Quantum state-resolved reactive scattering of F+CH4->HF(v,J)+CH3: Nascent HF(v,J) product state distributions

Article abstract of DOI:10.1063/1.1287398

State-to-state reactive scattering of F+CH4->HF(υ,J)+CH3 is studied using crossed supersonic jets and high-resolution (Δν ca. 0.0001 cm^-1) IR laser direct absorption techniques. Rovibrational state-resolved HF column-integrated absorption profiles are obtained under single collision conditions and converted to populations via appropriate density-to-flux transformation. Nascent rovibrational distributions in each HF(υ,J) state are reported. Summed over all product rotational levels, the nascent vibrational quantum state populations for HF(υ) [(υ=3) 0.106(3); (υ=2) 0.667(14); (υ=1) 0.189(27); (υ=0) 0.038(78); 2? error bars] are in agreement with previous flow cell studies by Setser, Heydtmann, and co-workers [Chem. Phys. 94, 109 (1985)]. At the rotational state level, however, the current studies indicate nascent distributions for HF(υ,J) that are significantly hotter than previously reported, ostensibly due to reduced collisional relaxation effects under supersonic jet conditions. Final HF rotational states from F+CH4 are observed near the maximum energetically accessible J values in both the υ=2 and υ=3 vibrational manifolds, which provides experimental support for a bent F-H-C transition state structure.

Full text of DOI:10.1063/1.1287398

Quantum state-resolved reactive scattering of F+CH 4 →HF (v,J)+ CH 3 : Nascent HF
v,J) product state distributions
(
Warren W. Harper, Sergey A. Nizkorodov, and David J. Nesbitt
Citation: The Journal of Chemical Physics 113, 3670 (2000); doi: 10.1063/1.1287398
View online: http://dx.doi.org/10.1063/1.1287398
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/113/9?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 113, NUMBER 9
1 SEPTEMBER 2000
Quantum state-resolved reactive scattering of F¿CH \HF„v,J…¿CH :
4
3
Nascent HF„v,J… product state distributions
Warren W. Harper, Sergey A. Nizkorodov, and David J. Nesbitt
JILA, National Institute of Standards and Technology and University of Colorado, and Department of
Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0440
͑
Received 12 April 2000; accepted 1 June 2000͒
State-to-state reactive scattering of FϩCH →HF(v,J)ϩCH is studied using crossed supersonic
4
3
Ϫ1
jets and high-resolution (⌬␯Ϸ0.0001 cm ) IR laser direct absorption techniques. Rovibrational
state-resolved HF column-integrated absorption profiles are obtained under single collision
conditions and converted to populations via appropriate density-to-flux transformation. Nascent
rovibrational distributions in each HF(v,J) state are reported. Summed over all product rotational
levels, the nascent vibrational quantum state populations for HF(v) ͓(vϭ3) 0.106(3); (v
ϭ2) 0.667(14); (vϭ1) 0.189(27); (vϭ0) 0.038(78); 2␴ error bars͔ are in agreement with
previous flow cell studies by Setser, Heydtmann, and co-workers ͓Chem. Phys. 94, 109 ͑1985͔͒. At
the rotational state level, however, the current studies indicate nascent distributions for HF(v,J)
that are significantly hotter than previously reported, ostensibly due to reduced collisional relaxation
effects under supersonic jet conditions. Final HF rotational states from FϩCH are observed near
4
the maximum energetically accessible J values in both the vϭ2 and vϭ3 vibrational manifolds,
which provides experimental support for a bent F–H–C transition state structure. © 2000
American Institute of Physics. ͓S0021-9606͑00͒00433-5͔
I. INTRODUCTION
improving due to rapid advances both in computational
chemistry and efficient algorithms for treating reactive scat-
tering in reduced dimensionality.
One important stimulus in the development of such
ab initio and dynamical efforts is the availability of experi-
mental results for reactive scattering at the fully state-to-state
resolved level, such as has recently been achieved for
The study of chemical dynamics in order to understand
the detailed mechanics of reactive processes has become in-
creasingly important in chemical physics. In recent years
there have been considerable parallel advances in both state-
of-the-art experiments1 and theory,
–8
9–13
in particular the
ability to ͑i͒ observe reaction dynamics at the fully quantum
state-to-state level, ͑ii͒ calculate potential energy surfaces
from first principles, and ͑iii͒ perform numerically exact
quantum scattering calculations on such potential surfaces. It
has become increasingly clear that for favorable systems the
field has progressed to a point where fully rigorous compari-
sons between theory and experiment are now feasible.
As one benchmark example, the elementary reaction
FϩH →HF(v,J)ϩH based on direct IR laser spectroscopy
2
1
on the nascent HF(v,J) product. Natural extensions
of this work into more complicated systems with an
increasing number of internal dimensions include
FϩH O ͑atomϩtriatom͒, FϩNH ͑atomϩtetra-atom͒, and
2
3
FϩCH ͑atomϩpenta-atom͒ reactions. The key advantages
4
of such systems are: ͑i͒ the high probability of chemical re-
action on each collision, ͑ii͒ the efficient funneling of chemi-
cal exothermicity into HF rotation/vibration, ͑iii͒ the pres-
ence of only two ‘‘heavy’’ ͑i.e., nonhydrogenic͒ atoms, and
͑iv͒ the low density of rovibrational energy levels for both
products and reactants. In conjunction with the well-studied
FϩH →HF(v,J)ϩH has been a prime focus of attention
2
from experiment, high-level ab initio theory, and numeri-
cally exact quantum reactive scattering dynamics. Indeed, as
noted in a recent review by Manolopoulos,14 reactive scatter-
ing for such ‘‘atomϩdiatom’’ systems is now theoretically
straightforward in all 3NϪ6ϭ3 internal degrees of freedom,
at least for adiabatic reactions confined to single potential
energy surfaces.
FϩH ͑atomϩdiatom͒ system, the above systems form a
2
natural quartet of hydrogen abstraction reactions that should
be cleanly accessible with full quantum state resolution un-
der crossed supersonic jet/single collision conditions.
Though the most challenging from a theoretical perspective,
By way of contrast, theoretical progress in
atomϩpolyatom systems has remained substantially more re-
calcitrant, essentially limited by the rapidly increasing inter-
nal vibrational degrees of freedom with molecular complex-
ity. What makes these theoretical calculations difficult is the
much greater number of ab initio points and fitting required
to adequately characterize the reactive potential surface, as
well as the significantly greater challenge in solving the
quantum reactive scattering problem in more than 3 internal
degrees of freedom. Nevertheless, this situation is quickly
we have investigated FϩCH as the second in this series, the
4
results of which form the primary thrust for the work de-
scribed in this paper. The availability of such quantum state
resolved results will hopefully provide the necessary stimu-
lus for both ab initio work on high-quality potentials as well
as the further development and implementation of new dy-
namical schemes for calculating reactive scattering on
atomϩpolyatom surfaces.
