Reactive scattering of F+HD→HF(v, J)+D: HF(v, J) nascent product state distributions and evidence for quantum transition state resonances

Article abstract of DOI:10.1063/1.1456507

The nascent distributions of HF quantum state distributions were studied for the F+HD→HF(ν,J)+D reaction, using a high-resolution direct infrared laser absorption study. The single collision reactive scattering dynamics of the reaction revealed strong evidence for quantum transition state resonance dynamics near E_com?0.6kcal/mol. Several rotational states in the HF(ν=3) vibrational manifold were also observed.

Full text of DOI:10.1063/1.1456507

Reactive scattering of F + HD → HF (v,J)+ D:HF (v,J) nascent product state distributions
and evidence for quantum transition state resonances
Warren W. Harper, Sergey A. Nizkorodov, and David J. Nesbitt
Citation: The Journal of Chemical Physics 116, 5622 (2002); doi: 10.1063/1.1456507
View online: http://dx.doi.org/10.1063/1.1456507
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/116/13?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 116, NUMBER 13
1 APRIL 2002
Reactive scattering of F¿HD\HF„v,J…¿D: HF„v,J… nascent product state
distributions and evidence for quantum transition state resonances
Warren W. Harper,a) Sergey A. Nizkorodov,b) 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 31 October 2001; accepted 11 January 2002͒
Single collision reactive scattering dynamics of FϩHD→HF(v,J)ϩD have been investigated
Ϫ1
exploiting high-resolution ͑⌬␯Ϸ0.0001 cm ͒ infrared laser absorption for quantum state resolved
detection of nascent HF(v,J) product states. State resolved Doppler profiles are recorded for a series
of HF rovibrational transitions and converted into state resolved fluxes via density-to-flux analysis,
yielding cross-section data for relative formation of HF(v,J) at EcomϷ0.6(2), 1.0͑3͒, 1.5͑3͒, and
1.9͑4͒ kcal/mol. State resolved HF(v,J) products at all but the lowest collision energy exhibit
Boltzmann-type populations, characteristic of direct reactive scattering dynamics. At the lowest
collision energy ͓EcomϷ0.6(2) kcal/mol͔, however, the HF(vϭ2,J) populations behave quite
anomalously, exhibiting a nearly ‘‘flat’’ distribution out to JϷ11 before dropping rapidly to zero at
the energetic limit. These results provide strong experimental support for quantum transition state
resonance dynamics near EcomϷ0.6 kcal/mol corresponding classically to H atom chattering
between the F and D atoms, and prove to be in remarkably quantitative agreement with theoretical
wave packet predictions by Skodje et al. ͓J. Chem. Phys. 112, 4536 ͑2000͔͒. These fully quantum
state resolved studies therefore nicely complement the recent crossed beam studies of Dong et al. ͓J.
Chem. Phys. 113, 3633 ͑2000͔͒, which confirm the presence of this resonance via angle resolved
differential cross-section measurements. The observed quantum state distributions near threshold
also indicate several rotational states in the HF(vϭ3) vibrational manifold energetically
2
inaccessible to F( P3 ) reagent, but which are consistent with a minor ͑Շ5%͒ nonadiabatic
/2
2
contribution from spin–orbit excited F*( P1/2). © 2002 American Institute of Physics.
͓
DOI: 10.1063/1.1456507͔
I. INTRODUCTION
than Born–Oppenheimer propagation on a single adiabatic
potential surface. This confluence of fully quantum state re-
solved experiment and theory has provided a powerful op-
portunity for testing potential surfaces and dynamical meth-
ods as well as the requisite ‘‘intellectual fuel’’ for numerous
controversies over the years.
The FϩH →HF(v,J)ϩH reaction has been of enor-
2
mous fundamental importance in the study of chemical reac-
tion dynamics. This system with its FϩHD, FϩD isotopic
2
variants represent the simplest exothermic three-atom bimo-
lecular reaction and has been subjected to increasing levels
Although the isotopically related FϩHD system shares
the same Born–Oppenheimer ͑i.e., adiabatic͒ potential en-
of scrutiny from both experimental1 and theoretical
–8
9–13
perspectives. This class of H atom abstraction reaction has
been experimentally investigated using methods ranging
ergy surface with FϩH , there are subtle but important dif-
2
ferences that have made it of compelling dynamical interest.
from the classic arrested relaxation infrared ͑IR͒ chemilumi-
First of all, the H symmetry is broken by a D atom substi-
2
nescence studies of Polanyi and co-workers,1
4,15
to crossed
tution, which makes reactive events at the two ends of the
molecule experimentally distinguishable. Thus, in the limit
of direct reactive scattering dynamics, one can isolate dy-
namical pathways semiclassically corresponding to F atom
attack on D or H end by detection of HF or DF product.
Second, this asymmetry eliminates the role of ortho/para
nuclear spin states in reagent HD, which therefore permits
efficient cooling in the supersonic expansion environment
into nearly a single (JϷ0) rotational level. Of primary dy-
namical importance for this work, however, is that D atom
substitution provides a F–H–D ‘‘heavyϩlight-heavy’’ transi-
tion state for F attack on the H atom, which has been
beam detection of HF/DF products via moderate resolution
energy loss methods,7 to recent high resolution crossed
,8
beam studies via Rydberg tagging and time of flight analysis
of H/D atom recoil.1
6,17
Full three-dimensional ͑3D͒ quan-
tum theoretical studies of these reactions are tractable due to
the presence of only a single heavy ͑i.e., nonhydrogenic͒
atom. Indeed, the FϩH system represents one of the few
2
reactions that have successfully permitted study in full di-
mensionality at the ab initio level, with converged calcula-
tions feasible without any dynamical approximations other
a͒Current address: Pacific Northwest National Laboratory, P.O. Box 999 MS
K5-25, Richland, WA 99352.
18
predicted to enhance quantum ‘‘transition state resonances’’
corresponding to excitation of quasibound vibrational motion
weakly coupled to the reaction coordinate. Indeed, the role of
b͒
Current address: California Institute of Technology, M/C 127-72, Pasa-
dena, CA 91125.
0021-9606/2002/116(13)/5622/11/$19.00
5622
© 2002 American Institute of Physics
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1

J. Chem. Phys., Vol. 116, No. 13, 1 April 2002
Reactive scattering of FϩHD→HF(v,J)ϩD
5623
versions can be readily rationalized by conservation of
energy in the reactive event, with the more internally ener-
getic upper states having less energy left for velocity recoil.
Although high resolution Dopplerimetry on FϩHD is sub-
stantially more difficult by virtue of smaller reduced mass for
the ejecting D atom, it represents a twofold improvement
such transition state resonances in the FϩH reaction system
has been one of long standing controversy, for which a full
2
consensus is still not yet achieved. However, there is now
strong theoretical evidence1
8,19
for a broad quantum transi-
tion state resonance in FϩHD at low collision energies
Ϸ0.5 kcal/mol͒, corresponding semiclassically to rapid H
͑
over FϩH kinematics and can indeed be partially resolved.
atom ‘‘chattering’’ between the heavier F and D atom. Ex-
perimental confirmation of such transition state resonance
dynamics has been elegantly provided in the Liu
2
Most importantly, however, studies with complete resolution
of rovibrational quantum states provide a rare opportunity
for rigorous benchmark comparisons between experiment
and theory for fundamental atomϩdiatom reaction dynamics
on a single, well characterized potential energy surface.
