Reactive excitation functions for F+p-H2/n-H2/D2 and the vibrational branching for F+HD

Article abstract of DOI:10.1063/1.1287840

The reactions of F+H₂ and its isotopic variants stand at a unique position in the field of reaction dynamics. A number of important issues about this reaction are addressed in this work. First, at the level of detail of the integral cross section the transition-state properties including the barrier height of this reaction are well characterized by the Stark-Werner potential energy surface (PES), despite the fact that from the ab initio point of view the correct PES for the F(²P_3/2) reaction should be the HSW which raises the barrier by 0.35 kcal/mol. Second, based on the excitation functions for F+p-H₂ and F+n-H₂, it is speculated that a resonance may indeed exist for the F+H₂ reaction, in support of the original suggestion by D.M. Neumark et al. (1985). Third, it is conjectured that the unusual energy dependence of the vibrational branching of the HF product provides another measurable signature for dynamical resonance in F+HD → HF+D. Finally, the nonadiabatic reactivity of the spin-orbit excited F^*(²P _1/2 ) atom is found to be small in F+HD over the entire energy range of this work.

Full text of DOI:10.1063/1.1287840

Reactive excitation functions for F +p- H 2 /n- H 2 / D 2 and the vibrational branching for
F+HD
Feng Dong, Shih-Huang Lee, and Kopin Liu
Citation: The Journal of Chemical Physics 113, 3633 (2000); doi: 10.1063/1.1287840
View online: http://dx.doi.org/10.1063/1.1287840
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 113, NUMBER 9
1 SEPTEMBER 2000
Reactive excitation functions for F¿p-H2 Õn-H2 ÕD2 and the vibrational
branching for F¿HD
Feng Dong, Shih-Huang Lee, and Kopin Liu
Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, Taipei, Taiwan 10764
͑Received 13 March 2000; accepted 8 June 2000͒
Complementary to our recent report on the FϩHD reaction, the reactive excitation functions for the
other isotopomers are presented. Through analysis of the differential cross section data, the
collisional energy dependencies of product vibrational branchings for FϩHD are also reported here.
Several important conclusions can be drawn from this work. First, the transition-state properties, in
particular the barrier height, of this reaction are well-characterized by the SW PES, despite its
neglect of spin–orbit couplings. Second, contrary to the theoretical conclusion in recent literatures,
an experimental observation is presented which seems to suggest that a resonance may indeed exist
for the FϩH2 reaction in support of the original interpretation proposed by Lee and co-workers.
Third, the vibrational branching for the FϩHD→HFϩD reaction elucidates another facet of
resonance effects in the integral cross sections. Finally, the nonadiabatic reactivity of the spin–orbit
2
*
excited F ( P1/2) atom is found to be small, which is in line with the conclusion inferred from a
most recent, full quantum mechanical multisurface calculation. © 2000 American Institute of
Physics. ͓S0021-9606͑00͒01233-2͔
I. INTRODUCTION
bending potential, but it cannot establish the reaction barrier
height because of the uncertainty in the dissociation energy
of the FHϪ2 anion. On the other hand, using the SW PES,
discrepancies between QM calculations and scattering ex-
periments still persist for FϩH2 ,16,17 and particularly more
so for FϩHD→HFϩD.18 More significantly, the original in-
terpretation of a resonant scattering mechanism proposed by
Lee and co-workers in 1985 was challenged by a QCT in-
vestigation on the SW PES.19 The QM calculations and
analysis performed later for FϩH2 seemed to confirm the
alternative QCT line-of-center model that the sharp forward
The reaction of F(2P)ϩH2 and its isotopic variants have
played a central role in the development of gas phase reac-
tion dynamics.1 These reactions have been extensively stud-
ied in a large variety of kinetic and dynamic experiments. A
major breakthrough on the experimental front was the 1985
crossed-beam study of Lee and co-workers for FϩH2 /D2 /
HD in the range of 0.7–3.4 kcal/mol collision energies.2,3
Anomalous forward scattering peaks in the vibrational state-
resolved angular distribution were observed, which was at-
tributed to quantum dynamical resonance phenomena. This
experimental result has since then inspired numerous theo-
retical works both on the potential energy surface ͑PES͒ and
on a series of quasi-classical trajectory ͑QCT͒ and quantum
mechanical ͑QM͒ calculations of its reaction dynamics.4
Meanwhile, impressive experimental investigations of this
reaction progressed. These include new crossed-beam ex-
periments with improved resolution for FϩD2 in an extended
collision energy range of 2–5.5 kcal/mol,5–7 a rotationally
resolved differential cross section measurement for a few
scattering of HF( ϭ3) in FϩH is attributed to tunneling
v
Ј
2
through the centrifugal barrier for large impact parameter
collisions.4,16 Hence, at this point it appears that the experi-
mental anomalies in angular distributions could be classical
mechanics in origin.