0021-9606/2000/113(9)/3670/11/$17.00
3670
© 2000 American Institute of Physics
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1

J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Quantum state-resolved reactive scattering
3671
though the earliest results were strongly influenced by vibra-
tional and rotational relaxation of the product HF(v,J), more
recent experiments2
2,23
have made substantial efforts to re-
duce these collisional effects. The first study under low pres-
sure conditions of the FϩCH product energy distribution
4
2
2
was performed by Nazar and Polanyi, which yielded a
highly inverted HF(v,J) vibrational distribution ͓v
ϭ3,2,1:0.10, 0.69, 0.21͔. The corresponding HF rotational
populations roughly resembled a Boltzmann distribution of
3
00 K, but with increased product density in higher J levels,
suggesting a largely, but not completely, relaxed rotational
manifold. This work was followed by a detailed FTIR study
of HF product state distributions for a series of FϩRH reac-
tions by Setser, Heydtmann, and co-workers, including
2
3
HF(vϭ1–3;J) rotational distributions from FϩCH4.
These arrested relaxation HF vibrational distributions for
FϩCH4 ͓vϭ3,2,1:0.09(1),0.73(7),0.17(2)͔ are in good
agreement with distributions from the chemiluminescence
studies of Nazar and Polanyi;22 however, the possibility of
partial rotational relaxation of the nascent HF and secondary
reactions24 could again not be ruled out. In analogous F
FIG. 1. Simplified view of the FϩCH hydrogen abstraction reaction. The
HF product recoils with a large fraction of the exothermicity in vibrational
and rotational energy.
4
atom abstraction experiments with larger hydrocarbon
The FϩCH →HFϩCH reaction system represents an
4
3
species,2
3,25–27
the evidence for rotational relaxation was
especially important prototype for highly exothermic hydro-
gen abstraction reactions of F with hydrocarbons ͑see Fig. 1͒.
There have been many theoretical investigations of the title
reaction at various levels of theory, including several studies
of the potential energy surface ͑PES͒. At the simplest
quite dramatic. In particular, the rotational distributions ex-
hibited pronounced shoulders or even double maxima. This
behavior was interpreted as arising from strongly
J-dependent rotational relaxation dynamics, which prevented
high J states from relaxing efficiently due to the large energy
gap while allowing the lower J states to become thermalized
on the time scale of the detection.
‘
‘pseudotriatomic’’ level, with the CH group treated as a
3
single ‘‘atom,’’ London–Eyring–Polanyi–Sato ͑LEPS͒ sur-
faces have been developed15 for the FϩCH reaction and
4
The potential influence of collisions in previous arrested
relaxation studies merits further clarification. Specifically,
different final quantum states will recoil with different ki-
netic energies and therefore exhibit different residence times
in the detection region. Since very little energy is deposited
into the CH3 fragment, HF quantum states with internal en-
ergy close to the exothermicity of the reaction (vϭ3) will
exhibit lower recoil energies than HF with smaller quanta of
internal energy (vϭ0,1,2). These quantum state dependent
recoil kinetic energies and free-flight residence times trans-
late into quantum state dependent detection sensitivities for
any absorption/emission based experiment. This is the es-
sence of the density-to-flux transformation, which couples
the magnitude of an absorption measurement to the residence
time of the absorbing chromophore, e.g., an individual quan-
tum state of HF. The density-to-flux transformation becomes
negligible with sufficient collisions to cause translational
equilibration of the product molecules; however, these colli-
sions unavoidably come with increased opportunity for rota-
tional relaxation. It is therefore especially interesting to re-
visit this system under single collision conditions, explicitly
taking density-to-flux considerations into account.
optimized to reproduce experimental results available at that
time. Although significantly below full dimensionality, this
LEPS surface has been used to calculate reaction cross sec-
tions as a function of collision energy, which have proven
successful in reproducing experimental thermal rate con-
stants. More recently, improved surfaces have been devel-
oped in full dimensionality1
6,17
including all vibrational co-
ordinates in the CH product. Two of the FϩCH surfaces
3
4
are empirical extensions of the ab initio HϩCH4
1
8,19
16
potential,
while the third version of the surface is ob-
tained from FϩCH semiempirical calculations ͑PM3-SRP͒
4
modified to reproduce known experimental data. Further-
more, high-level ab initio efforts20 have permitted the ex-
plicit reaction path and transition state for the title reaction to
be determined. The transition state geometry calculated20 at
the QCIsd/6-31G(d,p) level is found to have a bent structure
(
(
Є
F–H–Cϭ161.4°) and an elongated H–F bond length
rF–Hϭ1.360 Å; rC–Hϭ1.152 Å͒. Most importantly, this
bent geometry is indicative of an ‘‘early’’ transition state,
corresponding to a H–F distance significantly longer than the
equilibrium bond length ͑0.9168 Å͒, specifically falling be-
tween the HF classical outer turning points of
v
2
1
ϭ4(1.318 Å) and vϭ5(1.381 Å). Thus, from simple
Franck–Condon and impulsive recoil ideas, one expects both
substantial vibrational and rotational excitation in the HF
product.
In this work, the quantum state resolved dynamics of the
FϩCH →HF(v,J)ϩCH reaction have been investigated
4
3
based on direct absorption of a high resolution IR probe laser
under crossed supersonic jet conditions ͑see Fig. 2͒. By vir-
A number of experimental investigations have been per-
tue of the jet expansion geometry, the reagent CH molecules
4
formed on the FϩCH reaction, primarily using infrared
chemiluminescence and arrested-relaxation techniques. Al-
are supersonically cooled into the lowest rotational levels
allowed by the nuclear spin statistics prior to reactive scat-
4
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3672
J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Harper, Nizkorodov, and Nesbitt
the valve body, is held at ground potential forming the anode
and protects the valve body from degradation due to the
discharge. A 600 ␮m plastic spacer separates the anode from
the cathode, which consists of two stainless steel slit expan-
sion jaws in electrical contact. The two cathode electrodes
form the limiting aperture (400 ␮mϫ0.50 cm) for both
the expansion and discharge. This allows the gas between
the anode and cathode to rise to the valve backing pressure
͑
35–40 Torr͒, thereby achieving stable discharge conditions.