The organization of the rest of this paper is as follows.
Section II briefly summarizes the experimental method with
emphasis on details relevant to the present study. Section III
follows with Doppler resolved absorption results on FϩHD
reactive scattering, followed in Sec. IV by Monte Carlo
simulations of the density-to-flux transformation, which are
necessary to obtain nascent HF(v,J) product state distribu-
tions from direct absorption measurements as a function of
center-of-mass collision energy. Comparison of the experi-
mental HF(v,J) product state distributions with ab initio the-
oretical dynamics calculations by Chao et al. are discussed in
Sec. V, with particular focus on anomalous changes in the
HF(vϭ2,J) distribution topology at collision energies near
the predicted transition state resonance. Furthermore, analy-
sis of the near threshold HF(vϭ3,J) product distributions at
Ecomϭ0.6(2) kcal/mol indicate weak branching into rota-
tional levels energetically inaccessible to ground state
1
8,19
laboratory
by time-of-flight analysis of the D atom prod-
uct, specifically monitoring angular changes in the vibra-
tionally resolved differential cross sections as a function of
collision energy.
As a special motivating force for the current studies, an
anomalous and distinctive independent signature of this
quantum transition state resonance is also predicted in the
HF(v,J) rotational state distributions. Wave packet calcula-
tions by the Skodje group1
8,20
predict two qualitatively dif-
ferent classes of product state distributions for HF(v,J)
products. Far away from the resonance energy, product for-
mation is predicted to occur by ‘‘direct’’ reactive scattering,
yielding distributions with a gradual, ‘‘Boltzmann-like’’
dropoff in rotational J state. Products from the transition
state resonance channel, on the other hand, are thought to
occur via tunneling through a strongly noncollinear barrier,
which is therefore greatly enhanced by rotational excitation
of the nascent HF in the transition state region. As a result of
this competition between ͑i͒ J dependent enhancement of
resonance decay rate and ͑ii͒ J dependent drop off due to
energetic constraints, the HF(v,J) product states have been
2
F( P )ϩHD reactions, suggesting the presence of minor
3
/2
2
2
0
͑Շ5%͒ contributions from nonadiabatic F*( P1/2)ϩHD
predicted to yield nearly ‘‘flat’’ J distributions ͑although
with significantly local structure͒ right up to the energetic
cutoff. Such tests for the rotational ‘‘signatures’’ of quantum
transition-state resonance behavior requires complete experi-
mental resolution of the nascent HF(v,J) rotational state
populations as a function of collision energy, which repre-
sents the primary thrust of this paper.
channels. Section VI summarizes and concludes the paper.
II. EXPERIMENT
The crossed jet apparatus has been described in detail
previously;1
,2,21
only features pertinent to the current study
will be briefly summarized in this section. The reaction ves-
sel is a 65 L vacuum chamber pumped by a 10 in. diffusion
pump fitted with a water-cooled baffle trap and roughed with
a Roots23 blower. Two pulsed valves oriented at right angles
to the probe laser deliver short gas pulses of jet cooled F and
HD reagents, at total densities such that the collision prob-
ability is Ͻ1%; thus the probability of reagents/products ex-
periencing multiple collisions can be safely neglected. The
chamber is pumped out to a background pressure of Ͻ5
To achieve the necessary quantum state detection speci-
ficity, we have combined high sensitivity, single-mode IR
laser absorption methods with crossed beam reactive scatter-
ing for direct monitoring of nascent products under rigor-
ously single collision conditions. The crucial advantage of
single mode sources for studying reaction dynamics is the
Ϫ1
high spectral resolution ͑⌬␯Ϸ0.0001 cm ͒, which translates
into HF(v,J) product state detection with complete rovibra-
tional quantum state resolution. In fact, the intrinsic velocity
resolution is sufficiently good ͑Ϸfew meters/s͒ that the ab-
sorption profiles exhibit Doppler line broadening effects due
to HF translational energy recoil, the dynamics of which can
be studied for favorable kinematic mass combinations by
high resolution IR laser Dopplerimetry methods. This has
Ϫ6
Ϫ4
ϫ10 Torr and remains below 1ϫ10 Torr with both
valves running at 10 Hz. After the reaction event, the HF
product is detected by high-resolution IR laser absorption
monitored using two matched InSb detectors to record the
transient absorbance response for each HF rovibrational tran-
sition of interest. Figure 1 provides a schematic of the ex-
perimental setup, where the two jet expansion axes are mu-
tually orthogonal to each other and the detection laser. The
contours drawn in the jet intersection region ͑obtained from
detailed Monte Carlo simulations described in Sec. IV A͒
illustrate the probability of detecting HF after a reactive
event. These contours are very strongly peaked within a
been most recently demonstrated for FϩCH reactive
4
2
1,22
scattering,
for which the CH product provides a suffi-
3
cient mass for developing substantially high HF recoil
speeds in the reactive event. This capability permits detec-
tion and elucidation of frequency dependent Doppler profiles
from ͑i͒ stimulated emission ͑near line center͒ and ͑ii͒ ab-
sorption ͑at large detuning͒ due to velocity dependent popu-
lation inversions in the crossed jet reaction zone. These in-
3
small detection volume ͑Ϸ3 cm ͒ at the jet intersection re-
gion, with low probability tails that extend toward each
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5624
J. Chem. Phys., Vol. 116, No. 13, 1 April 2002
Harper, Nizkorodov, and Nesbitt
half maximum ͑HWHM͒ values of 19° and 40° for the lim-
iting cases parallel and perpendicular to the slit axis. Reac-
tive scattering experiments are performed with the slit paral-
lel to the laser axis ͑perpendicular to the HD expansion͒; this
configuration has the advantage of prefocusing the initial F
atom reagent ͑and thus HF absorption signals͒ into a nar-
rower Doppler velocity group without loss of absorption path
length. The F /Ar jet speed can be obtained either by direct
2
1
laser Dopplerimetry or time-of-flight of absorption signals;
the measured value of 560͑5͒ m/s agrees well with calculated
speeds from standard adiabatic expansion formulas.
The HD source consists of HD/argon gas mixtures ex-
panding through a piezoelectric valve24 with a 145͑5͒ ␮m
orifice and 200 ␮s gas pulse, timed to coincide with the F
atom source in the intersection region. The reagent HD jet is
characterized by recording Doppler profiles for small dopant
FIG. 1. Schematic of the crossed supersonic jet experiment for FϩHD re-
action dynamics. Nascent HF(v,J) product states are formed and detected
via shot noise limited direct absorption with a single mode IR laser multi-
passed 20 times through the jet intersection region in a Herriot cell configu-
ration. The set of contours ͑in 10% increments͒ represent Monte Carlo simu-
lations of events producing HF from a specific spot in the jet intersection
region ͑see text for details͒. The contours are strongly peaked in the detec-
tion volume, but extending slightly toward each valve.
levels of HF or CH in the argon/HD gas mixtures and in-
4
verting to angular distributions for each gas mixture. On-axis
jet speeds are measured using Dopplerimetry or optical time-
of-flight techniques,1 yielding 2310͑25͒ m/s ͑neat HD͒,
1
1
970͑30͒ m/s ͑3% Ar/HD͒, 1620͑40͒ m/s ͑9% Ar/HD͒, and
150͑40͒ m/s ͑25% Ar/HD͒ as a function of expansion dilu-
tion.
