Quantum state-resolved reactive scattering of F+H2 in supersonic jets: nascent HF(v,J) rovibrational distributions via IR laser direct absorption methods

Article abstract of DOI:10.1063/1.477592

A new direct IR laser absorption-based method that permits nascent rotational product distributions to be determined for F+H₂→HF+H reactions in crossed supersonic expressions under single collision conditions is described. Populations extracted from absorption and stimulated emission signals show very good overall agreement with the predictions of Castillo and Manolopoulos on the ground adiabatic potential energy surface of Stark and Werner, over most of the HF(v,J) state distribution. Comparison with the early arrested relaxation studies of Polanyi and Woodal indicates qualitatively but somewhat less satisfactory agreement with both the present results as well as theoretical calculations.

Full text of DOI:10.1063/1.477592

Quantum state-resolved reactive scattering of F+H 2 in supersonic jets: Nascent HF
v,J) rovibrational distributions via IR laser direct absorption methods
(
William B. Chapman, Brad W. Blackmon, Sergey Nizkorodov, and David J. Nesbitt
Citation: The Journal of Chemical Physics 109, 9306 (1998); doi: 10.1063/1.477592
View online: http://dx.doi.org/10.1063/1.477592
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/109/21?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 109, NUMBER 21
1 DECEMBER 1998
Quantum state-resolved reactive scattering of F؉H in supersonic jets:
2
Nascent HF„v,J… rovibrational distributions via IR laser direct
absorption methods
William B. Chapman,a) Brad W. Blackmon, Sergey Nizkorodov, and David J. Nesbittb)
JILA, University of Colorado and National Institute of Standards and Technology and Department
of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0440
͑
Received 18 June 1998; accepted 25 August 1998͒
Supersonically cooled discharge radical atom sources are combined with high-sensitivity IR
absorption methods to investigate state-to-state reactive scattering of Fϩn-H →HF(v,J)ϩH in
2
low-density crossed supersonic jets at center-of-mass collision energies of 2.4͑6͒ kcal/mole. The
product HF(v,J) is probed with full vibrational and rotational quantum state selectivity via direct
Ϫ1
absorption of a single mode (⌬␯Ϸ0.0001 cm ), tunable F-center laser in the ⌬vϭ1 fundamental
8
3
manifold with near shot noise limited detection levels of 10 molecules/cm /quantum state per
pulse. The high absorption sensitivity, long mean free path lengths, and low-density conditions in
the intersection region permit collision-free HF(v,J) rovibrational product state distributions to be
extracted for the first time. Summed over all rotational levels, the HF vibrational branching ratios
are 27.0͑5͒%, 54.2͑23͒%, 18.8͑32͒%, and Ͻ2͑2͒%, respectively, into vHFϭ3:2:1:0. The nascent
vibrational distributions are in good agreement with rotationally unresolved crossed-beam studies of
Neumark et al. ͓J. Chem. Phys. 82, 3045 ͑1985͔͒, as well as with full quantum close-coupled
calculations of Castillo and Manolopoulos ͓J. Chem. Phys. 104, 6531 ͑1996͔͒ on the lowest
adiabatic FϩH potential surface of Stark and Werner ͓J. Chem. Phys. 104, 6515 ͑1996͔͒. At a finer
2
level of quantum state resolution, the nascent rotational distributions match reasonably well with
full quantum theoretical predictions, improving on the level of agreement between theory and
experiment from early arrested relaxation studies. Nevertheless, significant discrepancies still exist
between the fully quantum state-resolved experiment and theory, especially for the highest
energetically allowed rotational levels.
S0021-9606͑98͒00545-5͔
© 1998 American Institute of Physics.
͓
after chemiluminescence,3 chemical laser, and crossed-
–5
6
I. INTRODUCTION
7
beam experiments began to yield the first quantum state-to-
A detailed understanding of fundamental chemical reac-
tion dynamics from first principles has represented a long-
standing challenge to the chemical physics community. Al-
though the ultimate achievement of this goal will require
much further theoretical and experimental effort, there has
been enormous progress in these directions in recent years.
This progress largely reflects rapid advances in ͑i͒ quantum
state resolved experimental techniques, ͑ii͒ development of
accurate high level ab initio potential energy surfaces ͑PES͒,
and ͑iii͒ theoretical tools for performing high-level dynamics
calculations on such surfaces in full dimensionality. By vir-
tue of the intrinsic complexity of polyatomic reaction dy-
namics, a logical focus of theoretical and experimental ef-
forts has been toward fundamental three-atom hydrogen
abstraction processes, the classic prototype for which has
state results.
The FϩH →HFϩH chemical reaction has played an
2
enormously important role in the development and testing of
theoretical reactive scattering methods for several reasons.
First of all, this system represents an excellent prototype of
low-barrier exothermic H-atom abstraction, yet it is small
enough in total electron number and nuclear degrees of free-
dom to be currently tractable with high-level ab initio meth-
ods. Consequently, there has been a large number of poten-
tial energy surfaces developed for this system with which to
investigate the dynamics of simple atom transfer
reactions.8
–12
The availability of these surfaces has facili-
1
3–16
17–19
tated detailed classical,
quasiclassical,
and quantum
mechanical2
0–25
studies of the reaction dynamics, in particu-
lar elucidating the final rotational, vibrational, and angular
distributions of the HF(v,J) products. One major break-
through in this direction has been the development of theo-
retical tools for fully converged quantum reactive scattering
calculations for atomϩdiatom systems. In conjunction with
high-quality ab initio methods, these combined capabilities
now open up exciting prospects for a truly rigorous, ‘‘first
principles’’ comparison between full quantum state-to-state
resolved experiments and exact quantum reactive scattering
been the FϩH →HFϩF reaction. Indeed, the reaction dy-
2
namics of this ‘‘benchmark’’ system has remained a central
target of chemical physics research1 nearly three decades
,2
a͒Permanent address: New Focus, Inc., 2630 Walsh Avenue, Santa Clara,
CA 95051.
b͒
Author to whom correspondence should be addressed.
0021-9606/98/109(21)/9306/12/$15.00
9306
© 1998 American Institute of Physics
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1

J. Chem. Phys., Vol. 109, No. 21, 1 December 1998
Chapman et al.
9307
dynamics, at least for reactions occurring on a single adia-
batic potential surface.2
6–28
The experimental literature on FϩH reactions is im-
2
pressively extensive. From a thermally averaged perspective,
there have been numerous temperature-dependent kinetic
studies of FϩH reactions, which have provided rate con-
2
stants, activation energies, and Arrhenius pre-exponential
2
9–31
factors
for the atom abstraction event. Such results pro-
vide useful experimental constraints with which to test both
potential surfaces and dynamics calculations, but the strength
of these comparisons is substantially weakened by extensive
thermal averaging over the initial and final quantum state
distributions of reagents and products. From a more quantum
state-resolved perspective, the exothermic FϩH reaction re-
2
sults in a strong vibrational and rotational population inver-
sion in the HF product, which has permitted detailed studies
of state-to-state reaction dynamics; for example, via tandem
chemical laser gain experiments by Pimentel and
FIG. 1. Schematic diagram of the crossed-jet apparatus for state-to-state
reactive scattering of FϩH →HF(v,J)ϩH under single collision condi-
2
tions.