For the production of fluorine atoms, a 10%:40%:50%
fluorine:neon:argon͒ mixture expands through the slit in a
ϳ2 ms gas pulse, while a Ϫ800 V pulse of shorter ͑500–700
s͒ duration on the cathode strikes and maintains the elec-
͑
␮
trical discharge. The transient discharge currents are typi-
cally 250–500 mA, stabilized with a 500 ⍀ ballast resistor.
At a 10 Hz repetition rate, this translates into Ϸ1 W average
power dissipation, which in vacuum necessitates water cool-
ing to maintain a constant valve temperature of Ϸ25 °C.
FIG. 2. Schematic of the experimental apparatus. See text for details.
tering. In addition, since these experiments are based on laser
absorption rather than spontaneous emission, one can probe
the full rovibrational manifold of product HF ͑i.e., down to
vϭ0͒ for the first time. Most importantly, the low super-
sonic jet densities and high detection sensitivity allow one to
perform the experiment in a regime that cleanly eliminates
contributions from collisional relaxation effects and/or sec-
ondary reactions.
The organization of the rest of this paper is as follows. In
Sec. II, relevant details of the experimental apparatus are
provided, followed by a presentation of the nascent HF(v,J)
absorbance results in Sec. III. The analysis of these data is
discussed in Sec. IV, which addresses Monte Carlo simula-
tion of the density-to-flux transformation and permits extrac-
tion of the nascent HF(v,J) rovibrational populations. These
results are then discussed in the context of previous work in
Sec. V. Section VI summarizes the conclusions.
The CH reactant is delivered through a piezoelectric
4
2
9
pulsed valve based on the design of Proch and Trickl,
backed with neat methane at pressures between 250–500
Torr. From the measured pulse duration, gas flow, and rep-
etition rate, the effective diameter of the expansion orifice is
determined to be 145Ϯ5 ␮m. This is in excellent agreement
with the actual 150 ␮m pinhole diameter, which implies es-
sentially full choke flow expansion conditions. The rotational
state distributions of the jet-cooled CH correspond to a tem-
4
perature of 20 K for each of the three A(Jϭ0), F(Jϭ1),
and E(Jϭ2) nuclear spin isomers, as readily determined via
direct infrared absorption. The ratio of nuclear spin isomers
in the stagnation region is approximately 5:9:2(A:F:E).
After supersonic expansion, 85%–90% of the population is
cooled into the lowest possible J state for each isomer. Due
to high vibrational frequencies, the CH population is nearly
4
II. EXPERIMENT
entirely in the ground vibrational state; even at room tem-
perature stagnation conditions, there is only about 0.1% and
The apparatus used for these reactive scattering experi-
ments has been described in the literature previously;1,2 only
features specifically relevant to the current study will be
summarized here. The crossed jet scattering reactions are
performed in a 65 L vacuum chamber pumped by a 10 in.
diffusion pump equipped with a liquid nitrogen cold trap and
backed with a Roots blower pump. As shown schematically
in Fig. 2, two pulsed valves oriented at right angles deliver
0
.6% population in the bending ␯ and ␯ vibrational modes,
2 4
respectively, with vanishingly small contributions in either
of the ␯ or ␯ stretching modes.
1
3
The infrared radiation is produced by a color center la-
ser, pumped by the red lines of an amplitude stabilized kryp-
3
0
ton ion laser and modified for continuous single mode
Ϫ1
scanning up to 0.8 cm intervals with 2 MHz resolution.
The laser beam is multipassed 18 times through the vacuum
chamber in a Herriott cell configuration to enhance detection
sensitivity. The multipassed IR laser beam forms an elliptical
pattern31 approximately 8 mm high by 5 mm wide centered
at the intersection region. HF(⌬vϭ1) rovibrational transi-
tional frequencies are calculated using the improved rota-
tional constants of Ram et al.,32 where residual errors are
well within the experimental Doppler width. Time-dependent
absorbance signals are recorded with a transient digitizer and
transferred to a computer for analysis on a pulse-to-pulse
basis. Dual software gates ͑100 ␮s width͒ are used to record
background and transient absorption signals, as well as ex-
clude very weak delayed signals due to HF molecules
formed by pulsed F atom reactions on the chamber walls.
Data collection is therefore restricted to the middle 400 ␮s
the F atom and CH reactants, where the distances between
the nozzle orifices and the probe laser axis are 5.1 cm and 5.5
4
cm, respectively. The background pressure is Ͻ5
Ϫ6
ϫ10 Torr (1 Torrϭ133.32 Pa) and rises to Ͻ2
Ϫ4
ϫ10 Torr with the pulsed valves operating at 10 Hz. The
HF product molecules are probed in the jet intersection re-
gion perpendicular to the plane formed by the two expansion
axes, utilizing cw direct infrared laser absorption in a dual
beam configuration with two matched InSb detectors. The
fluorine atom source used in this experiment1,2 is based on a
jet-cooled discharge expansion design previously used for
high-resolution jet spectroscopy of radicals.28 The source is
2
built around a pulsed solenoid valve body modified to have
a slit aperture (0.60ϫ0.20 cm) sealed by an O-ring. A thin
piece of stainless steel, in direct contact with the bottom of
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J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Quantum state-resolved reactive scattering
3673
of the 500 ␮s CH gas pulse, with the gates turned off before
4
the HF molecules have time to travel back into the detection
region. The absolute absorbance is recorded as the frequency
of the laser is scanned in 3–5 MHz increments over the
entire Doppler profile for each transition studied. Etalon
fringes are recorded simultaneously with the Doppler profile
to provide relative frequency calibration, while a phase
locked loop travelling Michelson interferometer33 is used
with a polarization stabilized HeNe laser to determine the
absolute IR laser frequency. Residual power fluctuations in
the IR light are monitored on the IR reference laser, which
are used with fast servoloop feedback electronics to control
the amplitude of the krypton ion pump laser.
Conditions have been chosen to make the effects of sec-
ondary reactions negligible by lowering the gas densities in
the jet intersection region. The reaction probability ͑P͒ can
be estimated from Pϭ␴NL, where ␴ is the reaction cross
Ϫ16
2
section ͑Ϸ5ϫ10
cm , inferred from the room tempera-
ture rate constant͒,34 N is the density, and L is the path length
FIG. 3. Network of HF absorption/stimulated emission transitions probed.
For the vϭ3,2 vibrational levels, we probe J up to the energetic limit, while
for vϭ1,0 we probe all levels within the tuning range of our F-center laser.
The high level of redundancy ͑ϳ1.5-fold͒ in the measurements enhances the
statistics of our population measurements.
for the reactants. The total F atom density from the discharge
source is estimated to be 7ϫ10 cm ͑in 1.5ϫ10 cm of
1
1
Ϫ3
14
Ϫ3
carrier gas͒ while the density of CH is about 7
4
1
2
Ϫ3
ϫ10 cm , each evaluated at the laser intersection region.