There are other unsettled issues about this reaction.
Since all experimental works performed so far involved an
F-atom source with unknown spin–orbit contents ͑the spin–
orbit excited P1/2 state lies 404 cmϪ1 above the P3/2
ground state͒, one of the long-standing questions is about
2
2
selected ( , j ) states of HF in FϩH at Ecϭ3.64 kcal/
v
Ј Ј
2
mol,8,9 newer measurements of the rovibrational state distri-
their relative reactivities. Could the nonadiabatic reactivity
2
butions of HF from FϩH2 at 2.46 kcal/mol,10 and the rota-
*
of F ( P1/2) account for the remaining discrepancies be-
tween theory and experiment? Facing this challenge, spin-
orbit effect has then been included in a refined version of the
SW PES ͑hereafter HSW PES͒.20 Its major effect was the
tional state distributions of HF( ϭ3) over the energy range
v
Ј
of 0.3–2.4 kcal/mol,11 and, most notably, the photodetach-
ment spectroscopic approach of FHϪ2 in direct probing the
transition-state region of PES.12–14
increase of the barrier on the ground adiabatic (1 2A ) PES
Ј
by 0.35 kcal/mol relative to its value on the spin-free SW
PES. Paradoxically, QM simulations on the HSW PES ͑still
single-surface calculations͒ for both FϩH2 ͑Refs. 20 and 21͒
and FϩD2 ͑Ref. 22͒ scattering experiments turned out to be
somewhat worse than with the SW PES. Recently, the first
‘‘exact’’ QM multisurface scattering calculation, which in-
cludes all three HSW PESs, derivative coupling, spin–orbit
The development of a highly accurate, state-of-the-art ab
initio PES by Stark and Werner ͑SW͒ around the mid-90’s
15
has really made possible quantitative comparison between
theory and experiments. Full QM calculations on the SW
PES led to an unprecedented, nearly quantitative agreement
with the photodetachment spectra.13,14 This confirms the
shape of the transition state to be bent with a relatively flat
0021-9606/2000/113(9)/3633/8/$17.00
3633
© 2000 American Institute of Physics
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3634
J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Dong, Lee, and Liu
FIG. 2. A schematic of the discharge F-atom beam source. The labels are
͑1͒, ͑2͒, and ͑4͒: Teflon or ceramic insulator; ͑3͒ and ͑5͒: S.S. electrodes;
͑6͒: skimmers. The O-rings are made of Kalrez 4079.
tion and the shape of the steplike feature at low energies are
well reproduced, although the magnitude is off by a factor of
2. The reactivity at higher energies ͑Ͼ1 kcal/mol͒ also agrees
well with experiment. As shown in Ref. 24, the peculiar
steplike feature turns out to be an unmistakable fingerprint
for resonance in the integral cross section of this reaction.
Since the ‘‘resonance hierarchy’’ is expected to
follow the trend: (FϩHD→HFϩD͒Ͼ͑FϩH2͒Ͼ͑FϩD2͒
Ͼ͑FϩHD→DFϩH), this new finding seems to reopen the
original resonance interpretation,2,3 particularly for the
FϩH2 reaction, of the landmark 1985 crossed-beam scatter-
ing experiments. This paper tries to shed some light on this
issue by presenting the similar excitation function measure-
ments for Fϩp-H2 /n-H2 and D2 . The collisional energy
dependencies of the product vibrational branchings for
FϩHD are also included to further elucidate the resonance
FIG. 1. Excitation functions for the two isotopic channels of the FϩHD
reaction. The experimental results are shown with dots. The QM and QCT
simulations on the SW PES are plotted with solid and dashed lines, respec-
tively. The experiment is normalized to theory by a single scaling factor for
both channels. ͑Adapted from Ref. 24.͒
and Coriolis coupling effects, has been performed for the
FϩH2 reaction.23 It was found that for Jϭ1/2 the reaction
2
*
probability of F ( P1/2) is less than 10% of that for
F(2P3/2). Although the reaction cross sections for F(2P3/2
)
effect on integral cross sections, and to delineate the
2
2
*
and F ( P1/2) are yet to be calculated, it appears that the
dominant feature of this reaction may very well be repre-
sented by the adiabatic dynamics on the lowest electronic
PES, i.e., the SW PES.