6
,32,33
co-workers.
Of special historical importance have been the pioneer-
ing ‘‘arrested relaxation’’ studies of Polanyi and co-workers,
which exploited FTIR chemiluminescence methods3–5 to
probe rovibrational distributions of the product HF(v,J)
states under low-pressure, continuous flow conditions. The
key advantage of these chemiluminescence methods for H-
atom abstraction is that IR emission from all rovibrational
levels of the HF(v,J) product can be readily resolved with
modest spectral resolution. Due to finite pressures and resi-
dence times in the FTIR region, however, the newly formed
HF products experienced multiple collisions and thus suf-
fered partial rovibrational relaxation prior to detection. Con-
sequently, the ‘‘nascent’’ ͑i.e., collision-free͒ rovibrational
distributions of HF could only be estimated by repeated ex-
periments as a function of flow cell densities and extrapola-
tion to the zero-pressure limit. Despite limitations due to
collision effects, however, the Polanyi studies provided a
major advance in our understanding of AϩBC reaction dy-
namics. Indeed, the legacy of these arrested relaxation meth-
ods has been an impressive body of state-resolved rate data
for several atomϩdiatom systems. In turn, these data have
been responsible for stimulating the development and testing
of many fundamental concepts in microscopic reaction rate
theory.
more limited information on rotational distributions ex-
tracted from detailed modeling and contour analysis of the
time-of-flight data. Nevertheless, due to exquisite angular
and center-of-mass energy resolution, these crossed-
molecular-beam methods have provided the most detailed
information to date on FϩH reactions, specifically on vibra-
2
tional state-resolved angular distributions of reactively scat-
tered HF. For example, the studies of Neumark et al.3
yielded first indications of a strong dependence of differen-
tial cross sections on vibrational state, shifting from pre-
dominantly backward- to forward-scattered HF(v) products
for the highest energetically accessible vibrational level.
4,35
These vibrationally state-resolved data stimulated consider-
able theoretical interest2
6–28,39–41
in the possible role of dy-
namical quantum scattering resonances of the FϩH poten-
2
tial surface.
Our group has recently been developing pulsed dis-
charge sources of jet-cooled radicals for investigation of
state-to-state reaction dynamics with high spectroscopic
resolution.4
2,43
The sources rely on striking a discharge be-
hind the limiting aperture of a supersonic slit or pinhole
nozzle, which effectively confines the plasma in the stagna-
tion region. In favorable systems the source can produce
15
3
With even more detailed control of the reactive event,
elegant crossed-molecular-beam methods developed by Lee
radical densities on the order of 10 /cm at the expansion
orifice. These high radical densities prove sufficient for reac-
tive scattering studies with a second jet of supersonically
cooled reagents,44 while yielding adequate product state den-
sities for detection via shot-noise limited direct absorption
with a high-resolution, tunable IR laser ͑see Fig. 1͒. The
7
,34,35
36–38
and co-workers
and Toennies and co-workers
have
been used to investigate differential reactive scattering of
FϩH ͑and isotopic variants͒ for a series of center-of-mass
2
collision energies. Under crossed-beam conditions, the num-
ber densities in the intersection region are low enough to
prevent collisional relaxation of the initial HF(v,J) product
state distributions, which can therefore be measured by time-
of-flight analysis of recoil velocities. However, even with
heroic improvements in these beam techniques by Faubel
powerful advantage of such an approach is that one can si-
Ϫ1
multaneously achieve spectroscopic ͑i.e., ⌬␯Ϸ0.0001 cm
͒
levels of complete product quantum state resolution, while
rigorously maintaining single collision conditions. In a very
interesting complementary direction, there have also been
recent molecular beam measurements from Keil and
3
6–38
et al.,
such time-of-flight methods still offer only rather
2
Ϫ1
45
modest kinetic energy resolution (Ϸ10 cm ) of the HF
product recoil in comparison with laser or chemilumines-
cence detection methods. As a result, these beam studies
yield data primarily on HF vibrational populations, with
co-workers that combine HF chemical laser excitation and
bolometric detection to probe angularly resolved, differential
reactive scattering into selected rotational levels in the
HF(vϭ2) manifold.
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9308
J. Chem. Phys., Vol. 109, No. 21, 1 December 1998
Chapman et al.
FIG. 2. Energy level diagram for FϩH2 reactions, demonstrating the
HF(v,J) product levels energetically accessible at 1.84͑14͒ kcal/mole colli-
sion energy (1 kcal/moleϭ4.184 kJ/mole). The bond dissociation energies
for H and HF have been determined to high precision from detailed spec-
2
2
troscopic work, which permits the reaction exothermicity for F( P3/2)
2
ϩH (jϭ0)→HF(vϭ0,Jϭ0)ϩH( S1/2) to be known to unusually high ac-
2
Ϫ1
curacy, i.e., ⌬Eϭ11 192͑5͒ cm ϭ32.001͑14͒ kcal/mole denoted by the
double-sided arrow.
The focus of the present work is to exploit the high-
resolution IR laser-based absorption method for extracting
FIG. 3. Details of the pulsed discharge source for F-atom generation.
nascent product state distributions from the FϩH reaction
2
under single collision conditions. Our approach is based on
the following. First, a primary pulsed supersonic discharge
source of F-atoms is collided with a secondary pulsed jet of
tial energy surfaces of Stark and Werner,27 with additional
comparisons made with previous experimental studies of Lee
and co-workers3
4,35
and Polanyi and co-workers. Conclu-
4
H molecules sufficiently far downstream of the nozzle to
ensure long mean-free-path length, molecular beam colli-
sions and directions for future work are summarized in Sec.
VII.
2
sions. Second, the H beam densities and intersection path
2
lengths are chosen to permit only a small fraction ͑Շ3%–
II. EXPERIMENT
4%͒ of the F-atoms to react, which for the current center-of-
mass collision energy ͓Ecomϭ2.4(6) kcal/mole͔ and reaction
exothermicity can energetically access HF products in up to
vϭ3 ͑see Fig. 2͒. Third, this product HF(v,J) is probed in
the intersection region by high-sensitivity direct absorption
of single mode tunable F-center laser light. As a function of
laser tuning, these spectral data yield Doppler limited pro-
files on reactively scattered product HF(v,J) over the com-
plete manifold of vibration/rotation quantum states. Finally,
in conjunction with previously measured rovibrational tran-
sition matrix elements for HF absorption/emission, nascent
product state distributions can be extracted for each of the
energetically accessible rovibrational levels.
