Isotope effects and excitation functions for the reactions of S(1D) + H2, D2 and HD

Article abstract of DOI:10.1016/S0009-2614(98)00535-1

Excitation functions for the title reactions were determined from 0.6 to 6 kcal/mol. Contrary to the analogous reaction of O(¹D), it appears that the reaction of S(¹D) proceeds solely through insertion over this energy range. Compared to other reactions, an intriguing H/D isotope effect was revealed. The propensity of the intramolecular H/D branching found under thermal conditions for A + HD reactions appears to be reverse for a supersonically cooled HD reagent. This finding implies that the reagent rotation could have profound influences on radical reactivity not only for an activated abstraction reaction, but for a barrierless inserted one.

Full text of DOI:10.1016/S0009-2614(98)00535-1

3
July 1998
Chemical Physics Letters 290 Ž1998. 323–328
Isotope effects and excitation functions for the reactions of
1
ž /
S D qH , D and HD
2
2
Shih-Huang Lee, Kopin Liu )
Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, Taipei, Taiwan 10764, ROC
Received 23 February 1998; in final form 27 April 1998
Abstract
Excitation functions for the title reactions were determined from 0.6 to 6 kcalrmol. Contrary to the analogous reaction of
1
1
OŽ D., it appears that the reaction of SŽ D. proceeds solely through insertion over this energy range. Compared to other
reactions, an intriguing HrD isotope effect was revealed. The propensity of the intramolecular HrD branching found under
thermal conditions for AqHD reactions appears to be reverse for a supersonically cooled HD reagent. This finding implies
that the reagent rotation could have profound influences on radical reactivity not only for an activated abstraction reaction,
but for a barrierless inserted one. q 1998 Elsevier Science B.V. All rights reserved.
1
. Introduction
branching measured for the room-temperature aver-
age of the ratio of the rate constants for the two exit
channels of the AqHD reaction. They found that
for a direct abstraction reaction with an entrance
channel barrier, such as FqHD, this ratio is usually
less than one. By contrast, a ratio of larger than one
was generally found for a number of reactions which
are believed to proceed through an insertion mecha-
nism Žsome of them are known to have little poten-
tial energy barrier.. Qualitative arguments, based on
either the screening of the D atom by the H atom in
a rotating HD molecule or the escape probability
from a HAD complex, were also presented to ratio-
nalize the observations.
Subsequent theoretical investigations w2–8x, based
on quasi-classical trajectory ŽQCT. results for a few
The elementary chemical reaction can be classi-
fied according to its reaction mechanism as a direct
abstraction, an Žend-on. addition–elimination, or an
Žedge-on. insertion–decomposition process, with the
latter two involving the formation of reaction com-
plexes. Knowledge accumulated over the past
decades in reaction dynamics allow us now to make
some generalizations or to ‘understand’ many of
dynamical attributes based on this simple classifica-
tion and its relationship to the dominant features of
the potential energy surface ŽPES. involved.
One aspect, which has recently received consider-
able attention both experimentally and theoretically,
is the isotope branching ratio, in particular for the
reaction with HD. In a seminal paper w1x, Bersohn
direct abstraction reactions, indicated that the inter-
pretation is actually far more complicated. The HrD
ratio depends not only sensitively on the shape of the
PES en route to the barrier Ži.e. oblate vs. prolate.,
and coworkers summarized the intramolecular HrD
)
Corresponding author. E-mail: kpliu@gate.sinica.edu.tw
0
009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.
PII: S0009-2614Ž98.00535-1