*
F ( P1/2) contribution to total reactivity of this reaction. The
latter is currently of considerable interests.4,10,11,20–23
Very recently, in a combined experimental and theoreti-
cal investigations of FϩHD, we reported our experimental
excitation function results.24 Conclusive evidence was pre-
sented for the existence of a reactive resonance in the HFϩD
product channel. For illustrations and for ready comparisons
with the other isotopic variants of this work, the results are
replotted here in Fig. 1. As is seen, both QCT25 and QM24
calculations on SW PES gave excellent account for the total
reactivity of the DFϩH isotope channel. The agreement be-
tween QM and experiment is in fact nearly perfect, except
for an experimental scaling factor. For the HFϩD product
channel, however, significant discrepancies by QCT are
seen. Specifically, the peculiar steplike feature observed for
EcϽ1 kcal/mol in experiment is entirely absent in the QCT
result, and at higher energies QCT also underestimates its
reactivity. By way of contrast, the QM calculation is in sig-
nificantly better agreement with experiment. Both the posi-
II. EXPERIMENT
The experiments were carried out in a crossed-beam
apparatus.26,27 The experimental details, except the F-beam
source, have been described previously,24,28 and thus will not
be reiterated here. A schematic of the beam source is de-
picted in Fig. 2. Basically it is a modification of a standard
piezoelectric transducer ͑PZT͒ pulsed valve. An extended
housing is attached to a PZT pulsed valve to act as a gas
holder so that the piezoelectric disk is not exposed to the
corrosive gases. A pair of electrodes is mounted further
downstream, and a dc high voltage, typically ϩ1.1 kV, is
applied to the front electrode. As the pulsed valve opens, the
gas inside the extended channel ͑1 mm ␾, 6 mm long͒ ini-
tiates the discharge and sustains it ͑i.e., a glow discharge͒
until the gas expands out of the channel. Also mounted be-
tween the two skimmers is a pair of deflection plates which
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J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Excitation functions and vibrational branching
3635
remove any discharge-generated ions from the beam. Typi-
cally, 5% F2 in He or Ne ͑total pressure at 15 atm͒ was used
in this work.
Two ways were used to characterize the mean speed of
the F-atom beam. It was found that there is always a trace
amount of discharge-generated H-atoms entrained in the
beam. Assume that all supersonically expanded gases travel
at the same speed. The Doppler-shift technique29 was then
employed to measure the beam speed through the ͑1ϩ1͒
REMPI detection of the entrained H-atoms. Alternatively,
one can monitor the ͑pulsed͒ discharge current. Knowing the
distance from nozzle to the scattering center, the measure-
ment of the time delay between the probe laser and the onset
of the discharge current pulse also provided a convenient
way to determine the beam speed. Agreement of these two
methods is always within Ϯ3%. The collision energy deter-
mined in this fashion is confirmed to be accurate within 0.05
kcal/mol from the rotational state-resolved differential cross
section measurements. It is known that discharge of F2 can
*
also generate a spin–orbit excited F atom. Unfortunately,
2
the relative amounts of F(2P3/2) and F ( P1/2) in the beam
*
FIG. 3. Excitation function for the FϩD2→DFϩD reaction ͑the upper
panel͒. Both the QM ͑Ref. 22͒ and QCT ͑Ref. 31͒ results are based on the
SW PES. The same scaling factor as FϩHD is used here. The open circles
are the experimental data points from Ref. 5. The low panel compares the
isotope effects. The experimental result for n-H2 is taken from Fig. 4, and
the theoretical curve ͑the solid line͒ is the corresponding QM result.
could not be measured with our setup. Hence, only a rough
estimate can be made. ͑Since the assumption involved is not
readily verified, one should not take this estimation too seri-
*
ously. In the following only the F contribution, not its rela-
tive cross section, will be reported.͒ The measured F beam
speeds correspond to an effective source temperature of
about 600 K for both seeded sources. Assuming the popula-
scaling factor used here is the same as that for the
FϩHD→DFϩH reaction; thus the agreement in magnitudes
is quite significant.
tions of the two spin–orbit states equilibrate at this tempera-
2
*
ture, this yields about 16% F ( P1/2) present in our beam.
Before presenting the experimental results, we want to
mention two more relevant points. First, the rotational tem-
peratures of our target beams were estimated to be 150 K for
H2 ͑both n-H2 and p-H2͒, 100 K for D2 , and 50 K for HD.28
Accordingly, the theoretical results reported below, which
are all based on the SW PES, have taken into account the
initial j-dependencies of reaction cross sections whenever
they are available. And the multisurface factor has been ap-
plied to all theoretical results in this work. Second, while the
experimental excitation functions are not in absolute cross
sections, they have all been normalized to one another.