The experimental apparatus for state-to-state reactive
scattering of FϩH is based on a modification of earlier ex-
2
periments for investigating state-to-state inelastic scattering,
schematically shown in Fig. 1. The main technical advance
that makes these reactive scattering experiments possible has
been the development of pulsed slit discharge sources to pro-
duce high densities/absorption path lengths of jet-cooled
radicals.4
3,44
The success of these techniques for high-
resolution, jet-cooled radical spectroscopy has prompted us
to further develop smaller pinhole and/or mini-slit apertures
for use in reactive scattering experiments, as elucidated in
Fig. 3. Basically, a thin ͑ϳ0.5 mm͒ discharge region is
formed by gated voltage pulses ͑Ϸ300–1000 V͒ applied
across a Vespel insulator between the valve body and shaped
electrodes that form the limiting expansion aperture. This
design fully localizes the discharge behind the nozzle orifice,
which therefore permits efficient jet cooling of the expanded
The rest of this paper is organized as follows. In Sec. II,
details of the experimental method are presented, followed in
Sec. III by sample data and necessary experimental diagnos-
tics. In Sec. IV we report rotationally resolved absorption/
emission data for the energetically accessible HF(vр3, J)
rovibrational manifold, which are used in Sec. V to extract
nascent state populations. A major focus of this work is to
provide the first rigorous comparison of measured rovibra-
tional HF(v,J) populations with theoretical predictions from
current state-of-the-art ab initio/quantum dynamics calcula-
tions. Specifically, our results are compared in Sec. VI
against fully converged, three-dimensional ͑3-D͒ quantum
reactive scattering calculations performed by Castillo and
radical species down to T Ϸ10–20 K. Furthermore, the
rot
thickness of the discharge region limits the residence time of
the precursor radical species in the discharge to Շ1 ␮s,
which effectively eliminates subsequent bimolecular or ter-
molecular radical chemistry from taking place. As noted in
previous work,4
3,44
it is also important that the voltage pulse
polarity across the electrode/aperture be negative with re-
spect to the valve body, which allows the heavier cations to
flow downstream while permitting higher mobility electrons
2
8
2
Manolopoulos on the lowest adiabatic F( P3 )ϩH poten-
/2
2
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J. Chem. Phys., Vol. 109, No. 21, 1 December 1998
Chapman et al.
9309
to flow upstream against the bulk gas flow. This promotes a
much more stable, volume-filling glow discharge instead of
spatially localized filamentary breakdown.
tational temperature is found to be on the order of Trot
Ϸ30 K, which provides a lower limit for the H distribu-
2
tions. However, even if cooled only to T Ϸ100 K, H2
rot
The pulsed discharge generates on the order of
would still be essentially collapsed into its lowest nuclear
spin-allowed states, namely jϭ1 ͑ortho͒ and jϭ0 ͑para͒ in a
3:1 ratio, with the first excited para (jϭ2) and ortho (j
ϭ3) state populations down by an additional 2–3 orders of
magnitude.
3
1
015 F-atoms/cm upstream of the limiting expansion orifice.
The stagnation gas for the current studies is 5% F in He at
2
50–100 Torr (1 Torrϭ133.3 Pascal), though other F-atom
precursors such as CF and SF have also been investigated.
4
6
The discharge strikes automatically by applying ϷϪ800 V
bias to the electrode/aperture during the Ϸ1–2 ms gas pulse.
Computer-controlled timing circuits limit the discharge to a
short temporal window ͑Ϸ500–700 ␮s͒ near the peak of the
gas flow. This serves both to better match the timing of the
The crossed jets intersect 4.5 cm downstream of the
nozzles, where for typical backing pressures and peak gas
densities in the intersection region, the F-atoms have
Շ3%–4% probability of colliding and reacting with H . This
2
is comparable to the probability of subsequent inelastic col-
lisions of the resulting HF(v,J) products in the reaction
zone; any rovibrational relaxation of the HF(v,J) distribu-
tions is therefore also limited to a few percent even for gas
kinetic processes, which is explicitly verified in Sec. IV by
stagnation pressure-dependent studies as a function of beam
H pulse and to eliminate occasional arcing in the vacuum
2
chamber between pulses. The resulting 10–40 mA peak cur-
rents are stabilized with a ballast resistor ͑1–5 k⍀͒ in series
with the discharge. The F-atoms are presumably formed
from F2 in the stagnation region by rapid associative
4
6
detachment
occurring at near Langevin rates (kL
density. The time profile of both F-atom and H gas pulses is
2
Ϫ7
3
Ϫ1 Ϫ1
Ϸ10 cm /mol /s ),
monitored with miniature hearing aid microphones mounted
inside the vacuum chamber on translatable stages, which fa-
cilitates temporal overlap of gas pulses in the intersection
region.
Ϫ
Ϫ
F ϩe →FϩF ,
͑1͒
2
energetically driven by the electron affinity of F.47
Both slit and pinhole modifications of the source have
been used for F-atom generation. Because the small slit
source (300 ␮mϫ5 mm) is used at an order of magnitude
longer distance ͑Ϸ4.5 cm͒ from the probe volume than the
slit length, the F-atom density in the beam intersection re-
gion is effectively similar to a pinhole orifice of the same
cross-sectional area. Indeed, relative HF(v,J) populations
measured with the two source geometries are identical within
experimental uncertainty, and thus the choice between pin-
hole and small slit aperture sources is largely a matter of
convenience. However, long-term stability of the discharge
is empirically found to be much better with the slit source,
providing over 100 h of operation between routine mainte-
nance. With pulsed valve repetition rates kept to р10 Hz, a
III. SAMPLE DATA AND DIAGNOSTICS
The HF(v,J) reaction products are probed on ⌬vϭ1,
P or R branch transitions with a single-mode, color-center
laser beam multipassed 16 times through the intersection re-
gion with a cylindrical Herriot cell.50 Near shot-noise limited
absorption sensitivities are achieved by a combination of ͑i͒
dual beam differential detection on matched InSb detectors
and ͑ii͒ electro-optic servo control of the color-center laser
intensity, with feedback from IR light on a reference detector
ϩ
used to correct the intensity of the Kr pump laser. This
servo-loop control permits readily detectable signals at
Ϫ5
Շ10
absorbance levels in a 10 KHz detection band-
1
0 inch diffusion pump equipped with a liquid N -cooled
width, which for Ϸ500 MHz Doppler-broadened lines
2
Ϫ5
baffle maintains a background pressure of Շ5ϫ10 Torr in
the 64 L vacuum chamber.
