The state-to-state photodissociation dynamics of HOD(A?)

Article abstract of DOI:10.1063/1.473625

HOD, rotationally state selected in the third and fourth OH stretching overtone (|04〉 |05〉) levels, has been photodissociated via the A? state at λ ? 288 nm. In accord with previous studies H + OD is the dominant dissociation channel, with the yield of OH photofragments being below the detection limit in both sets of experiments. Model Franck-Condon calculations suggest that the OD photofragment rotational state distributions, determined by OD(A-X) laser induced fluorescence (LIF), reflect primarily the rotational and zero-point bending motions in the selected rovibrational state of HOD(X?) However, in contrast to the state selected photodissociation of H₂O, the OD rotational distributions from HOD also reveal the influence of a small exit channel torque, which is enhanced in the photodissociation of the deuterated molecule by the shift in the OD centre-of-mass relative to that in OH. A modified Franck-Condon model, which accounts approximately for this modest impulsive torque, qualitatively reproduces the observed behaviour.

Full text of DOI:10.1063/1.473625

The state-to-state photodissociation dynamics of HOD (Ã)
M. Brouard and S. R. Langford
Citation: The Journal of Chemical Physics 106, 6354 (1997); doi: 10.1063/1.473625
View online: http://dx.doi.org/10.1063/1.473625
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˜
The state-to-state photodissociation dynamics of HOD(A)
M. Brouarda) and S. R. Langfordb)
The Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford, OX1 3QZ,
United Kingdom
͑
Received 8 November 1996; accepted 10 January 1997͒
HOD, rotationally state selected in the third and fourth OH stretching overtone (
͉
͘ ͘
04 , ͉05 ) levels,
˜
has been photodissociated via the A state at ␭Ӎ 288 nm. In accord with previous studies, H ϩ OD
is the dominant dissociation channel, with the yield of OH photofragments being below the
detection limit in both sets of experiments. Model Franck-Condon calculations suggest that the OD
photofragment rotational state distributions, determined by OD(A-X) laser induced fluorescence
͑
LIF͒, reflect primarily the rotational and zero-point bending motions in the selected rovibrational
˜
state of HOD(X). However, in contrast to the state selected photodissociation of H O, the OD
2
rotational distributions from HOD also reveal the influence of a small exit channel torque, which is
enhanced in the photodissociation of the deuterated molecule by the shift in the OD centre-of-mass
relative to that in OH. A modified Franck-Condon model, which accounts approximately for this
modest impulsive torque, qualitatively reproduces the observed behaviour. © 1997 American
Institute of Physics. ͓S0021-9606͑97͒00615-6͔
I. INTRODUCTION
refer to the number of quanta in the O–H and O–D local
mode stretches, respectively͒, and the dynamical tunnelling
The study of state-to-state molecular photodissociation
dynamics has for many years attracted much experimental
effort and provides a direct and rigorous test of the theoret-
ical understanding of the fragmentation process. The depen-
dence of the photodissociation dynamics on reagent state has
perhaps been most thoroughly explored, and understood, for
Ϯ
effect, which produces the local mode doublets
͉
nm
͘
in
16,17
17
H O,
is destroyed. Excitation of either of the two
2
stretching modes is localised and vibrationally mediated pho-
˜
todissociation ͑VMP͒ of HOD via the A state can result in
selective cleavage of the vibrationally excited bond. In the
1
8
light of this, the theoretical studies of Imre and co-workers
˜
˜
–7
the photodissociation of H O via its A←X transition. The
2
19,20
1
and Schinke and co-workers,
periments of Crim and co-workers2
HOD ͑4␯OH) at 218.5, 239.5 and 266 nm͒ and Rosenwaks
and the state-selected ex-
fully state resolved experimental studies
provided by a
0,21
͑photodissociating
number of researchers, show that the scalar ͑internal energy͒
and vectorial ͑momentum͒ disposals in the OH photofrag-
ments are profoundly influenced by the rotational and vibra-
tional motions of the parent molecule in its ground electronic
state, and are little affected by modest exit channel torques
and co-workers2
2,23
͑photodissociating HOD in the 1␯OH , 1
␯OD and 3␯OD modes at 193 nm͒, have focussed on the par-
ent vibrational state and photon energy dependence of the H
ϩ OD/D ϩ OH branching ratio. The theoretical predictions
are in qualitative agreement with the experimentally ob-
served trend: provided the supplied energy is less than that
required for excitation above the D ϩ OH → H ϩ OD
˜
generated on the dissociative A state. Theoretical modelling
of these observations, together with data from resonance
8
9,10
Raman and one-photon photodissociation
studies, have
provided a very detailed understanding of the photodissocia-
1
,3,5,11–15
˜
tion dynamics.
reaction barrier on the A state surface, the selectivity of the
A further chapter in understanding the photodissociation
dynamics of water has been opened by study of its partially
deuterated isotopomer, HOD. Photofragmentation from the
dissociation process is enhanced by increased initial vibra-
tional excitation in the bond to be cleaved. These results
have been shown to be in accord with classical expectation.20
˜
A state potential energy surface, at total supplied energies
When excitation occurs above the barrier ͑as in the case of
Ϫ1
20,21
Ͻ60000 cm , occurs via two distinguishable product chan-
the 218 nm photodissociation of HOD͑4␯OH),
the 193
nels, leading to:
nm photodissociation of HOD͑3␯OD) ͑Ref. 23͒, and the 157
24
nm direct photolysis experiments of Bersohn et al. ͒, the
branching ratios have been shown to be strongly dependent
on quantal interferences arising from the overlap of the
ground and excited state parent molecular wavefunctions,
and classical mechanics provides only a very qualitative pic-
2
2
D͑ S͒ϩOH͑X ⌸͒
˜
HOD͑A͒→
2
2
H͑ S͒ϩOD͑X ⌸͒.
In the ground electronic state, the reduction in symmetry
arising from substitution of a deuterium atom for a hydrogen
atom lifts the degeneracy of the local mode stretching vibra-
20
ture of the dissociation dynamics. Except for the 193 nm
photolysis of HOD͑3␯OD),1
͑
8,20,23,24
the measured and
quantum͒ calculated ratios in this energy regime are in near
quantitative agreement.