Hence, only a single scaling factor, which was based on the
FϩHD→DFϩH reaction,24 is involved in comparison with
theory for all isotopomers.
The only previously reported experimental excitation
function for this reaction is that by Faubel et al.5 Their re-
sults are depicted in Fig. 3 as the open circles for compari-
son. The scaling of their data is somewhat arbitrary by
matching the three higher energy points. Their lower energy
data clearly appear to be too low compared to either the
theory or the present result.
B. Excitation functions for F¿n-H2 Õp-H2
Figure 4 shows the excitation functions for the reactions
of Fϩn-H2 /p-H2 . The purity of p-H2 was greater than
98%, as reported previously.32 As expected, tunneling be-
comes more pronounced, in particular for the p-H2 case.
Even at energy as low as 0.2 kcal/mol, the reactive cross
section is still quite significant. Again, both the magnitude
and the global shape are reproduced reasonably well by a
QM coupled-state calculation.33 Similar to the comparison
shown in Fig. 1 for FϩHD→HFϩD, the QM calculation
appears to overestimate the reactivity of Fϩp-H2 at low en-
ergies ͑Ͻ0.5 kcal/mol͒. Another way to make a comparison
between experiment and theory is to examine the ratio for
different target molecules, as displayed in the lower panel of
III. RESULTS AND DISCUSSION
A. Excitation function for F¿n-D2
The excitation function for FϩD2→DFϩD is presented
in Fig. 3. As is seen, both the threshold and the general shape
are very much like that for FϩHD→DFϩH ͑Fig. 1͒, which
suggests that the FϩD2 reaction is also dominated by direct
scattering. Also shown in the figure are the QM22,30 and
QCT31 results and the adiabatic barrier height of the SW
PES. Small tunneling at low energy is discernible. The the-
oretical predictions, both QM and QCT, are in reasonable
agreement with experiment. In particular, the experimental
Fig. 3 for ␴ /␴ and of Fig. 4 for ␴
/␴
. In this
p-H
2
D
H
n-H
2
2
2
way, no scaling factor is involved; thus the experimental
absolute ratio is compared directly with the theoretical value.
Very good agreements can be seen in both cases. Based on
the comparisons shown in Figs. 1, 3, and 4, we conclude that
the main properties of the transition state including the bar-
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3636
J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Dong, Lee, and Liu
the FϩH2 reaction probability.16 There is, however, a signifi-
cant difference between the two reactions. For the
FϩHD→HFϩD reaction, at the resonance energy ͑i.e.,
‘‘peak A’’͒ there is little or no direct reactive scattering.
Thus it is an isolated resonance, which appears to survive the
partial-wave averaging and manifests itself as a distinctive
steplike feature in the integral cross sections ͑Fig. 1͒.24 In the
case of FϩH2 , the QM calculation16 indicated that the onset
for direct scattering shifts significantly closer toward its
‘‘peak A.’’ Consequently, we expect a substantial contribu-
tion to the integral cross section from direct scattering even
near the reaction threshold, which then blurs the resonance
signature ͑i.e., the steplike feature͒ in the integral cross sec-
tions. Nevertheless, QM calculations also indicated that the
‘‘peak A’’ intensities for both reactions diminish with even
one quantum of rotational angular momentum in either H2
͑Ref. 16͒ or HD24 reactant. In other words, the resonance
contribution, if it exists, should be more pronounced for
p-H2 than for n-H2 . The significant enhancement of reactive
cross section observed at low energies for p-H2 than for
n-H2 ͑Fig. 4͒ is entirely consistent with the resonance sce-
nario in FϩH2 . Furthermore, the opposite rotational depen-
dencies predicted by QM and QCT at low energies can also
be reconciled by the existence of a resonance state in this
reaction provided that the absorbing potential used in Ref. 33
was sufficiently far out without missing the resonance con-
tribution. A QM wave packet analsysis for FϩH2 , similar to
that reported for FϩHD,24 has recently been performed,
which firmly establishes the existence of a reactive resonance
on the SW surface.35 Thus, it seems that the theoretical bal-
ance is now tilt back in favor of the existence of a resonance
for the FϩH2 reaction, though the correct interpretation of
the landmark 1985 scattering experiment which was at
higher collision energies could still remain an open question.
In this regard, it is interesting to note that using semiclassical
Regge pole analysis, with the help of Pade approximation, of
the ‘‘exact’’ QM differential cross section for FϩH2 ,
Sokolovski and Castillo36 very recently argued that the
anomalous state-selective forward scattering has a major
resonance contribution.