Of special importance is the distribution of rotational
states in the HD jet. In the previous studies of FϩH dynam-
2
pulsed valve. These tails are due to single collision FϩHD
reactions occurring slightly upstream, yielding products re-
coiling collision free into the laser detection region. This
necessarily translates into a distribution of collision geom-
etries and thus a somewhat broader range of collision ener-
gies than could be obtained with skimmed beams. However,
the implementation of crossed jets as opposed to skimmed
beams is dictated by sensitivity demands for long absorption
path lengths, which provide necessary detection limits for
ics, complete cooling of the H (J) reagent distributions was
2
limited by ⌬Jϭ2 partially rotational energy differences and
lack of ortho/para spin relaxation channels. This absence of
full rotational relaxation for H expansions could be inferred
2
from the measured terminal jet speeds, which were slower
than predicted from adiabatic heat capacity formulas due to
1
unrelaxed H rotational energy. From a similar analysis of
2
terminal jet speeds for neat HD expansions, the rotational
temperature can be estimated to be р50 K, which would
predict HD populations of 0.812:0.186:0.002 for HD(J
ϭ0,1,2), i.e., largely confined to the ground state. In fact,
this HD rotational cooling improves dramatically with Ar
diluent, where reverse seeding is utilized to slow down the
HD reagent for the lowest collision energies sampled. Under
these Ar diluent conditions, we conservatively estimate the
HD rotational temperature to be р40 K, which translates
into upper limit HD(Jϭ0,1,2) populations of 0.892:0.107:
Ͻ0.001, respectively. This proves to be relevant for studies
of the transition state resonance dynamics at the lowest col-
lision energies sampled (EcomϷ0.6 kcal/mol), which there-
fore take place with nearly pure HD(Jϭ0) reagent and only
р11% contributions from any rotationally excited HD(J
у1).
7
3
absorbers such as HF down to Ͻ10 molecules/cm /quantum
state.
The reactive F atoms are produced in situ for each pulse
by passing a 5% fluorine/95% argon mixture through a
pulsed discharge valve located 5.1 cm from the intersection
region. The F-atom source consists of two electrodes
mounted at the exit of a solenoid valve, one of which is in
contact with the metal body of the valve. As the gas pulse
͑Ϸ1 ms duration͒ expands into the vacuum, a high voltage
pulse ͑ϷϪ800 V, 600 ␮s͒ is applied to the bottom of two
electrodes separated by a thin ͑550 ␮m͒ Kel-F spacer. The
resulting current pulse first crosses a 500 ⍀ ballast resistor
before going to the electrode, stabilizing the discharge and
allowing a convenient measurement of real time currents
͑Ϸ0.4–0.5 A peak͒. The limiting orifice of the valve is a 500
The HD gas is prepared using the exothermic reaction
␮mϫ5 mm slit, optimized to provide stable discharges on
LiD(s)ϩH O(1)→HD(g)ϩLiOH(s), which goes to
the week-long time scale between routine maintenance. As a
consequence of the slit valve, the angular distributions are
functions of both ␪ ͑angle from expansion axis͒ and ␾ ͑angle
about the expansion axis͒. However, these can be measured
2
completion even at high HD gas pressures. A vacuum tight
reactor is fabricated from a stainless steel pipe with flanges
welded on each end and gas line connections attached to one
end. LiD(s) reagent is placed in a stainless steel cage that
can be lowered in the reactor under vacuum into excess
deionized H2O. The reactor is assembled and evacuated
down to the vapor pressure of water in order to remove re-
sidual nitrogen and oxygen. The cage is then slowly lowered
directly by doping a small amount of HF or CH into the 5%
4
fluorine/argon mixture, recording Doppler absorbances, and
inverting these profiles analytically to obtain angular distri-
butions. The angular distributions for each ␾ can be well
n
characterized as power laws in cos (␪), with half width at
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J. Chem. Phys., Vol. 116, No. 13, 1 April 2002
Reactive scattering of FϩHD→HF(v,J)ϩD
5625
into the water to trigger a vigorous chemical reaction ͑cooled
with an alcohol bath of Ϫ10 °C͒, which can be conveniently
moderated by regulating cage height. The resulting HD prod-
uct is collected in a gas cylinder after passing through a
Ϫ100 °C silica bead trap to remove residual water vapor; HD
pressures of 300 psi can be easily obtained and controlled by
the amount of LiD reagent. The HD synthesis method is
limited by LiD isotopic purity to Ϸ99%, as directly quanti-
fied by rotationally resolved Raman spectroscopy on sample
gas aliquots. During experimental runs, a cold trap ͑Ϫ80 °C͒
removes any trace residual H O vapor present in the HD just
2
prior to the pulsed valve.
The infrared laser has been described previously.1
,21,25
ϩ
The cw IR source is a Kr pumped color center laser, retro-
fitted with tunable intracavity galvo plates and an etalon ser-
voloop for continuous, single mode scanning. The IR is split
into two equal signal and reference beams, with the signal
beam going through the vacuum chamber in a Herriot
2
6,27
cell
multipass configuration ͑20 passes͒ to enhance de-
tection sensitivity. Signal and reference photocurrents are
subtracted down to the shot noise limit using servoloop elec-
tronics with 10 -fold common mode rejection. The differ-
FIG. 2. Sample Doppler profile data on nascent HF(v,J) product states
from FϩHD reactive events.
5
ence signal is low pass filtered, recorded with a transient
digitizer, and transferred to a computer for analysis and data
storage. Software integration is used to isolate transient sig-
nal changes occurring in the temporal overlap between the
two crossed jets, with DC IR power levels monitored to yield
absolute absorbances. IR power levels are Ͻ100 ␮W to en-
sure negligible pertubation of rovibrational populations by
stimulated absorption/emission effects as well as maintain
Savitzky–Golay filtering process,28 which takes advantage of
the large number of laser frequency steps sampled over the
full scanning event. Additional S/N enhancement in the
overall data set is achieved by ͑i͒ scanning each transition
multiple times, ͑ii͒ probing redundant transitions out of the
same state, as well as ͑iii͒ integrating over Doppler profiles
to obtain column integrated densities. Reference data on the
vϭ3� 2; R(4) transition is recorded for normalization at
regular intervals during all experimental runs; this success-
fully corrects for low frequency drift and day-to-day fluctua-
tions in F-atom production efficiency. As an indication of
intentional redundancy in data acquisition, the total number
of Doppler scan measurements and quantum state popula-
tions determined are summarized in Table I for each collision
energy. In all cases, there are fourfold to sixfold more mea-
surements than the number of quantum states populated,
which is sufficiently over-determined to permit high S/N ex-
traction of populations.
detectors in a linear regime. Minimum detectable absorbance
Ϫ5
͑
in a nominal 20 kHz detection bandwidth͒ is Ϸ1ϫ10
,
6
translating into a sensitivity of 5ϫ10 HF(v,J)products/
3
cm /quantum state with modest signal averaging.