͘ ͘ ͘
tional states ͉nm and ͉mn ͑for the state ͉ab , a, and b
a͒
Author to whom correspondence should be addressed.
Present address: School of Chemistry, University of Bristol, Cantock’s
Close, Bristol, BS8 1TS, United Kingdom.
b͒
Less information is available on the effect of isotopic
substitution on the OH/OD photofragment rovibrational dis-
6354
J. Chem. Phys. 106 (15), 15 April 1997
0021-9606/97/106(15)/6354/11/$10.00
© 1997 American Institute of Physics
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˜
M. Brouard and S. R. Langford:: Photodissociation dynamics of HOD(A)
6355
tributions. Crim and co-workers,21 photolysing HOD͑4␯OH
)
found to be only slightly dependent on the intermediate vi-
brational state, a result which contrasts with the analogous
at 218.5, 239.5 and 266 nm, measured the relative yields of
the OH and OD photofragments produced in vϭ0 and 1.
Both fragments are produced predominately in their ground
vibrational states, with the relative yield of vibrationally ex-
cited products exhibiting a dependence on the photon energy.
5
H O experiments ͑photolysing H O͑4␯OH) and ͑5␯OH) at
2
2
2
82 nm͒ in which a strong dependence was observed. Cal-
culations using a modified Franck-Condon model, which in-
cludes an approximate treatment of the small exit-channel
torque, qualitatively reproduce the experimental data and
provide an insight into the dynamics of parent molecule dur-
ing the photodissociation.
20
Wavepacket propagation calculations on an ab initio poten-
tial energy surface25 reproduce these observations well.
However, at supplied energies corresponding to excitation
˜
below the barrier on the A state surface, the calculations
underestimate the yield of vibrationally excited fragments.
II. EXPERIMENT
The D ϩ OH/H ϩ OD branching ratio at these
2
0,21,23
energies
calculations,
was also underestimated by these
and by the calculations of Imre and
The apparatus employed has already been described in
2
0
5,26
detail elsewhere.
An excimer laser was used to pump two
1
8
co-workers, which used the same ab initio surface, suggest-
ing that some modification of the calculated A state surface
dye lasers, one to provide the overtone excitation radiation
(␭Ӎ720 and 590 nm for HOD͑4␯OH) and ͑5␯OH) respec-
tively͒ and the other to provide both the photolysis radiation
(␭Ӎ288 nm͒ and the OD/OH photofragment LIF probe ra-
diation, using the 1–0 band of the OD/OH͑A–X͒ transition.
Both beams were counterpropagated into a reaction cell with
their electric vectors parallel to the fluorescence detection
axis, and the photofragment fluorescence signal was detected
through a 310 nm interference filter ͑centered on the 1–1
OH/OD band͒ using a photomultiplier. The photomultipler
signal was recorded on a boxcar integrator and transferred on
a shot-by-shot basis to a PC for power normalisation and
averaging. The HOD was produced with a 5:1 mixture of
H O and D O ͑99.95% pure, Aldrich Chemical Ltd.͒, which
˜
is required, perhaps in the barrier height for the hydrogen/
deuterium exchange reaction. Discrepancy between the cal-
culated and measured OH product vibrational distributions
˜
arising from H O photolysis via the A state would likewise
2
9,10,13
suggest this to be necessary.
The OH rotational distributions generated in the state-to-
1
–5
state photodissociation of H O,
have been shown to be
2
satisfactorily modelled using the Franck-Condon model of
1
1
Balint-Kurti, implying that final state interactions in the
exit channel are of minor importance. Variations in the pho-
tofragment rotational distributions with increasing parent
molecule vibrational excitation and decreasing photolysis
wavelength have been shown to reflect changes in the bound
state rotational-bending motion of water, arising from pref-
erential dissociation from increasingly extended H–OH re-
2
2
was allowed to flow into the reaction cell at pressures of
ϳ50 mTorr.
Similar to the previously reported study of the VMP of
5
˜
5
gions of the potential. Small differences in detail between
H O(A) from this laboratory, the high intensity of the pho-
2
the calculated and experimental OH distributions are prob-
ably the result of the neglect of exit-channel torques in the
Franck-Condon calculations.1 The shift in the centre-of-
mass arising from the substitution of a deuterium atom for a
hydrogen atom in the water molecule should make the OD
photofragment rotational distributions produced in HOD
photolysis more sensitive indicators of these exit-channel ef-
fects. Resonance Raman spectra of HOD obtained by Sen-
tolysis radiation used in this study was sufficient to saturate
highly the photofragment LIF spectra. Therefore, no correc-
,5
tion for the OH/OD rotational linestrengths or rotational
alignment were made6
,27,28
and rotational population distri-
butions were determined from peak height measurements.
The close agreement between the rotational distributions ex-
tracted from the main and satellite transitions, which probe
the same product ground state level, substantiates the use of
this procedure.
The HOD ͑4␯OH) and ͑5␯OH) overtone transitions were
initially detected by recording the action spectra, detecting
the OD photofragment LIF and scanning the overtone exci-
tation radiation ͑Figure 1͑c͒͒. Rotational assignments were
8
sion and co-workers, exciting at 174.6, 171.4 and 160.0 nm
˜
͑
resonant with the A state͒, show no activity in the bending
mode, and therefore indicate that the OD photofragment ro-
tational population distributions should still be strongly in-
fluenced by the initial ro-vibrational motion of the bound
state HOD molecule. A state-to-state study of HOD photo-
dissociation should therefore provide detailed information on
the sensitivity of the photofragment rotational distributions
to the concerted influence of the motions of the parent mol-
ecule on both its ground and electronically excited state sur-
faces.
Presented in this article are the measurement and inter-
pretation of the OD photofragment rotational distributions
arising from the 288 nm photodissociation of HOD, initially
prepared in the third and fourth OH stretching overtone lev-
els. A branching ratio between the H ϩ OD and D ϩ OH
dissociation channels has also been estimated from OD and
OH LIF measurements. The OD fragment distributions are
made on the basis of rigid asymmetric rotor simulations of
the spectra3
0,31
͑Figure 1͑d͒͒, assuming predominantly
32,33
A-type rather than B-type character (ϳ 0.7:0.3͒.
