The dynamics of the reactions H+H2O→OH+H2 and H+D2O→OD+HD at 1.4 eV

Article abstract of DOI:10.1063/1.1356008

Fully quantum state-resolved OH and OD angular scattering and kinetic energy release distributions were established for the hot H atom reactions with H₂O and D₂O at a well-defined collision energy of 1.4 eV. OH and OD population dist

Full text of DOI:10.1063/1.1356008

The dynamics of the reactions H+H 2 O→OH+H 2 and H+D 2 O→OD+HD at 1.4 eV
M. Brouard, I. Burak, D. M. Joseph, G. A. J. Markillie, D. Minayev, P. O’Keeffe, and C. Vallance
Citation: The Journal of Chemical Physics 114, 6690 (2001); doi: 10.1063/1.1356008
View online: http://dx.doi.org/10.1063/1.1356008
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 114, NUMBER 15
15 APRIL 2001
The dynamics of the reactions H¿H O\OH¿H2
2
and H¿D O\OD¿HD at 1.4 eV
2
a)
M. Brouard, I. Burak, D. M. Joseph, G. A. J. Markillie, D. Minayev, P. O’Keeffe,
and C. Vallance
The Physical and Theoretical Chemistry Laboratory, The Department of Chemistry, University of Oxford,
South Parks Road, Oxford, OX1 3QZ, United Kingdom
͑
Received 14 November 2000; accepted 25 January 2001͒
OH͑OD͒ quantum state populations, rovibrational quantum state-resolved center-of-mass angular
scattering distributions, and H ͑HD͒ coproduct internal energy release distributions have been
2
determined for the hot H atom reactions with H O and D O at mean collision energies close to 1.4
2
2
eV. The experiments employ pulsed laser photolysis coupled with polarized Doppler-resolved laser
2
induced fluorescence detection of the radical products. The OH( ⌸ ,vЈϭ0,NЈϭ1,AЈ) and
1
/2
2
OD( ⌸ ,vЈϭ0,NЈϭ1,AЈ) angular distributions generated by the two isotopic reactions are quite
1
/2
distinct: that for the reaction with H O shows intensity over a wide range of center-of-mass
2
scattering angles, and peaks in the sideways direction, while the state-resolved angular distribution
for the reaction with D O displays more scattering in the backward hemisphere. For higher OH͑OD͒
2
angular momentum states the differences in the angular distributions for the two reactions are less
marked, with both systems showing a slight preference for backward scattering. The kinetic energy
release distributions are insensitive to OH͑OD͒ quantum state and to isotopic substitution, and
reveal that the H ͑HD͒ coproducts are born internally cold at 1.4 eV. OH͑OD͒ quantum state
2
averaged energy disposals in the two reactions are also presented. The new experiments provide
detailed mechanistic information about the two reactions and clarify the dominant sources of
product OH͑OD͒ rotational excitation. Current theoretical understanding of the reaction is critically
assessed. © 2001 American Institute of Physics. ͓DOI: 10.1063/1.1356008͔
I. INTRODUCTION
on the product OH quantum state-resolved scattering dynam-
3
7
ics of the forward reaction between H and H O, there have
2
The reaction
been only two measurements of angular scattering and ki-
netic energy release distributions for this system, namely the
crossed molecular beam studies of Casavecchia and
—
O
Ϫ1
HϩH O→OH͑vЈ, jЈ͒ϩH , ⌬ H ϭ61.9 kJ mol
2
2
r
0
͑
1͒
co-workers3 and, very recently, of Davis and co-workers
8,39
40
has played a key role in the development of reactive scatter-
ing theory. There are now several versions of the ground
electronic state potential energy surface ͑PES͒ available,1
produced either semiempirically or through fits to ab initio
of the reverse reaction between OH and D . In the latter
2
case, the angular distribution generated in the reverse reac-
tion was determined with HOD vibrational quantum state
resolution.
The present paper describes experiments to determine
the scattering dynamics of reaction ͑1͒ and the isotopically
substituted reaction
–7
4
,8–13
data, or a mixture of the two, and both quasiclassical
and quantum mechanical scattering calculations7
,14–23
of
ever-increasing degrees of sophistication have been per-
formed on them. There is also a wealth of experimental data
available to help motivate continued theoretical effort. The
majority of this experimental work has been devoted to mea-
suring quantum state populations, and inelastic and reactive
cross sections ͑or rate coefficients͒ for the forward reaction
between translationally excited ‘‘hot’’ H atoms and either
—
O
Ϫ1
HϩD O→OD͑vЈ, jЈ͒ϩHD, ⌬ H ϭ67.5 kJ mol
2
r
0
͑
2͒
using polarized, Doppler-resolved laser induced fluorescence
͑LIF͒ techniques.41 We present OH͑OD͒ rotational distribu-
vibrationally cold2
4–29
or vibrationally excited
29–31
water
2
tions, and OH͑OD͒( ⌸ ; ϭ0,N , f ) rovibrational quan-
vЈ
Ј Ј
⍀
molecules. The molecular frame alignment of vibrationally
tum state-resolved angular scattering and kinetic energy re-
excited H O molecules generated by inelastic scattering be-
lease distributions for reactions ͑1͒ and ͑2͒ at a mean
collision energy of 1.4 eV ͑ϵ138.0 kJ mol ͒, which is ϳ0.5
2
Ϫ1
tween thermal water molecules and translationally excited H
atoms has also been observed by Leone and co-workers.32
Some of this material has been the subject of recent
eV above the reaction barrier. OH͑OD͒ quantum state-
resolved rotational angular momentum polarization informa-
tion has also been obtained, but will be presented in a forth-
coming publication, as will the results of our continuing
experiments at a collision energy of 2.5 eV.42 In Sec. II we
outline the experimental and data analysis procedures em-
3
3–36
review.
However, apart from our own preliminary report
a͒Author to whom correspondence should be addressed. Electronic mail:
mark.brouard@chemistry.ox.ac.uk
0021-9606/2001/114(15)/6690/12/$18.00
6690
© 2001 American Institute of Physics
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1

6691
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
The reaction HϩH O→OHϩH
2
2
ployed, and in Secs. III and IV the results are presented and
discussed in light of previous experimental and theoretical
studies of the title reaction.