3
24
S.-H. Lee, K. LiurChemical Physics Letters 290 (1998) 323–328
but also on the reagent rotation. The reader is re-
ferred to Ref. w2x for an excellent review. Although
conflicting conclusions still remained w8–11x regard-
ing the exact interpretations of the role of reagent
rotation on reactivity, it is generally accepted that the
rotational effect is intimately related to stereodynam-
ics.
complex of H S on the ground state PES through the
2
insertion mechanism. The product is formed via
subsequent complex decomposition. The well-depths
of reaction complexes, H O and H S, for both reac-
2
2
tions are quite comparable, 118 and 90 kcalrmol,
respectively Žreference to the product channel.. The
exoergicity for the present system is, however, sub-
1
As to insertion reactions, either with or without a
barrier, much less has been investigated theoreti-
cally. In a very illuminating QCT study of the reac-
stantially smaller than that for OŽ D.qH , 6–7 vs.
2
;43 kcalrmol. Because of the deep potential well
and the small exoergicity, conventional wisdom will
then predict a long-lived complex being involved in
the title reaction and the statistical behavior might be
borne out w15x. Indeed, this is the conclusion drawn
1
tion dynamics for OŽ D.qH , D and HD w12x,
2
2
Schatz and coworkers found the intramolecular iso-
tope effect is strongly dependent on PES. The HrD
ratio varies from ;1.0 for the MC ŽMurrell and
Carter. surface to ;1.8 for the SL ŽSchinke and
Lester. surface. A detailed analysis of the reaction
from the measured isotope branching ratio and trans-
lational energy release in a recent investigation of
this reaction w16x. That study was conducted by the
1
mechanism was also performed to elucidate the
hot SŽ D.-atom technique in a room temperature
mechanistic origin of the difference. It is now proba-
cell, thus the initial collision energy distribution is
1
1
bly well-accepted that the reaction of OŽ D.qH is
relatively broad. Similar to the case of OŽ D., five
2
1
complicated by the additional microscopic abstrac-
tion pathway which proceeds initially on excited
surfaces w13,14x. The presence of a collinear barrier
of ;2 kcalrmol on the excited surface w13,14x
PESs are involved in the interactions of SŽ D. with
H . The degree of the participation of excited sur-
2
faces, which roughly speaking correspond to the
abstraction channel, in reactivity is unknown. The
questions we would like to address here are, over
what energy range does one need to consider the
abstraction pathway? What are the isotope branch-
ings for the insertion and abstraction pathways, re-
spectively? How do they compare with other reac-
tion systems?
makes the direct comparison of the HrD ratio more
complicated between theory Žif only the ground state
surface of H O is considered. and experimental re-
2
sults Žif the initial collision energy is too high or too
broad.. Nevertheless, the aforementioned theoretical
investigation is, by itself, quite insightful in that it
clearly showed that just like a direct abstraction
reaction, the long range orientation effects in the
entrance channel can have profound influences on
the observed HrD ratio for an inserted one, at least
for a reaction in which a short-lived complex is
2. Experiment
The experiment was carried out in a crossed-beam
apparatus with the procedure similar to that reported
1
involved such as OŽ D.qHD w12x. If this conclu-
1
sion is accepted, then the effects of rotational stere-
oselectivity might also be anticipated for an insertion
reaction. On the other hand, if the complex lives
sufficiently long, one might expect the dynamics
being governed by the complex decomposition and
all initial memories being lost. No reagent rotation
effect is then anticipated.
previously for the analogous reaction of OŽ D. w14x.
1
In brief, a skimmed SŽ D. beam was generated by
laser photolysis of CS Ž(0.5% CS seeded in He
2
2
at stagnation pressure of 15 atm.. at 193 nm ŽArF
laser. near the throat of a piezoelectric pulsed valve.
The subsequent supersonic expansion confined and
1
translationally cooled the SŽ D. beam which then
Reported here is our continuing efforts in under-
standing insertion reactions. The system studied is
collided with the target molecules ŽH , D and HD.
2
2
from the second pulsed beam. By alternating the
target gas pulses and taking the difference signal, the
reaction product of the H or D atom was interrogated
by a Ž1q1. resonance-enhanced multiphoton ioniza-
1
the reactions of SŽ D. atom with H and its iso-
2
1
2
topomers, SŽ D.qH ™SHŽX P.qH. Analogous
2
1
to the reaction of OŽ D., the interactions of the
1
divalent SŽ D. radical with H lead to the reaction
tionrtime-of-flight mass spectrometric detection
2