III. RESULTS
High-resolution Doppler profiles of HF(v,J) product
have been recorded over all relevant HF ⌬vϭϮ1 transitions
within the tuning range of the color center IR laser ͑2.5–3.3
␮m͒, and at each of four collision energies ͓EcomϷ0.6(2),
1.0͑3͒, 1.5͑3͒, and 1.9͑4͒ kcal/mol͔. Particular attention has
naturally been focused on transitions out of the vЉϭ2 and
vЉϭ3 manifold, where quantum transition-state resonance
and near threshold effects are predicted to be most relevant.
Transitions originating from the HF(vЉϭ1,J) manifold have
also been studied at the two highest collision energies, but
this proves unfeasible at current signal-to-noise levels due to
rapid decrease in signal intensity for collision energies below
The high resolution Doppler absorbance profiles, A(␯),
are integrated over the laser frequency and converted to
quantum state resolved column-integrated densities ͑CID͒
according to
8
␲3␯0
͉
m
͉
␮2
͐
͓HF͑␯Љ,JЉ͔͒dl
͑2JЉϩ1͒
͵
A͑␯͒d␯ϭ
ͫ
3
hc
Ϫ1
the activation barrier. Scans are performed over у0.1 cm
͐
͓HF͑␯Ј,JЈ͔͒dl
around the transition center, which for typical profiles corre-
spond to a 10-fold broader baseline than the Doppler
FWHM. Signal scans are corrected for weak background ab-
sorptions due to trace HF impurities in the F atom discharge
source ͑Ͻ10% of peak signals͒ by repeating the scans with
the HD valve on and off. Figure 2 shows representative
R-branch data at Ecomϭ1.9 kcal/mol collision energy, reveal-
Ϫ
,
͑1͒
ͬ
͑
2JЈϩ1͒
where ␯0 is the transition center frequency, mϭJЉϩ1
(ϪJЉ) for R(P) branch transitions, and ␮ represents the
transition dipole moment obtained from extensive studies by
Setser29 and Stwalley. Equation ͑1͒ has been used to least
squares fit the entire set of absorption data for each of the
four collision energies, yielding column-integrated densities
as a function of final HF(v,J) product state. Due to the large
number of redundant measurements for each J state, the
30
Ϫ4
ing ‘‘strong’’ absorbance signals of Ϸ2ϫ10 with the rms
Ϫ5
shot noise limited noise of Ϸ2ϫ10 and signal to noise
(
S/N)Ϸ10. Also shown are profiles obtained from a
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5626
J. Chem. Phys., Vol. 116, No. 13, 1 April 2002
Harper, Nizkorodov, and Nesbitt
TABLE I. Summary of probed HF(v,J) levels for each collision energy. Numbers reflect the total of all
repetitive measurements, with the values in parentheses indicating the number of unique transitions ͓i.e., vЈ
�
vЉ, R(J)͔ probed.
Collision
energy
Total number of
P-branch
R-branch
v,J populations
Number of
͑kcal/mol͒
transitions
transitions
transitions
determined
reference lines
1.9͑4͒
1.5͑3͒
1.0͑3͒
0.6͑2͒
176͑72͒
159͑59͒
147͑40͒
98͑30͒
96 ͑40͒
69 ͑29͒
60 ͑18͒
20 ͑10͒
80 ͑32͒
90 ͑30͒
87 ͑22͒
78 ͑20͒
40
39
24
20
86
66
66
42
variance–covariance matrix resulting from the least squares
fit describes the uncertainties in these column-integrated den-
sities reasonably well.
calculated from known speeds and collision geometries, ap-
propriately weighted by relative velocity vectors and reagent
densities, i.e., ϰ␳1␳2͉ ͉. Monte Carlo integration is per-
vrel
formed by randomly sampling over a sufficiently large num-
8
IV. ANALYSIS
ber of points (Ϸ10 ) inside the detection volume to ensure
convergence. Collision energy distributions for the four ex-
perimental conditions are shown in Figs. 3 and 4, with the
first and second central moments denoted by vertical and
horizontal lines, respectively. As expected, the collision en-
ergy uncertainties are dominated by the distribution of colli-
sion geometries and impacted to a much weaker extent by
the much narrower distribution of supersonic jet speeds. For
The primary data from these experimental studies are
column-integrated densities of nascent HF(v,J) product.
However, the more fundamental quantity characterizing re-
action dynamics is the reactive flux into a specific quantum
state, which therefore requires a careful consideration of the
density-to-flux transformation. For direct absorption mea-
surements, this transformation requires scaling integrated ab-
sorbance signals by the residence time in the laser beam for
a given HF(v,J) product state. Since the center-of-mass ve-
locity vector is largely carried by the F atom motion, these
density to flux scaling factors can be estimated from detailed
Monte Carlo simulations for a given experimental geometry,
with only modest theoretical input on angular scattering dis-
tributions, as described below. Indeed, these simulations also
permit many other useful statistics for the collision ensemble
to be obtained, such as the mean and spread in the distribu-
tion of sampled collision energies (Ecom). Finally, the ex-
perimentally inferred fluxes of HF(v,J) product states can be
translated into the desired relative cross sections from known
͗ ͘
vrel
reagent densities and the average relative velocity, .
A. Monte Carlo simulations
As mentioned above, to achieve suitable signal/noise
levels with shot noise limited IR laser absorbance methods,
the current experiments take advantage of unskimmed super-
sonic jets to provide significantly enhanced path lengths
͑Ϸ50 cm͒ while still maintaining single collision conditions.
This necessarily introduces a range of angles with which the
reagent species collide; even for supersonically cooled ex-
pansions this leads to a finite distribution of collision ener-
gies, P(Ecom). To obtain these distributions, we have utilized
Monte Carlo simulations, the details of which have been de-
2
1,22
scribed in previous work on the FϩCH reaction system.
4
As input data, high resolution IR laser Dopplerimetry tech-
niques are first used to measure the jet angular distributions,
while jet speeds along the expansion axis are characterized
using optical time-of-flight methods. To estimate the result-
ing spread in collision energies, points are randomly selected
in the experimental detection region, which is conservatively
approximated as a cube with the pulsed valves centered on
adjacent faces. The center-of-mass collision energy is then
FIG. 3. Energetics for the FϩHD reaction. The heavy solid line indicates
the 31.19͑1͒ kcal/mol reaction exothermicity, while the curves in the upper
right corner represent the additional center of mass collision energy ͑see also
Fig. 4͒. All HF(v,J) product states below a given collision energy distribu-
tion are energetically accessible. The blow up of this region ͑see inset͒
displays the threshold levels along with the energy available for each colli-
sion energy.