Based on an effective path length of 5 cm, the reaction prob-
ability for each F atom is Ͻ2%, thus reducing the probability
of sequential reactions to negligible levels ͑Ͻ0.02%͒. On the
Ͻ40 ␮s time scale that individual HF molecules arrive and
fly through the detection region, vibrational or rotational
state changing effects due to spontaneous emission can be
completely neglected. Furthermore, probe laser power levels
scanned over 0.2 cmϪ1 ͑у8 times the typical FWHM͒, and
integrated over all frequency steps to obtain integrated ab-
sorbances in absolute units. Finally, each Doppler profile is
also scanned with and without the CH valve operating to
4
correct for weak background absorbance ͑typically 0%–10%
of the peak signals͒ due to trace HF impurities present in the
F atom source. The development of such an extensive data
set necessarily reflects data collection over many weeks of
experimentation. Therefore, both to improve reliability on
individual lines as well as to combine data from different
days, a reference Doppler profile ͓vϭ4� 3;R(0)͔ is re-
corded after every third transition and used to correct for
͑Ͻ60 ␮W͒ are more than an order of magnitude below satu-
ration levels so as to insignificantly perturb the nascent
HF(v,J) populations. Under such expansion conditions, the
signal to noise ratio for the strongest absorption feature is
S/NϷ30 per pulse, with a rms absorbance noise floor of 7
Ϫ5
ϫ10
in a 20 kHz detection bandwidth. Since the inte-
grated absorbance measurement values reflect integration
over Ϸ1000 points across the Doppler profile, the resulting
S/N ratio for the product column integrated densities is fur-
ther enhanced by Ϸ15- to 20-fold.
slow variations in the pulsed F-atom/CH densities in the jet
4
intersection region. We find that this procedure works ex-
tremely well to improve the quality and reproducibility of the
data set.
Selected HF Doppler profiles for P- and R-branch tran-
sitions are shown in Fig. 5 and Fig. 6, respectively, and
immediately indicate several points worth noting. First, the
data testify to the high sensitivity of the measurements, typi-
cally with S/NϷ3–30 for absorbances at line center, and
improved to S/NϷ50–500 by integration over the Doppler
profile. Second, the line shapes are both positive and nega-
tive, i.e., corresponding to either absorption or stimulated
emission signals. This simply reflects the fact that an absorp-
tion measurement necessarily samples population differences
between the upper and lower probe states. For example, all
of the vϭ4� 3 data reflect pure absorption signals due to
insufficient reaction exothermicity to populate rotational
states in the HF(vϭ4,J) manifold. Conversely, the FϩCH4
reaction generates a strong population inversion between v
ϭ2 and vϭ1, which results in primarily stimulated emission
signals on each of the vϭ2� 1 probe transitions. Third,
there is considerable Doppler structure evident in these pro-
files, where the absorbance shifts from negative to positive
III. RESULTS
High-resolution IR absorption Doppler profiles have
been collected for all fundamental and hot band (⌬v
ϭϩ1)HF rovibrational transitions accessible within the tun-
ing range of the F-center laser ͑2.5–3.3 ␮m͒. A summary of
the full network of HF(vЈ,JЈ)� HF(vЉ,JЉ) transitions
probed is shown in Fig. 3, and the energetics are presented in
Fig. 4, where ⌬Ecom is the collision energy for a perpendicu-
lar collision geometry and ⌬Erxn is the 31.84͑3͒ kcal/mol
exothermicity of the reaction. It is worth noting that these
profiles are obtained on 50 populated rovibrational levels ͑up
to the vр3 energetically accessible manifold͒ connected by
45 P-branch and 29 R-branch transitions. As a test of internal
consistency, the number of independent measurements ex-
ceeds the number of inferred quantum state populations by
Ϸ1.5-fold. The Doppler profiles for each transition are re-
corded multiple times ͑typically 2–4͒ to enhance statistics,
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3674
J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Harper, Nizkorodov, and Nesbitt
FIG. 4. Energetics of the FϩCH reaction. The dashed line shows the total
4
FIG. 5. Representative HF(v,J) P-branch Doppler profiles. Doppler profiles
consist of pure absorption ͑vЉϭ3 manifold͒, stimulated emission (vЉϭ1),
or a combination of the two (vЉϭ2).
exothermicity of the reaction, including the contributions from ⌬H and the
center-of-mass collision energy ⌬Ecom . The vϭ3 manifold is accessible up
to Jϭ4 for a perpendicular collision geometry, and slightly higher for ob-
tuse collision geometries. Not shown is the energy contribution (⌬Eso
ϭ1.15 kcal/mol) from the spin–orbit excited fluorine, which would allow
vϭ3, Jϭ6 to be populated.
numbering index ͑mϭϪJЉ for P-branch transitions, mϭJЉ
ϩ1 for R-branch transitions͒. In Eq. ͑1͒, ␮ is the HF rovi-
brational transition dipole moment derived from extensive
for small and large Doppler detunings, respectively ͓e.g., v
ϭ3� 2; P(2)͔. In addition to these velocity dependent
population inversions between different rovibrational mani-
folds, line widths are also observed to change depending on
the HF quantum state. This is strong evidence that even the
translational energy distribution is not relaxed, providing ad-
ditional confirmation that the rotational and vibrational dis-
tributions are indeed nascent. As described elsewhere in
more detail, these Doppler profiles can be used to extract
partial information on the differential cross sections for re-
active scattering into a final quantum state.35
studies by Setser and Stwalley which correctly include rota-
36,37
tional Herman Wallis effects.
As noted above, the signals
reflect population differences in the upper and lower states,
which are mirrored by the absorption and stimulated emis-
sion terms in the right-hand side of Eq. ͑1͒. Specifically, the
integrals on the right-hand side of Eq. ͑1͒ yield HF(v,J)
column-integrated densities over the laser beam through the
detection region, which in turn are determined by simulta-
neously least squares fitting the integrated absorbance data
for the full set of lines to equation Eq. ͑1͒. The high redun-
dancy of the line measurements permits the least squares
goodness of fit parameter to be used with the variance-
covariance matrix to estimate standard errors associated with
each of these column-integrated densities.
The integrated absorbances are converted to column-
integrated densities according to
8
␲3␯0
͉
m
͉
␮2
͐
͓HF͑vЉ,JЉ͔͒dl
͑2JЉϩ1͒
͵
A͑␯͒d␯ϭ
ͫ
3
hc
IV. ANALYSIS
͐
͓HF͑vЈ,JЈ͔͒dl
Ϫ
ͬ
.