of HF translates into sensitivities on the order of
8
3
Շ10 mol/cm /quantum state per pulse. The laser wave-
lengths of specific HF rovibrational transitions5
1,52
are lo-
The H supersonic jet is formed through a piezoelectric
2
48
valve based on the design of Proch and Trickl. The condi-
tions are 100–400 Torr backing pressure of neat H or
H /rare gas mixtures with a typical pulse duration of 300 ␮s
and effective aperture diameter of 200 ␮m. The H stretch is
IR inactive, thus it is not possible to probe the rotational
distribution of the jet-cooled H reagent beam with direct
cated to within their Doppler widths using a traveling Mich-
elson interferometer of the Hall and Lee design.53 Sample
time domain absorption data is shown in Fig. 4, where the
laser is tuned to the top of the Doppler profile for the R(1)
line of the vϭ4←3 vibrational manifold and signal aver-
aged for Ϸ1000 pulses. The F-atom discharge voltage is
2
2
2
2
absorption laser methods. Alternatively, however, dopant
levels of IR absorbing molecules with comparable energy
spacings are used as a rotational ‘‘thermometer’’, based on
collisional equilibration in the expansion. Specifically, the jet
rotational temperatures have been independently character-
Ϸ500–700 ␮s long and centered on the H pulse; thus, the
nascent HF absorption signal directly maps out the 300 ␮s
2
profile of the H gas flow. The signals correspond to peak
2
absorbances of Ϸ0.14% and an rms absorbance noise floor of
Ϫ6
Ϸ7ϫ10
.
ized in separate experiments by adding 1% CH to the stag-
nation mixtures, and monitoring direct IR absorption out of
It is worth noting that direct IR laser absorption tech-
niques naturally yield absorbance signals in absolute units;
in conjunction with known IR transition moments, this per-
mits the absolute column integrated concentrations ͑or more
rigorously concentration differences͒ of HF(v,J) to be deter-
mined directly. For example, the peak HF absorbance signal
in Fig. 4 corresponds to an absolute column integrated den-
4
individual rotational levels in the ␯ CH stretch absorption
3
4
9
band. For typical stagnation pressures and expansion con-
ditions, the CH is almost completely cooled down into the
4
lowest A(Jϭ0), F(Jϭ1) and E(Jϭ2) levels allowed by
nuclear spin symmetry. From a Boltzmann analysis, the ro-
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9310
J. Chem. Phys., Vol. 109, No. 21, 1 December 1998
Chapman et al.
FIG. 4. Time domain signals for HF(vϭ3,Jϭ1) generated from FϩH2
reactions in the crossed jets, demonstrating the high signal-to-noise levels
achievable in the apparatus. These signals are obtained by direct absorption
of an amplitude-stabilized F-center laser tuned to the Doppler maximum of
R(1) and signal averaged for 1000 pulses. The maximum absorbance is
Ϫ6
0
.14%, with an rms noise floor of Ϸ7ϫ10 absorption units, correspond-
7
3
ing to a minimum detectable HF product density р10 mol/cm /quantum
state.
FIG. 6. Voltage deflection studies in order to test for possible HF formation
from ions formed in the discharge. The deflection voltages have been turned
on in the middle of the Doppler scan through an HF transition, with no
detectable effect on the observed absorption line profiles.
sity of 2.0ϫ1010 mol/cm2, which from Doppler measure-
ments of jet divergence translates into a quantum state-
resolved product density of ͓HF(vϭ3,Jϭ1)͔Ϸ3
9
3
51–54
ϫ10 mol/cm in the intersection region.
Based on the
observed signal-to-noise ratio ͑S/N͒, this corresponds to a
minimum detection level of ͓HF(v,J)͔ of Շ10 mol/cm3
per quantum state with only modest signal averaging.
By delaying the discharge voltage, these time domain
studies also provide a simple test that HF product is formed
only during the temporal overlap between F-atom and H2
pulses. This is shown in Fig. 5, which displays the time-
resolved HF absorption profile ͑centered at tϭ0͒ for vϭ4
7
←
3, R(1), with the discharge pulse ͑i͒ coincident with, ͑ii͒
partially overlapping, and ͑iii͒ prior to the H pulse. The data
2
illustrate that the HF signals faithfully map out the H den-
2
sity, and for partially overlapping F-atom and H pulses ͑see
2
middle panel of Fig. 5͒, the HF absorption signals decay
rapidly to zero when the discharge voltage is shut off. This
time decay of the HF signals is consistent with the angular
spread of the F-atom and H jets, which causes some disper-
2
sion in time-of-flight delay from the nozzle orifice to the
intersection region.
Although previous direct absorption studies indicate that
ion densities in the intersection region are down from radical
densities by at least 2 orders of magnitude,4
3,44
it is never-
theless important to test explicitly for contribution of any
charged species to the reactive scattering signals. To achieve
this, deflector plates (2.0ϫ4.0 cm) placed 8.0 cm apart, 0.5
cm downstream of the discharge aperture ͑see Fig. 6͒ are
charged up to a 1000 V potential difference, with the deflec-
tion voltage switched on as the laser is tuned through the
center frequency. The corresponding field strengths ͑up to
FIG. 5. Demonstration of temporal overlap between F-atom discharge with
HF absorption signals. The rectangular curves represent the F-atom dis-
charge current ͑scale on right͒, which have been progressively delayed with
respect to the H pulse centered at tϭ0. Note that the HF signals ͑scale on
2
1
25 V/cm͒ are at least an order of magnitude greater than
left͒ only occur during the precise overlap of the F-atom and H pulses, and
2
necessary to deflect charged species away from the jet inter-
section region. As shown clearly in Fig. 6, neither the inten-
that the HF signals rapidly go to zero when the F-atom discharge source is
shut off.
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1

J. Chem. Phys., Vol. 109, No. 21, 1 December 1998
Chapman et al.
9311
sity nor symmetry of the absorption profile is altered by the
presence of the electric deflection field, confirming negli-
gible contributions to the observed reactive scattering signals
from ion–molecule processes.
For comparison with previous theoretical and experi-
mental studies, the center-of-mass collision energy (Ecom) is
specified in two ways. First, IR chromophores ͑typically
CH ͒ are doped at 1% levels into the two beams and used to
4
characterize both the jet velocities and velocity distributions
49,55
by high-resolution IR laser Dopplerimetry.
However, one
can also measure the lab-frame speeds in situ for each of the
gas mixtures by translating a miniature hearing aid micro-
phone along the jet axis and measuring the time-of-flight
delay in the pulse arrival. This much simpler alternative
proves to be remarkably reliable, yielding centerline jet
speeds accurate to within a few percent, as quantitatively
confirmed both by the high-resolution Dopplerimetry studies
and detailed thermodynamic calculations of an adiabatic
5
6,57
expansion.