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1

J. Chem. Phys., Vol. 116, No. 13, 1 April 2002
Reactive scattering of FϩHD→HF(v,J)ϩD
5627
effects are insufficiently dominant to make a full Dopplerim-
etry analysis feasible. As a compromise, therefore, the
density-to-flux multipliers ͑DFM͒ are constructed from a
weighted sum:
iϭcos͑␲͒
Ϫ1
DFM͑v,J͒ϭ
͗
␶i,v,J
͘
ϫWi,v,J
,
͑2͒
ͫ
͚
ͬ
iϭcos͑0͒
where ͑i͒
͗
␶i,v,J
͘
are the average residence times calculated
for each HF(v,J) quantum state in a specific cos(␪ ) bin, and
i
͑
ii͒ wi,v,J 2 are normalized weights proportional to
0
theoretically calculated differential cross sections. While
this density-to-flux transformation relies on theoretical input,
this dependence is not overly strong since the residence time
␶
is largely dominated by forward center of mass motion in
the laboratory frame. As shown in Eq. ͑2͒, the density-to-flux
multiplier is equal to the inverse of the differential-cross-
section averaged residence time, so that the density-to-flux
transformation is achieved simply by multiplying by
DFM(v,J). The resulting fluxes have also been scaled by
argon dilution in the HD jet as well as by average collision
FIG. 4. Monte Carlo calculated collision energy distributions for each
collision energy studied in this work. Note that the distributions are near
Gaussian, with a slight asymmetry extending to higher collision energies.
The vertical and horizontal lines indicate average and variance for each
distribution.
vrel
speed (͉ ͉) to obtain results directly proportional to the
a simple rule of thumb, the FWHM values scale more or less
desired state-to-state reaction cross sections.
͗ ͘
linearly in Ecom , corresponding to a roughly 25% spread in
collision energies. ͑See Table II.͒
B. Nascent HF„v,J… populations and relative state-to-
To correctly determine final state fluxes ͑j͒ from column
integrated densities ͑␳͒ requires a density-to-flux transforma-
tion. The experimentally determined averages of these quan-
state cross sections
Table III reports relative cross sections for formation of
HF(v,J) product states at each of the four collision energies
studied. The full data set has been normalized to 100% only
for the highest collision energy ͓Ecomϭ1.9(4) kcal/mol͔, so
the v,J dependent changes in state-to-state cross sections
with decreasing collision energy are accurately reflected. The
DFM(v,J) values used in the density to cross-section trans-
formation differ by approximately equal twofold over all vi-
brational levels studied, but varying less than 20% within a
given rotational manifold. The error bars quoted reflect 1␴
estimates based on variance/covariance matrices obtained
from least squares fits to the column-integrated densities. Er-
rors estimated in this manner are most reliable when the
number of measurements is large compared to the number of
parameters determined. A simple statistical analysis based on
the student distribution33 and four to six measurements for
each HF(v,J) state ͑see Table I͒ predicts less than a 20%
increase in these error estimations.
tities are linked by
frame recoil velocity component perpendicular to the laser
probe axis. The average reciprocal speed 1/vЌ scales as the
͗ ͘ ͗ ͘
␳ ϭ j/vЌ , where vЌ is the laboratory
͗
͘
average residence time ͗␶͘ in the laser beam; thus the
density-to-flux transformation is simply proportional to 1/͗␶͘;
note that this differs from ͗1/␶͘ for any finite spread in ␶. One
advantage of the FϩHD system is that the reaction exother-
micity is known from spectroscopic measurements of HF
and HD bond strengths to Ϸ0.01 kcal/mol accuracy.3
Thus the recoil speed of any HF(v,J) product state can be
reliably obtained from conservation of energy and momen-
tum for a known incident collision energy and reaction exo-
thermicity. For a discretized bin of scattering angles in the
center-of-mass frame, the average residence time ͗␶͘ can
therefore be explicitly calculated. This also permits us to
construct predicted laboratory frame Doppler profiles for
scattering into a given center-of-mass angular range, which
represents the first step in a high resolution Dopplerimetry
analysis.
1,32
The HF(v,J) rotational distributions for vϭ2 and 3 are
represented graphically in Fig. 5 and indicate several inter-
esting trends. First of all, the HF(v,J) distributions at the
higher collision energies appear ‘‘Boltzmann-like,’’ i.e., ex-
hibiting a rapid initial growth followed by a gradual mono-
tonic decay with increasing J. This is qualitatively similar to
For light H or D atom ejection, however, the recoil
speeds imparted to the product HF(v,J) are only comparable
to the initial velocity spread in the jet. Though these recoil
distributions clearly impact the data via line broadening, the
previous quantum state resolved observations in FϩH and
2
FϩCH systems, and from comparison with theoretical cal-
4
TABLE II. Supersonic jet and collision characteristics.
culations ͑see below͒, the result appears to be characteristic
of direct reactive scattering dynamics associated with rapid
H atom abstraction from the HD. Second, there is a strong
dependence of cross sections on center of mass collision en-
ergy. This effect is most pronounced for the HF(vϭ3,J) dis-
tributions; specifically, the peak cross sections for HF(v
ϭ3,J) vary by over an order of magnitude for a threefold
vF (m/s)
% Ar/HD
vHD (m/s)
Eperp
Ecom
561
561
561
561
0.0
3.0
9.0
2310
1970
1620
1150
1.76
1.31
0.92
0.51
1.88͑43͒
1.46͑34͒
1.04͑25͒
0.59͑16͒
25.0
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5628
J. Chem. Phys., Vol. 116, No. 13, 1 April 2002
Harper, Nizkorodov, and Nesbitt
TABLE III. HF(v,J) state-to-state relative reaction cross sections. Results are after density-to-flux transformation, scaling for dilution by argon, and division
by the average collision velocity. The numbers in parentheses are 1␴ errors. The cross sections have been normalized such that summing over all Ecom
ϭ1.9 kcal/mol data gives 100%.