Rota-
tional transitions ͑P↑, Q↑ and R↑) up to JЉ ϭ 8 were unam-
biguously assigned in the ͑4␯ ) and ͑5␯ ) VMP OD ac-
OH
OH
Ϫ1
tion spectra recorded between 13706.1 and 13954.8 cm
Ϫ1
29
and 16730.8 and 17015.5 cm , respectively. The calcu-
lated rotational constants and the observed band origins are
given in Table I, along with the corresponding wavenumbers
of the ground and fundamental vibrational states.3
2,33
To en-
sure that only HOD molecules were state selected in the
photodissociation experiments, a comparison was made be-
tween the photoacoustic overtone spectra of pure H O and of
2
J. Chem. Phys., Vol. 106, No. 15, 15 April 1997
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˜
M. Brouard and S. R. Langford:: Photodissociation dynamics of HOD(A)
6356
FIG. 2. A plot of the water ground state potential of Jensen and co-workers
˜
͑
Ref. 40͒ and the A state potential of Staemmler and Palma ͑Ref. 25͒ against
the dissociation coordinate, RH-OD . Excitation to the excited state potential
in this study should preferentially occur from more extended H–OD con-
figurations than in the previous studies of Crim and co-workers ͑Ref. 20,21͒
and Rosenwaks and co-workers ͑Ref. 22͒.
FIG. 1. A segment of the rovibrational spectrum in the region of the third
OH stretch overtone of HOD using ͑b͒ photoacoustic spectroscopy and ͑c͒
recording a VMP action spectrum, fixing the probe radiation on the A
2
2
⌺
–X ⌸ ͑1–0͒ Q ͑1͒ LIF transition of OD and scanning the overtone
22
excitation radiation. Also shown are ͑a͒ the photoacoustic spectrum of pure
tation is reserved for the asymmetric rotor level in the upper
vibrational level of HOD͑X͒.͒ The majority of the photofrag-
˜
H O in the same region and ͑d͒ a simulation of the HOD͑4␯OH) band at 298
2
K.
ment LIF spectra were recorded using R↑ overtone transi-
tions, although the spectra were found to be insensitive to the
choice of the branch employed.34 The loss of information
concerning the effect of parent rotational alignment on the
photodissocation dynamics is attributed to the highly satu-
rated condition of the photofragment LIF spectra.
a H O and HOD mixture ͑see Figures 1͑a͒ and 1͑b͒͒. Only
2
HOD transitions that were clearly unblended with H O reso-
2
nances were used in the study. According to the simulations,
the HOD͑4␯OH) and ͑5␯OH) overtone transitions to Jϭ0,
000
←1 , were both overlapped with other HOD transitions,
III. (H ؉ OD)/(D ؉ OH) BRANCHING RATIO
01
Ϫ1
within the resolution of the laser radiation (ϳ 0.2 cm ),
and thus no data were obtained for photodissociation of
HOD͑J ϭ 0͒. ͑Throughout the text, the unprimed J
The 288 nm photodissociation of HOD, initially excited
into the third and fourth OH stretching overtone, provides
no-
Ϫ1
Ϫ1
K ,K
a
c
ϳ8000 cm
and ϳ11000 cm
excess energy, respec-
tively, for partitioning into the photofragments. This is con-
siderably lower than that provided in the 218.5, 239.5 and
TABLE I. The band origin energies and rotational constants for selected
20,21
2
66 nm experiments of Crim and co-workers
on HOD
O–H stretching vibrational states of HOD. The zero point energy of HOD is
Ϫ1
͑4␯OH) and the 193 nm experiments of Rosenwaks and
4
000.3 cm . The rotational constants quoted for ͑4␯OH) and ͑5␯OH) repro-
22
duce the line positions of transitions to levels with Jр8 to an estimated
co-workers on HOD͑1␯OH). Simple energy conservation
Ϫ1
˜
accuracy of Ϯ 0.2 cm
.
arguments suggest that excitation to the A state surface in the
present experiments should occur preferentially from larger
internuclear separations of the ground state than in previous
studies ͑see Figure 2͒.
Rotational constants cmϪ1
Vibrational level
Band origin
energies / cm
Ϫ1
(
␯OH , ␯bend , ␯OD
)
A
B
C
0,0,0͒ a
1,0,0͒
The OD͑H͒ LIF spectra, obtained subsequent to the pho-
͑
͑
0
3707
13844.8
16911.8
23.4139
22.3549
19.465
18.467
9.1034
9.0864
9.042
6.4063
6.3183
6.092
b
tolysis of HOD͑5␯OH) J
ϭ404 and shown in Figure 3,
K ,K
c
a
͑4,0,0͒
demonstrate that the relative yield of OH radicals is very
low: from the total LIF signals collected, the branching ratio
was estimated to be ⌽(OD,vϭ0)/⌽(OH,vϭ0)Ͼ23. A
similar result was found for the photodissociation of HOD
͑5,0,0͒
9.022
6.020
a
Taken from Ref. 32.
Taken from Ref. 33.
b
J. Chem. Phys., Vol. 106, No. 15, 15 April 1997
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˜
M. Brouard and S. R. Langford:: Photodissociation dynamics of HOD(A)
6357
2
FIG. 4. The OD( ⌸ 3) photofragment rotational distributions, for both
2
lambda doublet states AЈ (᭹) and AЉ (᭺), arising from the 288 nm pho-
todissociation of HOD͑4␯OH) JK ϭ313 ͑a͒, 404 ͑b͒ and 505 ͑c͒. The data
,K
a
c
͑
shown on the left͒ are compared with the distributions obtained in the 282
2
2
2
2
nm photodissociation of H O͑4␯OH) ͑Ref. 5͒.
FIG. 3. ͑a͒ OD A ⌺–X ⌸ ͑1–0͒ and ͑b͒ OH A ⌺–X ⌸ ͑1–0͒ LIF spectra
arising from the 288 nm photodissociation of HOD͑5␯OH) JK ϭ404
2
.
