but generates significant uncertainties forthe lowest (HF(v = 0, J < 6)) states arising from subtraction of weak and nearly equivalent
populations. Nevertheless, the present results provide first direct measurement of population in
the ground vibrational state, which had been inaccessible via previous IR chemiluminescencemethods.60-65

81
As noted previously, the experiment is conducted under rigorous single-collisionconditions, obtained from low reactant pulsed flow densities, but at the expense of product signal
strength. Based on our experimental conditions described above and an estimated49 reaction crosssection for F + HCl scattering of ≈ 1 Å2, fewer than 1% of the F atoms suffer a reactive collision
while transiting the secondary HCl jet. Of these 1% reactive events, the probability for elastic
and/or inelastic collisions prior to IR detection is predicted to be down by an order of magnitude.
Most collisions are with helium carrier gas, which is known to have small cross sections forrovibrationally inelastic scattering;36 hence, this represents an upper limit for redistribution of the
HF(v,J) population. By way of explicit verification, nascent HF(v,J) has been monitored on
several rovibrational transitions as a function of backing pressure in the HCl jet. The resulting
rotational distributions are summarized as a density ratio between two J states in the v = 3 and v =2 manifolds, as shown in Fig. 3.5. The observed ratio is much larger than the value for a room
temperature rotational distribution (dashed lines, Fig. 3.5), which furthermore remains constantwithin experimental uncertainty over more than a fourfold increase in gas density. Thismeasurement represents explicit verification of the nascent character of the quantum-state
populations. The lack of rotational redistribution is also consistent with the Doppler translational
excitation plotted in Fig. 3.4, further validating that the quantum state distributions can be
attributed to a single reactive collisional event.

82[HFJ=7]/[HFJ=3]

1.0

vHF=3

a)

0.5
0.03

(300K)
0.0[HFJ=8]/[HFJ=2]

1.0

b)

vHF=2

0.5
0.01

(300K)

0.0
0.0

0.5

[HCl] (10Figure 3.5

1.0
14

1.5

3

/cm )

HF(v,J) density ratios observed in two rotational states versus the HCl density inthe intersection region. (a) HF(v = 3) density ratio for J = 7 versus J = 3. (b) HF(v= 2) density ratio for J = 8 and J = 2. Dashed line is the ratio of densities at Trot =300 K. The solid line indicates the average ratio, with no systematic shift toward
thermalization as HCl density increases. Representative error bars are shown atthe ρHCl value used for full HF quantum-state distribution measurements.

83

3.3 Results
The data set consists of a series of high-resolution HF absorption Doppler profiles,
recorded on each HF line within the tuning range (2.5–3.3 μm) of the FCL. Mathematically, theabsorbance is related to differences in absolute HF densities by the Beer-Lambert law, i.e.
Aji (ν - ν0) = ∫dx ∫dν’ [σj→i(ν-ν’)κj(x,ν’-ν0) - σj←i(ν-ν’)κi(x,ν’-ν0)],(3.1)

where κi/j(x,ν’-ν0) is the spectral density (i.e., molecules/cm3/cm-1) of absorbers in states i or j, at
a position x along the absorption path with Doppler shifted center frequency ν’-ν0. σj←i(ν-ν’) andσj→i(ν-ν’) are the homogeneous absorption/emission lineshapes between states i and j, centeredaround ν’. Since the homogeneous lineshape is much narrower than the inhomogeneous Doppler
profile, the integral over ν’ can be readily performed to yield
Aji(ν-ν0) = Sj→i ∫dx κj(x,ν-ν0) - Sj←i ∫dx κi(x,ν-ν0),(3.2)

whereby the net absorption at a given Doppler detuning, ν−ν0, is related to the difference in HF
column-integrated spectral density between states i and j at ν−ν0, weighted by the appropriate
line strength Si↔j. We integrate over the absorption profile to obtain,∫A(ν-ν0) dν = Sj→i ∫dx ρj(x) - Sj←i ∫dx ρi(x),(3.3)

which, based on well-known absorption line strengths (Si↔j)85, permits the difference in columnintegrated densities for the lower and upper probe states to be extracted.
For the highly inverted vibrational populations observed in F + HCl reactive scattering,
significant HF density is often formed in both j and i, resulting in competition between stimulated
emission and absorption signals. By Eq. 3.3, this leads to correlation between upper and lower
state densities in a least-squares fit to the data. However, the correlation is effectively broken bytransitions out of the highest energetically accessible v = 3 manifold, for which there is zero
population in the upper state. Furthermore, the tunability of the IR laser permits observation ofboth P and R branch transitions out of many HF(v,J) lower states, adding further redundancy to

84
the data set. By employing a network of such expressions as Eq. 3.3, the full spectrum ofintegrated intensities has been fitted using linear least-squares analysis. The results of the fit
provide experimental values and uncertainties for the quantum state resolved HF(v,J) columnintegrated densities, as displayed in Fig. 3.6 and presented in Table 3.1.
The nascent population densities shown in Fig. 3.6 (discussed further in Sect. 3.4.)
immediately raise several interesting points. First, HF product is observed in a wide variety ofstates, from low J states in the v = 0 manifold to v = 3 states with high rotational excitation. The
measured uncertainty increases uniformly from the highest vibrational manifold to the groundstate because of the coupling of the observed absorption/emission lines in the least-squares fit tothe observed spectrum. Thus, the number of observations that influence any given state grows
with the number of upper state densities that also must be known, up to the highest energy,
unpopulated, state in a series of transitions that are related according to Eq. 3.3. Nevertheless,even densities in the lower vibrational manifolds are determined with repeatedly low
uncertainties.
The data reveal a strong propensity for vibrational population inversion. The maximum
HF densities are observed in the HF(v = 2) manifold, a somewhat smaller fraction in HF(v = 1),
and a yet smaller, but still significant, population in HF(v = 3). This trend is consistent with
Polanyi rules for strongly exothermic reactions with early barriers, which predict the formation of
the nascent HF population predominantly in high vibrational levels. In fact, the F + HCl reaction
is one of many systems studied by Polanyi and contemporaries60-65 via IR chemiluminescence
under arrested-relaxation conditions. The present study’s vibrational branching and that reported
in various chemiluminescence studies are compared in Fig. 3.7. The present HF densities are inexcellent agreement with the various arrested-relaxation studies. We note for later discussion,
however, that this level of agreement does not extend to rotational distributions in each HF(v)manifold.

85

v=3

2

HF Column Integrated Density (1010 #/cm2)

0

a

b

v=2

4

2

0
4

v=1

2

0

0

5

10

15

JHF
Figure 3.6

Column-integrated density distribution of nascent HF product formed from thereaction F + HCl. Values are obtained by least-squares fitting of the observed HF
IR spectrum to a network of transitions, as discussed in the text. Vertical dashedline a reflects the reaction exothermicity (near v = 3, J = 3); b includes the 4.3
kcal/mol collision energy (near v = 3, J = 9).

86Table 3.1 HF column-integrated densities (1010 molecules/cm2) for F + HCl → HF(v,J) + Cl.
Product fluxes have been inferred from detailed simulation of the reaction conditions. See text for
details.
v
0

1

2

3

J
6
7
8
9
10
11
12
13
14
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
0
1
2
3
4
5
6
7
8
9
10
11
12

∫dx ρHF(x)
-0.1
1.0
0.6
-0.1
0.5
1.3
1.4
0.9
2.2
1.3
2.5
2.0
2.2
1.4
1.2
1.0
0.5
0.5
0.4
1.2
1.3
0.8
2.1
1.0
0.9
0.9
1.4
2.3
2.9
2.4
2.3
2.0
1.9
2.3
2.5
3.6
4.4
4.2
3.6
1.0
0.4
-0.4
0.79
1.88
1.83
1.88
1.51
1.38
1.33
1.31
0.82
0.46
0.40
0.5
-0.2

error
(1.2)
(1.3)
(1.2)
(1.7)
(2.3)
(2.2)
(1.6)
(2.1)
(2.1)
(0.3)
(0.4)
(0.4)
(0.6)
(0.4)
(0.6)
(0.6)
(0.5)
(0.5)
(0.5)
(0.5)
(0.5)
(0.5)
(0.6)
(0.6)
(1.1)
(1.2)
(0.16)
(0.2)
(0.3)
(0.3)
(0.3)
(0.3)
(0.3)
(0.3)
(0.3)
(0.3)
(0.3)
(0.3)
(0.5)
(0.5)
(1.0)
(1.1)
(0.12)(0.17)(0.18)(0.19)(0.19)(0.19)(0.19)(0.17)(0.19)(0.18)(0.18)(0.4)(0.5)

Normalized Flux (%) error
-0.3
(2.3)
1.8
(2.4)
1.1
(2.1)
-0.2
(3.1)
0.8
(4.0)
2.2
(3.8)
2.3
(2.7)
1.4
(3.5)
3.5
(3.3)
2.1
(0.5)
4.1
(0.9)
3.2
(0.8)
3.5
(1.1)
2.2
(0.8)
1.8
(0.9)
1.5
(0.9)
0.8
(0.8)
0.8
(0.7)
0.6
(0.7)
1.7
(0.7)
1.8
(0.7)
1.1
(0.6)
2.6
(0.8)
1.2
(0.8)
1.0
(1.2)
1.0
(1.3)
1.8
(0.3)
2.8
(0.5)
3.6
(0.6)
2.9
(0.5)
2.8
(0.5)
2.3
(0.5)
2.2
(0.5)
2.6
(0.5)
2.7
(0.5)
3.7
(0.6)
4.3
(0.7)
3.8
(0.6)
3.0
(0.6)
0.7
(0.4)
0.2
(0.6)
-0.2
(0.4)
0.5
(0.2)
1.3
(0.4)
1.2
(0.4)
1.2
(0.4)
0.8
(0.3)
0.7
(0.3)
0.6
(0.2)
0.5
(0.2)
0.3
(0.2)
0.2
(0.14)
0.1(0.12)
0.1
(0.2)
-0.1
(0.2)

87

Fractional Population

0.8

this work (density)
Beadle et al.
Ding et al.
Tamagake et al.
this work (flux)

0.6

0.4

0.2

0.0
0

1

2

3

vHF
Figure 3.7

Vibrational HF product branching from F + HCl → HF(v) + Cl. The results ofarrested-relaxation studies from Ref. 60,62,65 are as indicated. Population in v =0 is directly observed for the first time; previous values are based on information
theory predictions. Data are normalized to HF(v = 1–3) summed populations,enabling meaningful comparison of measurements with and without HF(v = 0)information.

88Interestingly, direct absorption methods provide a first indication of finite nascentpopulation in the HF(v = 0, J) manifold, which does not emit in the near IR and thus had beeninvisible to early chemiluminescence studies. Any rotational structure within the small v = 0
signals is masked by the scatter between points because of the conjunction of low signal levels,
subtraction of trace HF background, and uncertainty propagation with decreasing v. However, the
HF v = 0 densities comprise 9.5(67)% of the total HF density observed, with the total population
clearly exceeding this value due to exclusion of J ≤ 5 background. Interestingly, the observed v =0 density is consistent with the 7–9% surprisal predictions reported by several of thechemiluminescence studies60,65. This qualitative agreement between information theory and direct
measurements of ground state HF confirms a dynamical propensity for a sizeable population in
low energy states following reaction of F with HCl.
On the other hand, significant HF density is clearly also produced in high-energy
rovibrational states. The dashed lines in Fig. 3.6 indicate the energetic limits for HF quantum
states accessible via the 33 kcal/mol reaction exothermicity [≈ EHF(v = 3, J = 3)] and those withthe addition of the 4.3 kcal/mol average center-of-mass collision energy [≈ EHF(v = 3, J = 9)]. For
HF produced in states exceeding the lower limit, the center of mass recoil energy of the products
is actually less than that of the reactant collision energy. Thus, the F + HCl reactive encounter
favors excitation of the nascent HF molecule to such an extent that some fraction of the products
are formed with all of the reaction energy plus some of the reactant translational energy
sequestered in the HF internal energy. Indeed, finite density is observed above the upper energetic
threshold, only dropping off to zero above v = 3, J = 11. Populating these highest states requires
an additional 1.9 kcal/mol of collision energy, most likely arising from the significant width (σ =1.3 kcal/mol, see inset of Fig. 3.1) in the crossed jet distributions. In principle, there may be an
additional energy contribution from reaction of spin orbit excited (2P1/2) versus ground state (2P3/2)
F atoms (Espin orbit = 1.1 kcal/mole) formed in a nearly statistical (2:4) ratio in the discharge

89source. Evidence for such nonadiabatic reaction dynamics has been demonstrated in previous
quantum state resolved F + H2 and F + HD collision studies,76,86 where Ecom had negligible
uncertainties with respect to spin orbit excitation energy. However, the high transition statebarrier and collision energies necessary for the present study preclude any definitive implicationof nonadiabatic dynamics.
A high degree of HF rotational excitation in lower vibrational manifolds is also evident
from the state distributions in Fig. 3.6. Of considerable dynamic interest is the highly
nonmonotonic structure apparent in the rotational distributions. This structure is particularly
evident in the v = 2 manifold, which demonstrates a clear peaking at both low (J ≈ 2) and high (J≈ 10) states. A qualitatively similar pattern of low (J ≈ 1–3) and high (J ≈ 11–13) state peaking is
also evident in the HF(v = 1) populations, though there appears to be additional structure in thatmanifold. Raw data from early arrested-relaxation studies60,61 also indicate HF formation in low J
levels of v = 2 and v = 1. However, these low-J population components were previously ascribedto rotational relaxation as a result of non-single-collision conditions and removed from theanalysis.60,61,67
The current results suggest grounds for reinterpretation. Data for the v = 1 and v = 2
manifolds are replotted in Fig. 3.8 along with the raw and “corrected” results from arrestedrelaxation studies.60,62 The crossed-jet studies, performed under much lower-density singlecollision conditions (see discussion in Sect. 3.1), clearly indicate the presence of a significant
bifurcation into both low and high J states. In principle, discrepancies between these studies could
arise from differences in thermal (Ecom ≈ kT = 0.6 kcal/mol) versus crossed supersonic jet (Ecom =4.3 kcal/mol) collision energies. However, a much more likely interpretation is that the earlystudies were in fact less rotationally relaxed than originally suspected, with partial rotational
relaxation simply adding to the true fraction of nascent product formed in low rotational states.

90

0.15

a)

HF (v=2,J)b)

HF (v=1,J)

Fractional Population

0.10

0.05

0.00
0.15

0.10

0.05

0.00
0

5

10

15

JHF

Figure 3.8

Rotational distributions for HF products in (a) v = 2 and (b) v = 1 manifolds,
obtained from arrested relaxation (solid, dotted lines)60,62 and the present crossed
jet experiments (circles with error bars). Distributions reported from previous
studies have been modified for presumed rotational relaxation, as illustrated byraw (dashed line) and corrected (solid line) results of Ref. 60.

91
It is also conceivable that the rotational distributions reported in arrested-relaxation studies of F +HBr and F + HI60,65,87 may also suffer from overcompensation for rotational relaxation and may
warrant study under lower density conditions.
It is apparent from Fig. 3.6 that the HF(v = 1,2; J) product distributions can not beadequately described by any simple statistical model. Indeed, these populations are remarkablefor both the wide number of J states populated and the significant bifurcation of the population
into low-versus-high rotational states in HF(v = 1) and HF(v = 2). By comparison, the reaction of
F with H2,74 CH4,75 or C2H6,88 each with comparable ≈ 30 kcal/mol exothermicities, produces
similar degree of vibrational inversion but with a much more modest amount of HF rotation.
Specifically, the rotational distributions peak at Jmax ≈ 2 for F + CH4 and F + C2H6, and at Jmax ≈ 6
for F + H2. In each case, the population decays monotonically for J > Jmax. The current results are
qualitatively different, with a relatively flat rotational distribution in HF(v = 3) extending out to J
≈ 5–6. The HF(v = 1) and HF(v = 2) manifolds are even broader, with local maxima occurringaround J = 10. One intriguing interpretation of these double maxima may be microscopic
branching in the reaction dynamics. For example, if reaction occurs through two dynamical
pathways, one producing HF in low rotational states and the other with a propensity for rotational
excitation, a bimodal distribution such as seen in Fig. 3.6 could arise naturally. One precedent forsuch bimodal and extensive rotational structure is the quantum transition-state resonancemediated reactions of F + HD, which will be discussed further in the following section.

3.4 Analysis
The results in Fig. 3.6 show nascent column-integrated densities for HF(v,J) produced
from the F + HCl reaction, as directly measured from the IR spectrum at the intersection of thereactant jets. However, it is the state resolved fluxes that represent the experimental quantity ofinterest; this requires consideration of the well-known89-91 density-to-flux transformation, i.e.

92
correctly taking into account the velocity-dependent detection sensitivity intrinsic in any density
based measurement technique. Modeling the effect of recoil energy on detection sensitivity
requires a detailed Monte Carlo (MC) simulation of the collision and absorption events based on
the explicit experimental geometry. Such a simulation has been described previously,92 is briefly
summarized here, and more completely detailed in Sect. 2.4(B) and Appendix E. The procedurestatistically calculates the relative signal contribution for a particular HF(v,J) quantum state
detected in some differential volume (dV) and Doppler detuning (dν) with respect to the probe
laser axis. This absorption signal arises from HF formation at another volume (dV’) in the jetintersection region, with recoil energy and angular direction consistent with incident reactant
velocities, reaction energetics and conservation of linear momentum for limiting forms of thedifferential cross section. The statistical averaging uses MC routines that simulate the distributionof reactant speeds, densities, collision angles, and scattering angles present under theexperimental conditions. The inputs to the model are as follows: i) probe and jet geometries, ii)
known reactant and product masses, iii) reaction exothermicity, iv) reactant jet angular
distributions and speeds, and v) the adiabatic, zero-point corrected transition-state barrier height(3.75 kcal/mol) obtained from high-level ab initio calculations,5,48,79 below which the reaction can
not proceed classically.
The key function of the MC simulation is to predict the probability distribution ofvelocities for HF detected in state (v,J) as a function of HF–Cl recoil energy. These distributions,projected onto to the IR probe axis, also can be used to predict Doppler widths plotted as thedashed line in Fig. 3.4. The agreement between predicted and measured Doppler widths serves as
an independent measure of model reliability, and increases confidence in the quantity of interest
from the MC simulation. The density-to-flux transformation is obtained fromΦ(v,J) = ∫dx ρHF(v,J)(x) /〈τ〉(v,J),

(3.4)

93
where Φ(v,J) is the state resolved flux per unit area (in HF molecules/cm2/s), ∫dx ρHF(ν,J)(x) is thecolumn-integrated density plotted in Fig. 3.6 and tabulated in Table 3.1, and 〈τ〉(v,J) is the averagetime HF(v,J) spends in the probe laser volume. Due to spatial averaging within the unskimmed
jets, the MC results are relatively insensitive to the assumed differential cross section, which istaken simply as isotropic. By way of support, MC simulations for extreme limits of i) sideways
and ii) forward/backward scattering yield ratios of density-to-flux transformation factors andquantum state resolved populations that differ less than experimental uncertainties for a given
vibrational manifold. The state resolved flux values calculated via Eq. 3.4 have been normalized
to yield branching ratios into a given HF(v,J) state, as also summarized in Table 3.1. The densityto-flux transformation results in a modest increase in product branching into low-energy HF(v,J)
states, yielding essentially identical trends for distributions of rotational HF column-integrated
densities discussed in Sect. 3.3. Net vibrational populations can be obtained by summing overrotational states for a given vibrational state, as shown by the flux and density branching ratios
illustrated in Fig. 3.7. This comparison generally provides very good agreement with previous
studies, supporting expectations that chemiluminescence conditions were indeed sufficient tocompletely arrest vibrational ineleastic collisions.

3.5 Discussion
Recent theoretical studies have reported the vibrational branching of HF product,
resulting in populations in [v = 0, 1, 2, 3] of [0.03, 0.31, 0.68, 0.01] on Kornweitz’s LEPS
surface71 and [0.01, 0.12, 0.72, 0.16] on the SHHG PES.66 Each of these studies consistently
overestimates the population in the highest (v = 2,3) manifolds compared to experimental
measurements, a trend continued by Hayes’ study73 on the new DHSN surface [0.001, 0.03, 0.43,
0.54]. Of particular importance, these calculations all reveal little or no population in the v = 0
manifold and a relatively insignificant fraction of v = 1 population. Such consistent over-94
prediction of HF vibrational excitation with respect to experiment may signal the need to address
remaining deficiencies in these QCT calculations, arising from either i) pure quantum effects suchas transition state resonances, ii) non-adiabatic surface hopping dynamics, or iii) deficiencies in
the previous ground state ab initio surfaces.
In light of the discrepancies in vibrational branching, it is not surprising that theoreticalstudies of the F + HCl reaction also fail to reproduce the highly structured rotational distributions
reported herein. Sayos’ QCT calculations66 found HF product almost exclusively in high J (J =10–16) v = 2. As discussed in the introduction, Sayos’ SHHG PES and the more recent DHSNPES both contain highly bent transition states. Such bent reaction geometry is likely tosignificantly torque on the nascent HF diatom and constrain motion across the transition state.73
The inability to explain lower-energy rotational populations has prompted us to further explore
the DHSN surface via QCT, as described below.
To help interpret the observed trends in HF product state distributions and address
remaining discrepancies with theory, a series of QCT calculations have been performed on the
DHSN surface using a fourth-order Runge-Kutta integration method.84 Using a time step of 5
atomic units = 0.12 fs, energy is conserved to better than 0.03 and 0.0002 kcal/mol for reactive
and non-reactive events, respectively, with typical trajectories of 1–2 ps duration. The surface has
been explored using trajectories starting in the entrance channel with an initial F–HCl distance of≈10 Å, collision energies of 4–10 kcal/mol, initial HCl angular momenta of J = 0–5, and impact
parameters of 0–4 Å. Representative calculations resulting from 50,000 trajectories starting in the
F + HCl channel at Ecom = 7 kcal/mol and JHCl = 2 are plotted in Fig. 3.9. The choice of collisionenergy enhances reaction probability; however, the qualitative aspects of the HF productquantum-state distributions for reactive events prove relatively insensitive to collision conditions.
Specifically, product HF is found exclusively in the v = 3 and v = 2 manifolds, with highestenergy rotational states primarily correlating with v = 2, as anticipated from conservation of

95

0.05

vHF=1

0.00

Fractional Population

vHF=2
0.10

0.05

0.00

vHF=3

0.10

0.05

0.00
0

5

10

15

JHF

Figure 3.9

QCT results on the DHSN potential energy surface. Rovibrational distributions in
v = 1, v = 2, and v = 3 are shown for trajectory calculations beginning far in theentrance channel (circles), and for trajectories beginning in the van der Waals
well (triangles).

96
energy. The results are qualitatively similar to those reported by Sayos et al.,48 who also foundonly rotationally excited HF in v = 2. The results of Sayos et al. are less vibrationally excited thanthe present DHSN calculations, but are performed on the SHHG PES, which has an empiricallylowered barrier that enabled study at lower collision energies. Nevertheless, trajectories on both
surfaces predict high vibrational excitation and, more specifically, only high rotational excitationin v = 2.
As a further test of these trends, a second set of trajectories has been performed, starting
simply in the transition state (TS) region of the DHSN surface with total energy 0.2 kcal/mol
above the classical barrier. Although these TS calculations have not been chosen to accuratelyreflect a distribution of reactive trajectories, they do reproduce the same propensity for i)
exclusive population in the v = 2 and (to a lesser extent) v = 3 manifolds, and ii) peaking of high J
state rotational excitation in v = 2. Thus, the DHSN surface clearly confirms results from earlier
surfaces, in which only the high-J HF(v = 2) and lower J HF(v = 3) products are predicted via
classical trajectory methods.
We have also used QCT methods to briefly explore the possible influence of the deep vander Waals well in the HF + Cl exit channel. These trajectories are motivated by the wealth ofvibrational predissociation studies of van der Waals complexes, as well as the possibility of long
lived resonance states that explore portions of the exit well not extensively visited by classicalreaction path. Exit-well trajectories are started in the vicinity of the HF–Cl van der Waals
minimum, in an initial distribution of HF rovibrational states obtained from full trajectory
calculations shown in Fig. 3.9 and with zero kinetic energy in the HF–Cl coordinate. In essence,these conditions mimic what might be expected if nascent reactive products were to becometrapped in the HF–Cl van der Waals well following reaction. The trajectories with non-rotating
but vibrationally excited HF were found to be nondissociative on the time scales explored; thiscorresponds roughly to vibrational predissociation, which is known to be exquisitely sensitive tothe hard inner wall of the PES and poorly modeled by QCT.93 However, the dissociation

97
probability of the HF–Cl complex does rise rapidly with increasing HF internal rotation, in effect,
rotationally predissociating to yield HF with reduced internal energy. The results of suchtrajectories are shown in Fig. 3.9, where the product HF fragments retain most of their vibrationalenergy while being “cooled” into lower angular momentum states. Thus, the Van der Waals exit
well may play a significant role in the formation of the low-J HF observed experimentally andmay even contribute to HF population in lower vibrational manifolds. Indeed, previous studies ofexit-channel dynamics by Orr-Ewing and coworkers in reactive trajectories found thatrotationally cold products with strong dipole moments can torque on recoiling fragments andthereby rotationally “heat up” in the exit channel.94 It would seem equally dynamically plausible
in the F + HCl system for highly rotationally excited HF to be “cooled” by angular forces in thevan der Waals exit channel, which would be an interesting direction for further theoretical
exploration.
As a final comment, we note that the broad bimodal rotational distributions observed in
the F + HCl system are not entirely novel. In fact, the resonance-mediated reaction F + HD
produces a similarly broad, highly structured distribution of rotational states in HF(v = 2), as
measured at Ecom = 0.6 kcal/mol by Harper et al.,76 and predicted by the quantum dynamical
calculations of Skodje et al.27 To facilitate comparison, the F + HD results for HF(v = 2, J) are
reproduced in Fig. 3.10 along with the distribution of HF(v = 2,J) fluxes from the present F + HCl
work. The distributions from each reaction share a number of qualitative features, including
highly nonstatistical populations, broad nearly constant intensities at low J and a sudden drop off
to zero population at high J. The calculations of Skodje et al. interpret the F + HD distribution as
the result of a transition state resonance due to H atom vibrational motion across the barrier, as
first observed in elegant differentially resolved scattering measurements by Liu and coworkers.
The qualitative similarity between rotational distributions in these two HLH systems therefore
suggest the presence of transition state resonance dynamics also playing an important role in

98

vHF=2

0.10

Fractional Population

0.05
F+HCl (current experiment)
Ecom = 4.3(1.3) kcal/mol

0.00

vHF=2

0.10

0.05

0.00

F+HD (Harper)
Ecom = 0.6(2) kcal/mol
0

5

10

15

JHF

Figure 3.10

HF(v = 2,J) rotational distributions from F + HCl (circles), in comparison with
the F + HD reaction (triangles) from Ref. 76. The broad and structured
populations from F + HD are dominated by a reactive transition state resonanceat ≈ 0.5 kcal/mol.

99
F + HCl reactive scattering. At the very least, this is an intriguing result worthy of further
experimental and theoretical attention. From an experimental perspective, we have constructed avelocity map ion imaging apparatus, which should permit reactive studies of F + HCl by probing
the Cl(2P1/2,2P3/2) product with energy and angular scattering resolution. From a theoreticalperspective, this has motivated our development of a full set of high-level multireference (MRCI+ Q), spin-orbit corrected potentials along with non-adiabatic terms coupling each of the surfaces.
It is our hope that such efforts will help further elucidate the dynamical richness clearly stillpresent in such a classic yet deceptively “simple” atom + diatomic reaction.

3.6 Summary and Conclusion
The reaction F + HCl → HF + Cl has been observed under rigorous single-collisionconditions for the first time, based on high resolution direct absorption IR laser spectroscopy on
the HF(v,J) product. The increased sensitivity of the direct absorption method permits operation
under much lower reactant densities, resulting in many orders of magnitude reduction in time
window for collisions of the nascent product. The absence of collisional relaxation is validated bystudies as a function of reactant backing pressure, as well as high resolution of Doppler profilesof translationally “hot” product species. The HF vibrational distributions are in excellent
agreement with results reported in early arrested-relaxation IR emission studies. The IR laser
absorption technique also permits branching into the HF(v = 0) manifold to be observed directly
for the first time. The HF rotational distribution reveals significant structure, with strongly
bimodal populations evident in both the v = 2 and v = 1 manifolds. The presence of both low andhigh J nascent rotational structure under single collision conditions is qualitatively similar to raw
data from early IR emission studies, for which the low J component was inferred to be due to“unarrested” rotational relaxation processes. The current studies offer indications that some

100
fraction of this low J component may have been truly nascent, which might warrant reanalysis ofsimilar IR emission data from other X + HY systems.
This novel bifurcation in J state distributions highlights the possible presence of
microscopic branching in the reaction, which might signal the presence of more complex
dynamics due to quantum effects and/or non-adiabatic coupling between electronic surfaces. By
way of example, the bimodal rotational distributions observed in F + HCl are qualitatively quite
similar to what is seen in the F + HD system, for which the presence of a FH(v = 3)–D quantum
transition state scattering resonance has been confirmed by both experiment and theory. In
analogy to the work of Orr-Ewing on more nearly thermoneutral systems, we propose a possible
alternate mechanism for microscopic branching between low J and high J rotational distributions
that involves partial internal HF rotor relaxation in the outgoing exit-channel due to the HF–Cl
van der Waals well. High-level multireference potentials will soon be available to permit full 3D
quantum reactive scattering on multiple non-adiabatic surfaces, and thereby stimulate more
rigorous comparison between theory and experiment and promote understanding of theunderlying reaction dynamics.

