Vibrationally mediated dissociation dynamics of H2O in the vOH=2 polyad

Article abstract of DOI:10.1063/1.1616915

The 193 nm photodissociation dynamics of gas-phase H₂O molecules was examined from selected rotational and vibrational quantum states within the v_OH=2 polyad. Data suggest a somewhat more restricted regime of applicability for the spectator model, specifically for vibrational states of H₂O at relatively high levels of local mode excitation.

Full text of DOI:10.1063/1.1616915

Vibrationally mediated dissociation dynamics of H 2 O in the v OH =2 polyad
Sergey A. Nizkorodov, Michael Ziemkiewicz, Tanya L. Myers, and David J. Nesbitt
Citation: The Journal of Chemical Physics 119, 10158 (2003); doi: 10.1063/1.1616915
View online: http://dx.doi.org/10.1063/1.1616915
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 119, NUMBER 19
15 NOVEMBER 2003
Vibrationally mediated dissociation dynamics
of H2O in the vOHÄ2 polyad
Sergey A. Nizkorodov,a) Michael Ziemkiewicz, Tanya L. Myers,b) and David J. Nesbittc)
JILA, University of Colorado and National Institute of Standards and Technology and Department
of Chemistry and Biochemistry, University of Colorado, Boulder, Colorado 80309-0440
͑Received 9 June 2003; accepted 18 August 2003͒
Vibrationally mediated photodissociation dynamics of jet-cooled H2O in the OHϭ2 polyad is
v
Ϫ
studied in a supersonic slit jet expansion. Single rotational states within
͉02 (ϵ␯1ϩ␯ in normal
͘
3
mode notation͒,
͉
02 ϩ(ϵ2␯1), 11 ϩ(ϵ2␯3), and 01Ϫ2 (ϵ␯ ϩ2␯ ) vibrational states of H O
͉
͉
͘
͘
͘
3
2
2
are selectively prepared with near IR overtone pumping, photodissociated at 193 nm, and the
resulting nascent internal state distribution of OH fragments probed via laser induced fluorescence.
Strong oscillations in rotational, spin–orbit, and lambda-doublet distributions are observed, often in
remarkably close agreement with H2O state-to-state photodissociation studies from both higher and
lower
polyads. The influence of initially excited bending and JK K levels of H2O on spin–
vOH
a c
orbit, ⌳-doublet, and rotational distributions of OH is examined in detail. Several new dynamical
trends are identified, for example, a clear propensity at high N for a strong ⌳ϩ versus ⌳Ϫ inversion
in the ⌸3/2 spin–orbit manifold, which reverses in the ⌸1/2 manifold, suggesting spin–orbit
sensitive stereodynamics in the ejection process. Furthermore, the results highlight significant
Ϫ
differences in photodissociation dynamics from gerade ͑e.g.,
͉
v
02 ϩ) versus ungerade ͑e.g.,
͉
02
͘
)
͘
vibrational states, specifically with respect to OH( ϭ1)/OH( ϭ0) branching ratios, and signaling
v
a breakdown of the ‘‘spectator’’ model at low vibrational excitation. © 2003 American Institute of
Physics. ͓DOI: 10.1063/1.1616915͔
I. INTRODUCTION
in the OHϭ1 vibrational polyad revealed surprisingly strong
v
oscillations in the OH fragment quantum state populations as
a function of NOH for a single spin–orbit/⌳-doublet mani-
fold. What made this observation particularly noteworthy
was that these same oscillations vanished for photodissocia-
tion of rotationally equilibrated water, even when cooled into
the lowest two nuclear spin states (JK K ϭ101,000) at super-
Photofragmentation of H2O in the first absorption band
(A 1B1 X 1A1) has long represented a fundamental para-
digm for direct dissociation on a single repulsive potential
energy surface ͑PES͒.1 In contrast to photodissociation in the
second absorption band (B 1B2 X 1A1), which involves
multiple product channels, conical intersections, and consid-
erable excess internal energy in the OH fragment,2 photoin-
duced bond-breaking via the A 1B1 state is less complicated,
in principle, permitting development of simple physical
models of the dissociation event. For example, A 1B1
X 1A1 excitation produces little change in the HOH bend
PES angular anisotropy, which largely accounts for the low
degree of rotational angular momentum transferred to the
nascent OH product.3 The moderate levels of OH vibrational
excitation observed can also be rationalized from a classical
perspective by preferred initial motion on the upper potential
surface along the symmetric stretch coordinate.1,4
a
c