The center-of-mass ͑c.m.͒ angular and kinetic energy re-
lease distributions were determined by a least-squares fitting
procedure to the LAB speed dependent composite profile,
ϱ
1
v
p
0
0
II. METHOD
D0͑0,0;vp͒ϭ
͵
␤0͑0,0;v͒P0ͩ ͪdv,
2
v
v
vϭvp
A. Experimental procedures
and the LAB anisotropy dependent profile,
The experimental procedure is similar to that described
3
7,42,43
ϱ
1
v
p
elsewhere,
and only a brief description will be pre-
2
2
0
D ͑2,0;v ͒ϭ
͵
␤ ͑2,0;v͒P ͩ ͪdv,
0
p
2
sented here. Polarized laser photolysis of H S at ␭
vϭv 2v
v
2
p
Ӎ225 nm was used to generate translationally excited H at-
using a series of basis functions, as described in detail
The analysis yielded the moments, anm , of
the joint c.m. distribution in scattering angle, ␪ , and frac-
oms, yielding mean collision energies of
͗ ͘
Et ϭ1.43
37,43
previously.
Ϯ0.10 eV͑HϩH O͒ and 1.44Ϯ0.10 eV͑HϩD O͒ with mean
2
2
4
4
t
translational anisotropy parameters ␤ӍϪ0.98. As noted in
our preliminary report,37 225 nm photolysis of H S provides
tional energy release into translation ft ,
2
a very clean source of near monoenergetic H atoms, well
suited to the requirements of the present experiments.
A 1:1 ratio of H S precursor and H O or D O target
df
t
P͑␪ ,w͒ϵP͑␪ , f ͒ͯ ͯ
t
t
t
dw
2
2
2
molecule gases were flowed through separate inlets into the
reaction chamber at a total pressure pр250 mTorr. The op-
tical delay ␶ between the photolysis and probe laser pulses
was ϳ20 ns. These conditions yield pressure times time-
delay values of pϫ␶ϳ5 Torr ns, which are sufficiently low
to ensure single collision conditions. OH(vЈϭ0) and
OD(vЈϭ0) radicals were probed on the 0–0 band of the
A� X transition using polarized, narrowband radiation at
wavelengths around 310 nm: In the current experiments the
1
4
dfЈ
t
ϭ
anmP ͑cos ␪ ͒P ͑ fЈ͒ͯ ͯ
,
͚
n
t
m
t
n,m
dw
where w is the c.m. speed of OH͑OD͒, and
dfЈ
mOH
w
t
fЈϭ͑2 f Ϫ1͒, ͯ ͯϭ2M
,
t
t
dw˜
mH2 EЈt,max
and EtЈ,max , the maximum possible kinetic energy release, is
given by
Ϫ1
dye laser bandwidth was determined to be 0.09Ϯ0.01 cm
using procedures discussed in detail previously.43 LIF signals
were detected through a 310 nm interference filter with a
UV-sensitive photomultiplier, and transferred to a micro-
computer for shot-to-shot normalization and signal averag-
ing. To improve the signal-to-noise ratios, approximately 20
scans of the Doppler-resolved profiles were recorded in each
of the laser pump–probe geometries A, B, and D.45 Broad-
band spectra were assigned and populations determined us-
ing output data from the program LIFBASE.46 Great care was
taken to avoid complications which might arise due to signal
saturation, and the broadband spectra were corrected for the
transmission curve of the interference filter.
—O
0
E
Ј
ϭϪ⌬ H ϩE ϩE ϪEOH
.
͑3͒
t,max
r
t
H O
2
M in these equations is the total mass, and E
and EOH
,
H O
2
appearing in the final expression, are the average internal
energy of the thermal H O͑D O͒ precursor molecules and the
fixed internal energy of the probed OH͑OD͒ level, respec-
tively. The scattering angle ␪ is defined as the angle be-
2
2
t
tween the c.m. velocities of the OH products and the H O
2
reactants, so that rebound dynamics would correspond to
backward scattered OH products. The moments of the c.m.
distribution were assumed to be independent of the compara-
tively narrow spread of reactant relative speeds, v . As
r
noted in our preliminary report,37 satisfactory fits to the data
could be obtained assuming a joint c.m. distribution of sepa-
rable form, for which the anm coefficients may be set equal
to a ϫb . Converged fits to the data were obtained with
B. Doppler profile analysis
Composite Doppler profiles, which depend separately on
moments of the joint LAB velocity-polarization distribution,
were constructed from linear combinations of sets of experi-
n
m
three moments in cos ␪ and four moments in f . Finally, the
error limits on P(cos ␪ ) and P(f ) were determined using a
t
t
t
t
4
7,48
4
3
mental data
recorded using the counterpropagating ͑cases
Monte Carlo technique, described in detail elsewhere ͑see
also the discussion in Sec. III͒.
In generating the basis functions employed in the fitting
of the experimental composite Doppler resolved profiles, we
have assumed that translationally excited H atoms react ex-
clusively with vibrational ground state H O and D O. If re-
A and B͒ and mutually orthogonal ͑case D͒ excitation-
4
5,48
detection geometries, and Q↑ and P/R↑ transitions.
The
composite Doppler line shapes ͑suitably convoluted with la-
ser line shape function͒ may be written as functions of the
component of the product velocity along the probe laser
2
2
4
7
propagation axis, vp :
actions involving vibrationally excited water had taken
place, the value of the internal energy E used in generat-
ϱ
H O
2
1
v
p
K
0
K
0
D ͑k ,k ;v ͒ϭ
͵
␤ ͑k ,k ;v͒P ͩ ͪdv,
1
2
p
1
2
k
ing the basis functions, and appearing in Eq. ͑3͒, would have
needed to be increased, reflecting the fact that reaction with
excited water molecules is more exoergic than reaction with
ground state water. The extent to which it is valid to assume
reaction occurs exclusively with the ground state of water
1
2
v
v
vϭvp
K
where ␤ (k ,k ;v) are the rescaled laboratory frame bipolar
moments, averaged over the spread of atomic and molecu-
0
1
2
4
7
lar reagent velocities, and the Pk1 are Legendre polynomials.