101

References for Chapter III
1

G. B. Moore and I. W. M. Smith, J. Phys. Chem. 100, 12848 (1996).

2

P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, S. D. Rosner, and C. E. Young, J. Chem. Phys.
44, 1168 (1966).

3

G. Capecehi and H. J. Werner, Phys. Chem. Chem. Phys. 6, 4975 (2004).

4

J. F. Castillo, B. Hartke, H. J. Werner, F. J. Aoiz, L. Banares, and B. Martinez-Haya, J.
Chem. Phys. 109, 7224 (1998).

5

M. P. Deskevich, M. Y. Hayes, K. Takahashi, R. T. Skodje, and D. J. Nesbitt, J. Chem.
Phys. 124, 224303 (2006).

6

P. F. Weck and N. Balakrishnan, J. Chem. Phys. 123, 144308 (2005).

7

S. Rogers, D. S. Wang, A. Kuppermann, and S. Walch, J. Phys. Chem. A 104, 2308
(2000).

8

D. J. Garton, A. L. Brunsvold, T. K. Minton, D. Troya, B. Maiti, and G. C. Schatz, J.
Phys. Chem. A 110, 1327 (2006).

9

D. J. Garton, T. K. Minton, B. Maiti, D. Troya, and G. C. Schatz, J. Chem. Phys. 118,
1585 (2003).

10

B. F. Parsons and D. W. Chandler, J. Chem. Phys. 122, 174306 (2005).

11

M. H. Alexander, G. Capecchi, and H. J. Werner, Faraday Discuss. 127, 59 (2004).

12

F. Dong, S. H. Lee, and K. Liu, J. Chem. Phys. 115, 1197 (2001).

13

D. Skouteris, H. J. Werner, F. J. Aoiz, L. Banares, J. F. Castillo, M. Menendez, N.
Balucani, L. Cartechini, and P. Casavecchia, J. Chem. Phys. 114, 10662 (2001).

14

N. Balucani, D. Skouteris, G. Capozza, E. Segoloni, P. Casavecchia, M. H. Alexander, G.
Capecchi, and H. J. Werner, Phys. Chem. Chem. Phys. 6, 5007 (2004).

102
15

D. G. Truhlar and Kupperma.A, J. Chem. Phys. 56, 2232 (1972).

16

R. D. Levine and S. F. Wu, Chem. Phys. Lett. 11, 557 (1971).

17

R. E. Continetti, B. A. Balko, and Y. T. Lee, J. Chem. Phys. 93, 5719 (1990).

18

S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N.
Zare, and E. Wrede, Nature 416, 67 (2002).

19

M. H. Alexander, D. E. Manolopoulos, and H. J. Werner, J. Chem. Phys. 113, 11084(2000).

20

S. C. Althorpe, Chem. Phys. Lett. 370, 443 (2003).

21

M. Baer, M. Faubel, B. Martinez-Haya, L. Y. Rusin, U. Tappe, and J. P. Toennies, J.
Chem. Phys. 108, 9694 (1998).

22

F. Dong, S. H. Lee, and K. Liu, J. Chem. Phys. 113, 3633 (2000).

23

M. Faubel, B. Martinez-Haya, L. Y. Rusin, U. Tappe, J. P. Toennies, F. J. Aoiz, and L.
Banares, J. Phys. Chem. A 102, 8695 (1998).

24

Y. T. Lee, Science 236, 793 (1987).

25

D. M. Neumark, A. M. Wodtke, G. N. Robinson, C. C. Hayden, and Y. T. Lee, J. Chem.
Phys. 82, 3045 (1985).

26

L. Y. Rusin and J. P. Toennies, Phys. Chem. Chem. Phys. 2, 501 (2000).

27

R. T. Skodje, D. Skouteris, D. E. Manolopoulos, S. H. Lee, F. Dong, and K. Liu, J.
Chem. Phys. 112, 4536 (2000).

28

R. T. Skodje, D. Skouteris, D. E. Manolopoulos, S. H. Lee, F. Dong, and K. P. Liu, Phys.
Rev. Lett. 85, 1206 (2000).

29

R. A. Sultanov and N. Balakrishnan, Astrophys. J. 629, 305 (2005).

103
30

S. Javoy, V. Naudet, S. Abid, and C. E. Paillard, Exp. Therm. Fluid Sci. 27, 371 (2003).

31

D. Gerlich, E. Herbst, and E. Roueff, Planet Space Sci. 50, 1275 (2002).

32

O. D. Krogh, D. K. Stone, and G. C. Pimentel, J. Chem. Phys. 66, 368 (1977).

33

M. J. Berry, J. Chem. Phys. 59, 6229 (1973).

34

C. Zhu, R. Krems, A. Dalgarno, and N. Balakrishnan, Astrophys. J. 577, 795 (2002).

35

D. A. Neufeld, J. Zmuidzinas, P. Schilke, and T. G. Phillips, Astrophys. J. 488, L141
(1997).

36

W. B. Chapman, B. W. Blackmon, and D. J. Nesbitt, J. Chem. Phys. 107, 8193 (1997).

37

C. X. Xu, D. Q. Xie, and D. H. Zhang, Chin. J. Chem. Phys. 19, 96 (2006).

38

S. C. Althorpe and D. C. Clary, Annu. Rev. Phys. Chem. 54, 493 (2003).

39

M. H. Qiu, Z. F. Ren, L. Che, D. X. Dai, S. A. Harich, X. Y. Wang, X. M. Yang, C. X.
Xu, D. Q. Xie, M. Gustafsson, R. T. Skodje, Z. G. Sun, and D. H. Zhang, Science 311,
1440 (2006).

40

Y. R. Tzeng and M. H. Alexander, J. Chem. Phys. 121, 5183 (2004).

41

J. D. D. Martin and J. W. Hepburn, J. Chem. Phys. 109, 8139 (1998).

42

W. T. Zemke, W. C. Stwalley, J. A. Coxon, and P. G. Hajigeorgiou, Chem. Phys. Lett.
177, 412 (1991).

43

B. P. Stoicheff, Can. J. Phys. 79, 165 (2001).

44

R. T. Skodje, Annu. Rev. Phys. Chem. 44, 145 (1993).

45

W. Jakubetz, D. Sokolovski, J. N. L. Connor, and G. C. Schatz, J. Chem. Phys. 97, 6451
(1992).

104
46

I. M. Waller, T. N. Kitsopoulos, and D. M. Neumark, J. Phys. Chem. 94, 2240 (1990).

47

F. Fernandez-Alonso and R. N. Zare, Annu. Rev. Phys. Chem. 53, 67 (2002).

48

R. Sayos, J. Hernando, J. Hijazo, and M. Gonzalez, Phys. Chem. Chem. Phys. 1, 947(1999).

49

E. Wurzberg and P. L. Houston, J. Chem. Phys. 72, 5915 (1980).

50

C. M. Moore, I. W. M. Smith, and D. W. A. Stewart, Int. J. Chem. Kinet. 26, 813 (1994).

51

I. W. M. Smith and D. J. Wrigley, Chem. Phys. Lett. 70, 481 (1980).

52

B. S. Ault, J. Chem. Phys. 68, 4012 (1978).

53

J. M. Merritt, J. Kupper, and R. E. Miller, Phys. Chem. Chem. Phys. 7, 67 (2005).

54

V. Aquilanti, D. Cappelletti, F. Pirani, L. Y. Rusin, M. B. Sevryuk, and J. P. Toennies, J.
Phys. Chem. 95, 8248 (1991).

55

A. V. Fishchuk, G. C. Groenenboom, and A. van der Avoird, J. Phys. Chem. A 110, 5280
(2006).

56

A. V. Fishchuk, P. E. S. Wormer, and A. van der Avoird, J. Phys. Chem. A 110, 5273
(2006).

57

J. Klos, M. M. Szczesniak, and G. Chalasinski, Int. Rev. Phys. Chem. 23, 541 (2004).

58

M. L. Dubernet and J. M. Hutson, J. Phys. Chem. 98, 5844 (1994).

59

M. Meuwly and J. M. Hutson, J. Chem. Phys. 119, 8873 (2003).

60

P. Beadle, M. R. Dunn, N. B. H. Jonathan, J. P. Liddy, and J. C. Naylor, J. Chem. Soc.,
Faraday Trans. II 74, 2170 (1978).

61

D. Bogan and D. W. Setser, in Fluorine-containing free radicals: kinetics and dynamics
of reactions: based on a symposium sponsored by the Division of Physical Chemistry at

105
the 169th meeting of the American Chemical Society, Philadelphia, Pennsylvania, April
7-11, 1975, edited by J. W. Root (American Chemical Society, Washington, 1978), pp.
237.
62

A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi, and J. L. Schreiber, Faraday
Discuss. 55, 252 (1973).

63

N. Jonathan, Melliar-Smith Cm, S. Okuda, D. H. Slater, and D. Timlin, Mol. Phys. 22,561 (1971).

64

J. P. Sung and D. W. Setser, Chem. Phys. Lett. 48, 413 (1977).

65

K. Tamagake, D. W. Setser, and J. P. Sung, J. Chem. Phys. 73, 2203 (1980).

66

R. Sayos, J. Hernando, R. Francia, and M. Gonzalez, Phys. Chem. Chem. Phys. 2, 523(2000).

67

D. S. Perry, Private Communication (2006).

68

D. Brandt and J. C. Polanyi, Chem. Phys. 35, 23 (1978).

69

L. J. Kirsch and J. C. Polanyi, J. Chem. Phys. 57, 4498 (1972).

70

J. C. Polanyi and K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).

71

H. Kornweitz and A. Persky, J. Phys. Chem. A 108, 140 (2004).

72

B. Y. Tang, B. H. Yang, K. L. Han, R. Q. Zhang, and J. Z. H. Zhang, J. Chem. Phys. 113,
10105 (2000).

73

M. Y. Hayes, M. P. Deskevich, D. J. Nesbitt, K. Takahashi, and R. T. Skodje, J. Phys.
Chem. A 110, 436 (2006).

74

W. B. Chapman, B. W. Blackmon, S. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 109,
9306 (1998).

75

W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 113, 3670 (2000).

106
76

W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 116, 5622 (2002).

77

D. Proch and T. Trickl, Rev. Sci. Instrum. 60, 713 (1989).

78

D. R. Miller, in Atomic and molecular beam methods, edited by G. Scoles (Oxford
University Press, New York, 1988), pp. 14.

79

I. Last and M. Baer, J. Chem. Phys. 80, 3246 (1984).

80

J. L. Hall and S. A. Lee, Appl. Phys. Lett. 29, 367 (1976).

81

A. S. Pine, J. Opt. Soc. Am. 66, 97 (1976).

82

D. Herriot, H. Kogelnik, and R. Kompfner, Appl. Optics 3, 523 (1964).

83

D. Kaur, A. M. Desouza, J. Wanna, S. A. Hammad, L. Mercorelli, and D. S. Perry, Appl.
Optics 29, 119 (1990).

84

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in
C: the art of scientific computing, 2 ed. (Cambridge University Press, New York, 1992).

85

E. Arunan, D. W. Setser, and J. F. Ogilvie, J. Chem. Phys. 97, 1734 (1992).

86

S. A. Nizkorodov, W. W. Harper, W. B. Chapman, B. W. Blackmon, and D. J. Nesbitt, J.
Chem. Phys. 111, 8404 (1999).

87

D. Brandt and J. C. Polanyi, Chem. Phys. 45, 65 (1980).

88

E. S. Whitney, A. M. Zolot, A. B. McCoy, J. S. Francisco, and D. J. Nesbitt, J. Chem.
Phys. 122, 124310 (2005).

89

H. W. Cruse, P. J. Dagdigian, and R. N. Zare, Faraday Discuss. 55, 277 (1973).

90

C. Naulin, M. Costes, A. Benseddik, and G. Dorthe, Laser Chem. 8, 283 (1988).

91

D. M. Sonnenfroh and K. P. Liu, Chem. Phys. Lett. 176, 183 (1991).

107
92

W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, Chem. Phys. Lett. 335, 381 (2001).

93

E. Tannenbaum, K. J. Higgins, W. Klemperer, B. Segev, and E. J. Heller, J. Phys. Chem.
B 106, 8100 (2002).

94

S. Rudic, C. Murray, J. N. Harvey, and A. J. Orr-Ewing, J. Chem. Phys. 120, 186 (2004).

108________________
Chapter IV F + H2O → HF(v,J) + OH: HF(v,J) nascent product state distributions formedin crossed molecular jets________________
4.1 Introduction
As demonstrated in the previous chapter, significant progress has been made inunderstanding gas-phase reaction dynamics in three-atom systems. However, significant hurdles
remain for larger systems because additional degrees of freedom dramatically increase thecomputational cost of characterizing the PES and performing quantum dynamical calculations onsuch surfaces in full dimensionality. Yet, even with the relatively modest increase from three tofour atoms, entirely new phenomena become feasible, such as mode-specific chemistry1-13 andenergy transfer into “spectator” degrees of freedom.14,15 Additionally, increasing system size andnumber of open channels necessitate considerably more detailed experimental observations tocharacterize adequately the product distributions at the quantum state-to-state level.
Recent work has demonstrated that the study of polyatomic (i.e. N ≥ 4) reaction dynamics
is on the horizon of computational feasibility. In particular, remarkable advances have been madein developing an accurate ab initio PES and performing exact quantum reactive scattering
calculations for the benchmark four-atom reaction system H + H2O ↔ H2 + OH.16-18 Recent
progress in this dynamically rich reaction suggests that full-dimensional ab initio studies of fouratom systems with more than one heavy (i.e., non-hydrogen) atom will be feasible in the near
future, and chemical systems with N > 4 are likely to become the outstanding computational
challenge in 3N-6 dimensions.
Direct dynamics methods present one interesting alternative to completely exploring
dynamics on a high-dimensional PES. This technique enables classical trajectory simulations to109
be performed in arbitrary dimensions by calculating the PES energy and its derivatives “on thefly,” at the nuclear coordinates traversed by a given trajectory.19-22 However, computational costs
in systems of high dimensionality restrict such calculations to relatively low levels of ab initio
treatment. Furthermore, this method relies intrinsically on classical dynamics, making inherently
quantum phenomena, such as zero point energy23 and reactions promoted by tunneling throughbarriers,24 difficult to model. The current intractability of full dimensional studies for all but thesimplest four-atom system emphasizes the need for further experimental efforts at the state-tostate level. Such work provides a crucial opportunity for benchmark testing of approximate
theoretical methods against detailed experimental measurements and stimulates the developmentof progressively more rigorous multidimensional quantum computational techniques.
The F + H2O → HF + OH reaction represents an ideal candidate for detailed comparison
between experiment and novel theoretical techniques. In addition to fundamental interest in 4atom bond-making and bond-breaking, this reaction plays an important role in Earth’s
atmosphere, where it is primarily responsible for scavenging F atoms introduced into thetroposphere by photolysis of partially fluorinated compounds.25 In astronomy this reaction may be
important in determining the fate of F atoms in the interstellar medium.26 The dynamics of thisatom + triatom abstraction process are dominated by a relatively low transition state barrier (ΔE ≈5 kcal/mol27) and yet a moderately high exothermicity (ΔH0 = -17.61(2) kcal/mol28,29).
Interestingly, these values are quite close to those found in the current state-of-the-art 4-atom
reaction system, H2 + OH, which features a similarly exothermic (ΔH0 = -14.4 kcal/mol28,30)
reaction path and low barrier (ΔE ≈ 6 kcal/mol)16 for formation of H2O product.
As shown in Fig. 4.1, many rovibrational quantum states of HF and OH products areenergetically accessible from reaction of F with H2O. From an experimental perspective, quantum
state resolved spectroscopic techniques have been developed that are capable of sensitively
probing reactive scattering and energy flow into both diatomic species.31-33 Alternatively, high-110

Energy (kcal/mol)

40
30(vHF,vOH)(3,0)
P(Ecom)20
100〈Ecom〉

(2,0)
(1,1)
(0,2)
(1,0)
(0,1)
(0,0)

Reaction Coordinate
Figure 4.1

Reaction coordinate for F + H2O → HF + OH on the two lowest adiabatic
potential energy surfaces, from calculation in Ref. 27. Both surfaces
asymptotically correlate to F(2P3/2) reactant, but result in ground OH(2P3/2) (solid2line) and spin-orbit excited OH( P1/2) (short dashes) in the product channel. The
inset plot is the calculated experimental collision energy distribution, whose
average value, Ecom = 5.4(1.3) kcal/mol above the reactant energy, is plotted as
the long dashed line. Various vibrational levels of HF and OH products areshown as dotted lines.

111level theoretical treatment may hope to attain chemically accurate ab initio results, while stillusing acceptably small basis sets to describe the second row atoms in this system. Recent
multireference configuration interaction studies of the F + H2O PES revealed that reaction on the
two lowest electronic PESs occurs over barriers of ΔE ≈ 5 kcal/mol and 25 kcal/mol, whichcorrelate adiabatically with the formation of ground (2Π3/2) and spin orbit excited (2Π1/2) productOH.27 Although these two surfaces exhibit quite different adiabatic barriers to reaction, they cancross via multidimensional “seams” of conical intersections, including nuclear configurations
close to the reactive transition state.
The importance of such non-adiabatic reaction considerations is emphasized by recent
crossed jet studies of F + H2O and F + D2O performed in our group.33,34 Though laser induced
fluorescence (LIF) measurements revealed that only OD(v = 0,N) is produced, with an averagerotational energy of Erot ≈ 1 kcal/mol, the reaction produces ground (2Π3/2) and spin-orbit excited(2Π1/2) OD products in roughly a 2:1 ratio. This result is surprising since spin-orbit excited radical
adiabatically correlates to reaction on the first excited electronic surface, whose ≈ 25 kcal/mol
barrier exceeds the collision energy by five-fold. Thus, multiple theoretical surfaces and nonadiabatic dynamical treatments will clearly be necessary to account for the apparent “surface
hopping” dynamics leading to OH(2Π1/2). The importance of such non-adiabatic dynamics
underlying this relatively simple four-atom reaction further motivates quantum-state resolved
studies of the HF(v,J) cofragment.
Both kinetic and dynamic studies of F + H2O have been performed previously.
Temperature dependent rates of the F + H2O/D2O reactions were reviewed by Stevens et al.,35
inferring a tunneling mechanism and a ΔE ≈ 4 kcal/mol estimate for the transition state barrierheight, in close agreement with the ΔE ≈ 5 kcal/mol value from ab initio theory.27 In a series ofpioneering dynamical studies, Setser and coworkers obtained rotationally resolved IR
chemiluminescence spectra of HF in the v = 1 manifold and inferred cold OH vibrations.36-38

112
Recent photodetachment studies of the anionic cluster FH2O- have also shed insight upon the title
reaction. Partial overlap between the FH2O- anion geometry and the F + H2O transition state
allows the reactive region of the PES to be accessed directly, resulting in a low energy tailattributed to formation of product HF + OH.39 Direct dynamics simulations of thephotodetachment process found substantial branching into the product channel, yielding
rovibrationally excited HF products and vibrationally cold OH with modest amounts of rotational
excitation.40 These studies stimulate further study of this fundamental four-atom reaction undercrossed beam conditions to resolve completely the energy partitioning in the HF fragment.
The following sections of this chapter describe the complete HF(v,J) product state
distribution following the reaction F + H2O → HF + OH, measured using the high-sensitivity
laser spectrometer and crossed jet apparatus described in detail in Ch. I. Crossed supersonic jets
enable the reaction to be studied with ≈ 1000-fold reduction in gas density compared tochemiluminescence studies. Furthermore, reverse seeding in a He diluent permits the supersonicjet reactants to more easily surmount the barrier by increasing the collision energy. Sensitive IR
laser absorption methods provide i) complete rovibrational state resolution, ii) high resolution
Dopplerimetry measurements along the probe axis, and iii) the first experimental measure of total
product branching into each of the v = 0, 1 and 2 vibrational manifolds.

4.2 Experiment
Detailed descriptions of the crossed jet experimental apparatus appear in Ch. II. The
specific conditions used in the present study are described here and illustrated in Fig. 4.2. The
H2O jet contains ≈ 30 Torr H2O, produced by bubbling He through liquid water heated to 30 °C at
a total pressure of 200 Torr. The remainder of the gas line, including the pulsed valve, is heated to
60 °C to prevent condensation. Fig. 4.3 displays IR measurements of H218O concentration, present

113

Schematic of the crossed jet apparatus, containing pulsed molecular jets of F and
H2O intersecting at 90° in a vacuum chamber. Product HF(v,J) is probed byquantum state resolved, high resolution IR laser absorption using a multipass celloriented perpendicular to the plane defined by the jets axes.

Observed
Expected

500
400
300
200

18

H2 O ∫A dν (kHz)

Figure 4.2

100
0
0

20

40

60

80

100

H2O Partial Pressure (Torr)
Figure 4.3

Measured spectral intensity of a isotopically substituted H218O line present innature abundance in the reactant water jet. The jet’s stagnation pressure isconstant at 200 Torr with helium carrier gas. Partial pressure of water is varied
by changing the liquid temperature.

114
in natural isotopic abundance. These measurements match the expected linear curve of growth as
H2O partial pressure increases up to the 30 Torr value used, confirming the absence of significant
H2O clustering in the reactant jet.
Given its high sensitivity, the IR probe detects trace HF gas produced in the radical
source by impurities in the 10% F2 90% He mixture passed through the high voltage plasma jet
source. Detailed characterization of this background was presented in Ch. 2.3(B). The measured
HF density corresponds to 1.0 ppm generated in the plasma source. Placing a liquid nitrogen cold
trap in the F2 gas line reduces this background approximately two-fold while leaving the reactive
scattering intensity unchanged. Background corrections are made by measuring the HF spectrum
in the presence and absence of H2O reactant, and correcting the reactively scattered results for the
background HF densities. This correction is most important in the v = 0 manifold at low J, as
demonstrated by the ≈ 60 K HF background temperature shown in Fig. 2.11. As a result,background HF can be confidently eliminated from the reactive product distributions, althoughproduct signals in the very lowest HF(v = 0, J ≤ 4) rotational states are not measured reliably andthus not reported. However, HF branching into these states is not expected to be dynamicallyfavored and does not change any of the conclusions drawn from the present results.
Doppler-resolved absorption measurements, such as those presented in Fig. 4.4(a,b), arerecorded for all HF(v” ≤ 2) IR transitions41 within 2.5–3.3 μm, for a total of about 500
observations of 42 lines. Fitting the lineshapes, such as that in Fig. 4.4(b), to a simple Gaussian
profile reveals translationally excited profiles (full width at half maximum [FWHM] of 880 MHz)following the reaction, corresponding to HF recoil speeds of ≈ 2.20 km/s. This value exceeds the1.25 km/s FWHM of the F + H2O center of mass (COM) velocity distribution. For statesoriginating in the v = 2 manifold [Fig. 4.4(a)], less energy is available for product translation, andthe observed Doppler widths decrease accordingly. However, the observed Doppler widths

115

aa)
20

v=3←2
J=1←0

∫Abs dνAbs (10-5)

0

0

-5
10

10

90

Δν=880MHz bb)

b)

v=2←1
J=2←1

5

∫Abs dν (kHz)Δν=610MHz

a)
5

60
30

0

Δν300K=330MHz-1000

Figure 4.4

0

1000

0
-1000

ν−ν0 (MHz)

0

1000

Sample Doppler-resolved absorption measurements originating from (a) HF (v =3←2; J = 1←0) and (b) HF (v = 2←1; J = 2←1) transitions, with total integrated
intensities with respect to laser detuning in (aa) and (bb) and indicated by solid
arrows. Solid lines in the left hand plots are least squares fits to Gaussianlineshapes, with Δν (FWHM) well in excess of the 300 MHz room temperature
HF linewidth [dashed line in (b)]. Doppler profiles have been smoothed with
Savitzky-Golay methods (4th order 25 point) relative to the high resolution
measurements; fits and integrals have been obtained from the raw data.

116
strongly indicate that the nascent HF remains translationally excited following the reactive
encounter, providing evidence for single collision conditions at the reactant jet intersection
region.
Reaction cross sections and experimental conditions for the present study result in HF
densities of < 2×109 #/cm3 per quantum state, requiring highly sensitive measurements of HF
transient absorption. As shown by the raw data in Fig. 4.4(a,b), the IR absorption at these low
densities is on the order of the fundamental photon shot noise limit of ≈ 1×10-5 absorbance in theexperimental 4.0 kHz bandwidth. Even at nearly shot-noise limited sensitivity, signals profit from
integrating each Doppler profile to improve the signal to noise as described in Ch. III. This
treatment reduces uncertainty by the square root of the 200–300 measurements under the Doppler
FWHM, as reflected in the ≈ 5 kHz integral absorbance uncertainty in Fig. 4.4(aa,bb), and results
in a detection sensitivity of ≈ 1×10-8 HF/cm3.
Since absolute HF densities are obtained from the IR absorption technique, the total
reaction cross section of σ ≈ 0.8(0.5) Å2 for F + H2O at 5.4(1.3) kcal/mol collision energy has
been obtained by calibrating the F atom density against F + H2 as described in Ch. 2.4(C). This
result agrees with measured thermal rate constant, which is approximately ten times lower thanthe molecular collision rate35 and suggests that the collision energy does not efficiently couple
into the reaction coordinate according to an intermediate- rather than early-barrier scenario. Ab
initio calculations support this conclusion, with the breaking O–H bond extended to r†(O–HA) =1.031 Å at the transition state, significantly longer than the 0.958 Å bond length in H2O, and thenon-reactive O–H bond only mildly stretched to r†(O–HB) = 0.971 Å.27,42 This comparison
suggests that vibrational excitation of OH stretching modes in water may selectively increase thereaction probability, an interesting area for future exploration.
As customary with the present experimental apparatus, nascent HF state distributions
have been directly confirmed experimentally. Absorption measurements originating in the HF(v =1171) manifold have been observed over a tenfold change in the collision rate, obtained bysimultaneously varying the distance dvalve from both jet sources to the intersection region on thelaser probe axis (see Fig. 4.2). Integral absorbances are scaled by their transition strengths to
produce a quantity roughly proportional to the HF rotational populations. These values have beennormalized and plotted in Fig. 4.5, from which HF rotations are found to be significantly excited
following the reaction event, since all three data sets appear significantly hotter than the 300 K
line in Fig. 4.4(b). This excitation remains unperturbed under the density conditions probed,
except perhaps at the highest collision densities explored (dvalve = 2.5 cm), which appears slightly
colder than the lower density measurements. Thus, the remainder of this study, including thesample data in Fig. 4.4, has been carried out at the middle density conditions (dvalve = 3.5 cm, withdensities of ≈ 5×1014 #/cm3 in the probe region), yielding sufficient signal for reasonablemeasurement uncertainties and maintaining rotationally unrelaxed conditions.

4.3 Results and Analysis
The observed HF spectral features are highly structured, as shown in the stick spectrumof measured integral intensities in Fig. 4.6. Specifically, both absorption and stimulated emission
result from the nascent HF state distribution. Indeed, most of the nascent HF population is formedin the v = 1 manifold, resulting in net emission signals in the fundamental (v = 1←0) band andabsorption on the v = 2←1 and v = 3←2 “hot bands”. No HF absorption signals are observable inthe v = 4←3 band, as expected based on the energy levels presented in Fig. 4.1.
The least squares analysis, described in detail in Ch. 2.4(A), has been performed using
the known HF(v,J) transition line strengths43 to obtain the nascent HF state resolved densities. All
500 observed HF line intensities are included in the fit, which matches experiment within
uncertainty, as shown in Fig. 4.6. The resulting HF densities for the 42 states whose population

118

Normalized ∫Abs dν/S0

(v,J)

0.25
0.20
0.15
0.10

dvalve=4.5
dvalve=3.5

0.05

dvalve=2.5

300K

0.00
0

1

2

3

4

5

6

JHF(v=1)

Figure 4.5

Normalized HF v = 1 integral absorbance measurements, scaled to the transitionlinestrength [S0(v,J)] at three different source geometries. Both F and H2O jet
nozzle distances (dvalve) are varied relative to the laser probe axis to change thereactant density in the intersection region. The dashed line represents a room
temperature rotational distribution, noticeably colder than the measured data.
Measurements confirm negligible rotational redistribution of HF population withincreasing gas density. Conditions used for all reported data in this study
correspond to dvalve = 3.5 cm.

vHF=1←0 P
vHF=2←1 P 7
vHF=3←2 R

6
3
0∫Abs dν (Abs×kHz)

50

5
2

1

1
2

3

0

-50
50

a) Observed

0-50b) Fit
3650

3700

-1

3750

IR Frequency (cm )Figure 4.6

A portion of the a) observed and b) fitted IR stick spectra for HF(v,J) formed by
the F + H2O reaction. Transition intensities are found by locally integrating each
Doppler-resolved measurement, as plotted in Fig. 4.4(aa) and (bb). Absorption
features have positive amplitude, while negative absorption intensities result
from stimulated emission on transitions originating from the vHF = 0 manifold
due to inverted vibrational populations in vHF = 1.