͑1͒
In any direct absorption detection experiment ͑and com-
mon to most laser based probe techniques͒, one directly mea-
sures the product densities, whereas the reaction cross sec-
tion is rigorously defined in terms of product fluxes. In
general, these two quantities are not identical and differ by
͑
2JЈϩ1͒
In this expression, A(␯) is the frequency dependent absorp-
tion coefficient integrated over the entire Doppler profile, ␯0
is the center transition frequency, and m is the rotational
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J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Quantum state-resolved reactive scattering
3675
FIG. 7. Newton diagram for the FϩCH reaction with perpendicular colli-
4
sion geometry. The vectors v represent lab frame velocities, while the vec-
tors u represent center-of-mass frame velocities. The center-of-mass scatter-
ing angle is given by ␪ and the azimuthal scattering angle ␾ ͑averaged over
in all of our calculations͒ traces a circle perpendicular and centered on vrel
,
HF and CH recoil from each other with velocities that are determined from
3
conservation of momentum and the internal energy for both molecules.
The Newton diagram in Fig. 7 shows an idealized geometry
for reactive scattering of FϩCH , where v (u ) and
4
F
F
vCH4(uCH4) denote the F atom and CH velocity vectors in
4
the laboratory and center-of-mass frame ͑COM͒, respec-
tively. The centerline magnitudes of v and v
are 641 and
CH
4
F
1
150 m/s, respectively, as calculated using standard super-
sonic jet formulas and confirmed by direct time of flight
measurements. This idealized perpendicular geometry corre-
sponds to a collision energy of Ecomϭ1.8(6) kcal/mol,
where the width is dominated by angular averaging over the
FIG. 6. Representative HF(v,J) R-branch Doppler profiles. Doppler profiles
primarily reflect absorption (vЉϭ3) or stimulated emission (vЉϭ1). How-
ever, for vϭ2, Jϭ0 a small amount of stimulated emission can be seen in
center of the profile. Although not immediately visible, there are also small
stimulated emission contributions in other transitions originating from the
vЉϭ2 vibrational manifold. Note the differences in the linewidths of various
transitions as a function of the HF quantum state.
finite distribution of angles between v and v
͑see Ref. 8
CH
4
F
for more details͒. After the reaction, HF is emitted in the
center-of-mass frame at some angle ␪ with respect to v ; for
rel
unaligned reagents, one integrates over the azimuthal angle
␾
͑i.e., the cone about v , to yield differential cross sections
rel
͑d␴/d⍀͒ for reactive scattering into a given final state. The
product molecules recoil in the COM frame with final veloc-
the density-to-flux transformation, which depends on several
factors including the magnitude of the energy release and
thus the final quantum state of the products. Therefore, in
order to facilitate rigorous comparison with theoretical and
other experimental results, the laboratory frame column-
integrated densities obtained in Sec. III must be properly
transformed into molecular fluxes in the center-of-mass
ity vectors uHF and uCH3; the product HF is then probed by
direct IR absorption where the Doppler shifts are easily cal-
culated from the lab frame velocity component of vHF ͑i.e.,
uHFϩvCOM͒ parallel to the probe laser axis. The relevant
weighting of these events ͑i.e., the density-to-flux transfor-
mation͒ is proportional to how long the product stays in the
laser beam, which is inversely related to v , i.e., the com-
Ќ
frame. For heavyϩlight-light systems such as FϩH , the ki-
2
ponent of vHF perpendicular to the probe axis.
nematics are quite favorable such that the desired HF fluxes
are closely proportional to the experimentally observed
column-integrated densities. However, the HF recoil effects
In the calculations, random points are chosen inside of a
small sampling volume at the jet intersection. The collision
energy along with the exothermicity of the reaction (⌬H
ϭϪ31.84 kcal/mol) provides the total energy available for
partitioning among the two product molecules. The relevant
quantity is therefore the recoil energy in the center-of-mass
frame, i.e.,
are much larger for FϩCH , which make this transformation
4
much more relevant to take into account, as treated below.
A. Monte Carlo simulation of density-to-flux
transformation
ErecoilϭEcomϪ⌬HϪEHFϪECH3
,
͑2͒
To address the issue of detection sensitivity on the resi-
dence time, detailed Monte Carlo simulations have been per-
formed to incorporate the density-to-flux transformation as a
function of Erecoil , or equivalently HF(v,J) quantum state.
where EHF and ECH3 represent the amount of total energy left
in internal quantum states of the product. Once this recoil
energy is specified, ͑vide infra͒, the collision energetics and
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3676
J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Harper, Nizkorodov, and Nesbitt
product speeds can be readily calculated from conservation
of energy and momentum. The HF product velocities are
then distributed in center-of-mass angle ␪ according to the
differential cross section, d␴/d⍀, which permits the calcula-
tion of the desired flux-to-density conversion factor (ϰvЌ)
for a given value of ␪ and averaged over ␾ϭ0–2␲.
used high resolution Dopplerimetry to obtain such informa-
tion for a selection of rovibrational product states in the
HF(vϭ1,2) manifold, as described elsewhere in more
detail.35 However, the product state distributions are rela-
tively insensitive to the form of these differential scattering
cross sections, primarily because f(v,J) depends on vЌ in
the laboratory frame, which is typically dominated by the
forward motion of the center-of-mass. Thus, based on differ-
ential cross sections obtained from high resolution Dopple-
rimetry for a series of J states in HF(vϭ1,2), we approxi-
For a known initial collision energy, reaction exother-
micity, and final HF(v,J) quantum state, the choice of Erecoil
depends only on the internal energy in the CH subunit. For-
3
tunately, as shown by Sugawara et al.,38 the internal energy
of CH is quite small compared to the exothermicity of the
mate the differential cross sections as d␴/d⍀ϰ͉cos(␪)͉,
3
reaction. Their study reports a relatively cold vibrational dis-
which roughly corresponds to forward/backward peaked dis-
tributions in the center-of-mass frame. This is also consistent
with a more complete Dopplerimetry analysis of HF(v
ϭ1,2).35 Unfortunately, Doppler information is not available
Ϫ1
tribution in the ␯2 ͑umbrella bending 606 cm ͒ mode of
CH , with fractional populations of 0.67(v ϭ0), 0.24(v
3
2
2
ϭ1), and 0.09(v ϭ2) ͑Ref. 38͒ ͑corresponding to T
2
vib
Ϸ1000 K͒. Furthermore, the nascent rotational energy distri-
bution appears to be approximately Boltzmann with a corre-
sponding temperature of 280͑40͒ K. By way of confirmation,
for differential scattering into the HF( ϭ3) manifold, since
v
the recoil energies are now too small to contribute signifi-
cantly to the experimental linewidths. However, the HF(v
ϭ3) populations also prove quite insensitive to the choice of
scattering model; specifically, forward, sideways, and isotro-
pic scattering models yield identical results within experi-
mental uncertainties ͑5%͒. We therefore have assumed an
isotropic distribution for HF(vϭ3), but note that the in-
ferred populations would increase slightly ͑Ϸ20%͒ in the
dynamically improbable limit of pure back scattering.