Ecomϭ1.9(4) kcal/mol
vϭ2
Ecomϭ1.5(3) kcal/mol
vϭ2
Ecomϭ1.0(3) kcal/mol
Ecomϭ0.6(2) kcal/mol
J
vϭ3
vϭ1
vϭ3
vϭ1
vϭ3
vϭ2
vϭ3
vϭ2
0
2.29͑10͒
4.42͑15͒
3.01͑13͒
1.38͑13͒
0.55͑15͒
0.12͑14͒
0.17͑14͒
0.04͑14͒
2.01͑14͒
5.69͑23͒
7.36͑26͒
7.65͑26͒
7.60͑18͒
7.20͑28͒
5.80͑27͒
4.73͑25͒
4.24͑26͒
3.25͑19͒
2.72͑21͒
2.07͑21͒
1.34͑27͒
0.82͑70͒
Ϫ0.28͑38͒
0.03͑60͒
0.59͑38͒
0.72͑47͒
1.32͑49͒
3.01͑44͒
3.21͑45͒
2.85͑41͒
2.10͑49͒
1.75͑47͒
1.15͑43͒
2.11͑45͒
1.07͑49͒
1.26͑42͒
1.58͑48͒
1.56͑78͒
1.52͑104͒
Ϫ0.03͑67͒
1.70͑5͒
3.03͑8͒
1.58͑7͒
0.49͑7͒
0.31͑8͒
0.12͑6͒
Ϫ0.02͑6͒
1.97͑11͒
4.90͑15͒
6.20͑20͒
6.31͑22͒
6.49͑13͒
5.73͑19͒
4.27͑19͒
3.94͑24͒
3.07͑14͒
2.75͑16͒
1.98͑9͒
1.72͑11͒
0.76͑12͒
Ϫ0.03͑32͒
0.03͑22͒
0.04͑11͒
0.15͑23͒
0.62͑38͒
1.14͑37͒
1.27͑55͒
1.41͑39͒
1.45͑30͒
2.04͑38͒
1.36͑35͒
1.37͑39͒
0.98͑34͒
1.56͑31͒
0.83͑27͒
1.16͑27͒
0.68͑26͒
0.33͑43͒
0.18͑46͒
1.01͑5͒
1.42͑8͒
0.86͑11͒
0.39͑8͒
0.25͑9͒
0.11͑6͒
1.63͑13͒
4.28͑20͒
4.81͑20͒
4.83͑32͒
4.61͑19͒
4.47͑22͒
3.92͑17͒
2.92͑32͒
2.50͑16͒
2.33͑13͒
1.53͑16͒
1.30͑15͒
0.65͑15͒
0.19͑16͒
Ϫ0.22͑39͒
Ϫ0.09͑8͒
0.29͑4͒
0.36͑7͒
0.21͑7͒
0.14͑8͒
Ϫ0.06͑6͒
0.02͑6͒
0.97͑10͒
1.75͑15͒
1.85͑17͒
2.26͑18͒
1.97͑18͒
1.59͑16͒
1.90͑20͒
1.48͑15͒
1.34͑13͒
1.86͑13͒
1.27͑22͒
1.22͑32͒
Ϫ0.05͑38͒
0.10͑45͒
1
2
3
4
5
6
7
8
9
0
Ϫ0.10͑8͒
Ϫ0.03͑4͒
1
1
1
12
13
14
15
nels into 1–2 rotational levels that should be energetically
decrease in Ecom . This heightened sensitivity is readily ra-
tionalized by conservation of energy constraints; the F
ϩHD(Jϭ0) reaction is insufficiently exothermic ͓31.19͑1͒
2
closed to F( P3/2)ϩHD(Jϭ0) at each E ; we will return
com
to this point in Sec V.
3
1,32,34
By way of contrast, there is a much reduced sensitivity
to collision energy in the HF(vϭ2,J) manifold, which varies
only by approximately equal threefold at low J for a similar
threefold change in Ecom . What is particularly noteworthy,
however, is that this decreased sensitivity to Ecom becomes
quite prominent at higher J values, resulting in only modest
changes in cross section at JϷ11 over the same threefold
range of collision energies. Stated differently, the HF(v
ϭ2,J) distributions noticeably ‘‘flatten’’ with respect to J for
the lowest collision energies sampled (EcomϷ0.6 kcal/mol),
as opposed to the more Boltzmann-type distributions in
HF(vϭ2,J) consistently observed at higher energies. From
detailed calculations by Chao and Skodje,20 this proves to be
kcal/mol͔
to form even the lowest state in the HF(v
ϭ3,J) manifold ͑32.52 kcal/mol͒ without the additional cen-
ter of mass collision energy. In fact, a closer comparison of
Figs. 3 and 5 indicates the presence of minor formation chan-
a
characteristic product state signature for quantum
transition-state resonance behavior in FϩHD, which is theo-
retically predicted to occur near EcomϷ0.5–0.6 kcal/mol.
V. DISCUSSION
The anomalous change in topology of the HF(vϭ2,J)
distributions with collision energy near the predicted FϩHD
transition state resonance provides a particularly useful op-
portunity for benchmark comparison with full quantum
wave packet calculations. The relevant data are illus-
trated more clearly in Figs. 6͑a͒ and 6͑b͒, which ex-
hibits HF(vϭ2,J) distributions at energies significantly
above ͓Ecomϭ1.9(4) kcal/mol͔ and essentially at ͓Ecom
ϭ0.6(2) kcal/mol͔ the FϩHD transition-state resonance.
Figure 6͑a͒ indicates that the HF(vϭ2,J) distributions at
higher collision energies exhibit a very hot but nevertheless
FIG. 5. HF(v,J) state-to-state reaction cross sections for vϭ2, 3 as a func-
tion of collision energy. The data are normalized such that the sum of all
cross sections at 1.9 kcal/mol collision energy is 100%. A rapid decrease in
vϭ3 cross sections is evident as the channel becomes energetically inacces-
sible. Note the much slower decrease in vϭ2 cross sections with energy,
and specifically the pronounced ‘‘flattening’’ of the rotational distributions
for collision energies ͓Ϸ0.6͑2͒ kcal/mol͔ near the predicted transition state
resonance.
‘
‘thermal’’ looking distribution, with a slow decay in the high
Ϫ1
J tail up to 3500 cm . Plotted also in Fig. 6͑a͒ are results
from Chao and Skodje,20 where the theoretical energy depen-
dent state-to-state cross sections have been obtained by full
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J. Chem. Phys., Vol. 116, No. 13, 1 April 2002
Reactive scattering of FϩHD→HF(v,J)ϩD
5629
qualitatively different from all other collision systems, i.e.,
FϩH , FϩNH , and FϩCH , studied thus far with the
2
3
4
crossed jet apparatus. Plotted again for comparison in Fig.
6
͑b͒ are the theoretical results of Chao and Skodje,20 convo-
luted over a Ecomϭ0.6(2) kcal/mol collision energy distribu-
tion and normalized to unity. The theoretical curves closely
recapitulate this anomalous ‘‘boxlike’’ dependence on the fi-
nal J state; indeed, the agreement between experiment and
theory is remarkably good out to the highest J values (J
Ϫ1
Ϸ11) near 2500 cm
.
As mentioned in the introduction, the source of this
anomalous, nearly ‘‘flat’’ distribution in J states at E
com
Ϸ0.6 kcal/mol has been identified by Chao and Skodje20 to
be tunneling dynamics out of the transition state resonance
region. In essence, the tunneling escape rate from the reso-
nance increases dramatically with final HF rotational state
due to a combination of ͑i͒ significantly noncollinear tunnel-
ing geometries and ͑ii͒ strong lowering of the rovibrationally
adiabatic tunneling barrier with asymptotic J value. The re-
sulting balance between a J dependent increase in tunneling
rates and J dependent decrease from phase-space consider-
ations predicts a more nearly ‘‘flat’’ cross section distribution
in J up to the energetic limit, in remarkably close agreement
with experiment. This provides strong additional support
from nascent quantum-state resolved populations for the ex-
istence of relatively broad quantum transition state reso-
nances in FϩHD at collision energies near Ecom
Ϸ0.5–0.6 kcal/mol, as first demonstrated in differential scat-
tering studies by Liu and co-workers.18
FIG. 6. Nascent HF populations for Ecomϭ1.9(4) kcal/mol and 0.6͑2͒ kcal/
mol. Panel ͑A͒ shows typical data at higher collision energies where the
dynamics are dominated by direct reactive scattering, yielding a more
Though the J state dependence of these reactive cross
sections appears to be well represented, it is worth noting
that some discrepancies between experiment and theory re-
main at the vibrational level. This can be seen in Fig. 7,
where the vibrational cross sections ͑summed over all rota-
tional states͒ are plotted against experimental results for
‘‘Boltzmann-type’’ distribution which peaks at low J and gradually drops
with increasing J. By way of contrast, panel ͑B͒ represents the qualitatively
different J distributions obtained at energies ͓EcomϷ0.6(2) kcal/mol͔ near
the quantum transition state resonance ͑Ref. 20͒, which are essentially ‘‘flat’’
in J out to Jϭ11, where they promptly drop to zero.