119
has been measured in the current experiment are presented in Table 4.1.
Also presented in Table 4.2 and plotted in Fig. 4.7 are the HF rovibrational branchingratios, PHF(v,J), obtained by consideration of the density-to-flux transformation,40 described in
Ch. 2.4(B) and discussed in more detail in Appendix E. This transformation is necessary sincelaser absorption methods measure the HF density, whereas branching ratios are proportional to
the state resolved product flux leaving the reaction volume. Based on detailed Monte Carlo (MC)modeling of the experimental apparatus,34,35 the expected residence time 〈τ〉(v,J) an HF molecule instate (v,J) spends in the detection volume can be predicted. This set of 〈τ〉(v,J)values represents
proportionality constants for converting column-integrated HF density (#/cm2) to flux (#/s/cm2),
which are then normalized to yield branching ratios. The MC model also provides a detailed
picture for the distribution of collision energies in the crossed jet apparatus, presented in the inset
of Fig. 4.1.

120

Table 4.1 HF column-integrated densities [∫dx ρHF(x)] observed following the reaction F + H2O→ HF(v,J) + OH, in units of 109 HF/cm2. Uncertainties in parenthesis are one standard deviationfrom the least squares fit.
J
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18

v=0
-----3 (14)
7 (13)
28 (12)15 (12)21 (12)6 (11)
8 (10)
4 (10)4 (9)
22 (9)
10 (8)3 (9)8 (7)-3 (7)v=1
64 (4)109 (5)112 (5)105 (7)78 (7)
51 (6)
38 (6)
23 (7)
22 (7)
7 (5)
0 (4)
9 (5)
3 (4)
7 (4)
6 (4)
0 (4)
----

v=2
21 (2)
16 (3)
13 (3)
7 (3)
0 (3)
0 (3)
0 (3)
-------------

Table 4.2 HF state resolved flux (normalized to 100 %) following the reaction F + H2O →HF(v,J) + OH. Uncertainties in parenthesis are one standard deviation from the least squares fit.
J
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18

v=0
-----0.4 (15)0.9 (14)3.5 (13)
1.8 (13)
2.6 (13)0.8 (12)1.0 (11)0.5 (11)0.5 (10)2.8 (10)
1.2 (9)0.4 (10)0.9 (8)-0.4 (8)v=1
7.9 (4)13.5 (5)13.9 (6)13.0 (8)9.7 (8)6.3 (6)4.6 (6)
2.8 (7)2.8 (7)0.8 (5)0.0 (5)
1.1 (5)0.4 (5)0.9 (5)0.7 (5)0.0 (4)----v=2
2.5 (2)2.0 (3)
1.6 (4)0.9 (3)0.0 (3)0.0 (3)0.0 (4)-------------

121

Figure 4.7

Observed nascent HF(v,J) populations produced by the F + H2O reaction.
Vertical lines represent the energetic limit based on the reaction energy (dotted)
and the reaction energy plus the experimental collision energy (dashed). Longdashed line in (b) represents a scaled HF(v = 1) distribution from the arrested
relaxation study in Ref. 28.

122

4.4 Discussion
The HF product distribution, summarized in Fig. 4.8, reveals significant rovibrational
excitation of the nascent HF fragment following the reaction F + H2O. The most populated
manifold is v = 1, and significant rotational excitation is observed in the v = 0 and v = 1
populations. The general trends in the observed population distribution are discussed in thissection.
Summing over the rotational levels produces HF vibrational branching ratios into v = [0,1, 2] of [0.21(6), 0.75(2), 0.046(6)]. Predominant formation in the highest thermochemicallyaccessible vibrational manifold, HF(v = 1), is in agreement with Polanyi rules48,49 for exoergic
reactions with early barriers, i.e. reactions characterized by reactant-like geometries (large F–H
distance) at the transition state. The high proportion of vibrationally excited HF confirms the
spectator nature of the OH fragment, which acts as an insignificant heat sink when compared tothe highly excited HF. The present results are also in good agreement with the [0.24, 0.76, 0.00]
vibrational branching estimates of Wickramaaratchi et al.,38 who used a surprisal analysis of the F+ D2O reaction to infer the v = 0 population for F + H2O. The agreement between predicted andobserved branching ratios reflects favorably on the use of information theoretic treatments topredict qualitatively vibrational partitioning into the nascent HF bond.
Interestingly, the present experimental conditions result in about 5% of the observed HF
population being formed in v = 2, which represents the first experimental observation of HF
product in this manifold. Earlier reactive studies36-38 at thermal collision energies (kT ≈ 0.6
kcal/mol) found no detectable v = 2 product, consistent with total available energy constraints.
However, recent estimates place the barrier for reaction at 4–5 kcal/mol,27,35 so any reactions seen
previously must have occurred either i) due to the “tail” of the thermal collision energy
distribution or ii) via quantum tunneling through the barrier. If tunneling were the dominant123

Arrested
Relaxation(300K)
PresentStudy(5.4 kcal/mol)DirectDynamics(11.3 kcal/mol)

Fractional Population

0.8

0.6

0.4

0.2

0.0
0

1

2

vHF
Figure 4.8

The vibrational branching for HF product found via: i) information theory
estimates in the arrested relaxation experiments in Ref. 38 (solid bars), ii)
measured in the present study (unfilled bars), and iii) calculated using direct
dynamics from the F–H2O anion geometry in Ref. 40 (striped bars). The energy
in excess of the F + H2O reactant asymptote due to experimental collision energy
or initial theoretical geometry is indicated in parenthesis.

124channel under thermal conditions, then the v = 2 manifold would not have been energeticallyinaccessible. Alternatively, thermal reactions may be dominated by improbably energetic
collisions, in which case branching into the HF(v = 2, J) manifold may have been present below
the previous detection sensitivity.
In the present study, the higher crossed jet collision energies guarantee a high probabilityof exceeding the classical barrier. Since the energetic threshold for formation of HF(v = 2)
exceeds the reaction enthalpy by ΔE ≈ 4.5 kcal/mol, the extra energy needed to create v = 2
population in the present study arises from the reactant’s Ecom ≈ 5.4(1.3) kcal/mol COM collisionenergy. Such efficient coupling of reactant translational energy into product internal degrees of
freedom has been observed previously in the reaction of F + HCl → HF + Cl,46 another systemcharacterized by a moderately large (E† ≈ 4 kcal/mol) and early barrier. A simple physical picture
for the coupling of reactant translational energy into product internal energy is based on theshifting nature of the reaction coordinate, which enables the barrier to be accessed via reactant
translation and closely resembles H–F vibration after the saddle point. Thus, the energy used toovercome the barrier can readily couple into product internal energy, in accordance with earlybarrier expectations.48,49
Supporting theoretical evidence for significant formation into HF(v = 2) population atthese higher energies has previously been reported via direct dynamics studies by Ishikawa etal.40 These trajectory simulations were started near the FH2O- ion complex minimum-energy
geometry (found to be near the transition state region) in order to simulate dynamics following
electron photodetachment from the negative ion complex. Starting geometries were found to be
11.3 kcal/mol above the reactant asymptote, corresponding to an additional 5–6 kcal/mol more
incident collision energy than available in the present experimental study. As expected, thesehigher energies lead to a larger proportion of HF forming in the (v = 2) manifold, reported as HF[v = 0, 1, 2] branching ratios of [0.23, 0.54, 0.23].

125
Trends for HF(v) branching in the three vibrationally resolved studies of the F + H2O
reaction are summarized in Fig. 4.8. With increasing energy with respect to the transition state(due to either Ecom or photodetachment starting geometry), the HF(v = 2) fractional population
grows, primarily at the expense of HF(v = 1). This trend is easily rationalized by the nearthermoneutral energetics for HF (v = 2) formation; small increases in the total energy enable thechannel to open, with population efficiently coupled into this manifold by early barrier dynamics.
As mentioned previously, total vibrational branching ratios in the F + D2O and F + H2O
arrested relaxation studies could only be inferred from surprisal analysis of the data, which
permitted the IR non-emitting DF(v = 0) and HF(v = 0) populations to be estimated indirectly.
Indeed, we have performed a similar statistical analysis (as described in Ref. 50,51) on the threedifferent vibrationally resolved data sets (the present study, direct dynamical calculations,40 and
the F + D2O chemiluminescence study38). The results yield linear plots with essentially identicalslopes, consistent with vibrational ratios matching a simple one-parameter surprisal model at eachof the various total energies. A more detailed description of these information theory analyses ispresented in Appendix D.
The degree of rovibrational excitation of the HF product measured in the present
experiment provides some information on the corresponding quantum states populated in the OH
cofragment. For example, based on the energy level diagram in Fig. 4.1, HF (v = 2) population
can only be accessed for the corresponding OH in its ground vibrational state. Similarly,
formation of both OH(v = 1) and HF(v = 1) is just barely energetically allowed, which would
leave insufficient energy for the high rotational excitation noted in HF(v = 1). Additionally, sucha channel would also be inconsistent with the broad Doppler lineshapes observed in the HF (v =1) manifold, which reveal a significant fraction of the remaining reaction exothermicity flowing
into product translational recoil. Thus, a conservative upper limit of the 21(5)% productbranching into OH (v = 1) can be attributed to co-formation of HF (v = 0). This estimate greatly
exceeds the < 1% OD (v = 1):OH(v = 0) vibrational populations observed in F + D2O/H2O via

126
LIF.33,34 Such results match Frank-Condon considerations of the ab initio transition stategeometry for F–H2O, where the non-reactive OH bond length of 0.971 Å closely matches the
0.970 Å bond length of the OH radical product,27 such that the unbroken OH bond is anticipatedto be a spectator to the reaction.
The HF rotational distributions presented in Fig. 4.7 reveal several features of dynamicalinterest. First of all, in comparison with the hot vibrational branching into HF vibrational states,
the rotational populations are relatively cool but still quite energetically excited. Indeed, of the 23
kcal/mol energy available, 41% or 〈Evib〉 ≈ 9.5(0.3) kcal/mol is deposited in HF vibration, while
the average rotational excitation is only 〈Erot〉 ≈ 2.1(0.4) kcal/mol. Secondly, appreciable
population is observed in rovibrational states higher than the 17.61(2) kcal/mol exothermicity,
due to efficient funneling of the incident collision energy (Ecom ≈ 5 kcal/mol) into internal energyof the products. Specifically, the thermochemical limit can only populate HF in the v = 1
manifold up to J = 10, above which finite population is observed up to the total energy limit
above J = 14. Indeed, such collision-energy assisted, endoergic reactions are responsible for all
population found in the HF(v = 2) manifold, as discussed above. The v = 2 rotational populations
are quite cold and decrease rapidly with increasing J, up to J = 4, which is inaccessible at the
average collision energy employed. Conversely, the observed HF (v = 0, J) rotational states arequite hyperthermal, with progressions extending up to the energetic limit at HF(v = 0,J = 17).
These trends match simple energetic expectations for populating higher rotationally excited states
in lower vibrational manifolds (and vice versa).
Interestingly, the current HF(v = 1, J) rotational distribution is remarkably similar to,though slightly colder than, what was observed previously using IR chemilluminescence,37
reproduced as the long dashed lines in Fig. 4.7. The main difference between the two distributions
is that the crossed jet population decreases rapidly above J ≈ 5, resulting in a lower averagerotational energy of 1.3(0.2) kcal/mol versus > 1.6 kcal/mol for the previous study, whose

127
population is not reported above J = 10. This similarity seems to vindicate earlier studies.
However, the level of agreement is also surprising, since these arrested relaxation measurements
were performed at rather different thermal (Ecom ≈ 0.6 kcal/mol) versus crossed jet [Ecom ≈5.4(1.3) kcal/mol] collision energies, and with an approximately 1000-fold increase in gas density
and secondary collision probability. Thus, the quite similar, yet slightly cooler, HF(v = 1)
rotational distributions may simply be the dynamical signature of the threshold HF(v = 2) channel
opening up energetically in the crossed beam and not observed via arrested relaxation methods.
More theoretical work will clearly be useful to help confirm or refute such a possible mechanism.
The nascent HF(v = 1,2) rotational distributions are found to be significantly non-thermal,
as revealed by the Boltzmann plots in Fig. 4.9. On one hand, the HF(v = 2) rotational distribution
shown in Fig. 4.9(a) appears quite cold, with most of the populated states falling on a 150 K slope
preceding a sudden increase for the J = 0 state. Cold rotations in HF(v = 2) are to be anticipatedbecause accessing this manifold requires translationally endoergic reactive collisions and the
additional energy needed to populate high J states is not available. On the other hand, the strongly
non-thermal HF(v = 1) rotational distribution contains significantly hotter components, as shownin the Boltzmann plot in Fig. 4.9(b). The curvature of this plot is qualitatively reproduced by a
two-temperature fit to the data, corresponding to components with 180 K at low J and ≈ 1200 K
at high J.
Similar rotational distributions, characterized by a near-thermal component at low J andhyperthermal decaying populations at high J, have previously been observed in polyatomic
scattering dynamics.21,47,52-54 In the present study, 33% of the HF population is found in stateswith more than 400 cm-1 rotational energy, due to the slowly decaying distribution in HF(v = 1)
and the broad HF(v = 0) distribution peaked near J = 7–9. Indeed, HF rotation contains dynamicalsignatures that are not readily anticipated from statistical considerations, as shown by thenonlinear surprisal plots presented in Appendix D.

ln[ P(JHF) / (2JHF+1) ]128a) vHF=2-4b) vHF=1

-3

-5
150K

-6
-7

-6

1200K

2.3K
-9

180K

-8
0

100

200

0

1000
-1

2000

3000

4000

Erot /cm

Figure 4.9

Boltzmann analysis of the HF product rotational populations in a) the vHF = 2 andb) vHF = 1 manifolds. Dashed lines represent thermal distributions, as labeled.
Significant curvature in the observed distributions motivates fitting to the sum of
two such thermal distributions, the total fit indicated by the solid line.

129
The structured rotational distributions may indicate multiple dynamical constraints, as
opposed to a single constraint that might lead to a linear surprisal plot. Alternatively, thecurvature in Fig. 4.9(b) may be caused by dynamical branching in the reaction mechanism, forexample, between ground (2Π3/2) and excited (2Π1/2) states of the OH product. Both of theseelectronic states have been observed via LIF studies of the OH and OD products following thereactions F + D2O/H2O, and it is conceivable that branching between electronic channels mightalso correlate with hotter and cooler rotational distributions of the HF coproduct. However, future
work will clearly be necessary to further elucidate possible non-adiabatic dynamics on the HF
fragment’s energy distribution.
Nonetheless, several physically motivated models anticipate highly rotationally excited
HF. We consider two mechanisms, differing by when, during the course of reaction, the HF bondreceives the torque necessary to create J > 9 states with more than 5 kcal/mol rotational energy.
One possible answer is that the torque occurs near the transition state. Highly bent transition stategeometries, such as the 103° F–H–O bond in the present reaction system,56 offer one efficientmechanism for coupling reaction exothermicity into rotation of the nascent diatomic bond.49 An
alternative interpretation arises from the large dipole moments of both OH and HF fragments,
which result in strong dipolar forces between diatoms in the ≈ 5.5 kcal/mol product channel well.
Previous direct dynamical studies21 have found sufficient dipole-dipole interaction in polyatomic
exit channel dynamics to excite significantly product rotations well past the transition state regionof the PES. Distinguishing between these two mechanisms would be an interesting avenue for
future theoretical study and a clear step toward fundamental understanding of four-atompolyatomic reaction dynamics.

130
4.5 Conclusions
The F + H2O → HF(v,J) + OH reaction has been studied by probing the nascent HF
rovibrational distribution under single-collision crossed molecular jet conditions using IR laser
spectroscopy. The results are summarized and discussed in light of recent ab initio
characterization of the reaction path and transition state geometry. This study represents the first
directly measured HF vibrational populations for this reaction, which are found to be highly
inverted, consistent with a large F–H distance comparable to “early barrier” transition stategeometry. These results generally agree with previous predictions, with branching into thethreshold HF(v = 2) manifold highly sensitive to the total system energy. HF rotational energy
increases monotonically as vibrational quanta decrease. The HF(v = 2,J) rotational distributions
prove to be quite cold, reflecting endothermic formation of v = 2 made possible by additional
incident kinetic energy in the crossed beam. The HF(v = 1,J) state distributions also exhibit
hyperthermal rotational structure that extends out to the energetic limit. Two possible
mechanisms, one due to energy release away from a strongly bent F–H2O transition stategeometry and the other induced by strong dipole-dipole interactions in the product well, areproposed to explain the propensity toward high J.

131

References for Chapter IV
1R. B. Metz, J. D. Thoemke, J. M. Pfeiffer, and F. F. Crim, J. Chem. Phys. 99, 1744
(1993).

2

M. Brouard, I. Burak, S. Marinakis, L. R. Lago, P. Tampkins, and C. Vallance, J. Chem.
Phys. 121, 10426 (2004).

3

A. Sinha, M. C. Hsiao, and F. F. Crim, J. Chem. Phys. 92, 6333 (1990).

4

A. Sinha, M. C. Hsiao, and F. F. Crim, J. Chem. Phys. 94, 4928 (1991).

5

S. Yan, Y. T. Wu, and K. P. Liu, Phys. Chem. Chem. Phys. 9, 250 (2007).

6

J. B. Liu, B. Van Devener, and S. L. Anderson, J. Chem. Phys. 119, 200 (2003).

7

J. R. Fair, D. Schaefer, R. Kosloff, and D. J. Nesbitt, J. Chem. Phys. 116, 1406 (2002).

8

B. R. Strazisar, C. Lin, and H. F. Davis, Science 290, 958 (2000).

9C. Kreher, J. L. Rinnenthal, and K. H. Gericke, J. Chem. Phys. 108, 3154 (1998).

10

K. Kudla and G. C. Schatz, Chem. Phys. 175, 71 (1993).

11

M. J. Bronikowski, W. R. Simpson, B. Girard, and R. N. Zare, J. Chem. Phys. 95, 8647
(1991).

12

J. M. Pfeiffer, R. B. Metz, J. D. Thoemke, E. Woods, and F. F. Crim, J. Chem. Phys. 104,
4490 (1996).

13

J. D. Thoemke, J. M. Pfeiffer, R. B. Metz, and F. F. Crim, J. Phys. Chem. 99, 13748(1995).

14

M. C. Hsiao, A. Sinha, and F. F. Crim, J. Phys. Chem. 95, 8263 (1991).

15

D. H. Zhang, M. H. Yang, and S. Y. Lee, Phys. Rev. Lett. 89, 283203 (2002).

16

R. P. A. Bettens, M. A. Collins, M. J. T. Jordan, and D. H. Zhang, J. Chem. Phys. 112,10162 (2000).

17

D. H. Zhang, J. Chem. Phys. 125, 133102 (2006).

18

D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 99, 5615 (1993).

19

K. Bolton, W. L. Hase, and G. H. Peslherbe, in Modern Methods for Multidimensional
Dynamics Computations in Chemistry, edited by D. L. Thompson (World Scientific,
River Edge, NJ, 1998), pp. 143.

20

W. Chen, W. L. Hase, and H. B. Schlegel, Chem. Phys. Lett. 228, 436 (1994).

21

S. Rudic, C. Murray, J. N. Harvey, and A. J. Orr-Ewing, J. Chem. Phys. 120, 186 (2004).

132
22

E. Uggerud and T. Helgaker, J. Am. Chem. Soc. 114, 4265 (1992).

23

G. H. Peslherbe and W. L. Hase, J. Chem. Phys. 100, 1179 (1994).

24

R. T. Skodje, D. Skouteris, D. E. Manolopoulos, S. H. Lee, F. Dong, and K. P. Liu, Phys.
Rev. Lett. 85, 1206 (2000).

25

R. von Glasow and P. J. Crutzen, in Treatise on Geochemistry, edited by R. F. Keeling,
H. D. Holland, and K. K. Turekian (Elsevier Pergamon, Amsterdam, 2003), Vol. 4, pp.
347.

26

D. A. Neufeld, J. Zmuidzinas, P. Schilke, and T. G. Phillips, Astrophys. J. 488, L141
(1997).

27

M. P. Deskevich, D. J. Nesbitt, and H. J. Werner, J. Chem. Phys. 120, 7281 (2004).

28

S. A. Harich, D. W. H. Hwang, X. F. Yang, J. J. Lin, X. M. Yang, and R. N. Dixon, J.
Chem. Phys. 113, 10073 (2000).

29

W. T. Zemke, W. C. Stwalley, J. A. Coxon, and P. G. Hajigeorgiou, Chem. Phys. Lett.
177, 412 (1991).

30

B. P. Stoicheff, Can. J. Phys. 79, 165 (2001).

31

A. Schiffman, W. B. Chapman, and D. J. Nesbitt, J. Phys. Chem. 100, 3402 (1996).

32

W. B. Chapman, B. W. Blackmon, S. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 109,
9306 (1998).

33

M. Ziemkiewicz, M. Wojcik, and D. J. Nesbitt, J. Chem. Phys. 123, 224307 (2005).

34

M. Ziemkiewicz and D. J. Nesbitt, manuscript in preparation.

35

P. S. Stevens, W. H. Brune, and J. G. Anderson, J. Phys. Chem. 93, 4068 (1989).

36

H. W. Chang, D. W. Setser, M. J. Perona, and R. L. Johnson, Chem. Phys. Lett. 9, 587(1971).

37

W. H. Duewer and D. W. Setser, J. Chem. Phys. 58, 2310 (1973).

38

M. A. Wickramaaratchi, D. W. Setser, H. Hildebrandt, B. Korbitzer, and H. Heydtmann,
Chem. Phys. 94, 109 (1985).

39

X. Yang, X. B. Wang, and L. S. Wang, J. Chem. Phys. 115, 2889 (2001).

40

Y. Ishikawa, T. Nakajima, T. Yanai, and K. Hirao, Chem. Phys. Lett. 363, 458 (2002).

41

R. B. Leblanc, J. B. White, and P. F. Bernath, J. Mol. Spectrosc. 164, 574 (1994).

42

G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules. (D. Van Nostrand
Company, New York, 1945).

133
43

E. Arunan, D. W. Setser, and J. F. Ogilvie, J. Chem. Phys. 97, 1734 (1992).

44

D. M. Sonnenfroh and K. P. Liu, Chem. Phys. Lett. 176, 183 (1991).

45

H. W. Cruse, P. J. Dagdigian, and R. N. Zare, Faraday Discuss. 55, 277 (1973).

46

A. M. Zolot and D. J. Nesbitt, J. Chem. Phys. 127, 114319 (2007).

47

W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 113, 3670 (2000).

48

J. C. Polanyi and W. H. Wong, J. Chem. Phys. 51, 1439 (1969).

49

J. C. Polanyi, Accounts Of Chemical Research 5, 161 (1972).

50

R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical
Reactivity. (Oxford University Press, New York, 1987).

51

J. T. Muckerman, J. Phys. Chem. 93, 179 (1989).

52

D. Troya, J. Chem. Phys. 123, 214305 (2005).

53

J. F. Castillo, F. J. Aoiz, L. Banares, E. Martinez-Nunez, A. Fernandez-Ramos, and S.
Vazquez, J. Phys. Chem. A 109, 8459 (2005).

54

E. S. Whitney, A. M. Zolot, A. B. McCoy, J. S. Francisco, and D. J. Nesbitt, J. Chem.
Phys. 122, 124310 (2005).

55

J. J. Valentini, J. Phys. Chem. A 106, 5745 (2002).

56

M. P. Deskevich, M. Y. Hayes, K. Takahashi, R. T. Skodje, and D. J. Nesbitt, J. Chem.
Phys. 124, 224303 (2006).

134________________
Chapter V Reactive scattering dynamics at the gas-liquid interface: Studies of F +squalane (C30H62) (liquid) via high-resolution infrared absorption of product
HF(v,J)________________
5.1 Introduction
Many practical chemical processes depend upon interactions at the gas-liquid interface,
including distillation, gas chromatography, biological respiration, and atmospheric chemistry on
aerosols and in bulk liquids. Despite such broad implications, relatively little is known about
elementary processes at the gas-liquid interface. In contrast, a much deeper level of understanding
has been established for gas-phase collision dynamics, where fundamental processes can bestudied in isolation and compared to high-level theoretical models. Molecular dynamics at thesurface of crystalline solids have also been probed in detail, largely motivated by interest inprocesses such as heterogeneous catalysis and corrosion. Dynamics in both gas phase and at gassolid interfaces have proven more accessible due to their inherent compatibility with vacuum andrelative theoretical accessibility via computational methods. Despite these additional challenges,
there remains a keen motivation for study of comparable inelastic and reaction dynamics at thegas-liquid interface.
Fenn and coworkers1 were the first to study the dynamics of gases scattering from liquidsurfaces using low vapor pressure liquids for molecular beam scattering studies. Nathanson andcoworkers have spearheaded the next generation of liquid scattering dynamics via flight-timemeasurements of scattered species with mass spectroscopic detection.2-6 Minton and coworkers
used similar methods to investigate reactive and inelastic scattering of Cl and O atoms fromliquid hydrocarbon surfaces.7-10 The first quantum-state resolved studies were performed by

135
McCaffery and coworkers, who detected I2 scattered from various liquids by laser induced
fluorescence (LIF).11-14 McKendrick and coworkers have also utilized LIF to study reactions of O
atoms with liquid hydrocarbon surfaces.15-22 Our group has developed the use of high resolution
IR absorption methods to probe inelastic scattering of CO2 from a series of perfluorinated,hydrocarbon and hydrogen bonded liquids.23-28 In this chapter, similar methods have been applied
to reactive scattering dynamics, using a modification of the crossed jet apparatus that was thefocus of the previous two chapters.
From these efforts, a general picture for scattering dynamics at the gas-liquid interface
has begun to emerge. The observations fit broadly into one of two mechanisms: trapping
desorption (TD), characterized by Boltzmann velocity and rotational state distributions matching
the liquid temperature, and impulsive/direct reactive scattering (DRS), in which recoiling
molecules retain a large fraction of their incident rotational and translational energy.
Significantly, molecular vibrations are largely decoupled from the surface temperature in either
TD or DRS scattering channels, indicating poor equilibration and suggesting an upper limit forsurface interaction on the 10–100 ps time scale for intermolecular vibrational energy transfer.
In comparison to inelastic scattering, reactions at the gas-liquid interface have only
recently begun to be characterized. Minton and coworkers used mass spectrometry to study thereactions of Cl, O, and O2 with liquid squalane at 5–125 kcal/mol collision energies.7-10
McKendrick and coworkers found modest vibrational excitation of OH formed by reaction of O
atoms with various hydrocarbons,15-22 and the v = 1 rotational temperature was found to be colder
than that for v = 0, particularly when the fast moving products were selectively probed.22 Excited
vibrational population was found to increase with surface temperature19 and depend on theparticular liquid reactant,18 trends ascribed to changes in the surface structure that influences
secondary collisions with the liquid following reaction. Thus, both vibrational and rotational
excitation strongly depends upon the degree to which product-surface interactions lead to energy
transfer into the surface.

136
Previous studies of nearly thermoneutral full7-10,15-20,22,29 or half30-33 reactions at the gasliquid interface have exploited either high incident translational energy or photolysis energy,
respectively, and revealed that product molecules generally retained some fraction of the initial
excitation. By way of contrast, the present study of H atom abstraction by F atoms at the liquid
squalane surface is conducted at approximately thermal collision energies, though the reaction ishighly exothermic. Fig. 5.1 schematically represents possible mechanisms for producing gasphase HF following reaction at the gas-liquid interface. The important features are that incident or
adsorbed F atoms (a, c in Fig. 5.1) may react and immediately eject product HF (b, c), or they
may suffer one or more collisions with the surface (d, e) before desorbing (f). Competition
between such direct or multiple encounters directly impacts the translational and internal energyof the recoiling products, as can be characterized spectroscopically using Doppler resolved
infrared absorption spectroscopy.
The multitude of reactive sites in the liquid reactant complicates discussion of thereaction energetics, as summarized in Fig. 5.2 and Table 5.1. For H atom abstraction from any of
the three types of C–H bonds present (primary, secondary or tertiary) HF product may be formed
anywhere from v = 0–3, with correspondingly higher rotational levels accessible for the lower
vibrational manifolds. The energetic threshold for HF(v = 4) formation exceeds the reaction
exothermicity even for the most weakly bound tertiary C–H site, though these products become
accessible with an additional 2.3 kcal/mol excitation. Based on the corresponding gas-phase
dynamics (i.e., “Polanyi rules”36), one would anticipate DRS to couple energy most efficiently
into the newly formed HF bond. In the TD mechanism, HF may remain trapped on the surface
long enough to accommodate thermally with the bulk prior to desorption, in which case thenascent reaction dynamics may be obscured. The present study reveals an energetic partitioning
between the DRS and TD extremes, interpreted with respect to the time-scale for desorption
following reactions at the gas-liquid interface.

137

a)

b)

Figure 5.1a) Possible reactive encounters between reactant F atoms and a liquidhydrocarbon interface. Incident F atoms (a) may react immediately upon contact(b), or after absorbing at the interface (c). HF product may recoil directly into thegas phase (b,c), or may remain trapped (d,e) before desorbing (f). b) The
chemical structure of squalane, a saturated hydrocarbon with a 24-carbon
backbone and six symmetrically placed methyl side groups.