Based on these approximate forms for the differential
scattering cross sections, an average residence time may be
calculated for a given Erecoil by the Monte Carlo methods.
The density-to-flux transformation factor f(v,J) is propor-
tional to the inverse of this residence time, which, when mul-
tiplied by the column-integrated density, results in a scat-
tered flux ͑or population͒. Erecoil is obtained by energy
conservation from the known reaction exothermicity, center-
of-mass collision energy, and internal energies in the
we have also observed CH infrared transitions based on the
3
␷3
CH stretch fundamental, albeit at tenfold higher CH4
backing pressures necessary to enhance detection sensitivity.
While no longer purely in the single collision regime under
these higher pressure conditions, the CH populations are at
3
least qualitatively consistent with the cold distributions ob-
tained by Sugawara et al. Based on these previous CH rovi-
3
brational distributions, the average internal energy
Ϸ1.61 kcal/mol, which represents a small fraction of the
1.84 kcal/mol reaction exothermicity. However, even this
͗
ECH3͘ is
3
average energy represents an overestimate for the highest
HF(v,J) states, which are populated up to the energetic
limit. Thus, as the simplest model consistent with experi-
mental results, ECH3 is assumed to be linearly anticorrelated
with EHF , i.e.,
͗
ECH3͘ϭ4.978Ϫ0.150
with the proportionality constants chosen to make ECH3 van-
ish at the energetic limit and ECH3͘ϭ1.61 kcal/mol when
͗
EHF
͘
,
͑3͒
HF( ,J) and CH products. Since the amount of energy in
v
3
the CH product is only a small fraction of the reaction exo-
3
thermicity, the extracted HF(v,J) rovibrational populations
͗
are insensitive to the CH internal energy distribution. In-
3
averaged over the nascent distribution of HF(v,J) product
states. It is worth noting that the reported HF(v,J) popula-
tions are quite insensitive to various modelings of the CH3
energy distribution, up to and including the complete neglect
deed, complete neglect of CH internal energy would result
3
in negligible differences ͑Ͻ2%͒ in the normalized popula-
tions of vϭ0,1,2 and only a small decrease in the vϭ3
populations ͑Ͻ10%͒.
Table I reports both ͑i͒ f(v,J), density-to-flux transfor-
mation factors, and ͑ii͒ nascent populations for each
HF(v,J) rovibrational level, based on d␴/d⍀ϰ͉cos(␪)͉ for
vϭ0,1,2 and isotropic scattering for vϭ3. The rotationally
of CH internal energy. The essential reason for this insensi-
3
tivity is that the 1.61 kcal/mol average internal energy of
CH is perturbatively small ͑Ϸ5%͒ compared to the overall
3
31.84 kcal/mol exothermicity of the reaction.
resolved populations are depicted graphically in Fig. 8. The
B. Nascent HF„v,J… populations
1
␴ confidence interval for the reported populations have
In order to convert the measured column-integrated den-
sities into state-resolved nascent populations, one needs the
density-to-flux conversion factor, f(v,J), for each final
HF(v,J) state. These f(v,J) can be obtained from the Monte
Carlo simulations described above by averaging over all
center-of-mass scattering angles ␪, and weighting the results
by the differential cross sections. Quantitative extraction of
the nascent HF(v,J) populations from any absorption/
emission experiment therefore requires some prior knowl-
edge of the state-resolved differential scattering cross sec-
tions of the product molecules. Toward this goal, we have
been propagated from the variance/covariance matrices ob-
tained from the least squares fit and given by the error bars in
Fig. 8 for each rovibrational level and listed in Table I. The
corresponding HF(v) populations, summed over all J for a
given vibrational manifold, have been plotted in Fig. 9 for
the present data as well as the previous studies of Polanyi
et al., Ref. 22 and Setser et al., Ref. 23. For vϭ3 popula-
tions, the calculated uncertainties are quite small but increase
systematically for the lower (vϭ0–2) vibrational levels.
This is because absorption measurements reflect population
differences between upper/lower states, which implies the
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J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Quantum state-resolved reactive scattering
3677
TABLE I. Nascent HF(v,J) rovibrational distributions and state specific density-to-flux transformation constants. The transformation constants result from
treating HF(vϭ0,1,2) with backward (d␴/d⍀ϰ cos(␪) ) scattering and HF(vϭ3) with isotropic ͑d␴/d⍀ϭconstant͒ scattering. Numbers in parenthesis are
͉
͉
1␴ errors.
vHFϭ3
vHFϭ2
vHFϭ1
vHFϭ0
JHF
Frac. Pop.
DF Const.
Frac. Pop
DF Const.
Frac. Pop.
DF Const.
Frac. Pop.
DF Const.
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
1.58͑1͒
3.25͑5͒
2.87͑6͒
1.85͑5͒
0.63͑6͒
0.25͑7͒
0.16͑7͒
0.565
0.570
0.580
0.593
0.610
0.629
0.652
0.677
4.5͑1͒
10.5͑2͒
12.5͑2͒
12.1͑2͒
9.9͑1͒
6.8͑2͒
4.1͑2͒
2.6͑2͒
1.6͑1͒
1.2͑1͒
0.4͑1͒
0.3͑1͒
0.2͑3͒
0.0͑3͒
0.0͑3͒
1.313
1.308
1.299
1.285
1.266
1.241
1.211
1.174
1.131
1.080
1.020
0.949
0.864
0.758
0.624
0.5͑2͒
1.6͑4͒
1.2͑4͒
1.1͑4͒
1.5͑4͒
1.8͑3͒
1.4͑4͒
1.6͑4͒
2.5͑4͒
1.5͑4͒
1.6͑4͒
0.9͑3͒
1.0͑3͒
0.7͑5͒
1.706
1.702
1.695
1.684
1.670
1.561
1.629
1.603
1.572
1.536
1.495
1.448
1.396
1.336
1.267
2.024
2.021
2.015
2.006
1.994
1.979
1.960
1.938
1.913
1.884
1.851
1.813
1.772
1.725
1.673
2.3͑22͒
1.8͑13͒
Ϫ1.1͑12͒
Ϫ1.5͑9͒
Ϫ0.2͑10͒
0.5͑9͒
0.8͑8͒
Ϫ0.0͑9͒
1.6͑9͒
Ϫ0.2͑8͒
0.1͑8͒
Ϫ0.6͑7͒
0.3͑7͒
a
0.00
1
1
1
1
1
0.2͑9͒
⌺
J
10.6͑1͒
66.7͑7͒
18.9͑14͒
3.8͑40͒
aParameter constrained to be positive.