1
8
HF(vϭ2,3) of Liu and co-workers and theoretical calcula-
tions by Chao and Skodje.20 For appropriate comparison
with the current crossed jet results, both the experimental
and theoretical data have been convoluted over the collision
energy distributions previously reported in Fig. 4. Finally,
since both experiments measure only relative cross sections,
all three data sets have been rescaled to sum to unity. In
general, the two sets of experimental results are in good
agreement, each indicating threefold to fivefold higher popu-
lations in HF(vϭ2) vs HF(vϭ3) at collision energies above
the transition state resonance, with a much steeper fractional
decrease in ␴vϭ3 vs ␴vϭ2 with Ecom . Theoretical predictions
are also in qualitative agreement with experiment, though
with two notable discrepancies. First of all, theory predicts a
much steeper increase in reaction cross section ͑from 0 to 0.6
kcal/mol͒ for HF(vϭ2) formation at the transition-state
resonance than is observed in either experiment. Such a reso-
nance feature is indeed confirmed in the data of Liu and
co-workers,18 though the magnitude of this enhancement is
considerably smaller ͑approximately twofold to threefold͒
than predicted by theory. The crossed jet data does reveal not
a significant enhancement in total cross section near Ecom
Ϸ0.6 kcal/mol, despite clear indications of resonance behav-
ior noted above in the HF(vϭ2,J) rotational distributions.
quantum wave packet reactive scattering on the Stark–
Werner potential surface and explicitly convoluted over the
measured experimental distribution in collision energies.
Since the crossed-jet apparatus determines only relative
state-to-state cross sections, the experimental and theoretical
distributions have been normalized to both sum to unity. As
clearly evident in Fig. 6͑a͒, the agreement between experi-
ment and theory is remarkably good. From the analysis of
Chao and Skodje, this qualitatively Boltzmann-type shape
of the rotational distributions is characteristic of direct reac-
tive scattering dynamics, where the reaction proceeds
smoothly and rapidly ‘‘over the top’’ of a reaction barrier,
without any quantum resonance dynamical effects due to
quasibound H atom motion between the F and D atoms.
Conversely, in Fig. 6͑b͒, the experimental distributions
are shown for HF(vϭ2) at Ecomϭ0.6(2) kcal/mol, where
resonance effects are theoretically predicted to be most im-
portant. The differences between direct reactive scattering
opposed to resonance mediated product state distributions
are immediately evident. The experimental distributions rise
quickly from Jϭ0 and remain relatively ‘‘flat’’ out to J
ϭ11, where the distribution rapidly decreases to zero for J
у12. This ‘‘boxlike’’ type of product state distribution is
2
0
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5630
J. Chem. Phys., Vol. 116, No. 13, 1 April 2002
Harper, Nizkorodov, and Nesbitt
FIG. 8. High resolution HF Dopplerimetry data showing velocity dependent
absorption profiles for Ecomϭ1.5(3) kcal/mol. By conservation of energy,
the upper vibrational state populations are formed at lower recoil velocities,
which preferentially lead to population inversion and thus stimulated emis-
sion near line center. These profiles also confirm the translationally unre-
laxed, single collision nature of the experiments.
FIG. 7. Experimental and theoretical cross sections for vϭ2 and 3 at the
four collision energies studied. To facilitate accurate comparison, the results
of Chao and Skodje ͑Ref. 20͒ have each been convoluted over the collision
energy distribution in this work, with each data set normalized to unity.
tween upper/lower state populations and velocity distribu-
tions can yield quite structured Doppler profiles, as shown in
Fig. 8 for a series of vЈϭ3� vЉϭ2P(J) transitions. Such
structure arises simply from the fact that the upper state is
moving more slowly than the lower state, which leads to
velocity dependent population inversions and therefore
stimulated emission and absorption behavior at small and
large detuning from line center, respectively. This behavior
However, it is likely that this enhancement is at least par-
tially masked by the broader energy resolution in the crossed
jet configuration.
Second, the wave packet calculations substantially un-
derpredict the vϭ3/vϭ2 branching ratios observed in both
experiments by more than an order of magnitude. One reason
for this discrepancy is that the HF(vϭ3,J) levels are formed
near the energetic limit, and governed by tunneling dynamics
exponentially sensitive18 to the barrier width and height. This
is relevant since the calculations were performed on the
has been observed previously in FϩCH scattering studies in
4
this laboratory,2
1,22
where the greater mass of the CH trans-
3
lates into much larger Doppler shifts for the recoiling HF
products, permitting information on quantum state resolved
nascent velocity distributions to be extracted. For the FϩHD
kinematics, however, the recoil energy is split much less fa-
vorably ͑Ϸ91%:9%͒ between D and HF products, which for
HF(vϭ2,Jϭ0) (Ecomϭ1.9 kcal/mol) translates into recoil
speeds of Ϸ650 m/s in the center-of-mass frame. For a
Maxwell–Boltzmann distribution of recoil velocities, this
would imply a Doppler width on the order of ⌬␯Ϸ0.011
3
5
Stark and Werner potential energy surface ͑SW–PES ͒. This
surface does not account for the effects of spin–orbit cou-
3
6
pling ͑included in HSW–PES ͒, which adds an additional
Espin–orbit/3Ϸ0.35 kcal/mol to the SW barrier height. More
⌬
relevantly near threshold, the SW potential surface underpre-
dicts the exothermicity of the reaction by Ϸ0.38 kcal/mol,
which can of course make significant differences in predicted
product state distributions very close to the energetic thresh-
old. In any event, both direct IR absorption and H atom
time-of-flight experimental methods consistently yield sub-
stantially larger relative branching ratios for formation of
HF(vϭ3) than can be accounted for theoretically. The
source of this discrepancy is currently being investigated by
Ϫ1
cm , which, when convoluted over experimental resolution
Ϫ1
͓⌬␯FWHMϷ0.0117(2) cm ͔ in the crossed jet configura-
Ϫ1
tion, gives 0.016 cm and compares well with the observed
Ϫ1
Doppler structure ͓0.017͑1͒ cm ͔. Thus, though the recoil
Doppler structure is not sufficiently extensive with respect to
the crossed jet resolution limit to warrant a detailed Dopple-
rimetry analysis, one can nevertheless demonstrate internal
consistency with the data. Furthermore, the presence of such
translationally unrelaxed Doppler structure confirms the rig-
orously single collision nature of the scattering dynamics
under investigation.
2
0
Chao and Skodje, in efforts to further elucidate the specific
dynamics for production into these threshold HF(vϭ3,J)
states.