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6692
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
Brouard et al.
depends on the vibrational enhancements of the reaction
cross section at a mean collision energy of 1.4 eV. At 300 K
the populations in the H O͑D O͒ bond stretching vibrations
2
2
are so small, and the necessary vibrational enhancements in
reaction cross section so large, that their participation in the
reaction at a collision energy of 1.4 eV can be safely dis-
counted. The enhancements in the cross sections for the hot
H atom reactions with H O and D O excited into their first
2
2
bending vibrational levels would need to be ϳ3000 and
ϳ400, respectively, to compete with reaction with the
ground state water molecules. As with the stretching modes,
these enhancements are much larger ͑by nearly two orders of
magnitude͒ than the typical values predicted for bend or
2
0
stretch excitation at elevated collision energies using QM
or QCT methods.4 The recent experimental rate coefficient
,11
3
1
measurements of Smith and co-workers reinforce the view
that bending excitation, in particular, leads to only modest
enhancements in reaction cross section. We therefore believe
that, on the current available evidence, it is safe to assume
that translationally excited H atoms react exclusively with
vibrational ground state H O and D O.
2
2
III. RESULTS
A. OHÕOD quantum state populations
OH and OD vЈϭ0 rotational population distributions
generated via the hot H atom reactions with H O and D O at
2
2
1.4 eV are shown in Figs. 1͑a͒ and 1͑b͒. The population data
have been averaged over OH͑OD͒ spin–orbit and ␭-doublet
levels. Although none of the previous population measure-
ments have been performed under precisely the same colli-
sion energy conditions that were employed here ͓and have
not generally been reported for the average over all OH͑OD͒
spin–orbit and ␭-doublet levels͔, both the HϩD O and
2
HϩH O data are in reasonable accord with previous
2
2
4,26,27,29
work.
There is a more extensive data set for the
HϩH O reaction ͓in particular for the AЈ␭-doublet level of
2
2
OH( ⌸3/2)͔, and in this case there appears to be a modest
increase in OH rotational excitation with increasing H atom
translational energy:24 Our OH( ⌸3/2) rotational distribu-
tions determined at 1.4 eV fall between those measured at
2
2
4
1
eV.
.0 eV, and those determined at 1.5, 1.8, and 2.5
2
4,26,27,29
The rotational distribution for OD from HϩD O
2
extends to higher NЈ than that for OH from HϩH O. How-
2
ever, the fractions of the available energy channeled into OH
or OD rotation in the two reactions are very similar ͑see
Tables I and II͒, with OD receiving a very slightly higher
share of the energy than OH. This pattern is confirmed by
replotting the population in the form of a Boltzmann plot
͓see Fig. 1͑c͔͒. The slightly higher OD rotational ‘‘tempera-
ture’’ evident from Fig. 1 is consistent with a slightly greater
transfer or release of energy to the OD fragment which arises
from the shift in the center of mass of the ‘‘spectator’’ OD
moiety in DOD relative to that of OH in HOH.29 We will
return to the origin of OH͑OD͒ rotational excitation in
Sec. IV.
In Fig. 2 we show the spin–orbit population ratios for
the OH and OD products of reactions ͑1͒ and ͑2͒. The data
have been corrected for differences in the degeneracies of the
FIG. 1. ͑a͒ HϩH O at 1.4 eV: ͑᭹͒ the OH(vЈϭ0,NЈ) rotational distribution
determined experimentally, averaged over lambda-doublet and spin–orbit
states; ͑᭺͒ results of the Franck–Condon model described in Sec. IV. ͑b͒
2
HϩD O at 1.4 eV: As in ͑a͒ but for the OD products of reaction ͑2͒. ͑c͒
2
Boltzmann plots of the rotational distributions for the reactions HϩH O ͑᭺͒
2
and HϩD O(᭹) at a collision energy of 1.4 eV. The dashed lines represent
2
linear fits to the data, the gradients of which yield rotational ‘‘temperatures’’
of 570 and 650 K, respectively.
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6693
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
The reaction HϩH O→OHϩH
2
2
FIG. 2. The OH ͑᭺͒ and OD ͑᭹͒ spin–orbit population ratios, corrected for
(
2jЈϩ1) degeneracy, generated via the reactions HϩH O and HϩD O at a
2 2
mean collision energy of 1.4 eV.
two sets of levels. In both cases, the statistical ratio of one is
approached at high NЈ, where the spin–orbit states become
4
9
mixed. However, the ratios tend to values close to two at
low NЈ, implying that the reactions preferentially populate
FIG. 3. ͑a͒ Composite Doppler resolved profiles obtained for the
2
the lower ⌸ spin–orbit state. Similar behavior has been
2
3
/2
OH( ⌸3 ,vЈϭ0,NЈϭ5,AЉ) fragments of the HϩH O reaction at a mean
/2
2
2
4,29
noted previously for the HϩH O reaction,
and also for
collision energy of 1.4 eV. ͑b͒ The same as for ͑a͒ but showing the com-
2
2
posite profiles for the OD( ⌸ ,vЈϭ0,NЈϭ1,AЈ) products of the HϩD O
the OH products generated by the HϩN O and HϩCO
1/2
2
2
2
5
0
reaction at 1.4 eV. In each case, the left-hand panel is the LAB speed
reactions, which have similar symmetry correlation dia-
grams to that of reaction ͑1͒. ͓Comparisons may also be
made between the correlation diagrams for the title reaction
0
dependent composite profile, D (0,0;v ), while the right-hand panel is the
0
p
2
composite profile dependent on the LAB translation anisotropy, D (2,0;v ).
0
p
The smooth lines are the fits to the data using the procedures described in
Sec. II B. The residuals to the fits are shown in the lower part of each panel,
offset for clarity by Ϫ0.5 and Ϫ0.75 in the two cases.