,K
a
c
2
IV. OD(X ⌸) ROTATIONAL DISTRIBUTIONS
A. The 288 nm photodissociation of HOD(4␯OH
)
͑
4␯OH), but reduced signal-to-noise levels meant that the
2
3
2
The OD͑X ⌸ ) photofragment rotational distributions
best estimate of the branching ratio was ⌽(OD,vϭ0)/
⌽
Crim and co-workers
2
data are consistent with an increasing preference for OD pro-
duction with increasing photolysis wavelength and parent
OH stretch excitation.
are shown in Figure 4 ͑plotted as a function of N, the total
angular momentum quantum number excluding spin͒, for
both lambda doublet states AЈ and AЉ, arising from the dis-
(OH,vϭ0)Ͼ12. Compared with the values obtained by
20,21
(ϳ1, Ͼ15 and Ͼ15 for the 218.5,
39.5 and 266 nm photodissociation of HOD͑4␯OH)͒, the
sociation of HOD͑4␯OH) J
ϭ313 ͑a͒, 404 ͑b͒ and 505 ͑c͒.
K ,K
a
c
For comparison, the corresponding data arising from the near
isoenergetic 282 nm photolysis of H O͑4␯ ) are also in-
cluded. Clearly the OD distributions are very sensitive to the
rotational state selected in the HOD intermediate overtone
level.
5
2
OH
The absorption cross-section for the ͑5␯OH) band,
␴(5␯
, is approximately an order of magnitude lower than
)
OH
that of ͑4␯OH).35 However, the overall VMP cross-section,
which is a product of ␴(5␯OH) and ␴elec ͑the state specific
B. The 288 nm photodissociation of HOD(5␯OH
)
photodissociation cross-section͒, was estimated to be ap-
The increased OD LIF signal-to-noise levels resulting
from the initial excitation of the fourth compared with those
from the third overtone meant that a more detailed study of
the 288 nm photodissociation of HOD͑5␯OH) was under-
taken. The resulting OD rotational distributions are sum-
marised in Figures 5͑a͒–5͑e͒ for a range of parent rotational
proximately twice as large as that for the VMP of HOD
͑4␯OH), based on an analysis of both the total LIF signals
and the observed signal-to-noise ratios. This would suggest
˜
that, at ␭ϳ 288 nm, the overlap between the A state con-
tinuum and ͑5␯OH) overtone wavefunctions is approximately
20 times larger than that of the ͑4␯OH) state. As is shown in
states ͑J
ϭ313 ͑a͒, 404 ͑b͒, 505 ͑c͒, 515 ͑d͒ and 606 ͑e͒͒.
K ,K
a c
Figure 2, on purely energetic grounds, 288 nm excitation
˜
from the ͑4␯OH) overtone to the A state should occur prefer-
The oscillations in the lambda doublet population distribu-
tions are clearly quite different from the corresponding OH
distributions obtained in the H O͑5␯ ) VMP study.5
entially from a classically forbidden region of the bound
state potential, where the vibrational wavefunction drops off
exponentially from a peak close to the classical turning
point. In contrast, excitation from ͑5␯OH) should occur from
near the maximum amplitude of the vibrational wavefunc-
tion, close to the outer turning point. This may well be the
primary cause for the differing VMP cross-sections, and will
be discussed further in Section V.
,34
2
OH
Comparing the OD distributions obtained from the photodis-
sociation of HOD͑4␯OH) and ͑5␯OH) ͑i.e. those shown in
Figures 4͑a͒–4͑c͒ with those in 5͑a͒–5͑c͒͒, there are small
but noticeable differences in parts of the oscillatory structure,
although the general forms of the lambda-doublet resolved
distributions remain very much the same. This contrasts with
J. Chem. Phys., Vol. 106, No. 15, 15 April 1997
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˜
M. Brouard and S. R. Langford:: Photodissociation dynamics of HOD(A)
6358
TABLE II. OD photofragment rotational temperatures, calculated from
Boltzmann plots of the lambda doublet averaged rotational distributions,
generated via the 288 nm photodissociation of HOD͑4␯OH) and ͑5␯OH
JK ͑J ϭ 3–7͒. Also shown are the corresponding OH product tempera-
)
,K
a
c
tures arising from the 282 nm photolysis of H O(4␯OH) and ͑5␯OH) ͑Ref.
2
34͒.
303
313
404
505
HOD͑4␯OH) ϩ 288 nma
•••
135Ϯ30 K 160Ϯ40 K 222Ϯ40 K
HOD͑5␯OH) ϩ 288 nmb 162Ϯ40 K 173Ϯ40 K 200Ϯ30 K 241Ϯ50 K
a,c
H O͑4␯OH) ϩ 282 nm
•••
•••
192Ϯ20 K 200Ϯ20 K 244Ϯ30 K
208Ϯ20 K 210Ϯ20 K 259Ϯ30 K
2
b,c
H O͑5␯OH) ϩ 282 nm
2
515
606
616
707
•
••
•••
•••
•••
2
2
2
33Ϯ50 K 250Ϯ40 K 280Ϯ60 K 292Ϯ60 K
46Ϯ20 K
•••
•••
•••
•••
59Ϯ30 K 292Ϯ20 K
355Ϯ20 K
a
Available energy for the photofragments ϳ8000 cmϪ1.
b
Ϫ1
Available energy ϳ11000 cm
.
c
Taken from Ref. 34.
H O͑4␯OH) ϩ 282 nm and HOD͑5␯OH) ϩ 288 nm with
2
H O͑5␯OH) ϩ 282 nm͒ clearly reveals a slight cooling of the
2
OD photofragment rotational distributions from HOD com-
pared with those of OH arising from H O photodissociation.