least uncertainty for the highest HF(vϭ3,J) vibrational
manifold. As a direct corollary, uncertainties accumulate
down the vibrational manifold, culminating in the largest un-
certainties in the HF(vϭ0,J) level, where rotational popula-
tions nearly vanish within experimental error bars ͑1␴͒. Al-
though a more detailed discussion of these distributions is
reserved until Sec. V, several comments are briefly worth
noting at this stage. First of all, the f(v,J) values range over
3.5-fold, illustrating the importance of a density-to-flux
analysis in any experiment with unequilibrated translational
degrees of freedom. Second, the nascent HF vibrational
populations summed over rotational states are in excellent
agreement with the arrested relaxation studies by both Pola-
nyi et al. and Setser et al. Finally, at the rotationally state-
resolved level, the distributions from this study are distinctly
hotter than previously obtained from early IR chemilunimes-
cence studies.
V. DISCUSSION
The HF(v,J)
rovibrational distributions from
FϩCH →HF(v,J)ϩCH have been previously character-
4
3
2
2,23
ized in two arrested relaxation studies.
However, partial
rotational relaxation and secondary reactions24 of the prod-
ucts could not be ruled out, and the population in the vϭ0
manifold could not be determined. The combined efforts23 of
the Setser and Heydtmann groups ͑SH͒ reported modest
agreement (vϭ3:0.09, vϭ2:0.73, vϭ1:0.17) between ar-
rested relaxation and flow reactor experiments, which were
2
2
in good agreement with the earlier work of Polanyi (v
3
9
ϭ3:0.10, vϭ2:0.69, vϭ1:0.21). Surprisal analysis esti-
mates of the HF(vϭ0) population predicted this to be neg-
ligibly small compared to the other vibrational levels. In-
deed, the present IR absorption measurements ͑which probe
vϭ0 directly͒ now confirm this prediction for the first time;
the total branching into HF(vϭ0) is 3.8Ϯ4.0%, with 1␴
FIG. 8. Nascent HF(v,J) fractional product populations. The filled circles
are the results of the current work after density-to-flux transformation ͑with
2
3
1␴ error bars͒, and the open circles are the results from Ref. 23 ͑SH͒. The
rotational distributions exhibit a consistent broadening as the vibrational
energy is decreased. Note the differences particularly in the vϭ1 manifold
between current and previous work ͑Ref. 23͒.
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1

3678
J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Harper, Nizkorodov, and Nesbitt
FIG. 9. Comparison of HF vibrational populations from Ref. 22 ͑Polanyi͒,
Ref. 23 ͑SH͒, Ref. 40 ͑Gonzalez͒, and the current work. The previous work
is based on IR emission, hence the population in vϭ0 could not be deter-
mined directly. Populations from Ref. 22 are given without error bars.
FIG. 11. Boltzmann plot for the current HF(vϭ1) populations and those of
Ϫ1
SH. The current work is characterized by a reciprocal slope of Ϸ1450 cm
.
The previous work indicates a room temperature initial slope at low J, while
error bars as large as the population. Taken one step further,
we have recalculated a vibrational surprisal plot based on
data in all HF(vϭ3,2,1,0) manifolds; the results are dis-
played and compared to the results of SH ͑Ref. 23͒ and the-
oretical predictions by Gonzalez40 in Fig. 10. The vibrational
distributions of HF are indeed remarkably well represented
by a single surprisal parameter, which corresponds to a
single constraint superimposed on a statistical ͑prior͒ distri-
bution.
the high J data gives slopes that approach our value. A 300 K equilibrium
Ϫ1
distribution would correspond to a reciprocal slope of 208 cm
.
higher rotational levels. These effects are particularly evident
in the vϭ1 vibrational manifold in Fig. 8, where the previ-
ous ͑SH͒ distribution peaks early at Jϭ2, while the present
distribution exhibits a much broader peak around JϷ8. Al-
ternatively, Fig. 11 compares data from the current and pre-
vious studies in Boltzmann plots for the rotational levels of
HF(vϭ1), where a straight line would correspond to a uni-
form rotational temperature. In this plot, the SH data exhibit
As shown in Fig. 9, excellent agreement exists between
past and present studies of HF vibrational energy
distributions ͓(vϭ3) 0.106(3); (vϭ2) 0.667(14); (vϭ1)
Ϫ1
a reciprocal slope of Ϸ200 cm ͑i.e., ϷkT at room tem-
0.189(27); (vϭ0) 0.038(78); (2␴)͔. However, the earlier
perature͒ for the lower J levels, while the higher J data ap-
rotational distributions appear to be somewhat relaxed in
each vibrational level when compared with the present work
Ϫ1
proaches a reciprocal slope of Ϸ1200 cm . By way of com-
parison, the current data show much less curvature at low J
values, and are adequately represented over all J by a recip-
͑Fig. 8͒. First of all, the present rotational distributions are
consistently broader in all vibrational levels than previously
reported. Second, the most populated J states occur at
Ϫ1
rocal slope of Ϸ1450 cm . This behavior would be qualita-
tively consistent with partial thermal equilibration in the pre-
vious work for low J rotational levels, where the smaller
rotational energy spacings make HF more susceptible to col-
lisional energy transfer effects.
As mentioned above, the previous studies have neglected
any effects due to density-to-flux transformations; the con-
nection between this and rotational relaxation are intimately
related. By neglecting this transformation, previous studies
are implicitly assuming translational equilibrium between
product states, though without any change in HF(v,J). This
assumption is based on the reasonable expectation that trans-
lational degrees of freedom relax on a faster time scale than
rotation and, in turn, much faster than vibration. Neverthe-
less, such equilibration of translational energy distributions
requires some collisions, which also necessarily introduces
the possibility of rotational relaxation effects. It is therefore
interesting to note that the agreement between current and
previous vibrational populations is significantly improved
when integrated over all J rotational levels. One self-
consistent interpretation would be that the previous experi-
FIG. 10. Vibrational surprisal analysis comparing the current results to that
of Ref. 23 ͑SH, experiment͒ and Ref. 40 ͑Gonzalez, theory͒. The vibrational
distribution is well characterized by a single constraint superimposed on a
statistical ͑prior͒ distribution.
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1

J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Quantum state-resolved reactive scattering
3679
upper limit already presumes no internal energy in the CH3
product, which provides an even tighter energetic constraint.