5
1
and that for the reverse isoelectronic FϩH reaction, al-
2
though in the present case the correlation diagram is simpler
2
because of the reduced symmetry of OH( ⌸ ) compared
⍀
2
52
with F͑ P ).͔ As with molecular photodissociation, the
J
spin–orbit branching ratio depends critically on the strength
of the spin–orbit coupling, and tends to unity in the Hund’s
case ͑b͒ limit, where the spin–orbit coupling is small relative
to the rotational energy.50 Quantitative modeling of these
spin–orbit propensities, however, would require quantum
scattering calculations on all relevant coupled potential en-
general features of the c.m. distributions derived from the
analysis ͑shown in the following͒ were unaltered by inclu-
sion of the extra parameters.
The c.m. angular scattering distributions derived from
the fits to Doppler profile data for reactions ͑1͒ and ͑2͒ are
shown in Figs. 4–7. For clarity, the Monte Carlo determined
errors in these distributions have been shown just at selected
ergy surfaces of the HϩH O system, as has been undertaken
2
5
1
for the FϩH reaction ͑see further discussion in Sec. IV͒.
2
4
3
values of cos ␪ and f . Figures 4 and 6 show the angular
t
t
2
scattering distributions for the OH͑ ⌸1 , vЈϭ0, NЈϭ1, AЈ͒
products of reaction ͑1͒ and the OD͑ ⌸1 , vЈϭ0, NЈϭ1,
/2
2
B. OH„OD… quantum state-resolved angular scattering
/2
distributions
AЈ͒ products of reaction ͑2͒. For this specific low rotational
AЈ state, and spin–orbit level, the scattering for the HϩD O
reaction is significantly more backward peaking than for the
2
Examples of the composite Doppler profile data are
shown in Fig. 3, together with the fits to the data obtained
using the procedures outlined in Sec. II and the residuals for
these fits. The residuals for the fits to the anisotropy depen-
dent profiles ͑shown in the right-hand panels͒ retain some
very slight structure, which becomes almost undetectable
when plotted on the same scale as the speed dependent com-
posite profiles ͑shown in the left-hand panels͒. Although this
structure could be removed by using a higher number of
same channel of the HϩH O reaction.
2
In Figs. 5 and 7 we compare the angular distributions for
2
the rotationally excited OH͑ ⌸ , vЈϭ0, NЈϭ5͒ and
3/2
2
OD͑ ⌸ , vЈϭ0, NЈϭ6, AЉ͒ products. The differences be-
3/2
tween the angular scattering for these specific channels are
much less pronounced than those between the OH and OD
2
products born with low NЈ in the upper ⌸1/2 spin compo-
fitting parameters, it was felt that the resulting reduction in
nent, discussed previously. Both the OH and OD fragments
are preferentially scattered into the backward hemisphere.
For the OH products of reaction ͑1͒, the angular scattering
2
␹
was insufficiently large to warrant inclusion of the high-
order fitting coefficients in the analysis. Furthermore, the
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6694
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
Brouard et al.
lease distributions, which by energy conservation reflect the
distributions over internal energies in the unobserved H or
2
HD coproducts. The kinetic energy release distributions are
shown in the lower panels of Figs. 4–7. The distributions are
very similar in each case, and vary little with deuterium sub-
stitution. It should be noted that the experimental error bars
in the kinetic energy release distributions tend to become
larger at high f values. We believe this to be an inherent
t
feature of the experimental technique, which arises because
fast moving products have large Doppler shifts, and therefore
contribute less to the amplitude of the LIF signal. This effect
is implicitly accounted for in the Monte Carlo error analysis
procedures.43 The combs shown in Figs. 4 and 6 indicate
approximately the f values of the H and HD rotational
t
2
quantum states in the two reactions. The experiments reveal
that at a mean collision energy of 1.4 eV, the H products
2
from reaction ͑1͒ and the HD products from reaction ͑2͒ are
both born vibrationally cold, with little rotational excitation.
The H ͑HD͒ energy disposal data are insensitive to OH͑OD͒
2
rotational state.
The kinetic energy release data shown in Figs. 4–7 may
be used to calculate the mean energy disposals in reactions
͑1͒ and ͑2͒. The averaging over OH͑OD͒ internal state is
approximate because the translational energy releases for
only a few OH͑OD͒ quantum states have been determined.
However, because the OH͑OD͒ populations span such a
small range of rotational levels in vЈϭ0, and because the
kinetic energy release distributions are so insensitive to
OH͑OD͒ quantum state ͑see Figs. 4–7͒, we believe that the
OH͑OD͒ quantum state averaged energy disposal data are
reliable. The data are shown in Tables I and II. The principal
conclusion from these results is that at a mean collision en-
ergy of 1.4 eV around 80% of the available energy is chan-
neled into product translational excitation.
IV. DISCUSSION
FIG. 4. The angular scattering distribution P(cos ␪ ) ͑a͒ and kinetic energy
t
release distribution P(ft) ͑b͒ for the HϩH O reaction generating
2
A. OH„OD… rotational excitation
2
OH( ⌸ ,vЈϭ0,NЈϭ1,AЈ) reaction products at a mean collision energy of
1
/2
1
.4 eV. For consistency with the distributions shown in Figs. 5–7, these data
Although the OH͑OD͒ product receives a small fraction
of the total available energy, mainly in the form of rotation,
it is of interest to identify the origin of this excitation. Sev-
are a reanalysis of the results presented previously ͑Ref. 37͒: the new analy-
sis yields very similar distributions to those presented previously. The scat-
tering angle ␪t is defined as that between the OH c.m. velocity, and the
2
9
eral sources of OH͑OD͒ rotation are available, including
momentum transfer from the incoming H atom ͑via a ‘‘bal-
listic’’ type mechanism, which imparts a torque on the
reactant H O velocity ͑see the text͒. Error bars represent 2␴ uncertainties.