FIG. 4. Excitation functions ͑the upper panel͒ for the Fϩp-H2 ͑᭹͒ and F
ϩn-H2 ͑᭺͒ reactions. The QM coupled-state results are taken from Ref. 33,
and the QCT simulation ͑for p-H2 only͒ is from Ref. 31. The experimental
scaling factor is the same as FϩHD ͑Fig. 1͒ and FϩD2 ͑Fig. 3͒. The lower
panel compares the initial j-dependencies. The solid line is the QM result.
rier height are well characterized by the SW PES, despite its
neglect of spin–orbit effects. ͑The inclusion of spin–orbit
effects will increase the barrier height spoiling the remark-
able agreements with experiments.͒ This conclusion corrobo-
rates with recent QM simulations of the other reaction at-
tributes using the HSW PES,20–22 as alluded to early.
A closer inspection of the experimental data also reveals
a subtle, yet significant dependence of reactivity on the ini-
tial j-state of H2 . At high collision energies, the rotation of
H2 apparently has a positive, abeit small, impact on its reac-
tivity. Similar propensity has previously been observed for
ClϩH2 ͑Ref. 32͒. Both QM33 and QCT31 ͑only p-H2 is
shown here for clarity͒ calculations display a similar trend.
Its physical origin is purely classical, and can be traced to the
long-range anisotropic interactions in the entrance valley.
This stereodynamics also manifests itself in the intramolecu-
lar isotope branching ratio, as discussed previously for the
FϩHD24,25 and the ClϩHD reactions.34 At lower energies
(EcϽ1.4 kcal/mol) such a j-dependency persists in the QCT
calculation ͑not shown; see Ref. 31 for the j-dependencies͒,
which is in sharp contrast with experimental observation. On
the other hand, QM coupled-state calculations for n-H2 and
p-H2 show the same propensity as experiment. Clearly,
something quantum in nature, and probably more than just
tunneling, must come into play at low energies. We conjec-
ture that it is reminiscent of the very same resonance state as
what we have recently found for the FϩHD→HFϩD
reaction.24
C. Vibrational branching for F¿HD
1. F¿HD\HF(vЈ)¿D
As depicted in Fig. 1 and discussed in details
elsewhere,24 the distinct steplike feature for FϩHD→HFϩD
is indeed an imprint of the long-searched reactive resonance
in the integral cross sections. The resonance fingerprint in
product angular distribution has also been uncovered.37 An
interesting question then arises: is there any other experi-
mental observable which signifies the existence of a reso-
nance? and in what way? Presented here is the product vi-
brational branching.
We used the Doppler-selected TOF approach to measure
the differential cross sections for FϩHD. The experimental
details have been given previously27 and the resulted state-
to-state differential cross sections for FϩHD will be reported
in the future. Here it suffices to say that once the product
velocity-flux contour map is obtained, the integration of all
The reason is the following. As shown previously,24 the
resonance state we identified for the FϩHD reaction corre-
sponds to ‘‘peak A’’ in its cumulative reaction probability.18
A similar feature ͑also labeled ‘‘peak A’’͒ is also present in
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J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Excitation functions and vibrational branching
3637
FIG. 5. A few examples of the product translational energy distributions for
FIG. 6. Collisional energy dependence of the HF product vibrational
branching ͑upper panel͒ and the vibrational-specific excitation function
the FϩHD→HFϩD reaction. Also marked in the figure are the energetic
2
onsets for the formation of HF( ) products from F(2P3/2) and F ( P1/2).
*
vЈ
͑lower panel͒ for FϩHD→HF( )ϩD. The ‘‘total’’ excitation function is
vЈ
These P(Et) distributions have been normalized to the excitation function
͑Fig. 1͒. Note the different scale for each collision energy, Ec in kcal/mol.
obtained by connecting the data points from Fig. 1. The oscillations at
higher energies are the experimental uncertainties. The small contributions
2
*
from F ( P1/2) ͑the shaded area, upper panel͒ were included in the indi-
vidual vibrational state-specific excitation functions ͑the lower panel͒.