2
V. FRANCK-CONDON CALCULATIONS
The OH photofragment lambda doublet population dis-
˜
1–5
tributions arising from the VMP of H O via the A state
2
have been successfully simulated using a simple Franck-
Condon model derived by Balint-Kurti.11 The model makes
the same basic assumptions as the earlier work of Beswick
and Gelbart36 and Morse and Freed, that exit-channel ef-
fects can be neglected and the transition dipole moment
function is independent of the nuclear coordinates, but also
takes into account the open shell character of the OH
37
2
FIG. 5. The OD( ⌸ 3) rotational population distributions in the AЈ (᭹)
2
and AЉ (᭺) lambda doublet levels generated via the 288 nm photo-
dissociation of the JK ,Kcϭ313 ͑a͒, 404 ͑b͒, 505 ͑c͒, 515 ͑d͒ and 606 ͑e͒ rota-
tional states of HOD͑5␯OH). The data ͑shown on the left͒ are compared with
the distributions obtained in the 282 nm photodissociation of H O͑5␯OH)
a
͑X ⌸) and H( S͒ photofragments. In the previous study,5
it was demonstrated that application of this model to VMP
experiments employing high intermediate stretching vibra-
tion overtone levels and low energy photolysis photons, re-
quires the use of extended values of the dissociation coordi-
nate R ͑throughout this paper, the Jacobi coordinates R, r
and ␥ will be used to describe the geometry of parent mol-
ecule - see Figure 6͑a͒͒. To simulate the OD rotational dis-
tributions observed in this study, the model ͑more specifi-
cally, Eq. ͑75͒ of Ref. 11͒ has been applied by fixing r at its
equilibrium value in free OD, r ϭ 0.970 Å, and varying R
from 0.970 to ϳ1.5 Å. The ground state water potential
function of Jensen and co-workers40 was used throughout the
calculations. By freezing r and R, the HOD ground state
Hamiltonian becomes that of a ‘‘rigid bender’’:
2
2
11
2
͑Ref. 5͒.
the VMP of H O, where excitation from the ͑4␯OH) and
5␯OH) overtone states yield dramatically different oscilla-
tory structure in the OH photofragment rotational distribu-
tions. Given the similar energetics of the HOD and H O
2
5
͑
2
experiments, the contrasting behaviours of the two molecules
must be associated with the differing nuclear motions on the
ground and excited surfaces accessed in the VMP processes.
Within the experimental errors, the OD spin-orbit popu-
lation ratios are approximately statistical. Averaging over the
lambda-doublet populations, for a given initial parent rota-
tional state, removes the oscillatory structure and yields OD
spin-orbit state-resolved population distributions which
could be characterized well by a Boltzmann distribution em-
ploying a single ‘‘rotational temperature’’. ͑Slight deviations
from Boltzmann behaviour at high N values may reflect the
modest preference for the AЉ lambda doublet state observed
at high N.͒ The photofragment rotational temperatures ob-
l2
j2
ˆ
Hϭ
ϩ
ϩV͑R,r,␥͒
͑1͒
2
␮R2 2␮OHr2
for which the bound state rotational-bend wavefunctions are
expanded in terms of an orthonormal set of parity adapted
11,38,39
angular basis functions,
tained in this study, and from the previous isoenergetic
H O study, are summarised in Table II. Comparing the val-
ues for the isoenergetic pairs ͑HOD͑4␯OH) ϩ 288 nm with
5
⌿JM͑R,r,E͒ϭ
Jp JMp
2
C Y ͑␥,⍀͒,
͑2͒
͚
j␭ j␭
j␭
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˜
M. Brouard and S. R. Langford:: Photodissociation dynamics of HOD(A)
6359
with only the phase of the oscillatory structure in the rota-
tional populations, for selected values of N, being correctly
predicted. Furthermore, the values of R returned by such an
analysis, are unrealistically small compared with those ex-
pected based on energetic considerations ͑see Figure 2͒. The
failure of the Franck-Condon model to reproduce the experi-
mental OD distributions from HOD photolysis, but its com-
parative success in accounting for those of OH from H O, is
2
likely to have its origins in the increased influence of the
excited state potential energy surface in the HOD photodis-
sociation dynamics, arising from the shift in the centre-of-
mass of the OD moiety further away from the oxygen atom,
as demonstrated below.
Reisler and co-workers41 have shown that for a fast dis-
sociation with a modest exit-channel torque, the final photo-
fragment rotational distribution may still reflect, in part, the
angular momentum distribution inherent in the parent mol-
ecule bound-state wavefunction. For such a system, they de-
veloped a modified form of the semiclassical ͑closed-shell͒
Franck-Condon model of Morse and Freed37 for parent mol-
ecules with Jϭ0, which includes an approximate treatment of
the small exit channel torque generated on the excited poten-
FIG. 6. The centre of mass body-fixed coordinate system used in the
Franck-Condon model calculations. The Jacobi coordinates are shown in ͑a͒.
The body-fixed axes used in this study and by Reisler and co-workers ͑Ref.
4
1͒ are shown in ͑b͒ and ͑c͒ respectively.
where
Y
1
41
JMp
j␭
JM
tial surface. Using the body-fixed axes shown in Figure
͑␥,⍀͒ϭ
͓Y ͑␥,⍀͒
j␭
ͱ
2͑1ϩ␦␭0
͒
6͑c͒, the semiclassical expression for the product rotational
37
distribution for a non-rotating parent molecule can be writ-
ϩ͑Ϫ͒Jϩp
Y
JM
jϪ␭
͑␥,⍀͔͒,
͑3͒
41
ten as
and38
n
n
ϩj
2ϩ
n 2
P ϳ͑
͉
C
͉
͉
C
͉
͒ϩinterference terms,
͑5͒
j
-j
1
2
J ϩ 1
2
where n is the reagent ͑bending͒ quantum state. ͑This expres-
sion is analogous to Equation 4, which, however, uses the
body-fixed axes defined in Figure 6͑b͒.͒ Equation 5 can be
interpreted in terms of the bound-state bending motion in the
parent molecule providing an equal source of clockwise
JM
J
Y ͑␥,⍀͒ϭ
ͩ
ͪ
Y ͑␥,0͒D ͑⍀͒.