Table 5.1 Bond strengths and exothermicities for hydrogen abstraction by fluorine atoms forvarious C–H bonds. The average F + squalane exothermicity has been estimated by weighting
according to the number of C–H bonds (NH) and functional groups (NCHx) in squalane.
Uncertainties in parenthesis are one standard deviation.
CH bond order D0 (kcal/mol) ΔHrxn (kcal/mol)a NH
Primary
Secondary
Tertiary
Squalanec
Squalaneda99.6(4)b96.9(3)b95.0(4)b97.7
97.3-35.7(4)-38.4(3)-40.3(4)
-37.5
-38.1

24
32
6

NCHx
8
16
6

D0(HF) = 135.27(1) kcal/mol from Ref. 34
Based on Ref. 35c
D0 as average for equal probability abstraction of all H atoms
dD0 as average for equal probability abstraction from all CHx groupsb

138

E (kcal/mol)

40
30

vHF=4

CH

vHF=3

CH2
CH3

20

vHF=2

10

vHF=1

0

vHF=0

Figure 5.2

Energy level diagram for HF, along with the exoergicity for reaction of F atoms
with different types of saturated hydrocarbon functional groups. Heterogeneous
bond energies for the various C–H bonds result in approximately 5 kcal/mol
uncertainty in the energy released following reaction of F with squalane. The 37–
42 kcal/mol reaction energy is sufficient to access HF states with energy well
above the v = 3, J = 0 level.

139

5.2 Static Liquid Experiment
The study employs the same high sensitivity IR laser spectrometer used in the previous
two chapters and in other state resolved studies of gas-phase collision dynamics in crossed
molecular jets.37-42 As a first attempt to probe the interactions at the gas-liquid interface, aminimal alteration configuration was implemented by placing stagnant pool of liquid squalane(commercially purchased) under the F atom plasma jet source, as illustrated in Fig. 5.3.
At room temperature the vapor pressure of liquid squalane is ≈ 10-7 Torr, i.e., negligible
compared to the ≈ 8×10-7 Torr base pressure of the vacuum chamber. However, the chamber mustbe evacuated slowly (over the course of about one hour) from atmospheric pressure, in order toprevent rapid outgassing and consequent “bumping” of the liquid reactant. The F atom source is
identical to that previously employed in crossed molecular jet studies, and described in detail in
Ch. 2.3(A). During the experiment, the F atom source operates at 10 Hz, and the average chamberpressure rises to ≈ 1.0×10-4 Torr. This low pressure prevents shocking in the supersonic
expansion. The nascent nature of HF recoiling from the surface has also been directly verified, as
discussed in more detail below.
A sample transient absorption waveform is shown in Fig. 5.4, recorded with an FCL
frequency of approximately 3693.682 cm-1, line center of the v = 3←2,J = 2←1 HF transition.
The rising edge of the absorption occurs approximately 250 μs from the start of the F discharge(dotted line in Fig. 5.4), in excellent agreement with time of flight predictions based on the 14.5
cm nozzle-to-liquid path length and 5.73 × 104 cm/s supersonic expansion velocity. The inset of
Fig. 5.4 emphasizes that the observed HF(v,J) signal duration is a convolution of the plasma
current pulse duration (td) and the source-to-surface flight time spread due to the F atom velocity
distribution. For short discharge pulses ( < 250 μs), the peak HF absorption signal grows linearlywith td. For longer discharge pulses ( > 250 μs), the peak signals remain constant with a width of

140

Schematic of the static liquid apparatus. A pulsed jet F atom source directs
reactant at a shallow Pyrex container of squalane. The infrared laser multipass
detects HF product 0.7 cm above the liquid surface with high resolution and ultrahigh sensitivity via direct absorption measurements.

% Absorbance

0.10

350μs
td=115μs

0.20

170μs

0.15

90μs

0.05

0.10
0.05

Idischarge (Amp)

Figure 5.3

0.00

0.00
0.0

Figure 5.4

0.5

1.0

time (ms)

1.5

2.0

Representative transient IR absorption measurement of HF v = 3←2, J = 2←1,
formed by reactive scattering of fluorine atoms from liquid squalane at 0.7(3)kcal/mol collision energy. The solid line is the measured absorption (left axis),
and the dotted line is the plasma current in the F atom source (right axis), withduration td = 115 μs. Inset plots show the signal waveform as a function of td. The
shaded region denotes the time domain of digital signal averaging used toconstruct HF absorption measurements.

141
approximately td. The limiting signal duration is readily anticipated from the 200(50) m/s FWHM
of the F atom velocity distribution, measured separately using IR Doppler measurements of the Fatom jet oriented nearly parallel the IR laser axis and doped with HF. A discharge width of td =115 μs is utilized for the remainder of this study, corresponding to ≈ 70% of the maximum
signal.
For the stagnant liquid surface study, the data is acquired in an identical fashion as in thegas-phase studies. Specifically, a transient recorder captures the time-dependent absorption andtransfers it to a personal computer for analysis as described in Sect. 2.3(B). The signal under a200 μs window centered on the peak HF signal, indicated by the shaded region in Fig. 5.4, isnumerically averaged, and only this value is recorded as a function of laser frequency to construct
the signal absorption profiles. Two such Doppler measurements, originating from different J
states in the v = 2 manifold, are presented in Fig. 5.5.
Single-collision conditions at the gas-liquid interface are necessary for the determinationof the nascent HF product state distribution. Placement of the nozzle orifice (≈ 0.01 cm2) a large
distance (14.5 cm) from the liquid ensures that the gas density is low at the surface. Under these
conditions, secondary radical-radical interactions at the liquid surface are negligible due to an F
atom coverage of approximately 0.001 monolayers per pulse. For these preliminary studies,
reacted liquid molecules must diffusively mix into the bulk, a likely process on the macroscopic
time scales for surface coverage. This concern is further allayed by the second-generation
experiment, described in the following section, which employs an actively refreshed surface, forwhich similar results have been obtained, as discussed in Sect. 5.4. The experimental conditions
are such that gas-phase interactions subsequent to reaction at the surface are also highly
improbable, since the total gas density at the liquid surface is approximately 1.5×1013 #/cm3, andthe mean free path (≈ 10 cm) exceeds the 0.7 cm surface-probe distance by more than an order ofmagnitude.

142

J=2

Absorption

0.004

0.002

0.000

J=6

Absorption

0.00080.00040.0000-800 -600 -400 -2000

200 400 600 80

ν−ν0 (MHz)Figure 5.5

Representative HF Doppler measurements following reaction of F at a liquid
squalane surface. Both lines are recorded on R-branch transitions originatingfrom the v” = 2 manifold, with J” as indicated. Solid lines denote raw absorption
measurements, and dotted lines are fits to Gaussian lineshape functions.

143
To establish nascent conditions unambiguously, the absorption profiles for transitions outof two rotational states shown in Fig. 5.5, the R-branch lines from J” = 2 and 6 in v” = 2, havebeen recorded at a series of nozzle-surface distances dv, shown in Fig. 5.3. Since gas density
varies with 1/dv2, this quantity is used as the x-axis in Fig. 5.6. To quantify the HF translationalenergy, the measured profiles are fitted to a Gaussian function according to Eq. 2.20. The fitted
widths Δν are scaled to the transition frequency ν, yielding a quantity directly proportional to thevelocity distribution’s full width at half maximum (FWHM). This value remains constant over aten-fold variation in the gas density, as shown in Fig. 5.6(a). Moreover, Δν/ν exceeds the value
expected at the 300 K surface temperature, and the J = 6 state exhibits more translational
excitation than J = 2. This trend for increasing translational energy release with increasing
internal excitation is measured throughout and is discussed in more detail with the Doppler
analysis presented in Sect. 5.5(B), where this correlation is further discussed. The density
independence of these high-resolution Doppler widths confirms that the observed HF
distributions are determined solely by nascent dynamics of the gas-surface reactive interaction
and not by secondary gas-phase collisions.
The measured HF absorbance intensities corroborate this conclusion. As seen in Fig.
5.6(b), the integral signals grow linearly with 1/dv2, as expected for signals linear in the F atom
density. In particular, the maximally populated rotational state at 300 K is J = 2, and the signal
from this state reveals no upward curvature with increasing density, which would be anticipated ifthermal relaxation were significant. Furthermore, the relative intensity ratio of 0.23(3) between
HF(v = 2, J = 6) and HF(v = 2 , J = 2) is significantly greater than the 0.07 value expected for a
300 K rotational distribution [dashed line in Fig. 5.6(b)], and the “hot” J = 6 density shows noevidence of decreasing with increasing gas density. The robust insensitivity of both translationaland rotational energy distributions to the experimental conditions indicates that the measured HF
state distributions can be confidently attributed to dynamics at the liquid surface. To be safe,

144

Δν/ν x 106

4

(a)

3
2

v=3I2 J=3I2
v=3I2 J=7I6
300K

1
0

∫Abs(ν)dν (MHz)

8

(b)

6

v=3I2 J=3I2
v=3I2 J=7I6300K J=6 expectation

4
2
0
0.00

0.01

0.02
2

0.03
-2

1/dv (cm )Figure 5.6

Jet density dependence of the observed HF absorption measurements, varied bychanging the distance from the F source to the squalane surface, dv. The total gas
density scales with 1/dv2, which is plotted along the abscissa. (a) Observed
Doppler widths from Gaussian fits of the HF lines v = 3←2, J = 3←2 (circles)
and v = 3←2, J = 7←6 (triangles). The FWHM of a 300 K distribution is plotted
as a dashed line for comparison. The solid arrow indicates the density used forthe remainder of this study. (b) HF integral absorption intensities for the sameobservations as in Fig. 5.5. Measured intensities scale linearly with gas density.
The dashed line is the expected J” = 6 intensity relative to the measured J” = 2
slope for a 300 K rotational distribution. Error bars are representative of typicaluncertainties.

145
however, the most conservative (i.e. lowest density) conditions are used for the remainder of thestudy, corresponding to dv = 14.5 cm, marked by arrow in Fig. 5.6(a), ≈ 1.5×1013 #/cm3.
Nascent HF rovibrational quantum state distributions have been determined from Doppler
profile measurements on all laser-accessible R and P branch rovibrational transitions connecting
the v + 1 ← v manifolds for v = 0,1,2,3. These measurements include a total of ≈ 300 Doppler
scans, typically repeated at least three times for each line. Data are normalized to the HF(v =3←2, J = 1←2) reference line to account for slowly drifting F atom production efficiency. As inprevious studies, numerically integrating the Doppler profiles provides net absorption intensities
for each spectral line, and the observed spectrum is fitted to obtain the HF(v,J) state resolved
column densities. These nascent densities have been normalized and are displayed as populationsin Fig. 5.7. Populations exhibit a simple rise and decay with increasing J state. However, closer
inspection reveals a highly non-thermal HF distribution in J. More detailed analysis is delayed
until Sect. 5.5, after the refreshed liquid surface experiment is described.

5.3 Continuously Refreshed Surface Experiment
Following the studies described in the previous section, a more sophisticated liquidsurface has been implemented, as illustrated in Fig. 5.8. This renewed surface is based on theinnovations of Fenn and co-workers1,43 and the design has been taken from Perkins et al.23 To
continuously refresh the liquid interface, a 15 cm diameter glass disk rotates at 0.3 Hz through acopper reservoir containing 200 mL of commercially purchased squalane. The motion of thewheel viscously drags a layer of squalane from the reservoir, and a steel razor blade, mounted 0.5mm from the glass disc surface, generates a uniform film of liquid while mechanically mixing theliquid at the surface. The IR probe passes ≈ 0.7 cm above the liquid 16 times via the Herriot
multipass cell.44

146

v=3
-0.0

v=2
0.06

Normalized Density

0.03

0.00

v=1
0.06

0.03

0.00
0.06

v=0

0.03

0.00
0

2

4

6

8

10

12

14

J

Figure 5.7

Normalized HF(v,J) density distributions, measured following reactive scatteringof F atoms from a static liquid hydrocarbon surface.

147

Figure 5.8

Schematic of the refreshed liquid apparatus. A rotating glass wheel iscontinuously recoated with liquid squalane as it passes through a trough of ≈ 100
mL liquid. The F source and IR detection are otherwise comparable to that
depicted in Fig. 5.3.

148
Similar low-density conditions as used with the stagnant liquid studies ensure nascent HF
populations scattering from the surface. Secondary radical-radical interactions at the liquidsurface can be neglected due to the F atom coverage of approximately 0.001 monolayers per
pulse. At the 0.3 Hz rotation rate of the wheel, the surface is exposed to < 2% of a monolayer of Fprior to being mechanically mixed with the bulk in the liquid reservoir. Thus, the present results
can be definitively attributed to the reactive scattering of isolated F atoms from squalane at thegas-liquid interface.
Sample absorption traces for detection of HF(v = 2,J = 1) product are presented in Fig.
5.9, along with the discharge current used for F atom generation. The 270 μs delay from the startof the discharge pulse to the rise of the HF absorption closely matches the expected 260(40) μs
flight time for F atoms in a 573(85) m/s argon jet and the 15.0(1) cm valve-surface distance. The
inset of Fig. 5.9 presents the time profiles for various td, comparable to those presented in Fig.
5.4. For the remainder of the present study, a discharge width of td = 200 μs is utilized, reflecting
a compromise between signal intensity (≈ 70% of the long discharge maximum) and time
resolution.
The fundamental experimental measurement consists of a series of IR absorption
waveforms, such as those in the inset of Fig. 5.9, as a function of probe laser frequency. A fast
digital acquisition card records the transient absorption waveform with a 500 kHz bandwidth,
while the FCL tunes in 3 MHz steps through a ≈ 3 GHz window approximately centered on agiven HF IR transition. Thus, raw data results in “three dimensional” measurement of absorption,
as a function of laser frequency and time. 3D absorption profiles, such as the one presented in thefalse color intensity plot in Fig. 5.10, have been recorded for every HF transition probed, enabling
reanalysis of various time windows to test for dynamical signatures as a function of time. For the
majority of this study, the analysis has been performed on a 200 μs window located at the risingedge of the signal waveform, as shown in the shaded region of Fig. 5.9. However, alternative time

149

0.20

40μs
120μs
210μs
280μs
400μs

0.00150.00100.00050.15
0.10

Idisch (A)Absorbance

0.00200.05

td=200μs

0.00

0.0000
0

1000

2000

3000

time (μs)

t (ms)

Figure 5.9

Transient IR absorption measurement of HF v = 3←2,J = 2←1, following
reaction of fluorine atoms at the refreshed liquid surface. The solid line is themeasured absorption (left axis), and the dashed line is the plasma current in the Fatom source (right axis), with duration td = 200 ms. Inset plots show the signal
waveform as a function of td. The shaded region denotes the time domain ofdigital signal averaging used to construct HF absorption measurements.

10
0Figure 5.10

0.6

1.2

Δν (GHz)

1.8

Sample 3D profile of the transition v = 3←2, J = 3←2 Infrared absorption isrepresented in false color, as a function of laser frequency (x axis) and time (yaxis). Vertical line-outs result in waveforms such as those in Fig. 5.9, and timedomain averages produce Doppler profiles as in Fig. 5.1

150
windows were also considered and will be discussed in more detail in Sect. 5.4.
Representative Doppler measurements are presented in Fig. 5.11, from which certain
features of the gas-liquid scattering experiment are immediately apparent. Many observed lines
exhibit large intensities, with peak absorptions (Fig. 5.9) approaching 0.5%, or ≈ 1010 HF/cm3 perquantum state. The rovibrational populations are broadly distributed in the v = 0–3 manifolds,
with significant inversion in HF vibration. Since IR absorption directly measures populationdifferences between upper and lower probed states, the HF lines can display either net absorption
or gain, depending on whether absorption from the lower state or stimulated emission from theupper state is stronger. This competition is clearly illustrated in Fig. 5.11 by net emission signals
observed for transitions involving the v" = 0 lower level, as considered in more detail in Sect. 5.5.
Nevertheless, the raw data illustrate that even with near-thermal collision energies, HF productdoes not remain trapped on the surface long enough to accommodate completely to the surface
temperature, and a significant fraction of the reaction exothermicity remains in the recoiling gasphase product.
Approximately 400 HF absorption profiles, such those shown in Fig. 5.11, have been
observed, originating from all energetically accessible HF quantum states having transitions
within the 2.5–3.3 μm tuning range of the FCL. In total, 87 transitions out of 59 quantum states
have been probed, spanning v = 0–4 and J between 0 and 15. Integrating the Doppler
measurements produces the “stick spectrum” of line intensities presented in Fig. 5.12(a). Fromthe procedure detailed in Sect. 2.4(A), this spectrum is least squares fitted to obtain the HF(v,J)
densities. The measured and fitted spectra agree within the 10 kHz experimental uncertainty ofthe measured intensities as shown in Fig. 5.12. The raw densities are presented in Table 5.2.
These results are quite robust, as demonstrated in Fig. 5.13 and discussed next.

151

J"= 0
v"=3

1

2

3

4

0.2% Abs

v"=2
2 GHz
v"=1
v"=0

Figure 5.11

Sample Doppler resolved HF absorption measurements following reactive
scattering from the liquid squalane surface.

a) Measured
0.6∫Abs(ν) dν (MHz)

0.3
0.0
-0.3

b) Fit
0.6
0.3
0.0
-0.3
3000

Figure 5.12

3250

3500

ν (cm-1)

3750

4000

Stick spectrum of the measured (a) and fitted (b) HF spectral intensities
following reaction of F at a liquid squalane surface. Shading indicates lower
vibrational state as follows: blue (v” = 3), green (v” = 2), red (v” = 1), and black(v” = 0). Absorption features are plotted with positive amplitude, whereas net
emission, created by population inversion on certain transitions, yields negative
absorption.

152
5.4 Comparing Results
Three sets of normalized data for F + squalane are presented in Fig. 5.13. The dots witherror bars are the “best set” data, i.e., the data acquired following scattering from the refreshedliquid surface, during the 200 μs rising edge of the transient absorption waveform, as described indetail in Sect. 5.3. The dashed line represents a reanalysis of the same raw data, where the timeaveraging gate has been moved 100 μs later, to the peak of the transient absorption signal. Thistiming matches that used in the static liquid surface experiment, detailed in Sect. 5.2, the resultsof which are replotted as dotted lines.
Overall, remarkable agreement exists among the data in Fig. 5.13. Nearly identical results
are obtained in both time windows, emphasizing that the observations are insensitive to thisexperimental choice for short time delays following the interaction of the F atom pulse with theliquid surface. Thus, the early portion of the time profiles likely can be attributed to the gas-liquid
reaction dynamics, whose temporal signatures are blurred over the > 100 μs F atom arrival time,
as shown in the insets of Fig. 5.9 and 5.4. The results obtained using the static liquid surface
agree remarkably well with those from the refreshed surface. The only significant difference isthe measured population in HF(v = 0, J = 2), the most populated state at room temperature. The
origin of this discrepancy remains unclear, but the otherwise broad agreement between thesestudies justifies the early study’s publication45 and confirms that the static surface reveals similar
dynamics as observed in the more rigorous study.
The falling edge of the absorption signal has also been analyzed to investigate thesurprisingly slowly decay of signal evident in Figs. 5.4 and 5.9. Significant absorption isobserved from various HF states for more than 1 ms after the rising edge, as shown in the sample
time profiles in Fig. 5.14. In order to better understand the nature of these delayed signals, thedata has also been analyzed using time gates located 250–3500 μs after the F atom plasma pulse,
as marked in Fig. 5.14. The resulting HF rotational state distributions are 300 K within

153

Table 5.2 HF column-integrated densities [∫dx ρHF(x)] observed following the formation of
HF(v,J) by reaction of F at the squalane surface. Values have been normalized to 100%.
Uncertainties in parenthesis are one standard deviation from the least squares fit, in units of theleast significant digit reported.
J
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14

v=0
2.17 (18)
5.19 (51)7.79 (42)4.47 (40)
2.60 (30)
1.19 (36)0.45 (34)0.14 (29)0.11 (31)0.25 (30)0.10 (24)0.11 (29)-0.11 (22)v=12.48 (6)6.57 (11)7.32 (15)
6.22 (15)
4.17 (16)2.28 (16)1.36 (18)0.93 (15)0.68 (14)0.64 (15)0.58 (15)0.41 (14)0.33 (15)0.32 (20)0.03 (24)v=22.26 (4)5.69 (7)7.51 (8)6.59 (10)4.69 (9)3.42 (9)2.10 (10)1.44 (10)1.17 (11)0.88 (11)0.64 (10)0.40 (11)0.28 (17)0.07 (20)0.05 (35)v=30.25 (2)0.74 (5)0.98 (6)0.91 (6)0.72 (6)0.31 (7)0.15 (6)0.05 (7)0.05 (6)-0.02 (5)-0.03 (7)-0.05 (15)-0.03 (18)ΣJ

24.46 (120)34.33 (61)37.17 (54)4.04 (30)

154

v=3

0.02
0.00

v=2

0.08
0.06

Fractional Population

0.04
0.02
0.00

v=1

0.08
0.06
0.04
0.02
0.00

v=0

0.08
0.06
0.04
0.02
0.00
0

2

4

6

8

10

12

14

JHF
Figure 5.13

Comparison of the normalized HF(v,J) densities observed for the F + squalane
reaction with the static surface (dotted line), and with the rising edge (solid lines,
data points) and peak (dashed line) timing from the refreshed surface.

155

0.0005v=4I3, J=3I2

0.00000.0020v=3I2, J=3I2

0.00150.0010Absorbance

0.00050.0000v=2I1, J=3I2

0.00050.00000.0005v=1I0, J=1I2
0.0000

0

1000

2000

3000

4000

time (μs)

Figure 5.14

Sample time domain profiles for the indicated transitions originating from v” =0–3. Pairs of vertical lines frame the timing domains used for temporal
averaging. The first pair of solid lines and the adjacent pair of dotted lines frame
the two time domains whose rovibrational state distributions are compared in Fig.
5.13.

156
uncertainty, while the shifting vibrational distributions are shown in Fig. 5.15. These data reveal asystematic shift toward a room-temperature HF internal state distribution with increasing time.
Although these observations could, in principle, be caused by equilibration of HF product trappedon from the surface, the required sub-kilohertz thermalization rate is inconsistent with 10–100 ps
vibrational relaxation times anticipated at the surface.46-49 On the other hand, this slow decay does
match that expected for product molecules reaching the edge of the vacuum chamber, relaxing
upon contact with the room temperature surface, and returning to the probe region. This
thermalization emphasizes the need to position the signal gate only 200 μs after the F atom pulse,
insuring insufficient time for the thermally recoiling HF to return to the probe region following
secondary collisions.

5.5 Analysis of Results
The high-resolution IR absorption measurements, such as those shown in Fig. 5.11,
contain two independent pieces of information about each HF quantum state: the total (state
resolved) transition intensity and detailed Doppler lineshape. Intensity information has been
integrated and fitted to obtain the state resolved populations presented in Table 5.2 and Fig. 5.13.
Additional information on the HF velocities, projected onto the probe axis, can also be obtained
via fitting of the observed lineshape. These two methods of analysis will be considered separately
in this section.

Fractional Population

157

1.0
0.8

v=0
v=1
v=2
v=3

0.6
0.4
0.2
0.0
-4.0

-3.5

-3.0

-2.5

-2.0

log10[time after discharge (s)]Figure 5.15

Vibrational distribution of HF product at three representative delay times,
marked in Fig. 5.14. Populations are in good agreement between the first two
gating windows, also compared in Fig. 5.13. After more than 1 ms delay, theapparent vibrational cooling appears to accelerate, as HF molecules relaxing at
the sides of the vacuum apparatus have time to return to the probe region.

158

A. HF(v,J) state distribution
The “best set” HF rovibrational state distribution, defined in Sect. 5.4, for F + squalane
has been obtained from the spectrum in Fig. 5.12(a), according the procedure in Ch. 2.4(A). The
results appear in Table 5.2 and Fig. 5.13. In the least squares fit, the HF density in all unprobed
states (generally with J > 15) and those in v = 4 is set to zero. Monotonically decaying intensities
versus J in each band in Fig. 5.12 and the unobservable signals originating from v = 4 justify thisapproximation. As a result, the higher state populations are less correlated and determined withgreater accuracy than those in lower vibrational manifolds, as can be seen by close inspection ofderived densities, shown in Fig. 5.13. Nevertheless, even for the v = 0 manifold, the peakcolumn-integrated rotational populations are determined to better than 5–10%, with precision
improving to 1–2% for the higher vibrational manifolds.
We previously noted that that the v = 4 manifold, at 42.4 kcal/mol above the groundstate, may be energetically accessible to F reacting with a tertiary C–H bond, within the certaintyof the bond strength and possible thermal activation. However, direct measurements of transitions
originating from the v = 4 manifold do not yield signals in excess of the ≤ 3×10-5 absorbancenoise limit, corresponding to less than 0.01% of the total HF population in any rotational state inthis manifold. Since detailed modeling of the liquid surface indicates that tertiary CH bonds areaccessible to impinging reactants,21,50,51 the lack of HF population in the v = 4 manifold can be
attributed to surface dynamics that do not favor extreme vibrational excitation, as also manifest in
the relatively small branching into v = 3.
The average state resolved density of HF above the liquid surface can be obtained byscaling the column-integrated densities in Table 5.2 by the quantity N×x, where N = 16 is thenumber of passes the probe laser makes through the Herriot cell and x =13(1) cm is the absorption
path length of HF above the liquid surface. The most populated states have a density of
approximately 1.2×1010 HF #/cm3 per quantum state, and the total HF density is approximately

159
1.5(2)×1011 HF #/cm3. Interestingly, this number is in excellent agreement with the estimated
1.5(3)×1011 #/cm3 F atom density impinging on the liquid surface, calibrated against the known F+ H2 rate constant,42,52 as described in more detail in Ch. 2.4(C). This calibration utilizes anumber of experimentally determined values, such that propagation of uncertainty results in the
20% fractional uncertainty in the predicted F atom density. However, within these error bars, it isclear that nearly all F atoms impinging on the surface react and return to the gas phase on the 200
μs time scale of the supersonic jet pulse. This analysis highlights a unique strength of highresolution direct absorption methods, whereby absolute absorbances can be used to accurately
infer absolute column-integrated densities of transient species.
Several interesting trends emerge from the HF state distributions following reaction withthe liquid squalane interface, plotted in Fig. 5.13. Summation over rotational states (Fig. 5.16)
reveals a rather broad distribution of vibrational state populations, with 25–35% of the total
population residing in each manifold between v = 0–2, and significantly less population entering
the v = 3 manifold. Also presented in Fig. 5.16 is the HF vibrational branching following gasphase reaction with ethane (gas), which has similar H–C bond strength. The gas-phase reaction
yields significantly more branching into v = 3, at the expense of v = 0–1.
The HF rotational state distributions for the reaction of F atoms with liquid squalane (seeFig. 5.13) appear nearly Boltzmann in nature, with maximum rotational population in each
vibrational manifold occurring at J = 2, the maximum for a 300 K distribution. However, closer
inspection reveals excess population formed in highly rotationally excited states, starkly evident
in the v = 2 and v = 1 manifolds. Boltzmann plots of degeneracy-scaled populations versus
rotational energy are presented in Fig. 5.17. These curves strongly deviate from the straight linescharacteristic of a purely thermal distribution. Indeed, the observed rotational distributions show asignificant kink at intermediate J values between two approximately linear regions. Thisobservation has prompted analysis of these rovibrational manifolds by a “two-temperature”

Fractional Population

160

F+squalane (liquid)
F+ethane (gas)

0.4
0.3
0.2
0.1
0.0
0

Figure 5.16

1

vHF

2

3

HF vibrational state distributions following the reaction of F atoms withhydrocarbons in the gas phase, and at the gas-liquid hydrocarbon surface, as
indicated.

161

vHF=2

26

1600(400)K

24

ln(ρ/(2JHF+1))

22
20 338(17)K
18
01000 2000 3000 4000

vHF=1

26

2400(500)K24
22

305(7)K
20
0

1000

2000
-1

3000

Erot (cm )Figure 5.17

Boltzmann plots of the HF rotational state distributions in the v = 1 and v = 2
manifolds, as indicated. Measured populations are data points with error bars.
The solid line is the result of the two-temperature fit, with the constituent highand low temperature thermal distributions plotted as the dashed and dotted lines,
respectively.