angles yields the desired product translational energy distri-
bution P(E )ϭd␴/dE . A few of them for the HF( )ϩD
v
Ј
t
t
isotope channel are shown in Fig. 5 for illustration. The en-
ergetic onsets for different product vibrational states are also
marked on the top. Quite obviously, the vibrational struc-
tures are well-resolved. Even after the integration of all
angles ͑note: the energy resolution in our experimental ap-
proach depends on the c.m. scattering angle͒, some rotational
structures for the most dominant vibrational state ϭ2 are
mation of HF( ϭ3) from the F(2P3/2) reaction becomes
energetically allowed, its population show a sudden boost. In
v
Ј
particular, at E ϭ1.18 kcal/mol, the contributions to HF(
v
Ј
c
2
ϭ3) from F(2P3/2) and F ( P1/2) are most evident as two
*
distinct features. Apparently, there is no delayed onset, i.e.,
no exit barrier, for the formation of HF( ϭ3). Using a
v
Ј
procedure similar to our previous work,38 we partitioned the
P(Et) distributions into product vibrational states. The re-
sults for 17 collisional energies ranging from 0.4 to 4.52
kcal/mol are summarized in Fig. 6. The vibrational branch-
ings are given in the upper panel, and the vibrational state-
specific excitation functions are in the lower panel. We first
v
Ј
still noticeable.
Also marked in Fig. 1 is the energetic onset for the for-
mation of HF( ϭ3) from the F(2P3/2)ϩHD reaction,
v
Ј
which occurs at Ecϭ1.16 kcal/mol. Yet, at Ecϭ0.4 kcal/
mol there is a prominent spike near zero kinetic energy re-
lease. Note that at 50 K only jϭ0 ͑82%͒ and jϭ1 ͑18%͒ of
HD need to be considered. The rotational energy for jϭ1 is
0.26 kcal/mol which is far too small to be responsible for this
spike. Similarly, a smaller peak at 0.4 kcal/mol can also be
seen for Ecϭ0.8 kcal/mol, which energetically does not cor-
note that the overall contribution ͑not cross section͒ from
2
*
F ( P1/2) ͑i.e., sum of all , in shaded area͒ is only a few
v
Ј
percent over the entire energy range of this work. That is true
even for E Ͻ1.1 kcal/mol when the formation of HF(
v
Ј
c
ϭ3) from F(2P3/2) is energetically closed.
respond to any high j-state of HF( ϭ2). Based on the en-
It is noteworthy that very recently Nesbitt and his
v
Ј
ergetic considerations, we ascribed them to F ( P1/2
)
co-workers10,11 also reported the experimental evidence for a
2
*
2
*
ϩHD→HF( ϭ3)ϩD which is a thermal neutral process.
finite nonadiabatic reactivity of F ( P1/2) in the reaction of
v
Ј
This is an unequivocal evidence for the finite reactivity of
Fϩn-H2 , which at first glance seems at variance with the
earlier crossed-beam scattering results.2,3,5–7 The present
work for F(2P)ϩHD indicated, however, that there is actu-
2
*
F ( P1/2), but its contribution to total reactivity is appar-
ently small even in the threshold region. It should be stressed
that this evidence rests only on thermochemistry, i.e., it is
completely independent of the barrier height of the SW or
HSW PES, and does not depend on the comparison with any
dynamical calculation. It can also be seen that once the for-
ally no significant conflict among all experiments provided
2
*
that there is no substantial isotope effects in F ( P1/2) reac-
tivities. First, the measurement of the HF( , j ) product
v
Ј Ј
state distribution by Nizkorodov et al.11 was made only for
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3638
J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Dong, Lee, and Liu
FIG. 8. As in Fig. 6, except for the FϩHD→DF( )ϩH reaction.
vЈ
FIG. 7. As in Fig. 5, except for the FϩHD→DFϩH reaction.
2
*
ϭ3. Thus the nonadiabatic contribution from F ( P1/2) in
v
Ј
integral cross sections. The low energy reaction is almost
entirely governed by resonant scattering.24,37 The resonance
state has been identified, in the local-mode picture, as ͑00°3͒
with three quanta of the H–F stretch and zero quanta of the
their experiment refers to ϭ3 only, whereas in all other
v
Ј
crossed-beam experiments, including the present one, they
are referenced to the overall reactivity. Since HF( ϭ3) is
v
Ј
not the dominant product channel in Fϩn-H2 even at low
H–D stretch and the bend. The dominance of the ϭ2 for-
v
Ј
collision energy ͑e.g., see Ref. 2, Fig. 3 for Ecϭ0.68 kcal/
mation follows the usual ⌬ -propensity rule in a vibrational
predissociation process, which says the larger the ⌬ ϭ
v vi
v
2
*
mol͒, an appreciable F ( P1/2) contribution to the formation
of HF( ϭ3) will still amount to a small contribution to
Ϫ
,
then the much less probable the vibrational
v
vf
Ј
total reactivity. Second, the evidence for nonadiabatic reac-
predissociation.1,39 We will loosely term a decay process for
tivity of F ( P1/2) presented by Nesbitt’s group10,11 depends
⌬ Þ0 a Feshbach-resonance decay.40 At higher energies
2
*
v
upon the theoretical prediction near the threshold region. If
the true barrier height for this reaction is, paradoxically,
closer to that on the SW PES, as suggested by the present
work, then the theoretical curve shown in the Fig. 7 of Ref.