j␭
j␭
␭M
4
␲
Neglecting the electronic fine-structure of the photofrag-
ments, the Franck-Condon expression for the ͑closed-shell͒
rotational probabilities is then given by
͑
m ϭϪj͒ and counter-clockwise ͑m ϭϩj͒ rotation of the di-
j
j
atomic fragment ͑caused by opening and closing of the bend-
ing angle, respectively͒.41 The interference of these motions
can be understood as the cause of oscillatory structure in the
product rotational distributions. The exit-channel torque is
treated in a time-dependent fashion and the resulting change
in the parent molecule equilibrium bending angle during dis-
sociation generates a time dependent, unidirectional angular
Jp
Jp 2
P ϰ
͚ ͉ j␭
C
͉
͑4͒
j
␭
Jp
in which Cj␭ are the expansion coefficients of the parent
ground state rotational-bend wavefunction. To make a com-
parison with the experimental measurements, the electronic
and spin degrees of freedom of the photofragments are in-
cluded within the model.11 A proper treatment of the sym-
metry and coupling of the electronic spin, s, and orbital an-
gular momentum, l, to the rotational angular momentum, j,
produces a more complicated, but analogous expression for
momentum J ͑t͒, superimposed on the product angular mo-
tq
menta derived from the parent bending motion. Calculating
J ͑t͒ at a time T when the Franck-Condon expansion is car-
tq
41
ried out, Reisler and co-workers rewrite Equation 5 as
11
the ͑open-shell͒ rotational probabilities.
Within the Franck-Condon framework, the photofrag-
ment rotational population distributions, characterized by the
n
j
P ϳF͓j - J ͑T͔͒ϩF͓Ϫj Ϫ J ͑T͔͒ϩinterference terms
tq
tq
͑
6͒
Jp
j␭
expansion coefficients C , simply reflect the bound state
with
rotational and bending motions of the parent molecule.
n 2
2
F͑x͒ϭ͉C ͉ .
x
3
Franck-Condon calculated OD( ⌸ ) lambda doublet popu-
2
lation distributions for HOD J
ϭ6 , calculated at in-
K ,K
06
A similar approach has been taken to modify the open shell
Franck-Condon model of Balint-Kurti,11 for parent rotational
states Jу0. The measured dissociation time for water in the
a
c
creasing values of R, are compared in Figure 7 ͑middle͒ with
the corresponding experimental distribution ͑left͒. A poor fit
to the experimental data can only be achieved by fixing both
bondlengths at their equilibrium values. The same is also
true for other initial parent molecule rotational states, but the
agreement is considerably worse than that shown in Figure 7,
˜
A state is between ϳ20 fs ͑Ref. 10͒ and ϳ40 fs ͑Ref. 6͒ and
it is assumed that the torque may be treated as impulsive.
Nearly all the available energy in the 288 nm photolysis of
Ϫ1
HOD͑4␯OH) and ͑5␯OH) (ϳ8000 and ϳ11000 cm respec-
J. Chem. Phys., Vol. 106, No. 15, 15 April 1997
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˜
M. Brouard and S. R. Langford:: Photodissociation dynamics of HOD(A)
6360
2
FIG. 7. The calculated OD( ⌸ 3) population distributions, for both lambda doublets AЈ (᭹) and AЉ (᭺), for HOD J
ϭ606 , as a function of R, using the
,K
c
K
a
2
original Franck-Condon model ͑middle͒ and the modified model ͑right͒ which includes an added impulsive torque. Also shown in the left of the figure is the
corresponding experimental distribution, photolysing HOD͑5␯OH) at 288 nm.
tively͒ is channelled into translational excitation of the pho-
tofragments, and a simple classical estimate suggests that an
additional ϳ 1.1 and ϳ 1.3 units of angular momentum are
generated in the OD fragment by the impulsive bond rupture,
for HOD͑4␯OH) and ͑5␯OH), respectively. In the simulations
that follow, Jtq is assigned a value of 1 ͑indeed, the modified
model only allows the ‘‘addition’’ of integral angular mo-
menta͒ and is chosen to lie in a direction specified by the
direction of the torque, which decreases the bending angle
s and l, the spin and orbital angular momentum of the pho-
tofragments, yields the exit-torque modified OD rotational
distributions. We note in passing that, for parent molecules
with Jϭ0, calculating the closed shell OD rotational distri-
bution using Equation 4, with the new set of coefficients,
yields the same results as obtained from the work of Reisler
and co-workers,41 employing Equation 6.
2
3
Modified Franck-Condon calculated OD( ⌸ ) rotational
2
population distributions obtained at three values of R for
͑i.e. a counter-clockwise rotation͒.
HOD J
ϭ606 are shown on the right hand side of Figure
K ,K
c
a
To modify the Balint-Kurti model, a new set of expan-
7
. Comparison of these distributions with those calculated
Jp
sion coefficients, C , were generated from the original co-
using the original Franck-Condon model, reveals that the exit
channel torque has a marked effect on the oscillatory struc-
ture of the lambda-doublet resolved populations. More im-
portantly, good agreement between experiment and the
modified theory is obtained using energetically realistic val-
ues of R. A selection of experimental and their correspond-
ing ‘‘best-fit’’ ͑modified͒ Franck-Condon calculated OD
photofragment distributions are shown in Figure 8 for HOD
j ␭
Ј
Jp
j␭
efficients, C ͑defined in Equation 2 and calculated using the
parent bound state Hamiltonian͒, using
Jp
Jp
C
j ␭ϭ͚j
͑j␭Jtq0
͉
jЈ␭͒Cj␭
͑7͒
Ј
and ͑ . .. ͉
. .. ͒ are Clebsch-Gordon coefficients.42 Thus,
within this modified Franck-Condon treatment, the effects of
the small exit channel torque are accounted for simply by
coupling the angular momenta generated on the bound and
dissociative electronic potential energy surfaces. Inserting
the new values of the coefficients into the expression for the
rotational population distribution ͑Equation 75 in Ref. 11͒,
which contains the remaining terms needed to couple jЈ with
J
ϭ313 ͑a͒, 404 ͑b͒, 505 ͑c͒, 515 ͑d͒ and 616 ͑e͒. The level
K ,K
a
c
of agreement between the experimentally measured and cal-
culated distributions is the same for both OD lambda-doublet
states, but for clarity only the AЉ lambda-doublet is shown.