S.-H. Lee, K. LiurChemical Physics Letters 290 (1998) 323–328
325
scheme. The 121.6 nm vacuum ultraviolet ŽVUV.
photon for the H or D atom Lyman-a transition was
generated by the frequency tripling technique from
the input UV light Ž;365 nm. in a Kr gas cell. One
unique feature of this apparatus is the ease in con-
trolling the initial collision energy by merely chang-
ing the intersection angle of the two molecular beams
without changing any other source parameters. The
translational energy resolution in this work was gov-
erned by the velocity spreads and the angular diver-
gences of the two skimmed molecular beams, and
was determined to be about 10% ŽD E rE .. By
c
c
virtue of the orthorpara nature of hydrogen Žde-
uterium. molecule, the supersonic expansion does
not relax the rotational degree of freedom fully. The
average rotational energies of the target molecules
were estimated to be 0.3 kcalrmol ŽTr;150 K.,
0
.16 kcalrmol Ž;100 K. and 0.05 kcalrmol Ž;50
K. for H , D and HD, respectively, as detailed
2
2
previously w14x.
The experiment was performed in the following
way. At a given beam-intersection angle Ži.e. initial
collision energy., the probe laser wavelength was
1
Fig. 1. Ža. Excitation functions for the reactions of SŽ D.qH ™
2
scanned. By integrating the difference signals over
the entire Doppler profile, which is proportional to
the total reaction rate at a given collision energy, the
reaction excitation function, i.e. the translational en-
ergy dependencies of the total reaction cross-sec-
tions, is readily obtained by repeating the measure-
ments at different intersection angles. Several back-
to-back wavelengths scans at fixed intersection an-
gles were performed for normalizing the reaction
cross-sections for different isotopomers. For that pur-
pose, care was taken to ensure that the experimental
conditions were identical, in addition a 1:1 mixture
1
SHqH Žlabeled as H , Ž`., SŽ D.qD ™SDqD Žas D , v.,
2
2
2
1
1
S
Ž
D qHD™SDqH as HD, I and S D qHD™SHqD
. Ž . Ž .
Žas HD, B.. For clarity the results for HD are scaled up by two as
indicated. The solid lines are the best-fits based on the empirical
form Ž1. from Table 1. Žb. The ratio of HrD yield for the
1
1
SŽ D.qH rSŽ D.qD reactions Ždashed line obtained from the
2
2
fits in Ža.. and for the SDqHrSHqD product channels in the
1
S
Ž
D qHD reaction the points are the experimental ratios and
. Ž
the solid line is from the fits in Ža...
the target molecule is not included. Contrary to the
analogous reactions for OŽ D. w12x, which all show
an unusual behavior Ži.e. rapid fall-off in reactivity
1
of H2 and D was used to check the normalization
2
factors and to cover a wider energy range. The
uncertainties in relative cross-section measurements
are all within "5%. The estimated overall errors are
probably less than "10%.
followed by a gradual rise as the collision energy
increases., in the present case the reaction cross-sec-
tion decreases monotonically with the increase in
collision energy. This behavior is characteristic of a
reaction governed by long range attractive force with
little potential barrier w15x. In consistency with the
1
3
. Results and discussion
interpretation proposed for the OŽ D. reaction that
the gradual rise in excitation function signifies the
participation of an additional abstraction pathway at
higher energies, the lack of such a signature in the
present case implies little contribution from abstrac-
tion. Presumably, it is because the collinear barrier
Fig. 1a summarizes the excitation functions for
1
the reactions of SŽ D.qH , D and HD. The colli-
2
2
sion energy here, E , refers to the translational en-
c
ergy of the reagents. The small rotational energy of

3
26
S.-H. Lee, K. LiurChemical Physics Letters 290 (1998) 323–328
Table 1
1
Fitting parameters for the excitation function SŽ D. with H and
2
its isotopomers
Parameter
H2
D2
HD
HD
Function Ž1.: A q A expŽy E r A .
1
1
2
c
3
A
6.70
7.37
6.56
38.1
0.56
8.58
46.0
0.60
A2
A3
16.5
0.66
30.5
0.89
y1
n
c
Function Ž2.: a E qa E
a1
a2
n
1
c
2
7.41
2.57
0.5
15.4
1.96
0.5
11.9
0.88
1
16.0
1.22
1
Note: Ec in kcalrmol.
height on the excited surface increases significantly
1
1
as one shifts from OŽ D. to SŽ D..
The notion that only the insertion pathway needs
to be considered in the present case is also supported
by the isotope branching ratio, as shown in Fig. 1b.
The HrD ratios remain nearly constant over the
Fig. 3. Same as Fig. 1, except an alternate form ŽFunction Ž2. in
Table 1. was used in fitting the experimental data.
entire energy range of this work, which is exactly in
accord with what was found previously for the reac-
1
tions of OŽ D. at lower energies below the onset of
the abstraction pathway.
To facilitate the comparison with future thermal
rate constant measurements, attempt was made to fit
measured excitation functions, as exemplified in Fig.
1
as the solid lines. The empirical form used is
s ŽE .sA qA expŽyE rA . and the fitting pa-
c
1
2
c
3
rameters are summarized in Table 1. The
Boltzmann-averaged thermal rate constants along
with the kinetic isotope ratios are depicted in Fig. 2.
As can be seen, the predicted rate constants show
little temperature dependencies. Considering the large
y10
rate constant measured at 300 K, 2.1=10
3
y1 y1
cm molecule
s
w17x which is essentially gas
kinetic, such a result is not surprising. Nevertheless,
it should be commented that the valid temperature
range of predicted rate constants depends somewhat
on the empirical form used in fitting excitation func-
tions, in addition to the intrinsic assumption that the
Fig. 2. The beam-derived rate constants based on the fits shown in
Fig. 1. The results are normalized to the kinetics data, the circle
1
Ž`., for SŽ D.qH at 300 K w17x. The symbols are the same as
2
Fig. 1.