11 should not be shifted upward by 0.38 kcal/mol. The re-
sulted discrepancy between experiment and theory will be
(Ecу1.16 kcal/mol) the decay of this resonance state into
HF( ϭ3), which is called a shape-resonance decay,40 be-
v
Ј
comes feasible. Hence, there is a competition between the
Feshbach- and shape-resonance decays, which explains the
abrupt rise in ␴( ϭ3) around this energy. The resonances
v
Ј
will be associated with larger partial waves with further in-
crease in collision energies. The centrifugal barrier for
shape-resonance decay becomes higher, lowering its prob-
ability, which could be the origin for the gradual decline for
greatly reduced—although the finite nonadiabatic reactivity
2
*
from F ( P1/2) might still be evident.
Perhaps more intriguing in Fig. 6 is the collisional en-
ergy dependency of the vibrational branching. At low ener-
gies, EcՇ1 kcal/mol, most of reactive fluxes ͑Ͼ90%͒ are
channeled into ϭ2. As soon as ϭ3 from F(2P3/2) be-
ϭ3 after 2 kcal/mol. Consequently, a prominent peak
v
Ј
shows up in both the state-specific excitation function and
the collision energy dependence of the vibrational branching
v
v
Ј
Ј
comes accessible, its branching rises sharply with a concur-
for HF( ϭ3). Of course, there is the direct scattering com-
v
Ј
rent drop for ϭ2. At even higher energies, Ec
ponent for Ecտ1.0 kcal/mol on SW PES,24 which also needs
to be considered. A thorough QM analysis is necessary for a
definite conclusion. Nevertheless, detailed analysis of our
v
Ј
տ2 kcal/mol, the branching for
ϭ3 declines gradually
v
Ј
whereas ϭ2 stays more-or-less constant following a small
v
Ј
initial increase. As to the branchings for ϭ1 and 0, both
differential cross section data indeed suggest that ϭ3 is
v
Ј
v
Ј
increase slowly with the increase in collision energies.
We will argue that this vibrational branching behavior
could be another ramification of dynamical resonance in the
totally dominated by resonant scattering at all energies,
whereas ϭ0–2 consists of both contributions from reso-
v
Ј
nant and direct scatterings for Ecտ1.1 kcal/mol.41
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J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Excitation functions and vibrational branching
3639
TABLE I. Comparison of vibrational branchingsa for the FϩHD→DF(
ϩH reaction at Ecϭ1.98 kcal/mol.
)
vЈ
conceivable that the previous forward-convolution
procedure3 might not yield a unique distribution as the
present direct-mapping approach, which also has higher
resolution. Alternatively, the rotational temperatures of the
HD molecules in these experiments are not the same: the
thermal one42 is at 300 K, the Lee’s beam experiment is
about 40 K ͑0.9 and 0.1 in jϭ0 and 1, respectively͒, and the
present work is about 50 K ͑0.82 and 0.18 in jϭ0 and 1,
respectively͒. If the dynamics of this reaction depends
strongly on the initial rotational state, it could be the origin
of these discrepancies. Similar effects have previously been
noted for the FϩD2 reaction.5 In any event, it is recognized
that the vibrational branching of this reaction is extremely
sensitive to the fine details of the PES.43–45 Further work is
warranted.
*
F
Method
ϭ4
ϭ3
ϭ2
ϭ1
ϭ0
vЈ
vЈ
vЈ
vЈ
vЈ
b
Expt. ͑Lee et al.͒
0.25
0.26
0.33
0.27
0.34
0.53
0.43
0.44
0.51
0.43
0.21
0.23
0.15
0.19
0.23
0.01
0.08
0.03
0.025
0.003
c
Expt. ͑Polanyi et al.͒
This workd
QMe
0.01 0.038
QCTe
aDefined as ␴ /͚
␴
.
v
Ј
v
v
Ј
Ј
bReference 3.
cReference 41.
dEcϭ2.0 kcal/mol.
eFor HD (jϭ0) only.
2. F¿HD\DF(vЈ)¿H
At last, it is interesting to note the appearance of a
double-peaked kinetic energy distribution for DF( ϭ3 and
v
Ј
The product P(Et) distributions for this channel are pre-
sented in Fig. 7. Again, the vibrational structures are readily
resolvable. The resulted vibrational branchings are summa-
rized in Fig. 8. Although the differential cross section mea-
surements for this isotope channel were performed at only
four different energies, Doppler profile measurements ͑//-
configuration͒ indicated a rather smooth variation over the
entire energy range.41 Thus the main feature of the energy
dependency of the vibrational branching should be captured.