Of particular note from this figure is that the differences
observed experimentally between the OD distributions aris-
J. Chem. Phys., Vol. 106, No. 15, 15 April 1997
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˜
M. Brouard and S. R. Langford:: Photodissociation dynamics of HOD(A)
6361
FIG. 8. The modified Franck-Condon model calculated OD 2⌸ ͑AЉ͒ rotational distributions ͑shown on the left͒ obtained at the values of R indicated for
3
2
JK ϭ313 ͑a͒, 404 ͑b͒, 505 ͑c͒, 515 ͑d͒ and 616 ͑e͒. On the right hand side are the experimental distributions.
,K
a
c
5
the VMP of H O, in which experiments conducted at lower
ing from HOD͑4␯OH) and ͑5␯OH) J
ϭ 505 ͓Figure 8͑c͔͒
c
2
K ,K
a
photolysis photon energies or via higher intermediate over-
tone levels tend to yield fragment rotational distributions in
good agreement with those from the calculations employing
more extended values of R. Secondly, the values of R given
in the Tables III and IV appear sensible. The outer maximum
of the HOD͑5␯OH) vibrational wavefunction occurs at Rϳ
can be reproduced by the model only if a larger value of R is
used for the lower overtone experiment.
These results are further summarised in Tables III and
IV, in which are presented the reagent rotational state-
specific and the averaged values of R at which experiment
and theory are in reasonable accord. Also shown in Table IV
are estimates of the values of R at which preferential excita-
18,20
1.35 Å and at Rϳ 1.30 Å for HOD͑4␯OH).
˜ ˜
However, the
˜
tion to the A state is expected to occur, R , based purely on
A–X transition moment function, which may be assumed the
same as that for H2O,15 decreases significantly with bond
extension. Excitation from HOD͑5␯OH) appears to occur
preferentially at R values very close to the maximum in the
bound state vibrational wavefunction, the position of which
is little affected by the decaying transition moment function
exp
simple energetic considerations. ͑The ground state potential
40
of Jensen and co-workers and the excited state surface of
Staemmler and Palma25 were used to make these estimates.͒
These tables serve to highlight two key points. Firstly, the
results are consistent with the Franck-Condon simulations of
TABLE III. The parent rotational state-specific approximate values of R required in the modified Franck-
Condon model in order for the calculated OD distributions to be in accord with the experimental measurements.
The length r is fixed at its equilibrium value for free OD of 0.97 Å.
HOD state
a
Parent Rotational State JK
,K
a
c
303
313
404
505
515
606
616
707
͑
4␯OH) ϩ 288 nm
1.48
Ϯ0.05
1.48
1.40
Ϯ0.05
1.40
1.34
Ϯ0.05
1.31
͑
5␯OH) ϩ 288 nm
1.43
1.43
Ϯ0.05
1.29
Ϯ0.05
1.29
Ϯ0.05
1.29
Ϯ0.05
Ϯ0.05
Ϯ0.05
Ϯ0.05
Ϯ0.05
aThe parent molecule intermediate vibrational state and the dissociation wavelength.
J. Chem. Phys., Vol. 106, No. 15, 15 April 1997
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˜
M. Brouard and S. R. Langford:: Photodissociation dynamics of HOD(A)
6362
TABLE IV. As in Table III but showing the state averaged approximate
values of R, , for which the modified Franck-Condon model described in
͗ ͘
R
the text yields OD distributions in reasonable accord with experiment. The
length r is fixed at its equilibrium value in free OD of 0.97 Å. Also shown
˜
are the energetically expected values of R, Rexp , where excitation to the A
state surface should preferentially occur from. These were estimated using
the ground state potential of Jensen and co-workers ͑Ref. 40͒ and the excited
state surface of Staemmler and Palma ͑Ref. 25͒.
HOD State
͗
R
͘
͑Å͒
Rexp ͑Å͒
͑
4␯OH) ϩ 288 nm
5␯OH) ϩ 288 nm
1.41 Ϯ 0.05
1.36 Ϯ 0.05
ϳ 1.49
ϳ 1.40
͑
FIG. 9. The change in the direction of the a-inertial axis of the ground state
parent molecule with respect to R, as R is increased for H O, ͑a͒ and ͑b͒,
2
with bond extension.15 For HOD͑4␯OH), in contrast, ener-
and HOD, ͑c͒ and ͑d͒.
getic considerations alone suggest that excitation occurs
from regions well beyond the outer maximum in the bound
state wavefunction, ie. in the classical forbidden region,
where the decreasing dipole moment function with bond ex-
5
by the component of J about the a-inertial axis. For HOD, a
corresponding change in the direction of the a-axis ͓Figures
9͑c͒ and 9͑d͔͒ requires a much larger extension of R than for
H O, because of the shift in the centre-of-mass in OD rela-
tive to OH. The OD photofragment rotational state distribu-
tions predicted by the model are thus less sensitive to bond
15
tension is expected to have its greatest influence: excitation
˜
2
to the A state, in this case, therefore occurs at slightly smaller
values of R than would be expected purely on the basis of
energetic considerations. Note, furthermore, that the values
of R required to obtain agreement between the modified
Franck-Condon calculated and experimental rotational distri-
butions ͑see Table IV͒ are also consistent with the experi-
mental observation that the VMP cross-section for HOD
extension than are those of OH arising from H O photodis-
2
sociation.
This rationale is supported by inspection of the bound-
state Hamiltonian for the rotational-bending motion of the
parent molecule. The centrifugal and Coriolis coupling ma-
trix elements arising from l , which depend on J and ␭ ͑the
component of J ͑and j͒ about R), vary with 1/R and switch
5
͑5␯OH) ϩ 288 nm is approximately 20 times larger than that
ˆ2
for HOD͑4␯OH) ϩ 288 nm.