2
The combs superimposed on the P(f ) distribution shown in the lower panel
t
indicate the approximate positions of the H (vЉϭ0,jЉ) levels. H fragments
2
2
born in vЉϭ1 would appear at f values Շ0.35.
t
‘‘spectator’’ OH moiety͒, impulsive energy release as the
HH–OH bond is ruptured, and transfer of momentum from
distribution is found to be insensitive to the choice of OH AЈ
or AЉ␭-doublet level ͑see Fig. 5͒. Although the variations in
angular scattering distribution with OH or OD quantum state
are comparatively small, the OH(NЈϭ5) products from re-
action ͑1͒ appear slightly more backward scattered than
OH(NЈϭ1), while the OD(NЈϭ6) products from reaction
rotational and bending motion in the parent H O͑D O͒ target
2
2
molecule. In a recent study of the hot H atom reaction with
4
3
N O we have shown that the kinetic energy release distri-
2
butions obtained in the bimolecular reaction, which reflect
the internal energy distributions in the ͑unobserved͒ N co-
2
products, are very similar to those generated upon photodis-
͑2͒ are somewhat less backward scattered than their NЈϭ1
sociation of N O subsequent to excitation to its first excited
2
counterparts.
electronic state. The response of the target N O molecule to
2
the incoming H atom appears to be very similar to its re-
sponse to photon excitation into its first electronic con-
tinuum. The reason for this similarity lies in the fact that, in
the exit channel of the reaction, the electron originally car-
ried by the fast incoming H atom is transferred into an orbital
C. Kinetic energy release distributions, and energy
balance
Analysis of the composite Doppler profile data also
yields OH or OD quantum state-resolved kinetic energy re-
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6695
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
The reaction HϩH O→OHϩH
2
2
FIG. 5. The angular scattering distributions P(cos ␪ ) ͑a͒ and kinetic energy release distributions P(f ) ͑b͒ for the HϩH O reaction generating
t
t
2
2
2
OH( ⌸ ,vЈϭ0,NЈϭ5,AЈ)(A) and OH( ⌸ ,vЈϭ0,NЈϭ5,AЉ)(B) reaction products. Note that the energetics associated with these specific OH channels
3
/2
3/2
are very similar to those indicated by the combs in Fig. 4͑b͒.
of very similar character to that occupied by an electron sub-
similar to that responsible for rotational excitation in the
sequent to promotion by photon excitation of N O. Similar
photodissociation of H O. On the basis of this comparison it
2
2
behavior is found here for the HϩH O and HϩD O reac-
would seem that momentum transfer from the translationally
excited H atom is unlikely to be a major source of rotation in
the bimolecular reaction.
The fact that the rotational excitation in the OH in-
creases with available energy, and is so similar for molecular
2
2
tions. To demonstrate this, we compare the OH distributions
generated via photodissociation of water at 193 and 157
5
2
nm with those observed in the bimolecular reaction by our-
selves at a collision energy of 1.4 eV, and by Wolfrum and
co-workers at 2.5 eV24 ͑see Fig. 8͒. These particular data
have been selected so that the total energies supplied to the
water molecule ͑either by a photon or by a translationally
excited H atom͒ are similar. The two sets of population dis-
tributions are remarkably similar, suggesting that the source
of OH rotational excitation in the bimolecular reaction is
photodissociation of H O and for the bimolecular reaction
2
HϩH O, suggests that some rotational excitation in these
2
systems comes from the impulsive release of energy in the
breaking ͑H͒H–OH bond. However, we do not believe such
a mechanism to be the major source of OH͑OD͒ rotational
excitation at the low energies used in the present study. Wol-
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6696
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
Brouard et al.
FIG. 6. The angular scattering distribution P(cos␪ ) ͑a͒ and kinetic energy
FIG. 7. The angular scattering distributions P(cos ␪ ) ͑a͒ and kinetic energy
t
t
release distribution P(ft) ͑b͒ for the HϩD O reaction generating
release distributions P(ft) ͑b͒ for the HϩD O reaction generating
2
2
2
2
OD( ⌸ ,vЈϭ0,NЈϭ1,AЈ) reaction products. The combs superimposed on
OD( ⌸
3/2 vЈ
Ј Љ
, ϭ0,N ϭ6,A ). Note that the energetics associated with these
1
/2
the P(f ) distribution shown in the lower panel indicate the approximate
specific OD channels are very similar to those indicated by the combs in
t
positions of the HD(vЉϭ0,jЉ) levels. HD fragments born in vЉϭ1 would
Fig. 6͑b͒.
appear at f values Շ0.40.
t
frum and co-workers have measured the OH rotational dis-
eral workers have used simple Franck–Condon models to
tributions for the bimolecular reaction HϩH O down to a
account for the product internal excitation in the bimolecular
2
collision energy of 1.0 eV:24 The resulting distribution is
only slightly colder than that obtained here at 1.4 eV. This
implies an additional source of fragment rotational excitation
which does not scale with available energy, the most likely
candidate being the thermal rotation, and zero-point bending
reactions HϩH O
14,55
and HϩHCN, where the OH and
56
2
CN moieties act as near-spectators. Here we compare the
results of the open shell Franck–Condon model, developed
˜
specifically to treat the photodissociation of water via the A
state,5
4,57
with the OH͑OD͒ rotational populations generated
motion in the target H O molecule. Again, the comparisons
2
by the bimolecular reactions ͑1͒ and ͑2͒. The results for H O
2
˜
with the photodissociation of H O via the A band are fruitful.
and D O are shown as the open points in Figs. 1͑a͒ and 1͑b͒,
2
2
At low available energies the OH distribution generated by
respectively. The calculations assume a 300 K distribution of
rotational levels in H O and D O, and include water mol-
ecule rotational states up to Jϭ14. The agreement between
photolysis of water can be modeled very well5
2,53
using a
by
2
2
modified
Franck–Condon
model
developed
5
4
Balint-Kurti. This model allows for the correct mapping of
the rovibrational wave function of the parent molecule onto
those of the open shell OH photofragment. Previously, sev-
the Franck–Condon theory and the present low energy ex-
periments is good, particularly for the HϩH O reaction, and
2
demonstrates that the majority of OH product rotational ex-
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6697
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
The reaction HϩH O→OHϩH
2
2
TABLE I. Energy disposal data for the HϩH O reaction at a mean collision energy of 1.4 eV. The mean
2
vibrational energy content in the H2 coproducts is an upper estimate based on the amplitudes ͑and error
estimates͒ of the P(f ) distributions shown in Figs. 4 and 5 in the region where H (vЉϭ1) is expected. The
t
2
experimental data are compared with the theoretical calculations cited in the last column. The potential energy
surfaces employed in the latter are given in parentheses in the penultimate column.