162
model, also used extensively in the study of inelastic scattering of CO2 from liquid surfaces.23-26
The two-temperature model describes the rotational populations as the sum of twothermal distributions:ρv(J)/g(J) = A{(α/T1) exp(-E(J)/kT1) + [(1- α)/T2] exp(-E(J)/kT2)} ,(5.1)

where ρv(J) is the density of HF(v,J), g(J) is the degeneracy, and E(J) is the rotational energy ofstate J, α is the branching ratio between the two distributions, and A is an overall scaling factor.
The present F + squalane reactive scattering data exhibit much more dramatic and obvious
curvature than similar Boltzmann rotational state plots for gases inelastically scattered fromliquids.23-26 Of particular dynamical interest, the low temperature components in both HF(v = 1)
and HF(v = 2) manifolds match the 300 K surface temperature (Ts), nearly within one standard
deviation of the fit. In contrast, the curvature in the plots for v = 3 and v = 0 is much lessdramatic, justifying fits to a simpler one-temperature Boltzmann distribution to reveal qualitativerotational energy trends. Such fits result in least squares values of 400(24) K and 315(30) K for v= 3 and 0, respectively.
Although there is no a priori reason to expect the dynamically determined rotational state
distributions to approximate thermal distributions, this analysis does reveal qualitative features ofthe distribution that are likely to prove robust to detailed dynamical modeling. Specifically, lower
vibrational manifolds, which may be strongly populated via longer lived trapping desorption (TD)dynamics at the gas-liquid interface, are characterized by rotational temperatures close to thesurface temperature, Ts = 300 K. On the other hand, high vibrational excitation is correlated withhyperthermal rotations. This behavior is exactly opposite to trends observed in the gas phase,38,41
where lower vibrational levels are generally accompanied by increasing rotational energy.
The v = 3 and v = 0 rotational state distributions readily conform to this picture. The v =3 rotational "temperature" of about 400 K exceeds Ts, as expected because strongly
accommodating TD interactions only serve to depopulate this high-energy manifold. Although

163
partial rotational relaxation is likely, the fully equilibrated molecules are simply missing from this
distribution because they have also vibrationally relaxed. In contrast, the v = 0 population does
not exhibit any significant hyperthermal rotational component. This observation is consistent with
HF(v = 0) being formed almost exclusively via strongly trapped interactions, and the 0.24(1)fractional vibrational branching into this manifold represents a clear upper limit for the HF
population component that spends an appreciable time on the surface as compared with the timefor vibrational energy transfer to the surface.
However, the v = 0 population represents only a relatively small fraction of the total
population. Most of the nascent HF escapes with v > 0, and a significant amount does so while
maintaining a nonthermal distribution of rotational energy. The simplest interpretation is that
surface interactions can occur with varying degrees of accommodation, and higher energy states
are selectively populated via processes that eject HF directly into the gas phase prior to complete
thermalization.
The intermediate vibrational levels (v = 1–2) appear to have both thermallyaccommodated and rotationally hot signatures in their rotational distributions, motivating the twotemperature fit in Fig. 5.17. The TD fraction (α), defined in Eq. 5.1, comprises 0.78(2) and0.69(4) of the v = 1 and v = 2 populations, respectively. A simple picture for the dynamics basedon the rotational state analysis is that 70–80% of the HF product in the vibrationally excited (v =1, 2) levels desorb after rotationally equilibrating with the liquid surface. However, thesemolecules have not interacted with the bulk 300 K squalane long enough to lose their highvibrational excitation, motivating their assignment to the DRS channel. Of course, this picture is
likely to be an oversimplification of the true dynamics, as gas-phase reactions, analogous to the
DRS component, have not been found to match the 2000 K Boltzmann distribution found for thehigh-temperature component of the rotational state distributions. Nevertheless, the v = 1 and v =2 populations appear to have both rotationally excited components, created by the DRS channel,
and 300 K components, from TD. More evidence for HF product-state-dependent residence times

164
on the liquid surface can be found from the observed absorption lineshapes, which we discuss
next.

B. Doppler lineshape analysis
The measured Doppler lineshapes directly reveal the HF velocity distribution, projectedalong the laser axis, i.e., parallel to the liquid surface. Sample Doppler profiles are presented inFig. 5.18 and fits have been obtained using the method described in this section.
Modeling of Doppler lineshapes is straightforward for transitions terminating in an
unpopulated upper state, such as those originating in the v = 3 manifold and v = 2 with J > 7. In
this case, only the velocity distribution in the lower state must be considered in the Doppler
analysis. Such transitions have been fitted to a simple Gaussian lineshape:A(ν) = A0 exp(-4ln(2)[(ν−ν0)/Δν]2) ,(5.2)

where Δν is the FWHM of the transition, A0 is the peak absorbance, and ν0 is the line center
frequency. The choice of this functional form is arbitrary yet empirically justified by the robust
agreement between the fitted to the observed measurements, such as that shown in the top trace in
Fig. 5.18. Fits to Gaussian lineshapes are physically motivated by anticipated quasi-thermal
Doppler measurements, and Boltzmann-like velocity distributions observed following inelastic
scattering from liquid surfaces.23-26
For lower manifolds, emission from the upper state necessitates consideration of thevelocity distributions of both the upper and lower levels simultaneously. Specifically, lineshapes
can be expressed as a sum of two Gaussian components:
A(ν) = Al exp(-4ln(2)[(ν − ν0)/Δνl]2) - Au exp(-4ln(2)[(ν − ν0)/Δνu]2) .

(5.3)

The subscripts l and u indicate components used to describe the lower and upper state
distributions, respectively. Correlations between Al and Au, and between Δνl and Δνu make a five-165

Absorptionv"=30.001 Abs

v"=2
v"=1

-600 -400 -200

0

200

400

600

ν−ν0 (MHz)Figure 5.18

Representative Doppler resolved absorption data (solid lines) and fits (dottedlines) for several HF J” = 2, ΔJ = + 1 transitions. Vibrational manifolds are as
indicated. Absorption originating from the v” = 3 manifold is well represented bya single Gaussian fit, as no measurable population has been observed in the v” =4 manifold. Doppler modeling of the v” = 1–2 levels includes contributions fromabsorbing molecules in the lower state (long dashes) and emission from the upper
state (short dashes).

166
parameter least squares fit of individual Doppler profiles using Eq. 5.3 intractable. However, thecorrelation between the peak absorbances can be broken by using the column-integrated state
densities shown in Fig. 5.13 to fix the ratio REA between the integrated emission and absorption
components of the Doppler profiles, given by
REA = Sov’J’→v”J” ∫dx∫dν ρv’J’(ν,x) / Sov’J’←v”J”∫dx∫dν ρv”J”(ν,x).

(5.4)

Integration over the absorption and emission profiles in Eq. 5.3 relates the peak absorbances via
Au = Al REAΔνl/Δνu. The correlation between Δνl and Δνu can be broken by simultaneously fitting
the Doppler profiles of transitions in which a given level is both the upper and lower level, e.g.
the v + 2, J” ← v + 1, J’ and v + 1, J’ ← v, J lines, whose frequencies are denoted ν0’ and ν0 ,respectively. In this case, Δνl of the former can be related to Δνu of the latter by scaling to theabsolute frequencies via Δνl = Δνu’(ν0/ν0’).
These relationships are used in several ways. In the simplest approach, the Doppler fitsusing Eq. 5.2 are carried out for transitions out of the highest energy states, which only have anabsorption component. The Δν parameters obtained from these fits are then used to fix Δνu in Eq.
5.3 to obtain fits of transitions out of the next lower vibrational manifold, and the process isrepeated for progressively lower levels. Uncertainties in the fitted Doppler widths are obtained bya propagation of errors analysis. Alternatively, Eq. 5.3 and 5.4 are employed to fit simultaneously
sets of paired transitions. Similar widths are obtained within the derived uncertainties from bothprocedures.
The Gaussian nature of the Doppler lineshapes suggests converting the fitted widths Δν
to translational temperatures Ttrans. Specifically, Ttrans for a Maxwell-Boltzmann distribution isrelated to the Doppler FWHM Δν and center frequency ν via
Ttrans = (cΔν/ν)2(mHF/8k ln2),(5.5)

where mHF, c, and k are the mass of the HF molecule, speed of light, and Boltzmann’s constant,respectively. The results of the Doppler analysis are presented in Fig. 5.19, which shows

167

vHF=3

Ttrans (K)

1200

vHF=2
vHF=1

900

300K

600
300
0
0

2

4

6

8

10

12

JHF
Figure 5.19

Results from the least squares fit to the measured absorption lineshapes
originating from the v = 3 (circles), v = 2 (triangles) and v = 1 (squares)
manifolds. Observed Gaussian linewidths have been converted to translationaltemperatures via Eq. 5.5. HF translational energy increases with increasing
rovibrational energy. Such translational dynamics indicate strongly statedependent surface residence times.

168
that the product HF translational degree of freedom is hotter than or equal to the 300 K surface
temperature. Overall, the Doppler widths increase with rovibrational excitation, revealing a
positive correlation between average translational energy and internal HF energy. Thisobservation is most evident in the propensity for hotter translational temperatures as J increases
within a given vibrational manifold. The translational temperature also increases with the productvibrational excitation, although this effect is less pronounced than the dependence upon therotation state.
Doppler widths for the v = 0 manifold are not presented in Fig. 5.19 because they cannot
be fitted reliably using the procedure detailed above. Careful inspection of the v” = 0 Doppler
measurements in Fig. 5.11 reveals less structure is this manifold than in the v” = 1,2 manifolds.
Specifically, the Doppler structure appears approximately Gaussian, because the Δν values in
HF(v = 0,J < 6) correspond to 300 K, i.e., nearly identical to those for the upper states, HF(v = 1,
J < 5). These similar Doppler widths result in strong parameter correlation through Eq. 5.3,
which prevents reliable least squares fitting of the v” = 0 manifold. Nevertheless, thermallyequilibrated HF(v = 0,J) Doppler profiles would be completely consistent the established trend
for more accommodation with the surface as internal energy decreases.
The strong positive correlation between increasing HF Doppler widths and increasing
internal HF rovibrational energy contrasts rather dramatically with that observed in previous
studies of H atom abstraction in the gas phase, where energy sequestered into product internalenergy necessarily reduces the amount available for recoil.38 This effect was most convincingly
demonstrated in studies of F + ethane, where the Doppler measurements of HF(v,J) translationalenergy proved to be linearly correlated with Eavail = Etot - EHF(v,J) and therefore yielded a negative
correlation with HF internal energy. Stated most simply, this trend results from energy
conservation and insufficient time during the collisional event for energy flow into the isolated
ethyl cofragment.

169
By way of contrast, the gas-liquid interface offers a quite different scenario for H atom
extraction reaction dynamics. In particular, new correlations arise from quantum-state dependent
residence times on the liquid surface. For example, translational energy is likely to be dissipatedinto the bulk liquid within one or two collisional interactions after the reaction event. Therefore,translationally hot HF might be expected to correlate with molecules that escape from the surface
almost immediately following reaction (i.e., the DRS channel) and therefore retain a maximal
amount of energy released during reaction.
Similarly, molecules that have lost translational energy from the reaction event throughmultiple collisions with the surface (i.e., the TD channel) may be linked with additional loss ofinternal energy as well. In particular, since rotations are expected to equilibrate with the surface
almost as rapidly as translations, this consideration suggests a simple mechanism for a positive
correlation between rotational and translational energies. Because of the large size of its quanta,
vibrational energy transfer to the surface may be expected to occur much more slowly, explaining
the much weaker trend in translational energies with respect to final vibrational state. From thisperspective, the key difference between gas-phase (e.g. F + ethane) and gas-liquid (e.g. F +squalane) reaction dynamics is the presence of many additional channels for subsequent energy
transfer after the primary reaction event. As one simple physical picture, the liquid surface offersa larger cross section for subsequent inelastic interactions with the nascent product and thus
substantially restricts its ability to behave like a spectator.

5.6 Discussion
Following reaction of F atoms at the liquid squalane surface, HF desorbs into the gas
phase with varying amounts of energy in vibrational, rotational, and translational degrees of
freedom. High HF internal energy, particularly rotation, is strongly correlated with hottranslational distributions. This observation suggests that reaction occurs via competing

170
dynamical pathways, by which product escapes with a large fraction of the reaction energy, theDRS channel, or partially accommodates with the room temperature surface via TD.
It is interesting to compare the present results with those reported by McKendrick andcoworkers for H abstraction by O from squalane and other liquid hydrocarbon interfaces.15-20,22
Such comparison is necessarily general because these two reactions are quite different.
Specifically, O atoms react with a significantly higher (5–10 kcal/mol) barrier,29 and theexothermicity is much less (≈ 5 kcal/mol). In addition to a single abstraction event, forming OH
as probed my McKendrick and coworkers,15,16,18-20,22,29,53 subsequent reaction events can lead to
H2O product.7,9 Nevertheless, both HF and OH products are vibrationally excited following
reaction at the liquid surface, although they retain less vibrational energy than observed fromanalogous gas-phase reactions. This result is consistent with the inefficient vibrational
accommodation following inelastic scattering of CO223-26 and I211-14 from liquid interfaces. The
OH and HF rotational distributions both closely match the surface temperature, but the fastest
moving OH(v = 1) products mimic the sub-thermal distributions expected from gas-phase
dynamics.15 Similarly, in the present study the hottest Doppler widths are observed for high HF
rotational levels; in this case hot rotations occur with rapidly recoiling molecules attributed to the
DRS mechanism. Recent theoretical simulations of O + squalane reaction have found similar
trends for increasing rotation and translational energy, though the much larger ( > 100 kcal/mol)incident energies in these studies complicates more detailed comparison.51
Further insight into energy transfer into the liquid can be gained by comparing the resultsof F + hydrocarbon reactions at the liquid interface and in the gas phase. We focus on the F +ethane reaction system for this comparison because it has very similar energetics and has alreadybeen studied using high-resolution IR methods. However, similar conclusions would be expected
for other F + hydrocarbon systems.41,54 Fig. 5.20 presents detailed energetic branching analysis, in

171

25

F+squalane (liquid)
F+ethane (gas)E (kcal/mol)

20
15
10
5
0

HF
vib
Figure 5.20

HF
rot

HF
trans

R

Energy partitioning following various F + hydrocarbon reactions in the gas phaseand at the liquid interface. Expectation values for energy deposited in theindicated modes are evaluated according to Eq. 5.6. R denotes energy assumed to
be sequestered in the unseen hydrocarbon radical.

172
which average values 〈Ei〉 of vibrational, rotational, or translational energy are presented. Here,〈Ei〉 is computed as〈Ei〉 = Σv,J P(v,J) Ei(v,J) ,(5.6)

where P(v,J) is the HF state distribution, and Ei(v,J) is the energy (i = vibration, rotation, ortranslation), and Etrans is taken as 2kTtrans(v,J), the energy of an effusive source at temperature
Ttrans, as derived in the present study via Doppler data in Fig. 5.18. The most dramatic change inenergy partitioning originates from the larger HF(v = 0,1) population formed via reaction at
liquid interface, primarily at the expense of HF(v = 3). The energy partitioning analysis presented
in Table 5.3 emphasizes this result. Approximately 60% of the available energy deposited in the
HF vibrational coordinate for various gas-phase reactions, versus < 40% for F atom abstraction at
the liquid squalane interface.
The presentation in Fig. 5.20 reveals that every HF mode retains less energy afterreaction at the liquid interface than in the gas phase, resulting in larger energy branching into theunseen hydrocarbon, denoted R. In general, gas-phase halogen-alkane reactions result in modest(4–12%) energy transfer to internal modes of the hydrocarbon radical product, which acts mostly
as a spectator to the reaction.38,55 By comparison, the HF product recoils from the liquid surface
after partial equilibration, during which the extent of relaxation in rotational, vibrational, andtranslational degrees of freedom relax according to the propensity for energy transfer based on thesize of the energy quantum, i.e., larger quanta relax more slowly than smaller quanta. This trend
results in the average HF translational energy of 1.47(3) kcal/mol being only 25% higher than the
300 K value of 1.18 kcal/mol. Rotations are also nearly equilibrated, with 1.04(8) kcal/mol
average energy, nearly 75% larger than kT, as expected for a linear rotor at 300 K. With respect tosurface residence time, the observation of rotationally and translationally excited HF clearly
indicates fractional branching of HF into a channel that remains in contact with the173

Table 5.3 Fractional energy partitioning (X) of reaction energy following reaction of fluorinewith liquid squalane and several gas-phase hydrocarbons. Uncertainties in parenthesis are one
standard deviation.

Reactant

XHFvibsqualanea
ethanebmethanec
neopentaned
toluenedbenzened37(3) 2.8(3) 4.1(3) 56(8)56(6) 3.9(4) 16(2) 23(2)60.6(7) 4.4(6)
64
55
63

a

XHFrotXHftrans Xcofragment

Uncertainty dominated by the heterogeneous C–H bond strength in squalane
From Ref. 38
cFrom Ref. 41
dFrom Ref. 54b174
surface for less than the sub-picosecond relaxation timescales for these modes. Finally,
vibrational excitation remains extremely hot, with 13.3(2) kcal/mol average energy, and only
partial relaxation occurs because of moderately slow (tens of ps) relaxation time on the liquidsurface. Indeed, theoretical studies indicate that vibrational relaxation times are extended by afactor of only two to four by the partial caging present at the interface,46-49 so even the TD
channel is likely to be characterized by a ≈ 100 ps surface residence time.
Very recent computations of F + squalane by the Schatz group50 have reproduced manyof the general features of the experimental results, such as hotter rotational distributions in lower
vibrational manifolds. At an even higher level of detail, this work has found that excited rotations
are more likely to remain excited following scattering events that spend a relatively small time
below the so-called Gibbs surface. Indeed, the predicted vibrational distributions strongly agreewith measurements, though the theoretical rotational distributions are much more structured andless Boltzmann-like than those presented here. These differences may arise from the very high F
atom translational energies (0.5, 1.0 eV) used in these studies, or the need for more accurate PES
calculations to reliably predict rotational distributions. Nevertheless, the results of these landmark
computational studies seem to confirm the present interpretation of the experimental results, andpresent the opportunity to begin developing more detailed physical pictures for gas-liquid
scattering processes.

5.7 Conclusions
The reaction of fluorine atoms at the gas-liquid interface of squalane reveals a wide
variety of surface energy exchange with recoiling HF products. Highly inverted vibrational
populations indicate that a significant amount of the reaction energy remains sequestered in the
diatomic fragment as it recoils from the surface, although significant branching into the groundvibrational manifold is also observed. In contrast, rotational and translational excitation of HF

175
product is moderate. At low J, population distributions closely resemble the 300 K surface
temperature, though a slowly decaying tail in the rotational population results from hyperthermal
populations. The observed rotational state populations are well described by either a thermal
distribution or the sum of two such distributions, depending on the vibrational manifold. The v =3 manifold is characterized by a hot (400 K) distribution, while the v = 0 rotational state
distribution closely resembles a thermal distribution at the surface temperature, and intermediate(v = 1–2) levels have rotational state distribution components characterized by thermalized (300K) and very hot (2000 K) temperatures. Doppler measurements reveal that the HF translationalenergy matches the liquid surface temperature for moderately excited states, whereas recoil
energy increases with HF internal energy. These results indicate microscopic branching of HF
interactions with the surface following the reactive event, with high energy components resulting
from brief “direct reactive scattering” interaction with the liquid surface, contrasted with “trapped
desorption” events during which the product may become translationally, rotationally, and evenvibrationally accommodated with the surface. The contribution from each of these components
varies with the resulting HF quantum state and is most readily deduced from the translationalenergy measurements. These observations match expectations for partial equilibration at thesurface following an initial reaction event analogous to gas-phase F + hydrocarbon reactions.
Results are also consistent with previous studies in which bifurcated dynamic pathways andrelaxation rates were determined by energy gap expectations. Recent theoretical studies reproduce
the general features observed experimentally, and increase confidence in the presentinterpretation.

176

References for Chapter V
1

S. L. Lednovich and J. B. Fenn, Aiche J. 23, 454 (1977).

2

G. M. Nathanson, P. Davidovits, D. R. Worsnop, and C. E. Kolb, J. Phys. Chem. 100,
13007 (1996).

3

M. E. Saecker and G. M. Nathanson, J. Chem. Phys. 100, 3999 (1994).

4

M. E. Saecker and G. M. Nathanson, J. Chem. Phys. 99, 7056 (1993).

5

M. E. Saecker, S. T. Govoni, D. V. Kowalski, M. E. King, and G. M. Nathanson, Science
252, 1421 (1991).

6

G. M. Nathanson, Annu. Rev. Phys. Chem. 55, 231 (2004).

7

J. M. Zhang, D. J. Garton, and T. K. Minton, J. Chem. Phys. 117, 6239 (2002).

8

D. J. Garton, T. K. Minton, M. Alagia, N. Balucani, P. Casavecchia, and G. G. Volpi, J.
Chem. Phys. 112, 5975 (2000).

9D. J. Garton, T. K. Minton, M. Alagia, N. Balucani, P. Casavecchia, and G. G. Volpi,
Faraday Discuss.387 (1997).

10

J. M. Zhang, H. P. Upadhyaya, A. L. Brunsvold, and T. K. Minton, J. Phys. Chem. B
110, 12500 (2006).

11

A. J. Kenyon, A. J. McCaffery, C. M. Quintella, and M. D. Zidan, Faraday Discuss. 96,
245 (1993).

12

C. M. Quintella, A. J. McCaffery, and M. D. Zidan, Chem. Phys. Lett. 214, 563 (1993).

13

A. J. Kenyon, A. J. McCaffery, C. M. Quintella, and M. D. Zidan, J. Chem. Soc.-Faraday
Trans. 89, 3877 (1993).

14

A. J. Kenyon, A. J. McCaffery, C. M. Quintella, and M. D. Zidan, Chem. Phys. Lett. 190,
55 (1992).

15

S. P. K. Kohler, M. Allan, H. Kelso, D. A. Henderson, and K. G. McKendrick, J. Chem.
Phys. 122, 24712 (2005).

16

H. Kelso, S. P. K. Kohler, D. A. Henderson, and K. G. McKendrick, J. Chem. Phys. 119,9985 (2003).

17

F. Ausfelder, H. Kelso, and K. G. McKendrick, Phys. Chem. Chem. Phys. 4, 473 (2002).

18

M. Allan, P. A. J. Bagot, R. E. Westacott, M. L. Costen, and K. G. McKendrick, J. Phys.
Chem. C 112, 1524 (2008).

177
19

M. Allan, P. A. J. Bagot, M. L. Costen, and K. G. McKendrick, J. Phys. Chem. C 111,
14833 (2007).

20

M. Allan, P. A. J. Bagot, S. P. K. Kohler, S. K. Reed, R. E. Westacott, M. L. Costen, andK. G. McKendrick, Phys. Scr. 76, C42 (2007).

21

S. P. K. Kohler, S. K. Reed, R. E. Westacott, and K. G. McKendrick, J. Phys. Chem. B
110, 11717 (2006).

22

S. P. K. Kohler, M. Allan, M. L. Costen, and K. G. McKendrick, J. Phys. Chem. B 110,2771 (2006).

23

B. G. Perkins, T. Haber, and D. J. Nesbitt, J. Phys. Chem. B 109, 16396 (2005).

24

B. G. Perkins and D. J. Nesbitt, J. Phys. Chem. B 110, 17126 (2006).

25

B. G. Perkins and D. J. Nesbitt, J. Phys. Chem. A 111, 7420 (2007).

26

B. G. Perkins and D. J. Nesbitt, J. Phys. Chem. B 112, 507 (2008).

27

B. G. Perkins and D. J. Nesbitt, Proc. Natl. Acad. Sci. U. S. A. 105, 12684 (2008).

28

B. G. Perkins and D. J. Nesbitt, J. Phys. Chem. A 112, 9324 (2008).

29

F. Ausfelder and K. G. McKendrick, Prog. React. Kinet. Mech. 25, 299 (2000).

30

A. Furlan, Chem. Phys. Lett. 309, 157 (1999).

31

A. Furlan, J. Phys. Chem. B 103, 1550 (1999).

32

A. Furlan and G. E. Hall, J. Chem. Phys. 109, 10390 (1998).

33

A. Furlan, Chem. Phys. Lett. 275, 239 (1997).

34

W. T. Zemke, W. C. Stwalley, J. A. Coxon, and P. G. Hajigeorgiou, Chem. Phys. Lett.
177, 412 (1991).

35

S. J. Blanksby and G. B. Ellison, Accounts Chem. Res. 36, 255 (2003).

36

J. C. Polanyi and W. H. Wong, J. Chem. Phys. 51, 1439 (1969).

37

A. M. Zolot and D. J. Nesbitt, J. Chem. Phys. 127, 114319 (2007).

38

E. S. Whitney, A. M. Zolot, A. B. McCoy, J. S. Francisco, and D. J. Nesbitt, J. Chem.
Phys. 122, 124310 (2005).

39

S. A. Nizkorodov, W. W. Harper, W. B. Chapman, B. W. Blackmon, and D. J. Nesbitt, J.
Chem. Phys. 111, 8404 (1999).

40

W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 116, 5622 (2002).

41

W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 113, 3670 (2000).

178
42

W. B. Chapman, B. W. Blackmon, S. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 109,
9306 (1998).

43

M. P. Sinha and J. B. Fenn, presented at the Proceedings of the 5th International
Symposium on Molecular Beams, France, 1975 (unpublished).

44

D. Kaur, A. M. Desouza, J. Wanna, S. A. Hammad, L. Mercorelli, and D. S. Perry, Appl.
Optics 29, 119 (1990).

45

A. M. Zolot, W. W. Harper, B. G. Perkins, P. J. Dagdigian, and D. J. Nesbitt, J. Chem.
Phys. 125, (2006).

46

I. Benjamin, J. Phys. Chem. B 110, 9375 (2006).

47

I. Chorny, J. Vieceli, and I. Benjamin, J. Phys. Chem. B 107, 229 (2003).

48

J. Vieceli, I. Chorny, and I. Benjamin, Chem. Phys. Lett. 364, 446 (2002).

49

J. Vieceli, I. Chorny, and I. Benjamin, J. Chem. Phys. 117, 4532 (2002).

50

B. K. Radak, S. Yockel, D. Kim, and G. C. Schatz, J. Phys. Chem. A (in press) (2009).

51

D. Kim and G. C. Schatz, J. Phys. Chem. A 111, 5019 (2007).

52

F. Dong, S. H. Lee, and K. Liu, J. Chem. Phys. 113, 3633 (2000).

53

F. Ausfelder, H. Kelso, and K. G. McKendrick, Phys. Chem. Chem. Phys. 4, 473 (2002).

54

D. J. Bogan and D. W. Setser, J. Chem. Phys. 64, 586 (1976).

55

S. Rudic, C. Murray, J. N. Harvey, and A. J. Orr-Ewing, J. Chem. Phys. 120, 186 (2004).

179________________
Bibliography________________P. M. Aker, G. J. Germann, and J. J. Valentini, J. Chem. Phys. 96, 2756 (1992).
M. Alagia, N. Balucani, P. Casavecchia, D. Stranges, G. G. Volpi, D. C. Clary, A. Kliesch, and
H. J. Werner, Chem. Phys. 207, 389 (1996).
M. H. Alexander, G. Capecchi, and H. J. Werner, Faraday Discuss. 127, 59 (2004).
M. H. Alexander, D. E. Manolopoulos, and H. J. Werner, J. Chem. Phys. 113, 11084 (2000).
W. A. Alexander, B. S. Day, H. J. Moore, T. R. Lee, J. R. Morris, and D. Troya, J. Chem. Phys.
128, (2008).
M. Allan, P. A. J. Bagot, M. L. Costen, and K. G. McKendrick, J. Phys. Chem. C 111, 14833(2007).
M. Allan, P. A. J. Bagot, S. P. K. Kohler, S. K. Reed, R. E. Westacott, M. L. Costen, and K. G.
McKendrick, Phys. Scr. 76, C42 (2007).
M. Allan, P. A. J. Bagot, R. E. Westacott, M. L. Costen, and K. G. McKendrick, J. Phys. Chem.
C 112, 1524 (2008).
S. C. Althorpe, Chem. Phys. Lett. 370, 443 (2003).
S. C. Althorpe and D. C. Clary, Annu. Rev. Phys. Chem. 54, 493 (2003).
S. C. Althorpe, F. Fernandez-Alonso, B. D. Bean, J. D. Ayers, A. E. Pomerantz, R. N. Zare, andE. Wrede, Nature 416, 67 (2002).
F. J. Aoiz, L. Banares, and V. J. Herrero, Int. Rev. Phys. Chem. 24, 119 (2005).
F. J. Aoiz, L. Banares, B. MartinezHaya, J. F. Castillo, D. E. Manolopoulos, K. Stark, and H. J.
Werner, J. Phys. Chem. A 101, 6403 (1997).
V. Aquilanti, D. Cappelletti, F. Pirani, L. Y. Rusin, M. B. Sevryuk, and J. P. Toennies, J. Phys.
Chem. 95, 8248 (1991).
E. Arunan, D. W. Setser, and J. F. Ogilvie, J. Chem. Phys. 97, 1734 (1992).
B. S. Ault, J. Chem. Phys. 68, 4012 (1978).
F. Ausfelder, H. Kelso, and K. G. McKendrick, Phys. Chem. Chem. Phys. 4, 473 (2002).
F. Ausfelder and K. G. McKendrick, Prog. React. Kinet. Mech. 25, 299 (2000).