4͒ at Ecϭ4.0 kcal/mol. A bimodal rotational distribution has
also been reported recently for the backward scattered
DF( ϭ2 and 3͒ from FϩD at 2.07 kcal/mol.6 Due to
v
Ј
2
space limitation, further discussion will be deferred to our
future report on the state-resolved differential cross section.
IV. CONCLUSIONS
The reactions of FϩH2 and its isotopic variants stand at
a unique position in the field of reaction dynamics. A number
of important issues about this reaction are addressed in this
work, from which several conclusions can be drawn.
First, at the level of detail of the integral cross section
the transition-state properties including the barrier height of
this reaction are well characterized by the SW PES, despite
the fact that from the ab initio point of view the correct PES
for the F(2P3/2) reaction should be the HSW which raises
the barrier by 0.35 kcal/mol. This conclusion corroborates
the finding from the recent QM simulations of the other re-
action attributes using the HSW PES.20–22
As is seen, in contrast with the HF( )ϩD product channel,
v
Ј
there is a more democratic distribution for this channel. Ex-
cept for ϭ4 ͑the least exothermic state͒, all other vibra-
v
Ј
tional states display a gradual increase in both the cross sec-
tion and the branching with the increase in collision energies.
2
*
The F ( P1/2) contribution to this isotope channel is again
rather small.
There are two previous experimental reports3,42 on the
vibrational branching, both at a single collision energy.
Table I summarizes the comparisons, along with the dynami-
cal calculations on the SW PES. Qualitatively, all three ex-
periments are consistent: an inverted distribution peaking at
Second, based on the excitation functions for Fϩp-H2
and Fϩn-H2 , we speculated that a resonance may indeed
exist for the FϩH2 reaction, in support of the original sug-
gestion by Neumark et al.3 This conclusion seems in conflict
with the classical line-of-center interpretation of the land-
mark 1985 scattering experiment drawn from the recent the-
oretical investigations,4,16,19 but the correct answer, classical
versus resonance, could just be a question of degree.
Third, it is conjectured that the unusual energy depen-
dence of the vibrational branching of the HF product pro-
vides another measurable signature for dynamical resonance
in FϩHD→HFϩD.
ϭ3. Quantitatively, however, some discrepancies are no-
v
Ј
ticed, which are beyond the experimental uncertainty ͑Ϯ3%
for ϭ2–4͒ of this work. The difference between the
v
Ј
present work and the Lee’s 1985 experiment rests mainly on
the ratio of ( ϭ4)/( ϭ3). On the other hand, Polanyi’s
v
v
Ј
Ј
result,42 for which the collision energy is less defined, indi-
cated a slightly more even distribution for ϭ2, 3, and 4.
v
Ј
Compared to the dynamical calculations, the QM result ͑for
jϭ0 only͒18 is in excellent agreement with the Lee’s experi-
ment, whereas the QCT result43 agrees better with the
present one for ϭ3 and 4. At first glance, these compari-
v
Ј
sons might be a bit confusing. First, in terms of total integral
cross sections ͑Fig. 1͒, the QM result is certainly in better
agreement with experiment than QCT. Yet, for vibrational
branching QM yields a somewhat larger variance with ours
than QCT. Second, while there are appreciable differences
from the two dynamical calculations, both gave an equally
good simulation to the experimental ͑DFϩH͒ laboratory an-
gular distribution.18,43 Clearly, neither the total excitation
function nor the product laboratory angular distribution for
this reaction provides a very stringent test of the calculation
for a reaction attribute such as the vibrational branching. It is
Finally, the nonadiabatic reactivity of the spin-orbit ex-
2
*
cited F ( P1/2) atom is found to be small in FϩHD over the
entire energy range of this work. This conclusion is in cor-
roboration of the other crossed-beam scattering
experiments,2,3,5–7 and of a most recent, full QM multisur-
face calculation.23
ACKNOWLEDGMENTS
We are indebted to Professors R. T. Skodje, D. E.
Manolopoulos, and F. J. Aoiz for stimulating discussions and
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3640
J. Chem. Phys., Vol. 113, No. 9, 1 September 2000
Dong, Lee, and Liu
critical comments of this paper, and to Professor Y. T. Lee
for his continued encouragement. The National Science of
Council of Taiwan and the Chinese Petroleum Corporation
supported this work.
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