OH
OH
H
H
2
͗
ft
͘
͗
fr
͘
͗
f
͘
͗
f
2
͘
int
͗ ͘
fv
Comments
This work
Ref.
v
0
.80Ϯ0.09
0.06Ϯ0.01
0.00Ϯ0.02
0.14Ϯ0.09
Շ0.05
0.75
0.64
0.57
0.70
0.68
0.09
0.08
0.02
0.09
0.04
0.00
0.00
0.00
0.03
0.00
0.16
0.27
0.41
0.17
0.28
0.02
0.12
0.30
0.05
0.12
QM ͑WDSE͒
QCT ͑WDSE͒
QCT ͑15͒
QCT ͑OC͒
QCT ͑WSLFH͒
20
10
10
12, 59
4
citation observed in the current experiments arises from ther-
mal motions in the target water molecule. ͓At room tempera-
ture, the Franck–Condon model predicts that the zero-point
bending and rotational motions in the target water molecule
contribute about equally to OH͑OD͒ rotational excitation.͔
One might argue that the experimental OH and OD rotational
distributions are very slightly hotter than those predicted by
the Franck–Condon theory, particularly so for the deuterated
system, leaving some scope for a minor impulsive contribu-
tion to product OH͑OD͒ rotational excitation under the
present, low collision energy conditions.
have equated the closed shell jЈ values used in the closed
shell calculations with NЈϪ1, where NЈ is the total OH an-
gular momentum apart from electron spin.͒ In the latter case,
the QCT calculations also predict the generation of some
OH(vЈϭ1) products, for which we find no experimental evi-
dence. Both sets of calculations predict significantly more
rotational excitation in the OH products than observed ex-
perimentally, even though both calculations assumed the tar-
get water molecule to be initially rotationally unexcited.
QCT calculations on the latest PES of Schatz and coworkers
yield a somewhat lower mean OH rotational excitation than
previous PESs ͑see Table I and the discussion to follow͒; it
would be of particular interest to see how both this surface
and the OC PES perform when tested using full-
dimensionality QM scattering calculations.7
In principle, the Franck–Condon model can also be used
to calculate the OH ␭-doublet propensities and spin–orbit
state population ratios.5
2,54
͑The former will be discussed
,20,22
elsewhere in the context of rotational polarization effects in
4
2
the title reactions. ͒ The model predicts spin–orbit ratios
close to unity for all OH rotational states,52 and is unable to
B. OH„OD… angular scattering distributions
2
reproduce the preferential population of the OH( ⌸3/2) state
We turn now to the OH and OD quantum state-resolved
angular scattering distributions observed in the hot H atom
reactions with H O and D O. In our previous preliminary
for low NЈ levels observed experimentally ͑see Fig. 2͒, with-
out very major ͑and unrealistic͒ changes being made to the
input OH͑OD͒ spin–orbit coupling constant.
2
2
Although the OH and OD rotational distributions gener-
ated by reactions ͑1͒ and ͑2͒ at a mean collision energy of
1.4 eV are well accounted for by the Franck–Condon model,
ab initio theory performs somewhat less satisfactorily. In
Fig. 9 we compare the OH rotational populations generated
by the reaction HϩH O at 1.4 eV ͑averaged over OH spin–
2
orbit and ␭-doublet level͒ with the Jϭ0 probabilities calcu-
lated at 1.5 eV using full-dimensionality wave-packet propa-
2
0
gation techniques, which employed the WDSE potential
1
energy surface. The experimental data are also compared
1
3
with the QCT calculations of Castillo et al., which em-
3
ployed the more recent PES by Ochoa and Clary, labeled
the OC PES henceforth. ͑As noted in the caption to Fig. 9, to
compare the experimental and theoretical distributions we
TABLE II. Energy disposal data for the HϩD O reaction at a mean colli-
2
sion energy of 1.4 eV. The mean vibrational energy content in the HD
coproducts is an upper estimate based on the amplitudes ͑and error esti-
mates͒ of the P(f ) distributions shown in Figs. 6 and 7 in the region where
t
HD(vЉϭ1) is expected.
OD
OD
HD
int
HD
FIG. 8. Comparison between the experimental OH rotational distributions
͗
ft
͘
͗
fr
͘
͗
f
͘
͗
f
͘
͗
f
͘
Comments
This work
v
v
for the HϩH O reaction at 1.4 eV ͑᭹͒ and 2.5 eV ͑᭡͒ ͑Ref. 24͒, and those
2
˜
0
.80Ϯ0.10
0.07Ϯ0.01
0.00Ϯ0.02
0.13
Շ0.05
observed in the photodissociation of water via the A state at 193 nm ͑᭺͒ and
57 nm ͑᭝͒ ͑Ref. 52͒.
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1
1

6698
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
Brouard et al.
energy ͑associated with rebound dynamics͒, moving to side-
ways or forward peaking differential cross sections as the
collision energy is raised.
There are several features of the new angular scattering
distributions presented here which deserve some comment.