The angular profiles of the free jets are also
independently determined via deconvolution of high-
resolution Doppler profiles in each of the expansions. These
center line speeds and angular distributions are then used in
Monte Carlo simulations of the jet intersection region to
evaluate the mean value and spread in center-of-mass colli-
sion energy, ͑i.e., Ecom and ⌬Ecom͒, averaged over all rel-
evant collision geometries. This proves to be especially cru-
cial for energy-dependent studies of the quantum state-to-
FIG. 7. Sample absorption data on ͑a͒ the HF(vϭ3,J) rotational manifold
and ͑b͒ selected J-levels in the HF(vϭ2,J) rotational manifold, indicating
full resolution of the product high-resolution Doppler line shapes. Only a
single pulse is accumulated for each Doppler detuning, which accounts for
the 30-fold-lower signal-to-noise ratio than observed in Fig. 4, where 1000
pulses have been averaged. Note the presence of both stimulated absorption
͑upper panel͒ and stimulated emission ͑lower panel͒ signals, depending on
whether the reaction leads to a population inversion on the transition of
interest. Note also that the profiles show definite Doppler structure ͑lower
panel͒ at high and low detuning, which reflects information on velocity
distributions of the nascent HF(v,J) products.
state FϩH reaction cross section, as reported elsewhere in
2
5
7
detail. For the present studies, however, we are interested
predominantly in nascent state distributions of HF(v,J) at a
single center-of-mass collision energy for neat ͑у99.99%͒
H and 5.00% F /He. These measurements yield jet speeds
2
2
5
5
of 2.50(8)ϫ10 and 1.48(7)ϫ10 cm/s, respectively, which
for the current right angle collision geometry corresponds to
center-line collision energies of 1.84 kcal/mole. When Monte
Carlo averaged over the angular spreads determined from
high resolution IR Dopplerimetry for the two jets, this trans-
lates into an average center-of-mass collision energy of
the laser line width (⌬␯Ϸ1 MHz), thus demonstrating
velocity-resolved Doppler profiles for the reactively scattered
HF(v,J) product. In principle, these Doppler profiles can be
analyzed to extract perpendicular velocity distributions in the
lab frame for quantum state-resolved HF products. However,
there are significant contributions to these linewidths due to
angular divergence of the jets; thus, a detailed Doppler
analysis of the recoil velocities is deferred until data in a
skimmed expansion geometry is available. For present pur-
poses, the signals are integrated over the observed Doppler
profiles, which rigorously yield absolute column-integrated
densities over the absorption path length.
2.4͑6͒ kcal/mole. Though somewhat larger, this is compa-
rable to the 1.84 kcal/mole center-of-mass collision energies
3
4,35
used by Lee and co-workers,
as well as in theoretical
calculations by Manolopoulos and co-workers,2
6,28,58
which
prompts us to make comparison with these previous studies.
IV. RESULTS AND ANALYSIS
For each rotationally resolved transition, the time-
resolved HF signals are captured by a transient digitizer, in-
tegrated over the central 100 ␮s portion of the pulse dura-
tion, and stored on computer as a function of laser detuning.
Sample results for J-dependent absorption signals in the
HF(vϭ3,J) manifold are shown in Fig. 7͑a͒, obtained for
single gas pulses with no signal averaging. Note the strong
rotational-state dependence of the signals, which drop rap-
idly to zero near the energetic upper limit of HF(vϭ3,J
ϭ5). This provides additional confirmation that the HF is
Formation of product HF(vϭ4,Jϭ0) is significantly en-
dothermic ͑Ϸ8 kcal/mole͒ and therefore energetically inac-
cessible at 1.84͑14͒ kcal/mole center-of-mass collision ener-
gies. Thus, the vϭ4←3 signals in Fig. 7͑a͒ reflect pure
absorbance due to optical excitation out of the HF(vϭ3,J)
manifold. However, direct absorption methods coherently
probe the competition between stimulated absorption and
emission phenomena; hence, the HF(v,J) signals reflect de-
generacy weighted population differences between the upper
and lower rovibrational states. This is especially relevant for
produced solely by neutral FϩH reactions and not influ-
strongly exothermic processes such as FϩH that populate a
2
2
enced by any secondary reactions of HϩF , which can ener-
getically form up to vϭ10. The spectral line widths (⌬␯
Ϸ500 MHz) are more than 2 orders of magnitude larger than
large manifold of vibrational levels. Figure 7͑b͒ illustrates
one such set of data obtained from vϭ3←2 transitions out
of the vϭ2 vibrational manifold, which for sufficiently low
2
5
4
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9312
J. Chem. Phys., Vol. 109, No. 21, 1 December 1998
Chapman et al.
Aruman et al.54 and Ram et al.51 Analysis of this data can
proceed in one of two ways. First, since vϭ3 is the highest
vibrational state populated by the reaction, the vϭ4←3 in-
tegrated absorption measurements probe the HF(vϭ3,J)
populations directly, which can be independently fit without
reference to any lower vibrational manifold. Next, the
HF(vϭ2,J) distributions can be extracted from least-squares
fits to the vϭ3←2 data alone, where the vϭ3 populations
are taken from the above least-squares fit. This procedure can
then be repeated for each successive vibrational manifold,
yielding rovibrationally resolved data on vϭ3, 2, 1, and 0. It
is worth noting that this study reflects the first rotationally
resolved product detection in the vibrationless HF(vϭ0,J)
channels, which underscores one unique advantage of IR ab-
sorption vs emission-based probe methods.
FIG. 8. Network of absorption transitions probed in HF(v,J) product from
FϩH reactions, which permits quantitative mapping-out populations in v
A corresponding disadvantage is that absorption meth-
ods tend to amplify experimental uncertainties for the lower
vibrational levels, since these depend on uncertainties in the
progressively higher vibrational levels. Specifically, all other
noise contributions being the same, one can easily show that
the uncertainty grows with the square root of vibrational
steps away from the highest populated level. To help mini-
mize these effects, the input data represent an average over
multiple spectroscopic measurements for each transition,
with as many as 80 separate experimental measurements on a
given vibrational manifold taken over the course of several
months. From these studies, the populations in HF(vϭ0,J)
are found to be zero within experimental uncertainty for each
of several rotational levels tested ͑i.e., Jϭ4–11͒. This is in
good agreement with the rotationally unresolved beam data
2
ϭ3, 2, 1 and 0 vibrational levels as a function of rotational J-state.
J-values access upper vϭ3 states directly populated by the
FϩH reaction. Thus, more generally speaking, the observed
2
signals reflect the lower (v,J) and upper (vЈ,JЈ) state popu-
lations according to54
8
␲3␯
͓HF͑v,J͔͒
2Jϩ1
2
͵
A͑␯͒d␯ϭ
͉
␮v v͑m͉͒ ͉m͑J͒
͉
ͩ
Ј
3
hc
͓
HF͑vЈ,JЈ͔͒
Ϫ
ͪ
•l,
͑2͒
2
JЈϩ1
where
͐
A(␯)d␯ is the integrated absorbance for a single
rovibrational transition ͑unprimed/primed quantities refer to
of Neumark et al.3
4,35
as well as theoretical predictions on
58
the lower/upper vibrational manifold͒; ␮ (m) is the tran-
vЈ,v
the Stark and Werner surface.27
sition dipole moment; and m(J)ϭϪJ or Jϩ1 for P- or R-
branch transitions, respectively. The signals can therefore ap-
pear as net stimulated absorption or emission ͑i.e., ‘‘negative
absorption’’͒ depending upon the sign of the degeneracy
weighted population differences.