This would predict that product states up to HF(vϭ3,
Jϭ5) and HF(vϭ2,Jϭ14) could be energetically popu-
lated, which can be compared with populations experimen-
tally observed up to HF(vϭ3,Jϭ5) and HF(vϭ2,Jϭ11) in
the vϭ3 and 2 manifolds, respectively. At the 1␴ uncer-
tainty level we also observe extremely weak signals in
HF(vϭ3,Jϭ6), which could be made energetically acces-
sible by nonadiabatic reactions with spin–orbit excited F at-
oms (⌬Espin–orbitϭ1.15 kcal/mol). Experiments on the vϭ3
manifold could in principle be used to interrogate possible
8
non-adiabatic aspects of the reaction, but would first require
further efforts to reduce the collision energy uncertainty.
The observed vibrational populations agree well with the
theoretical predictions20 of Corchado and Espinosa-Garcia.
They found that the HF stretching motion is strongly coupled
with the reaction coordinate in the exit channel, allowing
vibrational excitation of the HF product. They also find that
FIG. 12. Triangle contour plot for the HF product energy distribution. The
the CH bending mode is coupled weakly to the reaction
diagonal lines form an axis that gives the quantity E ϩE . We estimate
3
T
CH
3
that 80%–85% of this energy is due to translational energy (E ). The HF
product is in a nonstatistical distribution with a large fraction of the exo-
thermicity going into vibrational energy.
coordinate in the exit channel, and therefore little vibrational
T
excitation in CH is predicted. These results are consistent
3
with the fact that reaction proceeds via an early barrier where
the HF distance ͑1.360 Å͒ ͑Ref. 20͒ is quite extended, 48%
longer than the equilibrium HF bond length (re
ϭ0.9168 Å).2
1,32
In contrast, the CH distance ͑1.152 Å͒
ments were performed under conditions that permit nascent
vibrational distributions to be obtained, although with partial
rotational relaxation in the collisionally more susceptible
lower J levels.
In the spirit of the early dynamical analysis of Polanyi
and co-workers, a triangle plot ͑see Fig. 12͒ shows how the
͑Ref. 20͒ is only slightly extended ͑5%͒ over the CH bond
4
4
6
length (r ϭ1.094 Å). The HF distance in the transition
0
state falls between the ϭ4 and ϭ5 classical turning
v
v
points21 in isolated HF, which corresponds to highly vibra-
tionally excited HF product. The hot rotational distributions
are consistent with a bent transition state, where the H re-
FϩCH reaction exothermicity is distributed into the HF
4
product molecules. Since there are more than three atoms,
this triangle plot has the added feature that the diagonal axis
ceives recoil impulse from the CH group in the exit channel
3
due to H–C repulsion in the products. Indeed, as noted
above, rotational states in HF(vϭ2,3) are populated up to or
near the energetic limit. Furthermore, the HF(vϭ1) rota-
tional distribution is very broad ͑Fig. 8͒, with population
observed up to the highest J levels probed.
represents not just translational energy (E ), but a sum of E
T
T
and CH internal energy (E ). However, based on the
3
CH
3
modest internal energy of CH , the majority of this diagonal
3
axis is due to translational energy ͑80%–85%͒. One striking
feature of this triangle plot is the overwhelming fraction of
reaction exothermicity being funneled into HF vibration and
translational recoil. The plot is similar to the triangle plot for
We have performed a simple Franck–Condon analysis
of the transition state geometry in order to gain further in-
sight into the reaction dynamics. Our analysis consists of
evaluating one-dimensional overlap integrals between
asymptotic vibrational wave functions ͑for both HF and CH3
product molecules͒ and the ab initio transition state20 geom-
etry, where we focus on the HF stretch and CH bend mani-
folds. Numerically converged eigenvalues and wave func-
4
1
FϩH2, but with even slightly narrower rotational distribu-
tions. Such behavior is of course consistent with the dynam-
ics for reactions on an early barrier potential energy surface.
In light of our previous study of nonadiabatic effects in
8
the FϩH reaction, one interesting question is the potential
2
2
47
importance of spin orbit excited F*( P1/2) present in the
tions are calculated in a distributed Gaussian basis. HF
discharge F atom source. This is greatly aided by recent
high-resolution photoelectron experiments, which have de-
wave functions were calculated using a simple Morse
potential;21 the distribution of initial transition state geom-
etries is characterized by a Gaussian distribution ͑centered at
rH–Fϭ1.360 Å͒ ͑Ref. 20͒ with a width of 0.25 Å ͑based on
zero point amplitudes͒. The overlap integrals predict HF vi-
brational populations to increase rapidly with v, in good
qualitative agreement with the observation for HF(v
ϭ0–3). From a Franck–Condon perspective, this would re-
quire a rapidly changing C–H bond character at the transi-
tion state that results in vibrationally excited HF products.
4
2,43
termined the bond dissociation energy
for methane to be
Ϫ1
3
6 174͑9͒ cm . In conjunction with the well characterized
4
4,45
Ϫ1
HF bond dissociation energy
of 47 311͑5͒ cm , this pre-
dicts an overall reaction exothermicity of ⌬H
Ϫ1
ϭ11 137(10) cm
or 31.84͑3͒ kcal/mol, for the ground
2
spin–orbit state of F( P3/2) and the A-modification of meth-
ane (Jϭ0). The total energy to be distributed into the prod-
ucts is ⌬HϩECOMϭ11 767(210) cm , where the energy
Ϫ1
4
8,49
uncertainty is now completely dominated by the angular dis-
tribution of collision geometries. It is worth noting that this
Similar studies of the CH fragment
have been explored
3
for a Gaussian distribution of out of plane bending geom-
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3680
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H–C–H
Ј
2
0
ϭ107.2°), with a width of 12°. This Franck–Condon
analysis predicts significant excitation of CH3 bending
modes, which is not consistent with the previous experimen-
tal results by Sugawara.38 This behavior suggests that the
relaxation of the CH bend potential from methane ͑tetrahe-
3
dral͒ to methyl radical ͑planar͒ occurs over a longer range of
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1
1
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2
0
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3
1
1
2
3
VI. CONCLUSIONS
1
1
1
1
4
5
6
7
Nascent rovibrational HF product state distributions
have been obtained for the FϩCH →HF(v,J)ϩCH reac-
4
3
tion, using direct infrared absorption detection in a crossed
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Ϫ1
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an incentive for further efforts in both the development of
high quality ab initio potential surfaces as well as methods
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ACKNOWLEDGMENTS
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This research has been funded by the Air Force Office of
Scientific Research, with support from the National Science
Foundation in the development of the pulsed slit discharge
sources. W.W.H. thanks the National Research Council for a
postdoctoral research fellowship.
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1