180
J. D. Ayers, A. E. Pomerantz, F. Fernandez-Alonso, F. Ausfelder, B. D. Bean, and R. N. Zare, J.
Chem. Phys. 119, 4662 (2003).
M. Baer, M. Faubel, B. Martinez-Haya, L. Y. Rusin, U. Tappe, and J. P. Toennies, J. Chem. Phys.
108, 9694 (1998).
N. Balucani, G. Capozza, F. Leonori, E. Segoloni, and P. Casavecchia, Int. Rev. Phys. Chem. 25,
109 (2006).
N. Balucani, D. Skouteris, G. Capozza, E. Segoloni, P. Casavecchia, M. H. Alexander, G.
Capecchi, and H. J. Werner, Phys. Chem. Chem. Phys. 6, 5007 (2004).
V. J. Barclay, B. A. Collings, J. C. Polanyi, and J. H. Wang, J. Phys. Chem. 95, 2921 (1991).
R. J. Bartlett and G. D. Purvis, Phys. Scr. 21, 255 (1980).
P. Beadle, M. R. Dunn, N. B. H. Jonathan, J. P. Liddy, and J. C. Naylor, J. Chem. Soc., Faraday
Trans. II 74, 2170 (1978).
P. Beadle, M. R. Dunn, N. B. H. Jonathan, J. P. Liddy, J. C. Naylor, and S. Okuda, J. Chem. Soc.,
Faraday Trans. II 74, 2158 (1978).
I. Benjamin, J. Phys. Chem. B 110, 9375 (2006).
I. Benjamin, M. Wilson, and A. Pohorille, J. Chem. Phys. 100, 6500 (1994).
M. J. Berry, J. Chem. Phys. 59, 6229 (1973).
R. P. A. Bettens, M. A. Collins, M. J. T. Jordan, and D. H. Zhang, J. Chem. Phys. 112, 10162(2000).
S. J. Blanksby and G. B. Ellison, Accounts Chem. Res. 36, 255 (2003).
D. Bogan and D. W. Setser, in Fluorine-containing free radicals: kinetics and dynamics ofreactions: based on a symposium sponsored by the Division of Physical Chemistry at the169th meeting of the American Chemical Society, Philadelphia, Pennsylvania, April 7-11,
1975, edited by J. W. Root (American Chemical Society, Washington, 1978), pp. 237.
D. J. Bogan and D. W. Setser, J. Chem. Phys. 64, 586 (1976).
K. Bolton, W. L. Hase, and G. H. Peslherbe, in Modern Methods for Multidimensional Dynamics
Computations in Chemistry, edited by D. L. Thompson (World Scientific, River Edge,
NJ, 1998), pp. 143.
S. B. M. Bosio and W. L. Hase, J. Chem. Phys. 107, 9677 (1997).
S. E. Bradforth, D. W. Arnold, R. B. Metz, A. Weaver, and D. M. Neumark, J. Phys. Chem. 95,
8066 (1991).
D. Brandt and J. C. Polanyi, Chem. Phys. 35, 23 (1978).
D. Brandt and J. C. Polanyi, Chem. Phys. 45, 65 (1980).

181
M. J. Bronikowski, W. R. Simpson, B. Girard, and R. N. Zare, J. Chem. Phys. 95, 8647 (1991).
M. Brouard, I. Burak, S. Marinakis, L. R. Lago, P. Tampkins, and C. Vallance, J. Chem. Phys.
121, 10426 (2004).
R. A. Brownsword, C. Kappel, P. Schmiechen, H. P. Upadhyaya, and H. R. Volpp, Chem. Phys.
Lett. 289, 241 (1998).
G. Capecehi and H. J. Werner, Phys. Chem. Chem. Phys. 6, 4975 (2004).
P. Casavecchia, Rep. Prog. Phys. 63, 355 (2000).
J. F. Castillo, F. J. Aoiz, L. Banares, E. Martinez-Nunez, A. Fernandez-Ramos, and S. Vazquez,
J. Phys. Chem. A 109, 8459 (2005).
J. F. Castillo, B. Hartke, H. J. Werner, F. J. Aoiz, L. Banares, and B. Martinez-Haya, J. Chem.
Phys. 109, 7224 (1998).
D. W. Chandler and P. L. Houston, J. Chem. Phys. 87, 1445 (1987).
H. W. Chang, D. W. Setser, M. J. Perona, and R. L. Johnson, Chem. Phys. Lett. 9, 587 (1971).
S. D. Chao and R. T. Skodje, J. Chem. Phys. 119, 1462 (2003).
W. B. Chapman, B. W. Blackmon, and D. J. Nesbitt, J. Chem. Phys. 107, 8193 (1997).
W. B. Chapman, B. W. Blackmon, S. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 109, 9306
(1998).
W. B. Chapman, M. J. Weida, and D. J. Nesbitt, J. Chem. Phys. 106, 2248 (1997).
W. Chen, W. L. Hase, and H. B. Schlegel, Chem. Phys. Lett. 228, 436 (1994).
I. Chorny, J. Vieceli, and I. Benjamin, J. Phys. Chem. B 107, 229 (2003).
R. E. Continetti, B. A. Balko, and Y. T. Lee, J. Chem. Phys. 93, 5719 (1990).
H. W. Cruse, P. J. Dagdigian, and R. N. Zare, Faraday Discuss. 55, 277 (1973).
G. Czako, B. C. Shepler, J. B. Braams, and J. M. Bowman, J. Phys. Chem. A(in press) (2009).
S. Davis, D. T. Anderson, G. Duxbury, and D. J. Nesbitt, J. Chem. Phys. 107, 5661 (1997).
B. S. Day, J. R. Morris, W. A. Alexander, and D. Troya, J. Phys. Chem. A 110, 1319 (2006).
W. Demtroder, Laser Spectroscopy. (Springer, Berlin, 1996).
M. P. Deskevich, M. Y. Hayes, K. Takahashi, R. T. Skodje, and D. J. Nesbitt, J. Chem. Phys.
124, 224303 (2006).
M. P. Deskevich, D. J. Nesbitt, and H. J. Werner, J. Chem. Phys. 120, 7281 (2004).

182
A. M. G. Ding, L. J. Kirsch, D. S. Perry, J. C. Polanyi, and J. L. Schreiber, Faraday Discuss. 55,
252 (1973).
F. Dong, S. H. Lee, and K. Liu, J. Chem. Phys. 113, 3633 (2000).
F. Dong, S. H. Lee, and K. Liu, J. Chem. Phys. 115, 1197 (2001).
V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73, 2634
(2002).
M. L. Dubernet and J. M. Hutson, J. Phys. Chem. 98, 5844 (1994).
W. H. Duewer and D. W. Setser, J. Chem. Phys. 58, 2310 (1973).
T. H. Dunning, J. Chem. Phys. 90, 1007 (1989).
A. Eppink and D. H. Parker, Rev. Sci. Instrum. 68, 3477 (1997).
H. Eyring, J. Am. Chem. Soc. 54, 170 (1932).
H. Eyring and M. Polanyi, Z. Phys. Chem. B-Chem. Elem. Aufbau. Mater. 12, 279 (1931).
J. R. Fair, D. Schaefer, R. Kosloff, and D. J. Nesbitt, J. Chem. Phys. 116, 1406 (2002).
M. Faubel, B. Martinez-Haya, L. Y. Rusin, U. Tappe, J. P. Toennies, F. J. Aoiz, and L. Banares,
J. Phys. Chem. A 102, 8695 (1998).
F. Fernandez-Alonso and R. N. Zare, Annu. Rev. Phys. Chem. 53, 67 (2002).
A. V. Fishchuk, G. C. Groenenboom, and A. van der Avoird, J. Phys. Chem. A 110, 5280 (2006).
A. V. Fishchuk, P. E. S. Wormer, and A. van der Avoird, J. Phys. Chem. A 110, 5273 (2006).
A. A. Fokin and P. R. Schreiner, Chem. Rev. 102, 1551 (2002).
From, pp. http://nobelprize.org/nobel_prizes/chemistry/laureates/1986/.
A. Furlan, Chem. Phys. Lett. 275, 239 (1997).
A. Furlan, Chem. Phys. Lett. 309, 157 (1999).
A. Furlan, J. Phys. Chem. B 103, 1550 (1999).
A. Furlan and G. E. Hall, J. Chem. Phys. 109, 10390 (1998).
D. J. Garton, A. L. Brunsvold, T. K. Minton, D. Troya, B. Maiti, and G. C. Schatz, J. Phys.
Chem. A 110, 1327 (2006).
D. J. Garton, T. K. Minton, M. Alagia, N. Balucani, P. Casavecchia, and G. G. Volpi, Faraday
Discuss.387 (1997).

183
D. J. Garton, T. K. Minton, M. Alagia, N. Balucani, P. Casavecchia, and G. G. Volpi, J. Chem.
Phys. 112, 5975 (2000).
D. J. Garton, T. K. Minton, M. Alagia, N. Balucani, P. Casavecchia, and G. G. Volpi, J. Chem.
Phys. 114, 5958 (2001).
D. J. Garton, T. K. Minton, B. Maiti, D. Troya, and G. C. Schatz, J. Chem. Phys. 118, 1585
(2003).
W. Gellermann, J. Phys. Chem. Solids 52, 249 (1991).
D. Gerlich, E. Herbst, and E. Roueff, Planet Space Sci. 50, 1275 (2002).
S. Ghosal and S. Mahapatra, J. Phys. Chem. A 109, 1530 (2005).
J. L. Hall and S. A. Lee, Appl. Phys. Lett. 29, 367 (1976).
S. A. Harich, D. W. H. Hwang, X. F. Yang, J. J. Lin, X. M. Yang, and R. N. Dixon, J. Chem.
Phys. 113, 10073 (2000).
W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 113, 3670 (2000).
W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, Chem. Phys. Lett. 335, 381 (2001).
W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 116, 5622 (2002).
J. G. Harris, J. Phys. Chem. 96, 5077 (1992).
D. R. Hartree, Proc. Camb. Philol. Soc. 24, 111 (1928).
D. R. Hartree, Proc. Camb. Philol. Soc. 24, 89 (1928).
M. Y. Hayes, M. P. Deskevich, D. J. Nesbitt, K. Takahashi, and R. T. Skodje, J. Phys. Chem. A
110, 436 (2006).
D. Herriot, H. Kogelnik, and R. Kompfner, Appl. Optics 3, 523 (1964).
G. Herzberg, Infrared and Raman Spectra of Polyatomic Molecules. (D. Van Nostrand Company,
New York, 1945).
R. C. Hilborn, Am. J. Phys. 50, 982 (1982).
M. C. Hsiao, A. Sinha, and F. F. Crim, J. Phys. Chem. 95, 8263 (1991).
N. Isa, K. D. Gibson, T. Yan, W. Hase, and S. J. Sibener, J. Chem. Phys. 120, 2417 (2004).
Y. Ishikawa, T. Nakajima, T. Yanai, and K. Hirao, Chem. Phys. Lett. 363, 458 (2002).
W. Jakubetz, D. Sokolovski, J. N. L. Connor, and G. C. Schatz, J. Chem. Phys. 97, 6451 (1992).
S. Javoy, V. Naudet, S. Abid, and C. E. Paillard, Exp. Therm. Fluid Sci. 27, 371 (2003).

184
N. Jonathan, Melliars.Cm, D. Timlin, and D. H. Slater, Appl. Optics 10, 1821 (1971).
N. Jonathan, Melliar-Smith Cm, S. Okuda, D. H. Slater, and D. Timlin, Mol. Phys. 22, 561(1971).
J. V. V. Kasper, C. R. Pollock, R. F. Curl, and F. K. Tittel, Appl. Optics 21, 236 (1982).
D. Kaur, A. M. Desouza, J. Wanna, S. A. Hammad, L. Mercorelli, and D. S. Perry, Appl. Optics
29, 119 (1990).
H. Kelso, S. P. K. Kohler, D. A. Henderson, and K. G. McKendrick, J. Chem. Phys. 119, 9985
(2003).
A. J. Kenyon, A. J. McCaffery, C. M. Quintella, and M. D. Zidan, Chem. Phys. Lett. 190, 55(1992).
A. J. Kenyon, A. J. McCaffery, C. M. Quintella, and M. D. Zidan, Faraday Discuss. 96, 245(1993).
A. J. Kenyon, A. J. McCaffery, C. M. Quintella, and M. D. Zidan, J. Chem. Soc.-Faraday Trans.
89, 3877 (1993).
D. Kim and G. C. Schatz, J. Phys. Chem. A 111, 5019 (2007).
L. J. Kirsch and J. C. Polanyi, J. Chem. Phys. 57, 4498 (1972).
J. Klos, M. M. Szczesniak, and G. Chalasinski, Int. Rev. Phys. Chem. 23, 541 (2004).
W. Koechner, (Springer, Berlin, 1999), pp. 232.
S. P. K. Kohler, M. Allan, M. L. Costen, and K. G. McKendrick, J. Phys. Chem. B 110, 2771
(2006).
S. P. K. Kohler, M. Allan, H. Kelso, D. A. Henderson, and K. G. McKendrick, J. Chem. Phys.
122, 24712 (2005).
S. P. K. Kohler, S. K. Reed, R. E. Westacott, and K. G. McKendrick, J. Phys. Chem. B 110,11717 (2006).
K. L. Kompa and G. C. Pimentel, J. Chem. Phys. 47, 857 (1967).
H. Kornweitz and A. Persky, J. Phys. Chem. A 108, 140 (2004).
C. Kreher, J. L. Rinnenthal, and K. H. Gericke, J. Chem. Phys. 108, 3154 (1998).
O. D. Krogh, D. K. Stone, and G. C. Pimentel, J. Chem. Phys. 66, 368 (1977).
K. Kudla and G. C. Schatz, Chem. Phys. 175, 71 (1993).
P. J. Kuntz, E. M. Nemeth, J. C. Polanyi, S. D. Rosner, and C. E. Young, J. Chem. Phys. 44, 1168
(1966).

185
S. R. Langhoff and E. R. Davidson, Int. J. Quantum Chem. 8, 61 (1974).
I. Last and M. Baer, J. Chem. Phys. 80, 3246 (1984).
R. B. Leblanc, J. B. White, and P. F. Bernath, J. Mol. Spectrosc. 164, 574 (1994).
S. L. Lednovich and J. B. Fenn, Aiche J. 23, 454 (1977).
Y. T. Lee, Science 236, 793 (1987).
Y. T. Lee, J. D. McDonald, P. R. Lebreton, and D. R. Herschbach, Rev. Sci. Instrum. 40, 1402
(1969).
E. B. W. Lerch, X. C. Dai, S. Gilb, E. A. Torres, and S. R. Leone, J. Chem. Phys. 124, (2006).
R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical Reactivity.
(Oxford University Press, New York, 1987).
R. D. Levine and S. F. Wu, Chem. Phys. Lett. 11, 557 (1971).
G. Li, S. B. M. Bosio, and W. L. Hase, J. Mol. Struct. 556, 43 (2000).
G. S. Li and W. L. Hase, J. Am. Chem. Soc. 121, 7124 (1999).
J. J. Lin, J. G. Zhou, W. C. Shiu, and K. P. Liu, Rev. Sci. Instrum. 74, 2495 (2003).
J. J. M. Lin, J. G. Zhou, W. C. Shiu, and K. P. Liu, Chin. J. Chem. Phys. 17, 346 (2004).
F. Lique, M. H. Alexander, G. L. Li, H. J. Werner, S. A. Nizkorodov, W. W. Harper, and D. J.
Nesbitt, J. Chem. Phys. 128, (2008).
J. B. Liu, B. Van Devener, and S. L. Anderson, J. Chem. Phys. 119, 200 (2003).
K. P. Liu, Phys. Chem. Chem. Phys. 9, 17 (2007).
F. London, Z. Elektrochem. Angew. Phys. Chem. 35, 552 (1929).
D. E. Manolopoulos and M. H. Alexander, Phys. Chem. Chem. Phys. 6, 4984 (2004).
U. Manthe, G. Capecchi, and H. J. Werner, Phys. Chem. Chem. Phys. 6, 5026 (2004).
M. M. Maricq and J. J. Szente, J. Phys. Chem. 98, 2078 (1994).
J. D. D. Martin and J. W. Hepburn, J. Chem. Phys. 109, 8139 (1998).
E. Martinez-Nunez, A. Rahaman, and W. L. Hase, J. Phys. Chem. C 111, 354 (2007).
J. M. Merritt, J. Kupper, and R. E. Miller, Phys. Chem. Chem. Phys. 7, 67 (2005).
R. B. Metz, J. D. Thoemke, J. M. Pfeiffer, and F. F. Crim, J. Chem. Phys. 99, 1744 (1993).
M. Meuwly and J. M. Hutson, J. Chem. Phys. 119, 8873 (2003).

186
D. R. Miller, in Atomic and molecular beam methods, edited by G. Scoles (Oxford University
Press, New York, 1988), pp. 14.
L. F. Mollenauer, Rev. Sci. Instrum. 49, 809 (1978).
C. M. Moore, I. W. M. Smith, and D. W. A. Stewart, Int. J. Chem. Kinet. 26, 813 (1994).
G. B. Moore and I. W. M. Smith, J. Phys. Chem. 100, 12848 (1996).
J. R. Morris, P. Behr, M. D. Antman, B. R. Ringeisen, J. Splan, and G. M. Nathanson, J. Phys.
Chem. A 104, 6738 (2000).
J. T. Muckerman, J. Phys. Chem. 93, 179 (1989).
C. Murray, A. J. Orr-Ewing, R. L. Toomes, and T. N. Kitsopoulos, J. Chem. Phys. 120, 2230
(2004).
G. M. Nathanson, Annu. Rev. Phys. Chem. 55, 231 (2004).
G. M. Nathanson, P. Davidovits, D. R. Worsnop, and C. E. Kolb, J. Phys. Chem. 100, 13007(1996).
C. Naulin, M. Costes, A. Benseddik, and G. Dorthe, Laser Chem. 8, 283 (1988).
D. A. Neufeld, J. Zmuidzinas, P. Schilke, and T. G. Phillips, Astrophys. J. 488, L141 (1997).
D. M. Neumark, A. M. Wodtke, G. N. Robinson, C. C. Hayden, and Y. T. Lee, J. Chem. Phys.
82, 3045 (1985).
S. A. Nizkorodov, W. W. Harper, W. B. Chapman, B. W. Blackmon, and D. J. Nesbitt, J. Chem.
Phys. 111, 8404 (1999).
J. H. Parker and G. C. Pimentel, J. Chem. Phys. 51, 91 (1969).
B. F. Parsons and D. W. Chandler, J. Chem. Phys. 122, 174306 (2005).
B. F. Parsons, K. E. Strecker, and D. W. Chandler, Eur. Phys. J. D 38, 15 (2006).
J. K. Pearce, B. Retail, S. J. Greaves, R. A. Rose, and A. J. Orr-Ewing, J. Phys. Chem. A 111,
13296 (2007).
B. G. Perkins, T. Haber, and D. J. Nesbitt, J. Phys. Chem. B 109, 16396 (2005).
B. G. Perkins and D. J. Nesbitt, J. Phys. Chem. B 110, 17126 (2006).
B. G. Perkins and D. J. Nesbitt, J. Phys. Chem. A 111, 7420 (2007).
B. G. Perkins and D. J. Nesbitt, J. Phys. Chem. B 112, 507 (2008).
B. G. Perkins and D. J. Nesbitt, Proc. Natl. Acad. Sci. U. S. A. 105, 12684 (2008).
B. G. Perkins and D. J. Nesbitt, J. Phys. Chem. A 112, 9324 (2008).

187
D. S. Perry, Private Communication (2006).
G. H. Peslherbe and W. L. Hase, J. Chem. Phys. 100, 1179 (1994).
J. M. Pfeiffer, R. B. Metz, J. D. Thoemke, E. Woods, and F. F. Crim, J. Chem. Phys. 104, 4490
(1996).
A. S. Pine, J. Opt. Soc. Am. 66, 97 (1976).
J. C. Polanyi, Accounts Chem. Res. 5, 161 (1972).
J. C. Polanyi and D. C. Tardy, J. Chem. Phys. 51, 5717 (1969).
J. C. Polanyi and W. H. Wong, J. Chem. Phys. 51, 1439 (1969).
J. C. Polanyi and K. B. Woodall, J. Chem. Phys. 57, 1574 (1972).
W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in C: theart of scientific computing, 2 ed. (Cambridge University Press, New York, 1992).
D. Proch and T. Trickl, Rev. Sci. Instrum. 60, 713 (1989).
M. H. Qiu, Z. F. Ren, L. Che, D. X. Dai, S. A. Harich, X. Y. Wang, X. M. Yang, C. X. Xu, D. Q.
Xie, M. Gustafsson, R. T. Skodje, Z. G. Sun, and D. H. Zhang, Science 311, 1440 (2006).
G. Quemener and N. Balakrishnan, J. Chem. Phys. 128, (2008).
C. M. Quintella, A. J. McCaffery, and M. D. Zidan, Chem. Phys. Lett. 214, 563 (1993).
B. K. Radak, S. Yockel, D. Kim, and G. C. Schatz, J. Phys. Chem. A (in press) (2009).
B. Retail, J. K. Pearce, C. Murray, and A. J. Orr-Ewing, J. Chem. Phys. 122, (2005).
S. Rogers, D. S. Wang, A. Kuppermann, and S. Walch, J. Phys. Chem. A 104, 2308 (2000).
S. Rudic, C. Murray, J. N. Harvey, and A. J. Orr-Ewing, J. Chem. Phys. 120, 186 (2004).
L. Y. Rusin and J. P. Toennies, Phys. Chem. Chem. Phys. 2, 501 (2000).
M. E. Saecker, S. T. Govoni, D. V. Kowalski, M. E. King, and G. M. Nathanson, Science 252,
1421 (1991).
M. E. Saecker and G. M. Nathanson, J. Chem. Phys. 99, 7056 (1993).
M. E. Saecker and G. M. Nathanson, J. Chem. Phys. 100, 3999 (1994).
S. Sato, J. Chem. Phys. 23, 2465 (1955).
S. Sato, J. Chem. Phys. 23, 592 (1955).
R. Sayos, J. Hernando, R. Francia, and M. Gonzalez, Phys. Chem. Chem. Phys. 2, 523 (2000).

188
R. Sayos, J. Hernando, J. Hijazo, and M. Gonzalez, Phys. Chem. Chem. Phys. 1, 947 (1999).
A. Schiffman, W. B. Chapman, and D. J. Nesbitt, J. Phys. Chem. 100, 3402 (1996).
B. Scott Day, J. R. Morris, and D. Troya, J. Chem. Phys. 122, (2005).
W. Shiu, J. J. Lin, K. P. Liu, M. Wu, and D. H. Parker, J. Chem. Phys. 120, 117 (2004).
A. Simoes and K. Gavroglu, Stud. Hist. Philos. Mod. Phys. 31B, 511 (2000).
A. Sinha, M. C. Hsiao, and F. F. Crim, J. Chem. Phys. 92, 6333 (1990).
A. Sinha, M. C. Hsiao, and F. F. Crim, J. Chem. Phys. 94, 4928 (1991).
M. P. Sinha and J. B. Fenn, presented at the Proceedings of the 5th International Symposium on
Molecular Beams, France, 1975 (unpublished).
R. T. Skodje, Annu. Rev. Phys. Chem. 44, 145 (1993).
R. T. Skodje, D. Skouteris, D. E. Manolopoulos, S. H. Lee, F. Dong, and K. Liu, J. Chem. Phys.
112, 4536 (2000).
R. T. Skodje, D. Skouteris, D. E. Manolopoulos, S. H. Lee, F. Dong, and K. P. Liu, Phys. Rev.
Lett. 85, 1206 (2000).
D. Skouteris, H. J. Werner, F. J. Aoiz, L. Banares, J. F. Castillo, M. Menendez, N. Balucani, L.
Cartechini, and P. Casavecchia, J. Chem. Phys. 114, 10662 (2001).
J. J. Sloan, D. G. Watson, J. M. Williamson, and J. S. Wright, J. Chem. Phys. 75, 1190 (1981).
I. W. M. Smith and D. J. Wrigley, Chem. Phys. Lett. 70, 481 (1980).
D. M. Sonnenfroh and K. P. Liu, Chem. Phys. Lett. 176, 183 (1991).
K. Stark and H. J. Werner, J. Chem. Phys. 104, 6515 (1996).
P. S. Stevens, W. H. Brune, and J. G. Anderson, J. Phys. Chem. 93, 4068 (1989).
B. P. Stoicheff, Can. J. Phys. 79, 165 (2001).
B. R. Strazisar, C. Lin, and H. F. Davis, Science 290, 958 (2000).
R. A. Sultanov and N. Balakrishnan, Astrophys. J. 629, 305 (2005).
Z. G. Sun, S. Y. Lee, and D. H. Zhang, Chin. J. Chem. Phys. 20, 365 (2007).
J. P. Sung and D. W. Setser, Chem. Phys. Lett. 48, 413 (1977).
K. Tamagake, D. W. Setser, and J. P. Sung, J. Chem. Phys. 73, 2203 (1980).
B. Y. Tang, B. H. Yang, K. L. Han, R. Q. Zhang, and J. Z. H. Zhang, J. Chem. Phys. 113, 10105(2000).

189
E. Tannenbaum, K. J. Higgins, W. Klemperer, B. Segev, and E. J. Heller, J. Phys. Chem. B 106,
8100 (2002).
L. M. Tashiro, W. Ubachs, and R. N. Zare, J. Mol. Spectrosc. 138, 89 (1989).
E. H. Taylor and S. Datz, J. Chem. Phys. 23, 1711 (1955).
J. D. Thoemke, J. M. Pfeiffer, R. B. Metz, and F. F. Crim, J. Phys. Chem. 99, 13748 (1995).
R. L. Toomes and T. N. Kitsopoulos, Phys. Chem. Chem. Phys. 5, 2481 (2003).
R. L. Toomes, A. J. van den Brom, T. N. Kitsopoulos, C. Murray, and A. J. Orr-Ewing, J. Phys.
Chem. A 108, 7909 (2004).
D. Townsend, M. P. Minitti, and A. G. Suits, Rev. Sci. Instrum. 74, 2530 (2003).
D. Troya, J. Chem. Phys. 123, 214305 (2005).
D. Troya and G. C. Schatz, J. Chem. Phys. 120, 7696 (2004).
D. Troya and G. C. Schatz, Int. Rev. Phys. Chem. 23, 341 (2004).
D. G. Truhlar and Kupperma.A, J. Chem. Phys. 56, 2232 (1972).
Y. R. Tzeng and M. H. Alexander, J. Chem. Phys. 121, 5183 (2004).
E. Uggerud and T. Helgaker, J. Am. Chem. Soc. 114, 4265 (1992).
J. J. Valentini, J. Phys. Chem. A 106, 5745 (2002).
S. A. Vazquez, J. R. Morris, A. Rahaman, O. A. Mazyar, G. Vayner, S. V. Addepalli, W. L. Hase,and E. Martinez-Nunez, J. Phys. Chem. A 111, 12785 (2007).
J. T. Verdeyen, Laser Electronics, 3rd ed. (Prentice Hall, Upper Saddle River, NJ, 1995).
J. Vieceli, I. Chorny, and I. Benjamin, J. Chem. Phys. 115, 4819 (2001).
J. Vieceli, I. Chorny, and I. Benjamin, Chem. Phys. Lett. 364, 446 (2002).
J. Vieceli, I. Chorny, and I. Benjamin, J. Chem. Phys. 117, 4532 (2002).
R. von Glasow and P. J. Crutzen, in Treatise on Geochemistry, edited by R. F. Keeling, H. D.
Holland, and K. K. Turekian (Elsevier Pergamon, Amsterdam, 2003), Vol. 4, pp. 347.
I. M. Waller, T. N. Kitsopoulos, and D. M. Neumark, J. Phys. Chem. 94, 2240 (1990).
P. F. Weck and N. Balakrishnan, J. Chem. Phys. 123, 144308 (2005).
H. J. Werner and P. J. Knowles, J. Chem. Phys. 89, 5803 (1988).
E. S. Whitney, A. M. Zolot, A. B. McCoy, J. S. Francisco, and D. J. Nesbitt, J. Chem. Phys. 122,
124310 (2005).

190
C. D. Wick, J. I. Siepmann, and M. R. Schure, Anal. Chem. 74, 3518 (2002).
M. A. Wickramaaratchi, D. W. Setser, H. Hildebrandt, B. Korbitzer, and H. Heydtmann, Chem.
Phys. 94, 109 (1985).
K. R. Wilson, G. H. Kwei, D. R. Herschbach, J. A. Norris, J. H. Birely, and R. R. Herm, J. Chem.
Phys. 41, 1154 (1964).
N. Winter and I. Benjamin, J. Chem. Phys. 121, 2253 (2004).
S. H. Wu, P. Dupre, and T. A. Miller, Phys. Chem. Chem. Phys. 8, 1682 (2006).
Y. S. M. Wu, A. Kuppermann, and J. B. Anderson, Phys. Chem. Chem. Phys. 1, 929 (1999).
E. Wurzberg, A. J. Grimley, and P. L. Houston, Chem. Phys. Lett. 57, 373 (1978).
E. Wurzberg and P. L. Houston, J. Chem. Phys. 72, 5915 (1980).
C. X. Xu, D. Q. Xie, and D. H. Zhang, Chin. J. Chem. Phys. 19, 96 (2006).
S. Yan, Y. T. Wu, and K. P. Liu, Phys. Chem. Chem. Phys. 9, 250 (2007).
T. Y. Yan and W. L. Hase, Phys. Chem. Chem. Phys. 2, 901 (2000).
T. Y. Yan and W. L. Hase, J. Phys. Chem. B 106, 8029 (2002).
T. Y. Yan, W. L. Hase, and J. R. Barker, Chem. Phys. Lett. 329, 84 (2000).
T. Y. Yan, W. L. Hase, and J. C. Tully, J. Chem. Phys. 120, 1031 (2004).
T. Y. Yan, N. Isa, K. D. Gibson, S. J. Sibener, and W. L. Hase, J. Phys. Chem. A 107, 10600(2003).
M. H. Yang, D. H. Zhang, M. A. Collins, and S. Y. Lee, J. Chem. Phys. 115, 174 (2001).
X. Yang, X. B. Wang, and L. S. Wang, J. Chem. Phys. 115, 2889 (2001).
X. M. Yang and D. H. Zhang, Accounts Chem. Res. 41, 981 (2008).
R. N. Zare and Dagdigia.Pj, Science 185, 739 (1974).
W. T. Zemke, W. C. Stwalley, J. A. Coxon, and P. G. Hajigeorgiou, Chem. Phys. Lett. 177, 412(1991).
D. H. Zhang, J. Chem. Phys. 125, 133102 (2006).
D. H. Zhang, M. H. Yang, and S. Y. Lee, Phys. Rev. Lett. 89, 283203 (2002).
D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 99, 5615 (1993).
J. M. Zhang, D. J. Garton, and T. K. Minton, J. Chem. Phys. 117, 6239 (2002).