Alternatively, we have combined a least-squares fit to
the entire set of integrated absorbance data. Since we do not
have data on the HF(vϭ0,J) manifold for all energetically
accessible J-values, the populations for vϭ0 are fixed at
zero, consistent with the above analysis. This does not elimi-
nate the issue described above of propagating uncertainties,
since populations for the higher vibrational levels will be
successively less correlated with the lower vibrational mani-
folds and therefore better determined. Nevertheless, this
method is somewhat more reliable, since it permits a physi-
cally appropriate weighting of data by number of measure-
ments and propagation of errors throughout the rovibrational
manifold. The results for all HF(v,J) states populated by the
By way of example, the first profile in Fig. 7͑b͒ is a scan
over the vϭ3←2R(0) transition which near line center ap-
pears as stimulated emission, indicating that for slow HF
products the degeneracy weighted population of HF(vϭ3,J
ϭ1) exceeds that of HF(vϭ2,Jϭ0). However, the popula-
tion inversion changes sign symmetrically in the wings of the
Doppler profile, consistent with the greater HF velocity re-
coil anticipated for comparable J-levels in the vϭ2 vs 3
manifold. For vϭ3←2,R(2), both upper and lower popula-
tions are large, but the measured population difference is
small and integrates to a net absorption. Again, the Doppler
structure reveals subtle velocity structure in the degeneracy
weighted population differences. Specifically, the signal be-
comes slightly more positive in the high-velocity wings of
the Doppler profile. The third transition is vϭ3←2,R(5)
and appears as a pure absorption due to the absence of sig-
nificant population in HF(vϭ3,Jϭ6).
FϩH reaction are listed in Table I and plotted in Fig. 9,
2
where the total population summed over all J-levels is set
equal to 100%.
Since the HF product spends only a few ␮s in the laser
probe region, any change in nascent population due to spon-
taneous emission is completely negligible ͑i.e., Ͻ0.1%͒.
More potentially significant are effects due to the probe laser
itself, which can in principle modify the nascent populations
by stimulated emission processes. This is especially impor-
tant under collision-free conditions, where the homogeneous
absorption cross sections are limited predominantly by tran-
sit time broadening and can be much larger than the peak
cross sections under pressure-broadened conditions. How-
ever, by limiting the power of the probe laser to below 50
To extract nascent HF product distributions, we first ob-
tain an overdetermined set of integrated absorption signals
that interconnect rovibrational levels in the energetically ac-
cessible manifold ͑see Fig. 8͒. The necessary dipole matrix
moments and frequencies for each fully rovibrationally
specified HF transition are known from previous work by
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J. Chem. Phys., Vol. 109, No. 21, 1 December 1998
Chapman et al.
9313
TABLE I. Nascent HF(v,J) populations ͑in percent͒ from Fϩn-H reactive
2
collisions at Ecomϭ1.84(14) kcal/mole. The analysis indicates the HF(v
ϭ0) populations summed over all J to be Ͻ2% and are not included in the
final least-squares fits ͑see text for details͒.
Nascent HF(v,J) populations ͑%͒
J
vϭ3
vϭ2
vϭ1
0
2.59 ͑09͒
6.72 ͑06͒
7.76 ͑15͒
5.49 ͑17͒
2.84 ͑19͒
1.23 ͑15͒
0.34 ͑36͒
1.43 ͑09͒
3.72 ͑20͒
5.20 ͑17͒
6.12 ͑30͒
6.90 ͑26͒
7.60 ͑32͒
7.05 ͑20͒
5.48 ͑43͒
4.31 ͑27͒
2.80 ͑49͒
1.84 ͑150͒
1.22 ͑93͒
0.54 ͑120͒
0.40 ͑24͒
0.98 ͑46͒
1.39 ͑56͒
1.76 ͑49͒
2.26 ͑65͒
1.81 ͑43͒
2.44 ͑40͒
2.02 ͑36͒
1.46 ͑52͒
1.42 ͑50͒
0.81 ͑58͒
0.40 ͑170͒
0.22 ͑110͒
0.35 ͑150͒
0.32 ͑100͒
0.53 ͑48͒
0.26 ͑38͒
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
1
1
1
1
1
1
1
␮W, this contribution is less than a few percent, which is
considerably smaller than the quoted experimental uncertain-
ties.
As a final note in this section, the densities in the inter-
section region are kept intentionally low to prevent any col-
lisional relaxation of the nascent HF(v,J) distribution. This
can be explicitly tested by measuring rotational branching
FIG. 9. Nascent-state product distributions ͑open circles͒ for HF(v,J)
formed from FϩH2 reactions at Ecomϭ2.4(6) kcal/mole, extracted from
absorption/emission signals obtained over the network of transitions listed in
Fig. 8. Signals are all scaled to sum to 100% and statistical error bars are
denoted for each transition. For comparison, full quantum theoretical calcu-
lations by Castillo and Manolopoulos58 on the SW potential surface are
shown in black. Note the generally good qualitative agreement with theory,
though significant discrepancies are evident, most notably in the
vϭ3 manifold.
ratios into low and high J-states as a function of reagent H2
density. In the single collision limit, such ratios should, of
27
course, be independent of ͓H ͔, whereas if collisional relax-
2
ation were occurring, one would anticipate an
͓
H ͔-dependent shift in rotational distributions from higher
2
to lower J-values. Figure 10 displays the ratio of integrated
absorbances for vϭ3←2R(J) branch transitions out of
‘‘low’’ (Jϭ2) and ‘‘high’’ (Jϭ8) rotational states, over a
range of stagnation pressures that extends up to nearly three
times the H densities used for obtaining the HF(v,J) distri-
2
butions reported in this work. Within experimental uncer-
tainty, these ratios are independent of H pressure, providing
2
experimental confirmation that rotational relaxation in the
intersection region is indeed negligible.
V. DENSITY-TO-FLUX TRANSFORMATION
When integrated over high resolution Doppler profiles,
the direct absorption/stimulated emission signals yield abso-
lute column integrated densities of the HF products in the
intersection region. However, for comparison with theoreti-
cal calculations, the state-to-state reactive cross sections are
most usefully defined in terms of reactively scattered fluxes.
In order to implement rigorous comparisons with theoretical
cross sections or previous beam data, one must therefore
consider the density-to-flux transformation, in effect ac-
counting for the residence time of the IR chromophore in the
FIG. 10. Pressure-dependent tests of integrated HF(vϭ2) signal ratios ͑for
Jϭ2 and Jϭ8͒ as a function of H stagnation pressure density, confirming
2
5
5
probe region. This residence time is inversely proportional
to the component of the lab-frame HF velocity perpendicular
the absence of collisional relaxation of the HF(v,J) nascent distributions
over a fourfold range in backing pressure and H beam densities.