At the outset, it should be emphasized that the angular scat-
tering distributions obtained here are fully OH͑OD͒ quantum
state resolved. In particular, the angular scattering ͑and ki-
netic energy release͒ distributions for OH and OD NЈϭ1
2
have been measured specifically for the upper ⌸1 spin–
/2
orbit state of the products, while those for OH(NЈϭ5) and
OD(NЈϭ6) were measured for the lower spin–orbit state,
2
⌸3/2
. For the HϩCO reaction we have recently observed a
2
dependence of the angular scattering distribution on OH
spin–orbit state for those OH products born in the lowest
rotational levels.49 Although a similar dependence on prod-
uct spin–orbit state cannot be ruled out in the present reac-
tion, the general uniformity of the angular scattering and
kinetic energy release distributions for different OH͑OD͒
quantum states ͑shown in Figs. 4–7͒ suggests that choice of
product spin–orbit state is not a major controlling dynamical
factor in the reaction. As noted in Sec. III, to address this
issue rigorously, and to address the general question of the
role of nonadiabatic effects in the exit channel of the
7
HϩH O reaction discussed by Collins and co-workers,
2
would require full-dimensional scattering calculations over
all relevant coupled PESs correlating with the OHϩH prod-
2
ucts.
A particularly notable feature of the angular distributions
is the change in scattering upon isotopic substitution for
those OH͑OD͒ products born in low rotational states ͑in the
same spin–orbit states͒. It is known that the reaction cross
section for HϩH O is two to three times greater than that for
2
2
9
HϩD O. This probably arises largely because the latter
2
reaction has a bigger effective barrier to surmount, due to the
lower zero-point energy of the D O reactants. The lower
2
zero-point energy of the system would also reduce the cone
of acceptance for the deuterated reaction compared with the
protonated case, leading to enhanced backward scattering for
HϩD O relative to HϩH O. Changes in angular distribution
FIG. 9. ͑a͒ Comparison between the experimental rotational distribution ͑᭹͒
for the HϩH O reaction at 1.4 eV and probabilities derived from the full
2
dimensionality Jϭ0 wave packet calculations at 1.5 eV of Zhang and Light
͑
͑
᭺͒ ͑Ref. 20͒, which employed the WDSE potential energy surface ͑Ref. 1͒
b͒ The same as for ͑a͒ but comparing the experimental data with those
2
2
calculated at 1.43 eV using QCT methods ͑Ref. 13͒ using OC PES ͑Ref. 3͒.
Note that in ͑a͒ and ͑b͒ we have equated the open shell NЈ values used
experimentally ͑which represent the total OH angular momentum apart from
electron spin͒ with jЈϩ1, where jЈ is the rotational angular momentum used
in the closed shell calculations.
are also observed for the two reactions with increasing OH
and OD rotational excitation. Both sets of data imply that
OH and OD are not purely spectators to reaction, and that the
Franck–Condon model described in the previous section rep-
resents an approximate limiting case.
Comparisons of the OH(NЈϭ1) experimental angular
scattering distributions from reaction ͑1͒, and reported in our
preliminary publication,37 with those derived from QCT
communication about the HϩH O reaction37 we noted the
theory have been presented on several occasions in the
2
,10,13
very wide range of scattering angles observed at a collision
energy of 1.4 eV, compared with the strong backward scat-
tering obtained by Casavecchia and co-workers38 for the re-
verse reaction OHϩD2 at a collision energy just above
threshold. The behavior was rationalized in terms of an
opening of the cone of acceptance to the forward reaction
with increasing collision energy. The validity of this expla-
literature.4
Best agreement between the experimental re-
sults is obtained in comparison with the QCT calculations
10
performed by Bradley and Schatz using the I5 PES of
2
Isaacson. However, this surface accounts very poorly for the
experimental energy disposal data ͑see the following͒, and
has also been shown to yield unrealistically large thermal
4
reaction rate coefficients. In Fig. 10 we compare the angular
nation has since been supported by QCT calculations on a
all of which display broad
backward peaking differential cross sections at low collision
scattering distributions for the OH products born in NЈϭ1
number of different PESs,4
,10,12,13
with QCT data generated on the most recent OC and
13
4
WSLFH PESs. The calculations agree qualitatively with the
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6699
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
The reaction HϩH O→OHϩH
2
2
experimental results, with both sets of theoretical data show-
ing scattering over a wide range of c.m. angles. Although the
calculated OH angular distributions using either of the PESs
are somewhat more backward scattered than observed ex-
perimentally, notice that the calculations show somewhat en-
hanced backward scattering for the more highly rotationally
excited OH products of reaction ͑1͒,1
0,13
as we observe here
experimentally. Perhaps more significantly, QCT calcula-
tions on the OC PES at a collision energy of 2.2 eV show
significantly more backward scattering for the low rotational
5
8
states of OD born via the HϩD O reaction compared with
2
that observed for the rotational cold OH products of the
1
3
HϩH O reaction. This predicted behavior agrees qualita-
2
tively with that determined here ͑and discussed previously͒
at a mean collision energy of 1.4 eV.
C. OH„OD… kinetic energy release and average energy
disposals
As noted previously, the kinetic energy distributions pro-
vide information about the disposal of energy in the internal
modes of the H and HD coproducts of the title reactions.
2
The general conclusion from the distributions shown in Figs.
4
–7 is that the H and HD molecules are born rather cold at
2
a collision energy of 1.4 eV. This contrasts with the high
rovibrational excitation which Zare and co-workers observed
2
9
directly in the HD products of reaction ͑2͒ at much higher
collision energies, around ϳ2.6 eV, using resonantly en-
hanced multiphoton ionization techniques. A key difference
is in the extent of vibrational excitation: The high energy
experiments indicated roughly equal probabilities for pro-
duction of HD vЈϭ0 and vЈϭ1, while in the present low
energy measurements, we find no evidence for significant
production of vibrationally excited products for either reac-
tion ͑1͒ or ͑2͒. It is worth emphasizing that the energy avail-
able in the present experiments is much closer to the ener-
getic threshold for production of H vЈϭ1 and HDvЈϭ1
2
2
9
than in the direct study of Zare and co-workers. Moreover,
the general feature of rapidly increasing H and HD internal
2
excitation ͑both rotational and vibrational͒ with increasing
collision energy seems to be reasonably well reproduced by
the QM calculations of Zhang and Light,20 and to a lesser
4
,10
extent the QCT calculations of Schatz and co-workers,
and Castillo and Santamaria12 ͑see the following͒.