191
J. M. Zhang, H. P. Upadhyaya, A. L. Brunsvold, and T. K. Minton, J. Phys. Chem. B 110, 12500(2006).
J. G. Zhou, J. J. Lin, and K. P. Liu, J. Chem. Phys. 121, 813 (2004).
J. G. Zhou, J. J. Lin, W. C. Shiu, S. C. Pu, and K. P. Liu, J. Chem. Phys. 119, 2538 (2003).
C. Zhu, R. Krems, A. Dalgarno, and N. Balakrishnan, Astrophys. J. 577, 795 (2002).
M. Ziemkiewicz and D. J. Nesbitt, manuscript in preparation.
M. Ziemkiewicz, M. Wojcik, and D. J. Nesbitt, J. Chem. Phys. 123, 224307 (2005).
A. Zolot, M., P. Dagdigian, J., and D. Nesbitt, J., J. Chem. Phys. 129, 194705 (2008).
A. Zolot, M. and D. Nesbitt, J., J. Chem. Phys. 129, 184305 (2008).
A. M. Zolot, W. W. Harper, B. G. Perkins, P. J. Dagdigian, and D. J. Nesbitt, J. Chem. Phys. 125,(2006).
A. M. Zolot and D. J. Nesbitt, J. Chem. Phys. 127, 114319 (2007).

192________________
Appendices________________
Appendix A: F Center Laser Realignment
The FCL used in the present work was manufactured by Burleigh Instruments as part oftheir commercial color center laser line developed in the early 1980s. The FCL was discontinued
in 1996 and Burleigh was subsequently purchased by EXFO, who does not support any Burleighelectro optics products. This situation strongly compromises the ability to service and maintainthe FCL, and suggests that more robust modern technology, such as quantum cascade lasers, CW
optical parametric oscillators, and difference frequency generation, will be more suitable for thistype of apparatus in the future. Particular complications with using discontinued equipment arose
after an unfortunate series of events necessitated the complete factory alignment of the FCL.
Based on these experiences, I strongly advise FCL users to always fill the Dewar by hand, andNEVER use an automated filling mechanism, which is prone to fail and freeze the exterior of thecrystal chamber, creating vacuum leaks. After such an o-ring freezing and vacuum failure, criticalalignment of mirrors mounted on the base plate was lost. Specifically, the mounting of the cavity
end mirror using a single set screw on a post has been found to be a critical design flaw of thecurrent version of the FCL, and accidental perturbation of this and other optical elements
necessitated the extensive efforts described below.
Although Burleigh Instruments no longer exists, a company founded by former Burleighengineers, Bristol Instruments, does provide expert assistance on many of their former employer’s
devices. Unfortunately, they do not have any expertise in the FCL field. However, throughcontacts at Bristol instruments, I was able to talk to the retired Burleigh engineer who was
primarily responsible for the FCL assembly and alignment, and with his help I was able torecreate the FCL factory adjustments. This alignment used to be performed at the Burleigh

193
factory with specially machined alignment jigs that no longer exist, meaning a number of thefactory alignments had to be recreated. The details of this process follow in this appendix, toassist other workers who may want to resurrect a Burleigh FCL.
To aid the current discussion, Fig. A.1 provides a sketch of the FCL’s optical elements.
In regular operation, the krypton ion pump laser is guided into the cavity through input irises (IIa,and IIb), reflects off the input steering mirror (ISM), enters the crystal vacuum chamber through avacuum window, and is reflected from a dichroic beam splitter (DBS). The folding mirror (FM)focuses the pump beam onto the gain medium, mounted at Brewster’s angle. Finally, the pumpbeam retroreflects from the cavity end mirror (CEM), which is mounted on a gear-driven
translation stage to enable adjustments while under vacuum. The IR laser cavity follows the pumplaser path between the CEM and FM, but the DBS efficiently transmits the IR light. The beamthen passes through a Brewster window forming the vacuum seal into the tuning arm, and throughthe center of the cavity iris (CI), located close to the tuning arm input. An approximately 30 cm
gap between the CI and the output coupling grating provides space for additional cavity elements,
i.e., the galvo plates and thick etalon. Two interchangeable gratings provide coarse frequency
selection and are blazed to couple either 10% (the B grating) or 1.5% (the A grating ) of the lightout of the chamber in zeroth order with high retroreflection in first order. The gratings aremounted on a right angle corner mount with a high reflector, such that tilting the grating tunes thecavity wavelength without displacing the output laser beam. A final output-coupling mirror(OCM) steers the beam out of the cavity and through the final window, which forms the tuningarm vacuum seal.
The only benchmark for the alignment that was left unperturbed was the CI, though eventhis position could be recreated, if necessary, by carefully positioning it 3.4 cm above the laserbase plate and centering it on the tuning arm axis. To assist alignment, an output iris (OI) was
added in front of and centered on the output window. The OI and CI define the laser oscillation

194

Figure A.1

Essential elements of the FCL laser cavity. Abbreviations for optical elements are
as follows. Input Iris (IIa and IIb), Dichroic Beam Splitter (DBS), Folding Mirror(FM), Cavity End Mirror (CEM), Cavity Iris (CI), Output Coupling Mirror(OCM), Output Iris (OI).

195
path, along with the OCM and grating. However, the position of the OCM is not critical, since it
is after the output coupler, so this element is coarsely positioned in the middle of its adjustment
range and bolted firmly in place for the remainder of the alignment. Similarly, the horizontal tiltof the grating is not critical, as it simply determines the frequency of the laser oscillation.
However, the vertical adjust on the grating should be selected such that the grating does notproduce a dramatic vertical tilt in the beam height. It must therefore be readjusted as thealignment proceeds and beam path is optimized, as described next.
To perform the alignment, the round trip oscillator path is defined by directing a HeNebeam into the laser output. Two steering mirrors define this beam path, which must be centeredon the CI and OI. Next, the grating vertical tilt must be optimized. By turning the grating
horizontal tilt (via the sine bar drive), one grating reflection can be directed approximately
backwards along the incoming HeNe path. Adjusting the grating vertical tilt enables this beam tobe perfectly retroreflected into the incoming beam, but displaces the alignment onto the CI. Thus,
the CI, OI, and grating retroreflection adjustments must be iterated until the beam is centered on
both irises and retroreflected along the HeNe input. Adequate positioning of the irises and OCM
can be checked, as it results in the tracer beam being level in the tuning arm and parallel to thelong edge of the laser base plate.
Next, the crystal chamber optics are coarsely positioned. To attain the needed
displacement from going through an Brewster window, the vacuum coupling between the crystal
chamber and tuning arm must be unbolted from the chamber housing and attached to the tuningarm bellows, such that it occupies the position it would with the crystal chamber in place. Afterbolting the DBS and FM onto the base plate, correct angular positioning may be verified using aplumb bob measurement device or similar contraption to measure the HeNe path relative to somereference point. Such measurements can be used to verify that the DBS is at Brewster’s angle
relative to the alignment beam (56.3°), and the FM bends the beam by 18.4° toward the CEM, theangle at which the FM astigmatism compensates for the astigmatism induced by focusing the196laser light on the crystal at Brewster’s angle.1 Next, the CEM translation stage may be attached,and its tilt coarsely adjusted. The tilt of the stage can be observed by affixing a card to the stage
and observing any apparent “walk” of the HeNe spot on the card as the stage translates. Properly
angling the stage minimizes such walk, as achieved by loosening the bolts attaching the stage tothe base plate and gently moving the stage in its slotted boltholes.
To replicate the beam displacement by the gain medium, a 2.0 mm thick quartz (orsimilar material with index of refraction of ≈ 1.5, close to that of KCl and RbCl) dummy crystal
should be placed in the crystal cassette holder. Positioning the crystal cassette mount is the mostproblematic procedure without the Burleigh alignment jigs, due to translational and angular
freedom provided in bolting it to the base plate. Acceptable positioning can be found by
expanding the HeNe tracer in a telescope and finding the location of its focus after reflecting fromthe 3 cm focal length FM. This position defines the location of the beam waist between the two
curved mirrors, which should be the center of the F center crystal. Angular positioning of thecassette holder requires reflecting an additional HeNe beam from the lower right side of thecrystal (as drawn in Fig. A.1) and measuring the angle of the dummy crystal’s face in order toverify that it is close to 56.3° from the tracer beam, i.e., Brewster’s angle at 3 μm in the salt
crystals. The angular adjustment needs to only be close to Brewster’s angle, since the reflection isa slowly increasing function and actually varies a bit between the different F center crystals andoperating wavelengths.
After the crystal cassette position is approximately correct, the CEM translation stage togain medium distance must be optimized, such that the middle of the CEM translation stage
motion corresponds to a CEM – crystal distance of ½ the CEM focal length (f = 7.1 mm).
Burleigh did this adjustment using an alignment jig, equipped with a special crystal marked witha “cross-hair”, which could be illuminated and re-imaged on itself from the CEM. I recreated thiscrystal by gluing a thin piece of paper, etched with a cross-hair, between two 1 mm microscope

197
slides, cut to match the desired crystal dimensions. The cross-hair crystal is best illuminated frombehind, as achieved by removing the FM in a reproducible manner, i.e., by screwing it out of its
mount and counting how many turns are needed for it to be released. Then, the inverted image ofthe cross hair can be focused on itself by careful CEM positioning. At this point the worm screw,which enables CEM translation while in vacuum, should be adjusted such that the focusing
position approximately corresponds to the center of the translation range.
After replacing the FM and quartz dummy crystal, the unexpanded HeNe alignment beam
can be retroreflected along its incoming path by carefully positioning the CEM. A card with asmall hole centered on the incoming beam can be placed in the tuning arm to facilitate thisadjustment. However, the CEM mount consists of a post with a setscrew to hold it in place, so it
is difficult to get the alignment perfect using only the CEM. For small angular displacements, theFM mount angular adjust knobs can be used without significantly perturbing the earlieralignments. Once adequate alignment has been obtained, the CEM should be translated on its
stage and any walking of the retroreflected beam observed. For the greatest sensitivity to walk,observe the beam reflected off the DBS and toward the pump laser. Beam translation indicatesthat the CEM translation is not perfectly parallel the alignment beam because perfect
retroreflection has only been attained for one CEM position. Changing the CEM stage angle canlargely eliminate horizontal motion, but small horizontal walk and vertical displacements may becorrected by changing the FM angular adjust knobs and compensating with the CEM position.
The process of retroreflecting the beam and checking for walk must be repeated until perfect.
Once the CEM and FM have been positioned, the cavity has been aligned and the pumplaser beam path must be defined. The alignment beam’s reflection off the DBS can be centered on
IIa and IIb by adjusting the DBS and ISM. The ISM is readily adjusted to center the beam on IIa.
At this point, the beam should be close to centered on IIb. Viewing the closer iris is difficult andbest done by peering into the bulky ISM mount and looking at the inner surface of IIb in thereflection off the ISM. Horizontal DBS adjustment is performed by slightly loosening the bolts

198
attaching its mount to the base plate and using a screwdriver to pry this mount and angle it.
Vertically adjust the DBS by firmly placing a finger on the top of the optic, which is only held by
its base, and gently pressing it forward or back. After iterating the DBS and ISM adjustments andperfecting the iris alignment, a weak krypton ion pump beam can be used to check the cavity
alignment. Center the pump beam on the input irises and verify that the remnant of the pumpbeam that exits the FCL output follows the incoming alignment beam. Note the retroreflected
pump beam may not be perfectly aligned with its incoming path, which may require slightadjustments to the ISM to obtain. This slight fudging of the beam path is necessary because theclose (14 cm) spacing of the input irises is not sufficient to perfectly define the incoming beampath. However, translation of the CEM should not produce significant walk of the reflected beam,compared to the change in the beam divergence. Additionally, motion of the CEM should be
sufficient to change the retroreflected beam from somewhat diverging (at the closest crystal
distance), to collimated, to diverging again as the CEM is translated.
Following these adjustments, the cavity is ready to receive the crystal, and lasing
attempted. However, one more adjustment may be needed – perfecting the FM to crystal spacing,which centers the waist of the stable cavity in the gain medium. Unfortunately, this can only be
optimized via the long process of inserting the crystal, pumping down and cooling the chamber,
testing the laser performance, then warming up the Dewar, removing the crystal, translating the
FM in its threaded mount, re-perfecting the alignment (all of the preceding paragraphs in thissubsection), and going through the whole process again. I found that the laser output
characteristics (particularly threshold) changes with as little as 1/8th of a turn of the FM in its
mount. It is critical to follow the proper crystal handling procedures described in Sect. 2.2(A),particularly not exposing the warm crystal to white light and never letting the cold crystal
condense moist air. If properly aligned and using a good KCl crystal, with the 10% output
coupler, the FCL should have a threshold of about 0.5 W 647 nm pump power and output morethan 10 mW at 2.0 W pump power. (Note: it is important to be aware of possible “rollover” when

199
pumping the laser at high power, during which the gain medium heats to the point where its
output power fails to increase as expected, or even decreases with higher pump power. The
rollover power for the KCl crystal occurs above 2.0 W and above 1.0 W for the RbCl crystal.)
Other characteristics of a well-aligned, functional cavity are the beam waist (ω0 = 0.63 mm 1/eelectric field radius) and divergence (z0 = 48 cm) on the output grating, as inferred frommeasurements further downstream. In fact, using a fresh crystal, multi-mode powers of more than
20 mW may be obtained with pump power of 2.0 W of 647 nm light. The methods and equipment
for making more color center crystals are described by Mollenauer.2 The difficulties in handlingand producing the gain media are the primary handicap with this IR source. Although thisrealignment has been an unfortunate diversion from my graduate studies, it has been a valuable
learning experience as I have become fearless with respect to aligning complex optical systems.

200

Appendix B: Ion Imaging Apparatus
A great deal of effort has gone into the design and construction of a new experimental
apparatus for studying reactive scattering dynamics. Specifically, a velocity mapped ion imaging(VMII) apparatus, based on the experimental innovations of Houston,3 Parker,4 Suits,5
Kitsopolous,6 Liu,7 and others, has been designed to enable crossed molecular jet studies to be
performed. The implementation of this new experimental technique was motivated by the uniqueresults obtained in the F + HCl reactive scattering dynamics, described in detail in Ch. III. The
VMII technique’s strength lies in measuring the angular distribution of products and the state ofspectroscopically ionizable species, such as Cl atoms. The details of this experimental apparatus
are presented in this section.
The key features of the experimental apparatus are schematically presented in Fig. A.2.
The frequency doubled output of an yttrium aluminum garnet (YAG) laser pumps a dye laser,which is frequency tripled to provide tunable UV pulses with about 10 ns duration. A prism filter
separates the tripled light, at about 235 nm, from the lower harmonics. About 1 mJ of light at thiswavelength, focused via a 50 cm calcium fluoride lens, passes into the vacuum chamber. The
resulting intense UV field enables resonantly enhanced multiphoton ionization (REMPI) of
atomic and molecular species. The main advantage of REMPI is that ionization of chemical
species occurs state selectively, when the UV photon energy is one half of an electronically
excited state of the neutral. These excited states are readily ionized, so the two-photon transition
limits the detection process, which scales with the square of the laser intensity. In contrast,
analogous non-resonant multi photon ionization would not be state selective, and signal scaleswith intensity to the third power.
Once the ions have been created, they accelerate toward a position sensitive detector, in
this case a microchannel plate (MCP) with phosphorescent output. Chandler and Houston
pioneered this ion imaging technique.3 Eppink and Parker4 introduced the velocity map

201

Figure A.2

Schematic of the ion imaging apparatus. Skimmed molecular beams intersect in adifferentially pumped vacuum chamber at a 90° angle. Resonantly enhanced
multiphoton ionization (REMPI) detection of collision products is achieved via
intense tunable UV laser pulses, generated from third harmonic generation(THG) of a yttrium aluminum garnet (YAG) pumped dye laser. Ions are detected
on a spatially sensitive microchannel plate (MCP) detector with phosphorescentoptical output coupling. Accelerating electrode geometries produce velocity map
ion imaging conditions, such that the location at which ions are detected on the
MCP directly correlate to the product’s velocity projection in the plane of thedetector. A charge coupled device (CCD) yields spatially resolved detection, anda PMT provides time domain measurements. HV pulsing of the MCP enablesprecise time of flight selection of ions, and a TTL pulse delay generator
synchronizes the experimental timing and data acquisition.

202
improvement, which enables higher resolution using ion optics (and not just flat electrodes) toremove most blurring introduced by the spatial distribution of the ions prior to acceleration,
providing higher resolution velocity measurements.
The high gain provided by the MCP detector enables individual ion detection events to berecorded by the charge coupled device (CCD) camera focused on the phosphor screen. Selective
detection of the ion of interest results from the time of flight (TOF) spectrum of the accelerated
ions. A fast (τ = 60 ns) phosphor decay disperses the mass spectrum in real time, which can bemonitored using a photomultiplier tube (PMT) directed at the MCP output. A high voltage (HV)
pulser switches the MCP bias from about 2 kV (high gain ≈ 107) to 1.5 kV (low gain ≈ 105), suchthat time of flight selection images only the species of interest. Additional experimental
resolution enhancement results from “centroiding” individual ion detection events, i.e., analyzing
the photon distribution on the CCD from a single event and finding the “center of intensity”, andassigning the detection event to that location.
The details of the crossed jet apparatus are as follows. A 3.5 inch inner diameter tube
forms the differentially pumped chamber and ion flight tube, in the center of a 55 L vacuum
chamber, pumped by a 1250 L/s turbo pump. Three skimmed Proch-Trickl8 valves are positioned
around the flight tube, one centered on and directed along the TOF axis, and two others at 90° tothis axis and each other. At the top of the flight tube, a gate valve opens to expose the MCP toions and differentially pump the inner region of the flight tube via two 250 L/s turbo pumps. The
focus of the UV laser lies at the intersection of the three molecular beams, and the UV laser axis
is oriented at 45° and 135° to the two non-axial beams.
The intersection of the molecular beams and laser defines the region where ions are
created. This location is centered between the first two ion optics electrodes, separated from the
MCP detector by a 55.4 cm ion flight distance. The electrodes are a series of 1/16th inch thickstainless steel disks with a 2.75 inch diameter. Each disk has a central hole with diameter d for the203passage of ions and bending of electric field lines to create the ion lenses. Table A.1 summarizes
the spacing between the electrodes, and the electrode disk hole diameters. The VMII and TOF
conditions have been modeled using the Simion electrostatic modeling package (version 7.0), theresults of which are summarized in Fig. A.3. Velocity mapping conditions are demonstrated inFig. A.3(a), where the trajectories of several 1 eV Cl + ions are presented. The ions begin at threelocations along the laser axis, and with initial velocities oriented in 45° increments away from the
TOF axis. Varying the ratio of voltages between the repeller plate and first ion lens changes thelens’ focal distance. Thus, ions created at different locations, but with the same initial velocity
component parallel the detector plane are detected at the same position on the MCP. Distances in
the image plane are directly proportional to this same velocity component, giving rise to the term
“velocity mapping.” The insensitivity to spatial origin when measuring velocities is what is meant
by VMII conditions.
An intuitive picture of the ion lens behavior can be gained by considering the surfaces
defined by the curved potential lines illustrated in Fig. A.3(b). Since the electrostatic forces bend
the ion velocities toward the surface normal, i.e., toward the field gradient, equipotential surfaces
play a role analogous to interfaces between regions with different indices of refraction in ray
optics – they bend diverging rays and enable the possibility of focusing optics.
Elementary electrodynamical considerations can be used to anticipate scaling of the
VMII conditions with respect to ion mass. Specifically, the local trajectory taken by an ion with agiven velocity vector can be described by the radius of curvature (rn) caused by the velocity
component normal to the local force (vn), according to
rn = vn2/a,(A.1)

where a is the acceleration caused by the applied force. In this case, the acceleration is simply
q|E|/m, where q is the ion’s charge, |E| is the magnitude of the electric field, and m is the ion

204

Table A.1 Geometry of the ion optics electrodes used in the ion imaging device.
Electrode H (mm)a
Repellerc 0.0
Lens 1
13.4
Lens 2
31.8
Lens 360.2

d (mm)b0 , 2.0 , 4.0
12.0
24.0
30.0

a

Height of electrode above the bottom, repeller plate.
Diameter of the central aperture in each lens.
cRepeller plate also acts as collimator for the on-axis molecular beam, necessitating several
interchangeable electrodes to match beam dimensions.
b

a)

b)

Figure A.3a) Simulated ion trajectories illustrating the velocity map ion imaging techniquein the experimentally used, cylindrically symmetric flight tube geometry. As
shown in the inset magnifications, 1 eV Cl + ions with initial velocities
progressively angled by 45° in the plane of the trajectory diagram. Initial ion
positions are displaced by 1 mm from each other perpendicular to the flight tube.
The velocity mapping conditions illustrated result in ions landing on the detector
at nearly the same location if they have the same velocity projection, regardlessof the start location. b) Equipotential lines between the accelerating electrodes.
Curved field lines in the vicinity of the central holes in the electrodes bend the
trajectories and act as ion lenses.

205
mass. Thus, the local radius of curvature becomesrn = mvn2/ q|E|.

(A.2)

The numerator in this equation is proportional to the ion’s kinetic energy, T, and otherwise only
depends upon the direction of the initial velocity vector in the constant E filed. Thus, ions formedat the same position and with parallel velocity vectors will follow the same three-dimensional
path through the electric field if they also have the same kinetic energy. Note that this result iscompletely general, and applies to ions in electrostatic fields. The additional advantage of VMII
is that, to a very good approximation, the end point of the trajectories is also independent of
position in the vicinity of the region the ion lenses are mapping onto the detector plane. Thus,
ions with mass m and velocity components (vx, vy, vz) striking a given detector position all havethe same √(mvx2 + mvy2), where the z-axis is the direction perpendicular to the detector axis.
Under most conditions only a single mass is selected and so this conditions produces a map of theions’ velocities projected onto the xy plane.
Careful inspection of Fig. A.3(a) reveals that VMII cannot distinguish between velocities
with the same vector component in the plane of the detector, but different absolute velocities.
Traditionally, this problem was resolved by studying systems with an axis of cylindricalsymmetry parallel to plane of the detector, such that the two dimensional information recorded inx, z directions could be converted to cylindrical polar coordinates (r, z) via the inverse Abeltransformation or similar mathematical methods.9 The two non-axial molecular beams in Fig. A.2
produce a relative velocity vector in the plane of the jets, satisfying such a condition. However,new VMII experimental techniques have made such symmetry considerations and datatransformation unnecessary. By turning on the MCP HV pulse for a very short time period (≈ 10ns) compared to the spread of ion velocities perpendicular to the detector (≈ 200–400 ns) one canselect the ion velocities along the TOF axis. Such “slicing” of the velocity map was first
implemented by the Suits and Kitsopoulos groups.5,6 For optimal slicing resolution, it is therefore

206
useful to maximize the spread of the ions along the TOF axis, which can be practically expanded
to several hundred nanoseconds by lowering the electric field strength between the repeller andfirst ion lens. Thus, 5–10% of the ion cloud can be sliced, avoiding the need for inverse Abeltransformation. Changing the lens voltage necessarily alters the ion focusing conditions, requiring
the use of a second lens to restore VMII conditions. For this reason, the current design was builtwith a second variable electrode (lens 2) in addition to the final, grounded one (lens 3).
Following the construction of such a complicated device as the VMII apparatus, eachcomponent was carefully characterized. In particular, many of the components shown in Fig. A.2
detect individual particles, such as photons on the PMT and CCD camera, and ion, electron, or
photon events on the MCP. These devices are characterized by measuring the gain G (orcalibration on the CCD analog to digital conversion) to verify proper functioning. Suchcalibration is performed by measuring two independent quantities that are related to G, i) the
device output and ii) the noise on the output. Mathematically, the device output signal S when N
events are detected is given by
S = GN.

(2.23)

Under the same shot noise limited conditions, repeat measurements of S result in a standard
deviation σS according to

σS = G√N.

(2.24)

Thus, when both signal and noise are measured under shot noise limited conditions, a plot of σS2versus S will yield a linear plot with a slope of G. Such calibrations result in the following. The
Lavision FlowMaster 3S CCD camera has a calibration of 2.15 photoelectrons (e-) per analog todigital unit (ADU), very close to the factory specified 2 e-/ADU. Similarly, the Burle PS33189
MCP detector with 2.0 kV bias and 5.0 kV phosphor potential exhibits 29 ADU/event whencalibrated with the CCD camera. The MCP gain increases with the applied bias according to an
exponential curve with 120 V characteristic voltage. Finally, the electron tubes 9924QB PMT

207gain was also calibrated, and fitted to the form G = Ae-V/V’ with A = 4500, and characteristic
voltage V’ = 143 V.
The ultimate velocity resolution of the VMII experiment may be limited by several
different factors. The translational temperature of the jet determines the spread of the unionizedspecies velocities parallel the jet direction, and for a helium carrier gas with a v/Δv ≈ 3, thelimiting resolution is about 300 m/s. However, perpendicular to the jet axis, the skimmer
geometry determines the velocity resolution, and for the on-axis valve, velocity spreads as small
as 10 m/s may be obtained. This value is sufficiently low that the recoil kinematics of theionization event also become significant. For Cl atoms ionized by three photons at 235 nm, theelectron recoils from the Cl with 2.8 eV excess energy, imparting a kick of 16 m/s to the Cl + ion.
In the limit that the electron recoils isotropically, this recoil produces an effective blurring of the
Cl atom’s initial velocity.
The REMPI spectral resolution has also been measured in two ways. Firstly, a jet of Cl or
HCl is introduced to the chamber, and the laser is scanned through a transition. The measured≈ 0.5 cm-1 linewidth exceeds the 0.04 cm-1 expected from Doppler broadening and the 0.1 cm-1
laser linewidth. This measurement is confirmed by imaging Cl2 photolysis with the doubled 353
nm dye laser light. This process produces Cl atoms with 1660 m/s laboratory-frame velocities,
and resulting in atoms with a maximum 0.47 cm-1 Doppler shift. At line center, the edges of theimage have about ½ the center’s intensity, again revealing a homogeneous width of about 0.5
cm-1. These measurements indicate that power broadening dominates, and the time a Cl atom
spends in the upper state is about 60 ps before a third photon ionizes it. This observation makes
sense, as the REMPI process is limited by the two-photon transition, and the final ionization step
strongly saturated.
The detection efficiency has also been calibrated by measuring the number of ionsgenerated with a known gas density in the ionization region. Bleeding gas into the source

208chamber produces a constant density of molecules in the ionization region, and the absolutedensity can be measured directly on ion gauges in the source chamber and the detector chamber.
However, neither of these gauges directly measures the pressure in the ionization region of theflight tube, which can only be inferred via conductance measurements of the intervening vacuum
components. Such measurements are performed by measuring the throughput between the sourceand differentially pumped vacuum regions via ion gauge readings as a function of gas bleed.
Removing a single element (e.g., the ion lens stack) changes the conductance between the two
measured regions and provides a relative measure of that element’s conductance. Absolute
conductance values can be obtained via a region with known throughput, for example thespecified pumping speed of the detection region’s turbo pumps. Conductances measured this way
agree to within a factor of three to the infinitely thin “effusive source” expectation. More
importantly, the relative conductance provides an accurate measure of the pressure drop between
regions, and the ionization region has been calibrated to have 6% of the gas density produced by
the bleed in the source chamber, which is measured directly. Thus, the absolute density ofmolecules in the ionization region can be known.
Next, the volume in which the UV laser ionizes 100% of the REMPI active species, i.e.,
the effective ionization volume can be inferred and calculated. Estimates of this volume can bemade from first principles considerations. For a Gaussian laser beam with 2.5 mm 1/e electricfield radius (ω), a 45 cm focal length lens (measured at 235 nm) produces a waist with ω0 = 24
μm. If the laser saturates the two-photon transition at the beam waist, the effective ionization
region can be calculated as 5.4×10-7 cm3, or about 20% of the focal volume, 2πω02z0, where z0 is
the confocal beam parameter. This estimate anticipates about 14 ions being produced per pulse
with an HCl density of 2.5×107 #/cm3 of HCl(J = 0) in the ionization region, very close to the 10–
20 ions observed with about 1.3 mJ pulse energy.