2
More detailed inspection of the data presented in Table
III, reveals that the returned estimates of R, required to fit the
modified Franck-Condon product state distributions to those
of the experiment, decrease with increasing parent rotational
state. As mentioned further below, the data may suggest that
coupling between the H—OD stretching and rotational-
bending degrees of freedom, not accommodated within the
Franck-Condon Model, also influences the OD product rota-
tional state distributions.
off as R increases. The remaining potential matrix elements
and those arising from j are both independent of J, but the
ˆ2
former do depend on ␭. As R increases, the overall rota-
tional motion of the ground state parent becomes more
prolate-top in character and the photofragment rotational dis-
tributions reflect the zero-point bending motion in the inter-
mediate bound vibrational state together with the component
of J about the a-inertial axis, K , which, at large R, approxi-
a
mately equals ␭.
The present study provides an additional insight into the
factors which affect the product state distributions and their
variation with increasing R ͑that is, with increasing OH
stretching quanta in the intermediate overtone level and/or
decreasing photon energy͒. Accounting approximately for
the effects of the small torque applied by the departing H
VI. DISCUSSION
5
Prevous Franck-Condon simulations of the OH distribu-
tions arising from the VMP of H O(A) ͑Refs. 1,2,4,5͒ have
˜
2
demonstrated that increasing values of R must be used in the
model calculations to reproduce the data from experiments
employing increasing vibrational excitation in the dissociat-
ing bond and/or decreasing energy of the photolysis photon.5
The origin of the variations in the oscillatory structure of the
product lambda-doublet resolved rotational population distri-
butions is rationalised by the effect that changing R has on
the inertial properties of the ground state parent molecule.
˜
atom on the OD photofragment on the A state surface, brings
the predictions of the modified Franck-Condon model into
qualitative accord with the experimental distributions, em-
ploying energetically realistic values of R for all of the initial
parent rotational states studied. The simulations suggest that
the phase and shape of the oscillatory structure in the
lambda-doublet population distributions primarily reflects
the ground state rotational-bending motion of the parent mol-
ecule ͑described above͒, perturbed by the influence of a
small final-state interaction. This result also helps provide a
rationale for the values of R required in the ͑original͒
Franck-Condon model to simulate the OH distributions ob-
These effects are illustrated schematically for H O in Figure
2
9͑a͒ and 9͑b͒. As R is increased, the a-inertial axis tends to
lie increasingly parallel with the vector R, and the equilib-
rium bond angle, ␥, becomes closer to 90°. As a conse-
quence, at large R (ϳ 1.5 Å͒, the calculated OH distributions
arising from levels with different J, but the same value of
1,2,4,5
K ͑and parity p͒, resemble those for J ϭ 0, but are shifted
a
tained in the VMP of H O,
which were found to be
2
J. Chem. Phys., Vol. 106, No. 15, 15 April 1997
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˜
M. Brouard and S. R. Langford:: Photodissociation dynamics of HOD(A)
6363
TABLE V. H O rotational state averaged approximate values of R,
2
cribed by Crim and Schinke and co-workers to exit channel
͗
R
͘
H2O , for with the ͑original͒ Franck-Condon model yields OH distribu-
effects.3
tions in reasonal accord with experimental distributions obtained in the
˜
VMP of H O via the A state ͑Refs. 1,2,4,5͒. Also shown are the energeti-
2
˜
cally expected approximate values of R, Rexp , where excitation to the A
VII. CONCLUSIONS
state potential surface should occur from.
HOD molecules, rotationally state selected in the third
and fourth OH stretching overtones levels have been photo-
dissociated at 288 nm via the A state. A branching ratio
between the H ϩ OD and D ϩ OH dissociation channels is
estimated to be ⌽͑OD͒/⌽͑OH͒ Ͼ23 and Ͼ12 for the higher
and lower overtone experiments respectively. The small shift
in the centre-of-mass arising from deuterium atom substitu-
tion is shown to have a marked effect on the rotational dis-
tributions of the OD photofragment, which are more sensi-
tive to the exit-torque applied by the departing H atom than
H O state
͗
R
͘
͑Å͒
H O
2
Rexp ͑Å͒
2
˜
a
a
a
a
͑5␯OH) ϩ 288 nm
͑4␯OH) ϩ 288 nm
͑4␯OH) ϩ 240 nm
͑1␯OH) ϩ 193 nm
1.26 Ϯ 0.10
1.11 Ϯ 0.09
1.06 Ϯ 0.06
1.05 Ϯ 0.04
ϳ 1.40
ϳ 1.49
ϳ 1.27
ϳ 1.27
aTaken from Ref. 5.
are the OH distributions produced in H O dissociation. Cal-
2
considerably smaller than those expected on energetic
culations using a modified Franck-Condon model, which ac-
counts approximately for the effects of an impulsive exit-
channel torque, are able to reproduce qualitatively the
experimental distributions at values of R that are in agree-
ment with those expected energetically, based on the current
grounds and to fluctuate over a considerable range (ϳ0.2
5
Å͒. These parent molecule state-averaged values of R,
͗
R
͘
, are shown in Table V along with the energetically
H O
2
expected values of R. The original Franck-Condon model
poorly͒ reproduces the experimental OD rotational distribu-
͑
˜
˜
knowledge of the X and A potential energy surfaces. These
calculations indicate that, in addition to being sensitive to
small changes in the inertial properties of the bound state
parent molecule, the OD photofragment rotational distribu-
tions ͑and to a lesser extent the OH distributions from the
tions from the VMP of HOD using values of Rϳ 0.97 Å ͑see
Figure 7͒, much smaller than those required in the H O
2
simulations. The torque produced by the departing H atom in
HOD dissociation generates approximately one unit of angu-
lar momentum in the rotating OD fragment, whereas in HOH
dissociation, the same torque generates only ϳ0.7–0.8,
which the modified Franck-Condon model cannot accommo-
date. This would suggest that the OH photofragment rota-
VMP of H O͒ are also sensitive to the small final-state in-
2
teraction on the dissociative potential surface.
1
͑
a͒ P. Andresen, V. Beushausen, D. Hausler, H. W. Lulf, and E. W. Rothe,
tional distributions arising from the VMP of H O VMP are
2
J. Chem. Phys. 83, 1492 ͑1985͒; ͑b͒ R. Schinke, V. Engel, P. Andresen, D.
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