By virtue of conservation of energy and momentum,
there is a perfect anticorrelation between internal HF rovi-
brational energy and the energy released into translational
recoil degrees of freedom. As a result, the observed Doppler
shifts narrow substantially with increasing internal energy
deposited in HF, varying by nearly 50% between HF(vЉ
As a final comment, we consider the threshold popula-
tions observed in HF(vϭ3,J), which are formed near the
energetic limit. The exothermicity3
1,32,34
for the F( P3/2)
2
ϩHD(Jϭ0) reaction is very accurately known ͓31.19͑1͒
kcal/mol͔, which in combination with the distribution of col-
lision energies (Ecom), determines a rigorous upper limit on
Ϫ1
ϭ2, low J͒ ͓⌬␯ϭ0.017͑1͒ cm ͔ and HF(vЉϭ3, low J͒ ͓⌬␯
Ϫ1
ϭ0.0111͑2͒ cm ͔ transitions. Indeed, this competition be-
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J. Chem. Phys., Vol. 116, No. 13, 1 April 2002
Reactive scattering of FϩHD→HF(v,J)ϩD
5631
HF(v,J) states that may be energetically populated. The in-
set in Fig. 3 illustrates the relevant overall reaction energetics
for forming HF(vϭ3,J) states and the experimentally deter-
mined spread in collision energies. At Ecom
Ϸ1.9(4) kcal/mol, there is significant population in up to
HF(vϭ3,Jϭ4), which is consistent with the collision en-
ergy. As Ecom is decreased, however, HF(vϭ3,J) product
states continue to be formed that should be energetically
2
inaccessible from F( P3/2)ϩHD(Jϭ0) reactions. For ex-
ample, HF(vϭ3,Jϭ4) is clearly formed at Ecom
ϭ1.5 kcal/mol, and HF(vϭ3,Jϭ3,4) are both detected at
Ecomϭ1.0(3) kcal/mol, despite a vanishingly small fraction
2
of F( P3/2)ϩHD(Jϭ0) collisions predicted from Fig. 4 to
have sufficient energy. These discrepancies are most accen-
tuated at Ecomϭ0.6(2) kcal/mol, where no state in the v
ϭ3 manifold is energetically accessible; nevertheless, small
but finite experimentally measured populations are clearly
evident into Jϭ0, 1, 2, and 3 ͑3 at the 2␴ level͒. It is impor-
tant to stress that this comparison is based solely on experi-
mentally well determined asymptotic properties HF and HD,
and therefore completely independent of any residual inac-
curacies or approximations implicit in the ab initio Stark and
Werner FϩHD potential surface. It is also worth noting from
Fig. 7 that similar results for anomalous formation of ener-
getically inaccessible HF(vϭ3) states at low collision ener-
gies are obtained in the time of flight experiments of Liu and
FIG. 9. Threshold HF(vϭ3) rotational distributions at Ecom
ϭ0.6(2) kcal/mol, plotted as a function of HF(v,J) internal energy. The
curves represent the distributions of total energy ͑i.e., EcomϩErxn͒ available
for product formation, based on HD(Jϭ0,1) reaction with ground state
2
2
F( P3 ) atoms ͑solid line͒ or spin–orbit excited F*( P1/2) atoms ͑dashed
/2
line͒. Note that at Ecomϭ0.6(2) kcal/mol there is insufficient energy to form
any HF(vϭ3,J) levels from ground state F atom reactions, which suggests
minor but finite ͑Ͻ5%͒ contributions from nonadiabatic reactions with F*.
(⌬Espin–orbitϭ1.15 kcal/mol), which based on beam studies
1
8
37
co-workers.
of Cassavecchia and co-workers should be present in
The formation of up to Jϭ3 ͑but not Jϭ4͒ at Ecom
Ϸ0.6(2) kcal/mol necessitates an additional source of energy
on the order of Ϸ1 kcal/mol. This is also consistent with
nearly statistical ͓͑F*͔/͓F͔Ϸ2:4͒ concentrations in the dis-
charge expansion. Additional support for this scenario is
shown in Fig. 9, which depicts the observed rotational dis-
tributions for HF(vϭ3) plotted as a function of the mini-
mum energy required to access each quantum state. Plotted
also are the distributions of energies for reactions with
previous quantum state resolved studies of FϩH dynamics
2
as a function of center-of-mass collision energy, which also
report nascent HF(v,J) product states Ϸ1 kcal/mol higher
than can be accounted for by reaction energetics. We have
carefully considered and rejected several possible sources of
this additional collision energy. First of all, fractional uncer-
tainty in the collision energy is appreciable due to angular
distribution in the crossed jet configuration; however, this
uncertainty scales with Ecom and is minor ͑Ϸ0.2 kcal/mol͒
under threshold collision conditions. Rationalizing these dif-
ferences on the basis of ‘‘wings’’ in the center-of-mass col-
lision distribution would require Ecom out near Ϸ1.7 kcal/
mol, i.e., Ͼ5␴ higher than the average value of Ecom
Ϸ0.6(2) kcal/mol. Another possibility would be rotationally
2
2
ground state F( P3 ) and spin–orbit excited F*( P1/2) at-
/2
oms, respectively, including all HD(J) species thermally
populated in the jet. Specifically, nascent distributions in sev-
eral HF(vϭ3,J) states inaccessible to FϩHD are quite ap-
preciable, but drop to zero ͑within experimental uncertainty͒
at the energetic limit for F*ϩHD. By summing over the total
HF(v,J) populations, the fraction of nascent product appear-
ing in states energetically inaccessible to FϩHD can be es-
timated to be Ͻ5%. This is quite comparable to findings
previously reported for FϩH reactions, where equivalent
2
discrepancies suggest the small but finite role of nonadia-
batic reaction dynamics in these systems. The presence of
such nonadiabatic contributions would be qualitatively con-
excited HD reagent in the beam with E Ͼ1 kcal/mol. How-
rot
ever, this would require at least HD(Jϭ3), which is negli-
gibly populated ͑Ӷ1%͒ at 50 K jet temperature conditions.
Indeed, the present FϩHD studies were specifically moti-
vated to eliminate the ortho/para nuclear spin statistical con-
1
9
sistent with the experimental results of Liu and co-workers,
as well as high level theoretical calculations by Alexander,38
which predict F* to exhibit a small but finite reactivity at
these low collision energies. Furthermore, in contrast to the
major impact on product state distributions evident near
threshold, the small size of these nonadiabatic effects is ex-
pected to have only minor influence for HF(vр2,J). Indeed,
this supports our use of purely nonadiabatic predictions from
Chao et al.20 for comparison between theory and experiment.
It is important to note, however, that even these state-of-the-
straints with H reagent and thereby eliminate any rotational
2
relaxation bottlenecks. A third possibility to consider would
be reactions with residual H in the HD jet, which by virtue
2
of zero point energy differences could provide an additional
Ϸ0.8 kcal/mol. However, the magnitude of the observed ef-
fects is simply inconsistent with H impurity limits ͑Ͻ1%͒
2
measured experimentally, only a minor fraction of which
proceeds to populate the HF(vϭ3,J) manifold.
art theoretical predictions are based on FϩH potential sur-
2
The most plausible source of this internal energy is from
F*( P1/2), i.e., the spin–orbit excited electronic state
faces that currently underpredict the experimentally known
reaction exothermicity by Ϸ0.6 kcal/mol. The effect of this
2
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5632
J. Chem. Phys., Vol. 116, No. 13, 1 April 2002
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ACKNOWLEDGMENTS
37
M. Alagia, V. Aquilanti, D. Ascenzi, N. Balucani, D. Cappelletti, L. Carte-
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This research has been supported by funds from the Air
Force Office of Scientific Research and the National Science
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for a postdoctoral research fellowship.
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