S.-H. Lee, K. LiurChemical Physics Letters 290 (1998) 323–328
327
tope ratio is about 0.7, which is noticeably smaller
than the previously reported values of 0.9–1.0 under
bulk conditions w16x. The latter is more in line with
the statistical argument. That difference becomes
more significant when one compares it with a few
other currently available reaction systems under sim-
ilar circumstances, as indicated in Table 2. As al-
luded to earlier, the thermal results led to the previ-
ous classification w1x that the HrD ratio is in general
less than one for a direct abstraction reaction, whereas
it is slightly larger than one for an inserted one.
Under the crossed-beam conditions, the generaliza-
tion appears to be reverse Ž!.. Although the crossed-
beam HrD ratios for insertion reactions,
1
1
OŽ D.rSŽ D.qHD, still cluster around one, they
tend to be on the lower side. The ratios for abstrac-
tion, on the other hand, are significantly larger than
one, opposite to the thermal results.
The apparent discrepancy between two sets of
data could be attributed to the rotationally cold HD
reagent in crossed-beam experiments. The effects of
the HD rotation on the HrD isotope branching ratio
for an abstraction reaction with an entrance barrier
have been amply discussed theoretically in the litera-
tures w2–8x, most notably for the reaction FqHD.
Fig. 4. The predicted thermal rate constants based on the fits
shown in Fig. 3.
While the room temperature kinetics measurements
thermal Boltzmann average over the translational
degree of freedom alone is sufficient. Shown in Fig.
yielded HrDs0.8 w20x, the QCT calculation on the
most accurate ab initio SW–PES found a strong
dependency of this ratio on the HD rotational state,
3
is an alternative fit, where the empirical form of
s ŽE .sa E qa E is adapted, and the fitting
y1
n
c
1
c
2
c
parameters are also listed in Table 1. Clearly, the fits
to the data are as good as those depicted in Fig. 1.
The only significant difference between the two fits
lies in the low energy extrapolation. As a result, the
predicted low temperature rate constants rise rapidly,
Fig. 4. Due to the extrapolation uncertainty, we then
conclude that the predicted rate constant will not be
reliable for temperatures -250 K. The same conclu-
sion has been drawn for the previously reported
results for the OŽ D. reaction w14x.
Perhaps the most surprising finding of this work
is the isotope effect. First, the magnitudes of total
reaction cross-sections follow an unusual trend, sHD
Table 2
Intramolecular isotope branching ratio ŽHrD. for the reaction of
AqHD
A
HrD
Refs.
Žcrossed-beam.
Ž‘thermal’.
1
SŽ D.
0.72"0.07
1.17"0.1 Žinsertion.
0.9–1.0
1.33"0.08
w16x
w18x
1
1
a
OŽ D.
1
.13"0.07
w x
a
;2.8 Žabstraction.
1
b
Cl
F
;3
;0.6
;0.8
w19x
w20x
c
1.2–3
a
From Ref. w14x. There is a small error in the previously reported
1
result. The cross-sections for OŽ D.qHD™ODqH should be
)
sD2 )sH2 , over the entire energy range. Conse-
scaled up by 1.15.
b
From this laboratory w21x, the HrD ratio actually depends on the
quently the beam-derived rate constants become kHD
collision energy. The quoted value here represents the mean value.
)
kH2 fkD2 , which is to be contrasted to the predic-
c
No crossed-beam data available. The quoted values are the QCT
tion of kH2 )kHD )kD2 from a simple transition
result for HD ŽÕs0, js0. from Ref. w7x, its variation arises from
the collision energy dependency.
state theory. Second, the intramolecular HrD iso-

3
28
S.-H. Lee, K. LiurChemical Physics Letters 290 (1998) 323–328
and for HD ŽÕs0, js0. it also varied from ;3 to
Compared to a few other currently available reaction
systems under either the crossed-beam or the ‘ther-
mal’ condition, intriguing intramolecular isotope ef-
fects are revealed. The discernible ‘less than one’
HrD ratio for the title reaction calls for further
investigation.
1
.2 with the collision energy w7x. The mass asymme-
try effects discussed in details by Johnston et al. w3x
clearly play the dominant role in favor of the FD
formation for js0 at low energies. The decrease of
the HrD ratio with collision energy was accounted
for by the long range reorientation effects on the
SW–PES w7x. Theoretical investigations for several
other abstraction reactions, such as HqHD w6x and
ClqHD w4,5x, on various types of PESs all have
Acknowledgements
This work was supported by National Science
reached similar conclusions: at low j, the D-end is
preferentially abstracted. The crossed-beam results
reported in Table 2 represent the first few experi-
mental confirmations of this theoretical prediction.
Interestingly, when HD is rotationally excited, the
opposite propensity is often observed as in the ther-
mal measurements. Thus, the contrast between the
supersonic crossed-beam and thermal data on the
HrD ratio suggests a sensitive means to gain deeper
insights into the interplay of the relevant topological
feature of PES and rotational stereoselectivity.
Council of Taiwan ŽNSC 87-2119-M-001-009-Y. and
China Petroleum.
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