209
After completing construction and calibration of the VMII apparatus, we attempted to
study the reaction F + HCl via velocity map imaging the product Cl atoms. Unfortunately,
unanticipated background from the photo fragmentation/ionization process,HCl + 3hν → Cl + + H,

(A.3)

which occurs resonantly with the Cl transitions, swamps the signal. Indeed, a jet of 10% HCl in
He should produce about ten Cl + ions per shot under favorable reaction and detection conditions.
However, these ten ions are outnumbered by the 30–1200 ions per shot produced from theprocess in Eq. 2.25, as shown in background the spectrum presented in Fig. A.4. Consequently,
any measured reaction dynamics would be masked by background at least three times higher than
the anticipated signal. Subtracting the background with only the HCl jet present from thereactively produced “signal” with both reactants was attempted, but did not reveal any
meaningful structure within uncertainty. Thus, this project has been sidelined while seeking
methods to surmount this hurdle. Despite such difficulties, VMII presents a powerful newtechnique for the study of state resolved reaction dynamics, and one on which we anticipate
fruitful results in the areas of photolysis and collision dynamics in the near future.

Ions/Pulse at m/q = 35210

Cl lines
Cl* lines

1000
800
600
400
200
0

41800 42000 42200 42400 42600 42800

ν (cm-1)

Figure A.4

Background ion spectrum of the 10% HCl jet in He, resulting in ions with mass
to charge ratio equal to 35. Measurements have been made at frequencies
corresponding to resonant ionization of ground state Cl (solid lines) and spin
orbit excited Cl* (2P1/2) (dashed lines).

211

Appendix C: F + HCl Quasi-classical Trajectory Simulations
We have performed a QCT study of the reaction F + HCl → HF + Cl using the DHSN
surface and a fourth-order Runge-Kutta integration method.10 Varying the time step for numericalintegration produces a very rapid change in the energy conservation, found to scale withapproximately the 5th power of the step size, as shown in Fig. A.5. Yet, the computational costscales inversely with the step size, as shown in Fig. A.6, such that the choice of integration
parameters is a compromise between accuracy and computer cost. Reasonable accuracy is readily
obtained by choosing a time step of 5 atomic units = 0.12 fs, which conserves energy to better
than 0.03 and 0.0002 kcal/mol for reactive and non-reactive events, respectively, for typical 1–2
ps trajectories which require about 10 seconds of CPU time. Such fast calculations enable many
thousand trajectories to be run for various starting conditions in order to obtain reasonablestatistics.
Trajectories were started in the entrance channel with an initial distance of ≈ 10 Å
between the F atom and the HCl center of mass, and stopped when the F–Cl distance again
exceeded 10 Å. At this distance, the potential energy between the reactants/products is less than
0.001 kcal/mol and completely negligible. 4–10 kcal/mol collision energies were utilized in order
to simulate experimental conditions. Impact parameters of 0–4 Å were explored, though theprobability for reaction approached zero above 2 Å. The HCl reactant’s zero point energy was
explicitly included by beginning the trajectory with the H–Cl distance stretched to the zero pointlevel’s outer classical turning point. In order to randomly sample the phase of the HCl vibration
during the collision, the F–HCl distance was varied by 1 Å. The relative orientation of the
products was also randomly sampled.

log(ΔE /kcal/mol)

212

0
-2

m≈5.0

-4

m≈5.2

-6
-8

reactive
non-reactive

-10
-12
-0.5

0.0

0.5

1.0

1.5

log(time step /atomic units)log(cpu time /s)

Figure A.5

The scaling of energy conservation (ΔE) versus the size of the integration time
step used for QCT calculations. Very rapid scaling (t5) is anticipated from the 4thorder Runge-Kutta integration method.

2m≈-1.0
1

0
-0.5

0.0

0.5

1.0

1.5

log(time step /atomic units)
Figure A.6

Simple reciprocal scaling of the CPU time required to compute a single QCT
trajectory as a function of the integration step size.

213
The calculated of reaction cross sections σ shown in Fig. A.7 are 2–3 orders ofmagnitude smaller than anticipated from experiment at all collision energies studied. Modest
increases in reaction probability are obtained for higher collision energies and for rotationallyexcited HCl, as noted by Hayes and Sun.11,12 Significantly, the reaction cross section remains
negligible at the experimental collision energy, which is above the classical barrier to reaction.
The low probability for reaction is discussed in more detail, below.
Following each reactive trajectory, the HF product is calculated using quasi-classicalapproximation. The results of many such calculations are histogrammed and representative resultsfrom 50,000 trajectories starting in the F + HCl channel at Ecom = 7 kcal/mol and JHCl = 2 areplotted in Fig. A.8. Although collision energy and HCl rotation enhance reaction probability, thequalitative aspects of the HF product quantum-state distributions for reactive events prove
relatively insensitive to collision conditions. Specifically, for all initial conditions studied,product HF forms exclusively in the v = 3 and v = 2 manifolds, with high energy rotational states
primarily correlating with v = 2, as anticipated from conservation of energy. The results are
qualitatively similar to those reported by Sayos et al.,13 who also found only rotationally excited
HF in v = 2. Sayos et al.’s results are less vibrationally excited than the present DHSN
calculations, but were performed on the SHHG PES, which has an empirically lowered barrierthat enabled study at lower collision energies. Nevertheless, trajectories on both surfaces predicthigh vibrational excitation and, more specifically, only high rotational excitation in v = 2. Thus,
full trajectory QCT methods do not qualitatively reproduce the observed HF state distributions.
Very recent wave packet calculations on the DHSN surface have been performed at substantiallylower energy than used in the present study, also resulting in branching primarily into high J in v
= 2.14 Thus, the DHSN surface reproduces the propensity for high J HF(v = 2) and lower J HF(v =3) products first observed on older surfaces.

σrxn (Å2)

214

JHCl=1
JHCl=2
JHCl=5

0.002

0.001

0.000
0

2

4

6

8

10

Ecom (kcal/mol)Figure A.7

Theoretical F + HCl reaction cross section from QCT calculations on the DHSN
surface for reaction with HCl in the rotational states indicated. Reaction events
are not observed until the center of mass collision energy well exceeds the 4
kcal/mol barrier. Modest rotational enhancement is evident, though computed
cross sections remain nearly 1000 times smaller than experimentally determined.

v=3

0.10

Fractional Population

0.05

0.00

v=2

0.10

0.05

0.00
0

2

4

6

8

10

12

14

16

J
Figure A.8

HF product state distribution for QCT scattering calculations on the DHSN
potential energy surface. Initial conditions are Ecom = 7 kcal/mol, JHCl = 2. These
results were obtained following 50,000 scattering trajectories.

215
In order to test the validity of the full collision calculations, a second set of trajectories
has been performed, starting simply in the transition state (TS) region of the DHSN surface withtotal energy 0.2 kcal/mol above the classical barrier. Although these TS calculations have notbeen chosen to reflect accurately a distribution of reactive trajectories, they should represent thetype of distributions obtained for reactive trajectories that surmount the classical barrier. As
shown in Fig. A.9, trajectories starting near the transition state and proceeding to the HF + Cl
channel exhibit similar features as the full trajectory results, i.e., population forms exclusively inhighly vibrationally excited states (v = 2 in this case), and high J state rotational excitation isfavored. Thus, the full trajectory results are indicative of the qualitative features of general
trajectories traversing the transition state.
We have also used QCT methods to explore briefly the possible influence of deep van der
Waals well in the HF + Cl exit channel. These trajectories are motivated by the wealth ofvibrational predissociation studies of van der Waals complexes, as well as the possibility of longlived resonance states that explore portions of the exit well not extensively visited by classicalreaction path. Exit-well trajectories are started in the vicinity of the HF–Cl van der Waals
minimum, in an initial distribution of HF rovibrational states obtained from full trajectory
calculations shown in Fig. A.8 and with zero kinetic energy in the HF–Cl coordinate. The starting
position is chosen to be within 0.5 kcal/mol of the bottom of the van der Waals minimum, and thetotal energy varies by this amount. In essence, these conditions mimic what might be expected if
nascent reactive products were to become trapped in the HF–Cl van der Waals well following
reaction. The trajectories with non-rotating but vibrationally excited HF were nondissociative on
the time scales explored; roughly corresponding to vibrational predissociation, which is known to
be exquisitely sensitive to the hard inner wall of the PES and poorly modeled by QCT.15
However, the dissociation probability of the HF–Cl complex does rise rapidly with HF rotation,in effect rotationally predissociating to yield HF with reduced internal energy. The results shownFractional Population

216

v=2
0.4

0.2

0.0
0

2

4

6

8

10

12

14

16

J
Figure A.9

HF distribution for trajectories started in the transition state region. Total energy
is constrained to exceed the classical barrier by 0.2 kcal/mol and initial kinetic
energy is randomly distributed. All reactive trajectories correspond to populationin the v = 2 manifold.

217
in Fig. A.10 reveal that product HF fragments retain most of their vibrational energy while being“cooled” into lower angular momentum states. Such relaxation suggests the Van der Waals exit
well may play a significant role in the formation of the low J HF observed experimentally andmay even contribute to HF population in lower vibrational manifolds. Indeed, previous studies ofexit-channel dynamics by Orr-Ewing and coworkers in reactive trajectories found thatrotationally cold products with strong dipole moments can torque on recoiling fragments andthereby rotationally “heat up” in the exit channel.16 It would seem equally dynamically plausible
in the F + HCl system for highly rotationally excited HF to be “cooled” by angular forces in thevan der Waals exit channel, which would be an interesting direction for further theoretical
exploration.

218

v=3

0.10

0.05

Fractional Population

0.00

v=2

0.10

0.05

0.00

v=1

0.10

0.05

0.00
0

2

4

6

8

10

12

14

16

J
Figure A.10

Quantum state distribution obtained by starting trajectories in the HF–Cl van der
Waals well. Initial HF rovibrational energy distribution is that plotted in A.8, andinitial HF–Cl kinetic energy is fixed at zero.

219

Appendix D: Surprisal Analysis of HF State Distributions Produced By F + H2O
The surprisal analysis works as follows. The “prior” distribution Pprior is defined as theone with maximum entropy, the case where all states (described by the rotational, vibrational, andtranslational states of the products) that are energetically accessible are equally likely to be
populated. Thus, the prior distribution is related to the degeneracy g(N) of each level N,
according to
Pprior(N) = g(N)/ΣNg(N),(A.4)

for N such that the energy of state N is less than the total energy. From information theory, thesurprisal17,18 I(N) is generated by comparing the calculated Pprior (N) to the observed distribution,
Pobs(N), via
I(N) = -ln[Pobs(N)/ Pprior(N)].

(A.5)

A linear plot of I(N) versus a quantity fN indicates a “constraint” on the quantity fN over the courseof reaction. Likely constraints are energy E(N) or the HF angular momentum JHF. The nearlycollinear surprisal plot in Fig. A.11 reveals that vibrational branching matches a simple oneparameter surprisal model that is nearly the same at all studied energies.
Unlike the vibrational populations, statistical analysis fails to even qualitatively describe
the measured rotational distributions. Surprisal analyses of the v = 1 rotational distributions arepresented in Fig. A.12, using JHF and E(N) as fN, defined in the discussion of Eq. A.5. These plots
are constructed by summing over the unseen parameters in the state indicator N, such as the OH
rovibrational quanta. Neither of the plots in Fig. A.12 is linear over the entire range of HF
rotational states probed, and recently proposed modified surprisal analyses21 result in similarly
non-linear trends. Thus, simple statistical considerations are not sufficient to explain the observed
rotational distributions, even if they do match the vibrational trends in Fig. A.11 reasonably well.
Since no physical mechanism has been proposed to predict the slope of such surprisal plots fromfirst principles, even in when observed trends exhibit linear surprisals, they shed little insight.

Vibrational Surprisal

220

IR chemiluminescencepresent study
direct dynamics

1
0
-1
-2
-3
-4
0.0

0.2

0.4

0.6

0.8

1.0

E(v) / ETotal
Figure A.11

Surprisal analysis of HF vibrational partitioning observed in the present F + H2O
study, inferred from comparison to F + D2O chemiluminescence in Ref. 19, andcomputed in the theoretical study in Ref. 20.

221

a)

-ln(Pobs/Pprior)

1
0
-1
-2
-3

0.5

0.6

0.7

0.8

0.9

E(v,J) / Etotb)-ln(Pobs/Pprior)

1
0
-1
-2
-3
0

2

4

6

8

10

12

JHF
Figure A.12

Surprisal plots of the vHF = 1 rotational distribution, plotted as a function of (a)fractional energy deposited in the HF product, and (b) HF angular momentum
quantum number , JHF.

222

Appendix E: Estimated State Resolved Branching Ratios
The precise HF branching ratios are obtained following the density-to-flux conversion,and performed via Monte Carlo modeling of the crossed jet conditions, as described in detail in
Chapter 2.4(B) This model produces the average residence time, 〈τ〉, for product HF in each (v,J)
state, which varies with the assumed differential scattering distribution. The calculated 〈τ〉 valuesfor HF formed in the reaction F + HCl are presented in Fig. A.13(a) and Table A.2 for several
differential scattering cross section limits. Defining θ as the angle between the F and HF
velocities in the center of mass frame, the limiting cases considered here are defined as follows:
isotropic (-1 ≤ cos(θ) ≤ 1), forward (0.33 ≤ cos(θ) ≤ 1), side (-0.33 ≤ cos(θ) ≤ 0.33), andbackward (-1 ≤ cos(θ) ≤ -0.33). Although 〈τ〉 varies by a factor of 0.57–1.7, depending on theunknown differential scattering limit, angular measurements on similar reactions have not foundthis quantity to vary rapidly between adjacent product rotational states.22 Essentially, the reactions
tend to proceed through one or more mechanisms that do not turn on and off abruptly between
product states, such that the entire HF population distribution may be obtained using one
universal differential cross section assumption.
The density-to-flux analysis has been performed for each of the angular scattering limits
presented in Table A.2, resulting in the normalized fluxes in Fig. A.14. This presentation reveals
that the uncertainty in the branching ratio introduced by the assumed differential cross section issmaller than the experimental uncertainty in the measured HF densities, at least to the extent thatthe differential cross section (dσ/dΩ) does not vary with HF state. This insensitivity largely arises
from the similar shape of the curves in Fig. A.13 and is explained by substantial blurring of theangular resolution of the experiment caused by spatial averaging within the unskimmed jets.
Therefore the exact choice of scattering limit is arbitrary, and for the analysis that follows, theisotropic limit has been used, as presented in Fig. A.14 and Table 3.1.

223

a)

Isotropic
Backward
Side
Forward

40

20

-10

ln(〈τ〉 /s)〈τ〉 (μs)60b)m=-1/2-11

Isotropic
Backward
Side
Forward

-12

-13

0
0

10

20

〈Eavail〉 (kcal/mol)Figure A.13

30

-2

-1

0

1

2

3

ln( 〈Eavail〉 /kcal/mol )a) Calculated HF residence times from Monte Carlo simulation of the F + HClcrossed jet experiment. Computed values are shown for four limiting cases ofdifferential scattering cross section, as discussed in the text. b) Log-log plot of
the same data. For sufficiently high recoil energy, 〈τ〉 scales with available
energy (Eavail) to the -½ power, i.e., with the inverse of the recoil speed.

224

Table A.2 HF(v,J) state resolved residence times in the probe region following the reaction F +HCl → HF + Cl, as calculated via Monte Carlo simulation of the crossed jet conditions. The
crossed jet conditions are as described in Ch. III. Average residence times are presented for theisotropic differential cross section limit〈τi〉. Ratio of residence times to this value are also
provided for the other three differential scattering limits, backward scattering 〈τb〉, side scattering〈τs〉, and forward scattering 〈τf〉, as defined in the text.
v
0

J
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1 0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16

〈τi〉(μs) 〈τb〉/〈τi〉 〈τs〉/〈τi〉 〈τf〉/〈τi〉
5.89
5.91
5.90
5.93
5.93
6.01
6.01
6.17
6.21
6.33
6.45
6.59
6.73
6.85
7.14
7.00
7.00
7.01
7.10
7.16
7.29
7.33
7.44
7.94
7.81
7.94
8.20
8.55
8.94
9.36
9.91
10.62

0.57
0.57
0.57
0.57
0.57
0.57
0.58
0.57
0.57
0.57
0.57
0.57
0.57
0.58
0.57
0.57
0.57
0.57
0.57
0.58
0.57
0.58
0.58
0.55
0.58
0.58
0.58
0.58
0.58
0.58
0.59
0.59

1.57
1.56
1.57
1.56
1.58
1.58
1.58
1.57
1.58
1.57
1.57
1.57
1.57
1.59
1.57
1.58
1.58
1.59
1.57
1.59
1.57
1.58
1.58
1.51
1.57
1.59
1.60
1.59
1.58
1.58
1.59
1.61

0.59
0.59
0.60
0.59
0.60
0.59
0.60
0.59
0.59
0.60
0.60
0.59
0.59
0.60
0.59
0.59
0.60
0.59
0.60
0.59
0.59
0.59
0.59
0.57
0.59
0.60
0.59
0.59
0.59
0.59
0.59
0.59

J 〈τi〉 (μs) 〈τb〉/〈τi〉 〈τs〉/〈τi〉 〈τf〉/〈τi〉
0
9.12
0.59
1.59
0.59
1
9.16
0.58
1.58
0.59
2
9.25
0.58
1.57
0.59
3
9.36
0.58
1.58
0.59
4
9.49
0.58
1.58
0.59
5
9.58
0.59
1.61
0.59
6
9.90
0.59
1.58
0.59
7
10.13
0.59
1.60
0.59
8
10.52
0.59
1.60
0.59
9
11.10
0.59
1.58
0.58
10 11.63
0.60
1.60
0.58
11 12.54
0.60
1.60
0.58
12 13.80
0.61
1.58
0.57
13 15.56
0.62
1.60
0.56
14 19.31
0.63
1.60
0.52
15 28.48
0.59
1.66
0.46
3 0
16.85
0.62
1.60
0.55
1
16.93
0.63
1.60
0.55
2
17.60
0.63
1.61
0.54
3
18.32
0.64
1.62
0.54
4
20.23
0.63
1.60
0.52
5
22.50
0.64
1.62
0.50
6
26.64
0.62
1.73
0.48
7
31.90
0.63
1.65
0.47
8
32.21
0.59
1.68
0.58
9
30.78
0.65
1.56
0.73
10 36.48
0.54
1.37
0.73
11 43.18
0.53
1.21
0.75
12 45.55
0.57
1.26
0.83

V
2

225

v=3

0.03

0.00

v=2
0.03

Normalized Flux

0.00

v=1
0.03

0.00

v=0

Isotropic
Backward
Side
Forward

0.06

0.03

0.00
0

2

4

6

8

10

12

14

16

J
Figure A.14

Calculated HF state resolved flux following the reaction F + HCl → HF + Cl for
four limiting cases of reactive differential cross section. All data have beennormalized such that they sum to 1. The agreement shown here reveals the highconfidence in the present results, limited by the unknown state-dependent
differential cross sections.

226
It is important to note that the structured rotational distributions in Fig. 3.6 cannot beascribed to varying detection sensitivity. With the present scaling, the local maxima at low andhigh J in the v = 1 and v = 2 manifolds have comparable magnitudes. Thus, even if the dynamical
processes leading to these features are correlated with radically different differential crosssections, the detection sensitivity changes by at most a factor of about 2.7 between the largest andlowest 〈τ〉 values presented in Fig. A.13. Thus, for the most extreme case, any portion of theresults in Fig. A.14 cannot change by more than three-fold, which is insufficient to mask therelevant bimodal structure. Additionally, if such extreme differential scattering structure were
present, it would further support bifurcated dynamics in the F + HCl reaction event.
Similar Monte Carlo modeling of the F + H2O experiment provides the 〈τ〉 values foreach HF(v,J) state for that system. In order to model the F + H2O reaction kinematics, the recoil
energy, and thus the HF and OH internal states, must be specified. Although the OH state
distribution is not explicitly measured in the current experiment, it has been found to be a smallheat sink (with respect to the total energy),23,24 consistent with the spectator bond approximation.
Indeed, varying the energy deposited in the OH fragment between zero and 1 kcal/mol (theaverage rotational energy observed in the OH product in Ref. 23) changes the density-to-flux
results by a completely negligible amount.
The resulting residence times are presented in Table A.3, for limiting cases of thedifferential cross section (dσ/dΩ). Since dσ/dΩ as a function of HF state is unknown, it is notpossible to perform the transformation with 100% certainty. However, in the limit that all productstates are formed with similar angular scattering dependence – consistent with the monotonic
distribution of product states and measurements of dσ/dΩ on other reactive systems – the choiceof dσ/dΩ does not significantly alter the results. This insensitivity is exploited in Fig. A.15,
which presents the normalized flux for each limiting case of dσ/dΩ. In v = 0 and v = 1, each of

227

Table A.3 HF(v,J) state resolved residence times (μs) in the probe region following the reaction
F + H2O → HF + OH, as calculated via Monte Carlo simulation of the crossed jet conditions. The
crossed jet conditions are as described in Ch. IV. Data are organized as in Table A.2.
v J 〈τi〉(μs) 〈τb〉/〈τi〉 〈τs〉/〈τi〉 〈τf〉/〈τi〉
0 0
8.86
0.53
3.03
0.36
1
8.87
0.54
3.02
0.36
2
8.93
0.53
3.03
0.36
3
9.02
0.53
3.04
0.36
4
9.08
0.53
3.05
0.36
5
9.29
0.53
3.04
0.36
6
9.44
0.53
3.05
0.36
7
9.63
0.53
3.06
0.36
8
9.90
0.53
3.08
0.36
9 10.25
0.52
3.09
0.36
10 10.64
0.52
3.13
0.36
11 11.21
0.51
3.17
0.36
12 11.83
0.51
3.22
0.36
13 12.75
0.50
3.30
0.35
14 14.23
0.48
3.42
0.35
15 16.31
0.45
3.71
0.33
16 20.56
0.40
4.28
0.30
17 26.04
0.35
4.61
0.30
18 25.60
0.41
4.08
0.33

v J 〈τi〉 (μs) 〈τb〉/〈τi〉 〈τs〉/〈τi〉1 0 13.45
0.49
3.35
1 13.53
0.49
3.38
2 13.81
0.49
3.38
3 14.08
0.48
3.43
4 14.59
0.47
3.49
5 15.26
0.47
3.56
6 16.420.45
3.72
7 18.03
0.43
3.90
8 19.94
0.41
4.29
9 23.18
0.37
4.48
10 24.82
0.37
4.70
11 26.02
0.39
4.38
12 25.17
0.43
3.81
13 22.04
0.53
3.02
14 25.60
0.54
2.72
15 29.34
0.61
2.51
2 0 22.20
0.56
2.71
1 23.56
0.54
2.79
2 22.93
0.59
2.71
3 23.27
0.58
2.62
4 25.100.58
2.55
5 25.37
0.62
2.48
6 28.20
0.63
2.36
7 31.83
0.64
2.17〈τf〉/〈τi〉
0.35
0.35
0.35
0.34
0.34
0.34
0.33
0.33
0.30
0.30
0.30
0.31
0.36
0.46
0.49
0.56
0.48
0.48
0.47
0.51
0.52
0.73
0.59
0.67

228

v=2

0.03

0.00
0.15

v=1

Normalized Flux

0.12

Isotropic
Backward
Side
Forward

0.09

0.06

0.03

0.00

v=0
0.06

0.03

0.00
0

2

4

6

8

10

12

14

16

18

J
Figure A.15

Observed nascent HF(v,J) populations produced by the F + H2O reaction,
obtained from the measured densities via the density-to-flux transformation. Data
points, and dotted, solid, and dashed lines indicate the results from various
assumed differential cross section scattering limits used in the density-to-flux
conversion, as defined in the text.

229
these limiting cases results in rovibrational population distributions that agree well within thereported experimental error bars, and the v = 2 populations are only slightly shifted by the chosen
angular scattering limit. The F + H2O results are particularly insensitive to changes in dσ/dΩ
because of i) the large amount of spatial averaging in the unskimmed jet geometry, ii) the
relatively small reaction exoergicity, compared to reactions such as F + HCl,25 or F + CH4,26 andiii) the narrow distribution of HF states populated, primarily v = 1, J < 5. Thus, for the bulk of
Ch. IV, the results obtained assuming isotropic differential scattering have been discussed, aspresented in Table 4.2.
In the gas-phase studies in Ch. III and IV, Monte Carlo simulations of the recoil
dynamics enabled the density-to-flux transformation to be performed and state resolved branchingratios to be estimated. In Ch. V, the reaction at the gas-liquid interface may have similar statedependent sensitivities. However, complications arise at the liquid interface because the dynamics
of the highly exothermic reaction event and subsequent interactions at the liquid interface
completely determines the state-dependent HF velocities in the laboratory frame. Thus, any
prediction of recoil velocities necessitates detailed dynamical commutation of the gas-liquid
scattering event. However, the Doppler measurements do provide direct experimental information
about the HF recoil velocities. As discussed in more detail in the next Chapter 5.5, the HF
velocities are quite close to thermal, and only change slowly with quantum state. Although
Doppler measurements in the current experimental arrangement only reveal velocities parallel theliquid surface, a physically motivated cos(θ) angular distribution of HF velocities escaping thesurface can be used to infer residence times in the probe volume and compute the state resolved
HF flux. Fig. A.16 presents the normalized flux values, along with the normalized columnintegrated densities from Table 5.2. This presentation reveals that the fluxes and densities agreenearly quantitatively in the present study. Thus, any flux correction results in only a slightincrease of the fractional branching into v = 3 and v = 2, at the expense of the slowly moving

230

v=3

0.02
0.00

v=2

0.08

Normalized Density
Normalized Flux

0.06

Fractional Population

0.04
0.02
0.00

v=1

0.08
0.06
0.04
0.02
0.00

v=0

0.08
0.06
0.04
0.02
0.00
0

2

4

6

8

10

12

14

JHF
Figure A.16

Normalized HF densities and inferred fluxes following reactive scattering of F
from a liquid squalane surface.

231(nearly translationally equilibrated) molecules in v = 0 and v = 1. Since the effect of suchweighting does not change the populations within the experimental uncertainty, we have focused
our attention on interpreting the measured densities. This approximation is complicated by recent
theoretical work by Schatz and coworkers,27 revealing a propensity for recoiling HF to be directedalong the surface normal. However, the high F atom translational energy used in this theoretical
study (0.5, 1.0 eV) makes direct comparison to the present study difficult.

232

References for Appendices A–E
1

W. Koechner, (Springer, Berlin, 1999), pp. 232.

2

L. F. Mollenauer, Rev. Sci. Instrum. 49, 809 (1978).

3

D. W. Chandler and P. L. Houston, J. Chem. Phys. 87, 1445 (1987).

4

A. Eppink and D. H. Parker, Rev. Sci. Instrum. 68, 3477 (1997).

5

D. Townsend, M. P. Minitti, and A. G. Suits, Rev. Sci. Instrum. 74, 2530 (2003).

6

R. L. Toomes and T. N. Kitsopoulos, Phys. Chem. Chem. Phys. 5, 2481 (2003).

7

J. J. Lin, J. G. Zhou, W. C. Shiu, and K. P. Liu, Rev. Sci. Instrum. 74, 2495 (2003).

8

D. Proch and T. Trickl, Rev. Sci. Instrum. 60, 713 (1989).

9

V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73,
2634 (2002).

10

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in
C: the art of scientific computing, 2 ed. (Cambridge University Press, New York, 1992).

11

M. Y. Hayes, M. P. Deskevich, D. J. Nesbitt, K. Takahashi, and R. T. Skodje, J. Phys.
Chem. A 110, 436 (2006).

12

Z. G. Sun, S. Y. Lee, and D. H. Zhang, Chin. J. Chem. Phys. 20, 365 (2007).

13

R. Sayos, J. Hernando, R. Francia, and M. Gonzalez, Phys. Chem. Chem. Phys. 2, 523(2000).

14

G. Quemener and N. Balakrishnan, J. Chem. Phys. 128, (2008).

15

E. Tannenbaum, K. J. Higgins, W. Klemperer, B. Segev, and E. J. Heller, J. Phys. Chem.
B 106, 8100 (2002).

16

S. Rudic, C. Murray, J. N. Harvey, and A. J. Orr-Ewing, J. Chem. Phys. 120, 186 (2004).

17

R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical
Reactivity. (Oxford University Press, New York, 1987).

18

J. T. Muckerman, J. Phys. Chem. 93, 179 (1989).

19

M. A. Wickramaaratchi, D. W. Setser, H. Hildebrandt, B. Korbitzer, and H. Heydtmann,
Chem. Phys. 94, 109 (1985).

20

Y. Ishikawa, T. Nakajima, T. Yanai, and K. Hirao, Chem. Phys. Lett. 363, 458 (2002).

21

J. J. Valentini, J. Phys. Chem. A 106, 5745 (2002).

233
22

X. M. Yang and D. H. Zhang, Accounts Chem. Res. 41, 981 (2008).

23

M. Ziemkiewicz and D. J. Nesbitt, manuscript in preparation.

24

M. Ziemkiewicz, M. Wojcik, and D. J. Nesbitt, J. Chem. Phys. 123, 224307 (2005).

25

A. M. Zolot and D. J. Nesbitt, J. Chem. Phys. 127, 114319 (2007).

26

W. W. Harper, S. A. Nizkorodov, and D. J. Nesbitt, J. Chem. Phys. 113, 3670 (2000).

27

B. K. Radak, S. Yockel, D. Kim, and G. C. Schatz, J. Phys. Chem. A (in press) (2009).