2
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1

9314
J. Chem. Phys., Vol. 109, No. 21, 1 December 1998
Chapman et al.
to the probe laser, i.e., v , which in turn depends upon the
Ќ
product’s final state and scattering angle. Although this
transformation can in principle be achieved by detailed
analysis of the Doppler profiles, the FϩH scattering system
2
offers several dynamical simplifications that make this un-
necessary.
First, conservation of energy and linear momentum dic-
tates that most of the recoil energy is carried off by the light
H-atom. Specifically, only m /(m ϩmHF)Ϸ5% of the total
H
H
recoil velocity appears in the HF. Second, as a result of such
limited HF product recoil, v is nearly equal to the lab-frame
Ќ
center-of-mass velocity, making the dispersion in vЌ also
small. Finally, from detailed Monte Carlo simulations for the
experimental geometry, any residual effect of HF recoil ve-
locity upon these measurements is preferentially suppressed
for backward-scattered products. Since previous differential
cross section measurements of vibrationally resolved FϩH
2
reactive scattering34 show clearly that HF(vϽ3) products
are predominantly backward scattered, this further limits any
influence of recoil velocity on the observed signals. There is
strong forward scattering of HF into the highest vibrational
level, vϭ3; however, these HF(vϭ3,J) rotational states
have less overall excess kinetic energy to distribute into HF
product recoil, which compensates for this small effect.
Thus, the density-to-flux transformation for the current scat-
tering geometry of FϩH is expected to be largely insensi-
2
tive to quantum state.
This important point can be quantitatively justified as
follows. For a given product state, collision energy and
center-of-mass scattering angle ␪, the range of possible final
lab-frame velocities depends on the azimuthal angle ␾, about
which the scattering is symmetric. For a given HF(v,J), this
can be calculated from conservation of energy and numeri-
FIG. 11. Diagnostic tests of the density-to-flux transformation behavior for
FϩH in the right angle crossed-jet collision geometry depends on the av-
2
erage final HF(v, j) velocity component perpendicular to the probe laser
beam axis, which can be predicted from theoretical differential cross section
calculations by Castillo and Manolopoulos.58 Top: Perpendicular velocities
as a function of center-of-mass scattering angle for a series of vibration/
rotation levels. Bottom: Perpendicular velocities integrated over all center-
of-mass scattering angles as a function of J for HF(v) in vϭ1, 2, and 3
manifolds. Note the remarkable insensitivity to HF(v,J) product state.
cally integrated over ␾. In Fig. 11͑a͒, the resulting v (␪)
Ќ
speeds are shown vs ␪ for several representative HF(v,J)
product states for a perpendicular collision geometry. Note
that even for the most extreme cases, the range of v (␪)
Ќ
varies with HF(v,J) by only Ϯ10%. Also, for all final states,
vЌ(␪) is nearly constant for ␪տ␲/2, indicating that differ-
ential cross sections dominated by backward scattering will
result in only very small corrections to perpendicular speeds
in the data analysis. To take this one step further, one can use
the v,J-specific differential cross sections calculated theo-
ferential and integral cross sections into given HF(v,J) lev-
els on the ground-state adiabatic potential surface of Stark
and Werner.27 These differential cross sections can be related
to the experimentally observed column-integrated popula-
tions by the standard center-of-mass to lab-frame transforma-
tion. As discussed above, however, the resulting flux-to-
concentration transformation between integral cross sections
and populations for the current scattering geometry, kine-
matic mass combinations and energetics is essentially inde-
pendent of HF(v,J). Thus, we can directly compare the ex-
perimental column-integrated populations with the
theoretical integral cross sections, averaged over the 1:3
nuclear spin distribution of jϭ0 ͑para͒ and jϭ1 ͑ortho͒ H2
58
retically by Castillo and Manolopoulos, on the Stark and
2
7
Werner potential to integrate v (␪) over ␪ for each of the
Ќ
final HF(v,J) states. The results are shown in Fig. 11͑b͒ and
indicate that the perpendicular speeds are predicted to be
constant to within 5% for all HF(v,J) product states. Thus,
to well within the reported experimental uncertainties, the
fractional quantum state-resolved product densities shown in
Table II also reflect the quantum state-resolved fluxes, which
can therefore be directly compared with full close-coupling
theoretical results in the following section.
TABLE II. Nascent vibrational HF populations ͑summed over J͒.
V
Population ͑%͒
VI. DISCUSSION
0
1
2
3
Ͻ2͑2͒
18.8͑32͒
54.2͑23͒
27.0͑5͒
The highest level theoretical studies done to date on the
FϩH (j) system have been the quantum reactive scattering
2
28
calculations performed by Castillo et al., which predict dif-
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J. Chem. Phys., Vol. 109, No. 21, 1 December 1998
Chapman et al.
9315
FIG. 12. Comparison of the rotationally resolved HF(vϭ2,J) product state
5
8
distributions with ͑a͒ exact quantum close coupled theory on the SW po-
2
7
4
tential surface and ͑b͒ arrested relaxation studies by Polanyi and Woodall.
FIG. 13. Comparison of rotationally unresolved branching ratios into v
4
ϭ1, 2, and 3 from ͑a͒ arrested relaxation studies of Polanyi and Woodall,
4,35
͑
b͒ crossed-molecular-beam studies of Neumark et al.,3
͑c͒ the current
5
8
work, and ͑d͒ theoretical predictions by Castillo and Manolopoulos.
in the low-temperature jet. These comparisons are displayed
in Fig. 9, which shows measured and predicted product state
distributions ͑in % of total͒ for Ecomϭ2.4(6) and 1.84
kcal/mole, respectively.
The data indicate several points worth noting. First of
all, the qualitative overall trends in experimental rovibra-
tional populations are in remarkably good agreement with
exact quantum theoretical predictions by Castillo and
gion. Furthermore, the crossed-jet data are insensitive to a
fourfold increase in this crossing density, as indicated in Fig.
10. This is qualitatively different from arrested relaxation
studies, where the data required explicit correction for
pressure-dependent effects. Finally, it is worth noting that
the experimental distributions for vϭ1 and 2 appear less
symmetric than theoretically predicted from quantum calcu-
lations by Castillo and Manolopoulos on the lowest adiabatic
surface, which also differs from the more symmetric distri-
butions for these two manifolds reported by Polanyi and
Woodall.4
2
8,58
Manolopoulos
on the Stark and Werner ͑SW͒ potential
2
7
energy surface. In the vϭ2 manifold, for example ͓Fig.