The internal excitations in the H and HD products of
2
reactions ͑1͒ and ͑2͒ have been calculated using both QCT
and QM methods on a variety of different PESs. The QCT
calculations, in particular, tend to overestimate the OH and
H internal excitation generated by reaction ͑1͒, as seen from
2
Table I. In Fig. 11 we compare the kinetic energy release
distribution determined experimentally for the OH͑vЈϭ0,
NЈϭ1͒ products of the HϩH O reaction ͓i.e., that shown in
2
FIG. 10. ͑a͒ Comparison between the experimental angular scattering dis-
Fig. 4͑b͔͒ with those determined from ͑a͒ the H quantum
2
tribution ͑smooth line with error bars͒ for the HϩH O reaction born in
2
state-resolved Jϭ0 QM reaction probabilities of Zhang and
2
OH( ⌸1 ,vЈϭ0,NЈϭ1), and that derived from the QCT calculations of
/2
2
0
Light for the WDSE PES, and ͑b͒ the H quantum state
Schatz and co-workers ͑᭹͒ ͑Ref. 4͒ using the WSLFH PES. ͑b͒ The same as
for ͑a͒ except the QCT calculations are those of Aoiz and co-workers using
the OC PES ͑Ref. 13͒. In both ͑a͒ and ͑b͒ the QCT data are specific to
2
populations obtained in the QCT calculations of Castillo
1
3
et al. using the OC PES. In both cases, the H internal state
2
channels yielding OH(vЈϭ0,jЈр2.) ͑c͒ The same as for ͑b͒ except the
populations determined by the calculations have been used to
2
experimental data are for OH( ⌸3 ,vЈϭ0,NЈϭ5,AЈ) and QCT calculated
/2
simulate the measured P(f ) distributions using the proce-
dure described in Ref. 13. This involves convolution of the
data are specific to OH(vЈϭ0) products born in the range 4рjЈр6
t
͑
Ref. 13͒.
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6700
J. Chem. Phys., Vol. 114, No. 15, 15 April 2001
Brouard et al.
found that the primary source of the discrepancy between
QCT theory and experiment was due to an overestimation of
the predicted amounts of vibrationally excited H produced
2
in the reaction,13 a point which is illustrated again here ͓see
Fig. 11͑b͔͒. The energy disposal data shown in Table I also
reinforce the view that the QCT calculations overestimate
the internal excitation generated by the HϩH O reaction,
2
particularly in the H product. Although the origin of the
2
discrepancy between experiment and QCT theory could
partly be due to experimental error, which ͑as discussed in
Sec. III͒ becomes large at high f , we believe the discrep-
t
ancy most likely reveals either inadequacies in the QCT
method, possibly associated with difficulties in ‘‘binning’’
trajectories into quantum mechanical states, or with the PESs
employed. Although it is encouraging that the QM calcula-
tions on the WDSE PES20 show considerably less H vibra-
2
1
0
tional excitation than predicted using QCT methods on the
same PES, it is worth emphasizing that the QM calculations
are restricted to Jϭ0. QM scattering calculations for Jу0
3
,4
on the more recent PESs,
which according to QCT
calculations4 generally show higher kinetic energy releases
,12
than the older surfaces,1 would clearly be desirable.
,2
V. CONCLUSIONS
We have presented fully quantum state-resolved OH and
OD angular scattering and kinetic energy release distribu-
tions for the hot H atom reactions with H O and D O at a
2
2
well-defined collision energy of 1.4 eV. OH and OD popu-
lation distributions and quantum state-averaged internal en-
ergy disposals have also been reported under the same con-
ditions. The experimental data provide a grueling test for ab
initio QCT and QM scattering theory, and of the potential
energy surfaces they employ. Overall, the experimental find-
ings are accounted for qualitatively by theory, but quantita-
tive agreement is still lacking. QM scattering calculations
using either wave-packet7
,19–21
or time independent meth-
22
ods on the most recent PESs3 would clearly be helpful at
,4
FIG. 11. Comparison between the experimental kinetic energy release dis-
this stage.
tribution ͑smooth line with error bars͒ for the HϩH O reaction generating
2
OH(vЈϭ0,NЈϭ1) products at a mean collision energy of 1.4 eV ͑shown in
Fig. 4͒, and those simulated using ͑a͒ the H2 rovibrational probabilities
obtained in the full dimensionality Jϭ0 wave packet calculations of Zhang
and Light at 1.4 eV ͑Ref. 20͒, which employed the WDSE PES ͑Ref. 1͒, and
ACKNOWLEDGMENTS
We are very grateful to the Leverhulme Trust, the Royal
Society, and the EPSRC for research grants, and to the
EPSRC for the award of a studentship to G.A.J.M. EU sup-
port through the RTN project HPRN-CT-1999-00007 is also
gratefully acknowledged. We also would like to thank Pro-
fessor F. J. Aoiz and Dr. J. F. Castillo ͑Complutense Univer-
sity, Madrid͒, and Professor G. C. Schatz for very helpful
discussions over a number of years, and for communicating
their QCT results to us. I am also indebted to Professor F. J.
Aoiz and Dr. J. F. Castillo for their helpful comments on
several versions of this manuscript.
͑
b͒ the H rovibrational populations determined by QCT calculations ͑Ref.
2
1
3͒ on the OC PES ͑Ref. 3͒. The QM calculations in ͑a͒ ͑shown as the
dashed line͒ predict a small ϳ3% population in H (vЉϭ1) which is not
2
included in the simulation, while the simulations based on the QCT calcu-
lations, reproduced form Ref. 13, are shown with ͑dotted͒ and without
͑
dashed͒ inclusion of the contributions from H (vЉϭ1). The QM simula-
2
tions employed OH quantum state averaged H2 rotational quantum state
resolved Jϭ0 reaction probabilities ͑Ref. 20͒, while the QCT results are the
average for OH(vЈϭ0) products born in 0рjЈр2.
populations, plotted as a function of f , with a Gaussian
t
‘
‘instrument-resolution’’ function of width ⌬EЈϳ0.1 eV.
t
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2
3
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6
7
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2
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