͑b͔͒, both experiment and theory indicate a broad J-
9
distribution rising from low J and peaking at Jϭ5. The mea-
sured drop-off in population at higher J is slightly sharper
than predicted theoretically, but the relative populations at
Jϭ11 and 12 are again comparable. The distribution of v
ϭ1 rotational states is broader still and reasonably well
matched by theory ͓Fig. 9͑c͔͒. The sharp peaking of the v
ϭ3 rotational distributions near JϷ1–2 is also well repro-
duced, although more significant deviations are clearly evi-
dent at higher J-values. Nevertheless, the overall level of
agreement is impressive and indicates strong support both
By summing over all rotational states in a given vibra-
tional manifold, we can also include previous crossed-beam
studies by Neumark et al.3
4,35
in these comparisons. These
vibrational branching ratios for all three experimental studies
are presented in Fig. 13, and compared again with the theo-
28
retical predictions of Castillo et al. on the SW lowest adia-
batic potential energy surface.27 First, the results indicate
fairly good agreement between the present crossed-jet and
previous crossed-beam studies. This is especially impressive
since the two methods utilize fundamentally different detec-
tion schemes ͑i.e., IR absorption/emission vs electron bom-
bardment ionization͒ for characterizing the product state vi-
brational distributions. Second, the overall agreement
between experiments and theory is quite reasonable, al-
though some significant differences can be noted. Specifi-
cally, theory predicts less population in vϭ1 by nearly two-
fold than is observed. This would suggest, despite the
remarkably good agreement between theory and experiment
for trends in the rotationally resolved quantum state distribu-
tions, that there still may be qualitatively important issues to
be addressed in either the ab initio surfaces or the dynamics
calculations.
27
for the SW potential surface as well as the quantum dy-
namical calculations of Castillo and Manolopoulos.58
Though the main thrust of this paper is to compare with
quantum theoretical predictions, it is also worth briefly com-
paring with HF(v,J) populations observed in the early ar-
rested relaxation studies of Polanyi and co-workers.3–5 Since
the HF(vϭ2) rotational levels represent the majority of the
reactive flux, this vibrational manifold is chosen for compari-
son in Fig. 12, where the Polanyi data reflects their best
extrapolation to zero-pressure, fully ‘‘arrested’’ experimental
conditions. Although the two sets of experimental results are
qualitatively similar, significant differences are also clearly
evident. Specifically, the crossed-jet distributions start at
nonzero values at Jϭ0 and grow to a maximum by Jϭ5,
whereas the arrested relaxation studies suggest vanishing J
ϭ0 and 1 populations that grow to a more symmetric maxi-
mum at Jϭ7. This trend in the crossed-jet results toward
lower J-state distributions might, at first, suggest partial ro-
tational relaxation. However, this is quite unlikely, since the
crossed-jet data are obtained for more than 2 orders of mag-
nitude lower average pressures in the beam intersection re-
In this regard, it is interesting to look more closely at
discrepancies between theory and the current experimental
results. These are most clearly evident in the vϭ3 manifold
͓Fig. 9͑a͔͒ for which calculations on the SW surface predict
a significantly steeper decrease in population with increasing
J than experimentally observed. Specifically, the fraction of
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9316
J. Chem. Phys., Vol. 109, No. 21, 1 December 1998
Chapman et al.
vϭ3 population measured in Jϭ3 is nearly twofold larger
than theoretically predicted, while this factor grows to nearly
sixfold for Jϭ4. This effect is even more dramatic in Jϭ5,
which is predicted to be an energetically closed channel on
the Stark and Werner surface ͑i.e., the integral cross section
vanishes identically͒, whereas strong experimental signals at
Jϭ5 are clearly evident. The source of this qualitative dis-
crepancy can be easily traced to errors in the potential energy
ground adiabatic potential energy surface of Stark and
Werner,27 over most of the HF(v,J) state distribution. Com-
parison with the early arrested relaxation studies of Polanyi
4
and Woodall indicates qualitatively good but somewhat less
satisfactory agreement with both the present results as well
as theoretical calculations, especially for rotational distribu-
tions in the maximally populated vϭ2 manifold. Summed
over all rotational states, the current product state distribu-
tions are in reasonable agreement with previous vibrationally
2
7
surface of SW. Specifically, the dissociation energies of
Ϫ1
both H2 (D ϭ36 118.6(5) cm
)
and HF (D0
resolved crossed-beam measurements of Lee and
0
Ϫ1
34,35
ϭ47 311(5) cm ) have been determined to high precision
co-workers
obtained under lower energy resolution con-
from detailed spectroscopic studies.5
9,60
Thus, the corre-
ditions, as well as with the theoretical predictions of Castillo
and Manolopoulos.2
8,58
sponding overall reaction exothermicity for ground spin orbit
2
excited F( P
)
with para H (jϭ0)
is ⌬E
In terms of nascent state populations, the present rovi-
brationally resolved results represent the most rigorous test
of both ab initio and dynamics theory to date; the very fa-
vorable agreement indicates strong support for both the qual-
ity of the potential as well as the ability to perform accurate
full quantum coupled calculations on a single adiabatic sur-
face. At a more detailed level of inspection, however, there is
clear evidence for outstanding discrepancies between theory
and experiment that warrant further attention. Specifically,
theory significantly underpredicts population in the highest
energetically accessible rotational levels in the vϭ3 mani-
fold states, by as much as factors of 5 or more. This point is
most clearly made in the HF(vϭ3,Jϭ5) level, which is en-
ergetically closed on the Stark and Werner surface27 at 1.84
kcal/mole, yet still energetically accessible from accurate
thermochemical predictions and experimentally observed.
This highlights the need for further refinement of the exit and
3
/2
2
Ϫ1
ϭ11 192(5) cm ͓32.001͑14͒ kcal/mole͔. With ortho H (j
2
ϭ1) reagent, this makes the HF(vϭ3,Jϭ5) product chan-
nel exothermic by Ϸ0.7͑6͒ kcal/mole at the collision ener-
gies used in this work. By way of contrast, the Stark and
Werner surface yields an overall reaction exothermicity of
only ⌬Eϭ31.77 kcals/mole, which is 0.23 kcals/mole
smaller than experimentally determined, and is the reason
why the theoretically predicted HF(vϭ3,Jϭ5) populations
vanish identically at Ecomϭ1.84 kcal/mole. These discrepan-
cies underscore the necessity of improving the asymptotic
exit/entrance channel properties of the SW surface in order
to reliably predict quantum state-resolved reaction dynamics
near the energetic threshold.
As a final note, closer inspection of Fig. 9 and Table I
reveals that there is also some finite population observed in
HF(vϭ3,Jϭ6). This state is at the energetic upper limit and
thus essentially requires the full center-of-mass collision en-
ergy plus the reaction exothermicity to access, even for the
limiting case of zero kinetic collision energy recoil in the
products. Such product state behavior is more dramatic in
studies at lower collision energies, which reveal HF(v
ϭ3,J) population in several rotational levels above the en-
ergetically accessible limit for reactions of ground spin-orbit
entrance channels on the FϩH surface in order for such
2
threshold phenomena to be reliably explored with fully rig-
orous quantum dynamics calculations.
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1