sonic jet temperatures.11 This oscillatory behavior has since
been unambiguously verified in single rovibrational state
photodissociation studies of H2O for higher OH stretching
polyads for OHϭ3–5.5,7,9,10 Subsequent experimental and
v
theoretical studies have demonstrated that these oscillations
result from coupling between OH angular momentum states
in the exit channel. Specifically, a Franck–Condon model
projecting the initial HOH wave function into asymptotic
OH states was developed by Balintkurti.12 This has provided
an excellent qualitative ͑and in some test cases, semiquanti-
tative͒ description of the nascent OH populations,8 clearly
confirming the extreme sensitivity to the initial rotational and
bending states of H2O. Indeed, this analysis provided the
necessary framework to explain how the presence of two
JK K ϭ101 , 000 nuclear spin isomers in the early beam ex-
However, when examined on a fully state-to-state basis,
this rather simple picture for photodissociation of H2O
proves somewhat deceptive, and indeed becomes far richer
and dynamically more interesting.5–10 The first experiments
on photodissociation dynamics of water from single rovibra-
tional excited states were due to Andresen and co-workers.6
a
c
periments of Andresen11 had been sufficient to average out
all oscillations in the observed OH rotational distributions.
From the perspective of vibrationally mediated control
of photofragmentation dynamics, state-selection of H2O via
overtone excitation offers special advantages. As first eluci-
dated by Lawton and Child, the OH stretch structure for H2O
can be best described by polyads, with each polyad contain-
Their pioneering experiments on state-selected H2O(JK K
)
a
c
a͒
Present address: Department of Chemistry, University of California at Irv-
ine, Irvine, CA 92697.
b͒
Present address: Pacific Northwest National Lab, Richland, WA 99352.
Electronic mail: djn@jila.colorado.edu
c͒
ing OHϩ1 levels corresponding to
quanta distributed
vOH
v
0021-9606/2003/119(19)/10158/11/$20.00
10158
© 2003 American Institute of Physics
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J. Chem. Phys., Vol. 119, No. 19, 15 November 2003
Dissociation dynamics of H2O
10159
TABLE I. Summary of vibrationally mediated photodissociation dynamics
studies of H2O in the first absorption band (A 1B1 1A1). The H2O states
are labeled using notation
mnϮk , where m and n are the number of quanta
between the two identical bonds. By virtue of anharmonic
X
detuning effects that increase with OH , these quantum states
v
͉
͘
can often be quite well described by a single symmetric or
antisymmetric linear combination of pure ‘‘local mode’’ ex-
in the OH local mode stretches and k is the number of quanta in the bend ͑if
any͒. Excess energy refers to the total excitation energy above D0(H–OH)
ϭ5.118 eV (41 280 cmϪ1). In some studies, H2O is excited in Franck–
Condon forbidden region, i.e., substantially below the saddle point on the
citations ͑e.g.,
bative contributions from other nearby members of the same
polyad ͑e.g., Ϸ2Ϫ1/2
nϮ1,mϯ1 Ϯ mϯ1,nϮ1 ). At least
͉ ͉n,m Ϯ͉m,n ) with pertur-
nm ϮϷ2Ϫ1/2
͘ ͘ ͘
͕ ͖
A
1B1 PES, which is located some 16 000 cmϪ1 above D0 . OH populations
͉
͉
͕
͘
͘
͖
are normalized to the sum of OH( ϭ0)ϩOH( ϭ1).
v
v
for higher polyad numbers ( OHϭ3,4,5), this has led to the
v
OH in ϭ0 OH in ϭ1
v
v
␭
Eexcess
‘‘spectator’’ paradigm, i.e., a strong propensity for cleavage
of the OH bond with greater local mode vibrational excita-
tion, with the surviving OH bond retaining its initial local
mode excitation.13 For example, elegant experiments in the
photolysis
H2O state
͑nm͒
͑cmϪ1
͒
͑%͒
͑%͒
Reference
ϩ
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
͉
00
00
01
193
157
193
193
193
193
193
248
248
248
248
218.5
218.5
282
10 530
22 410
14 290
17 400
17 730
17 780
17 980
9 640
Ͼ99.8
Ͻ0.2
16
11
͘
͘
͘
50a
50a
ϩ
Ϫ
b
6, 8
This work
This work
This work
Crim group demonstrated that 220–250 nm photodissocia-
b
01Ϫ2
͘
Ϫ
tion of H2O in
͉
04 local mode state predominantly results
͘
ϩ
02
͘
02
͘
11
͘
03
͘
03
͘
12
͘
12
͘
63͑3͒
97.8͑3͒
37͑3͒
2.2͑3͒
53͑5͒
Ϫ
ϩ
ϩ
Ϫ
ϩ
Ϫ
in OH( ϭ0) fragments, whereas dissociation of the nearly
v
Ϫ
isoenergetic ͉13 state produces mostly OH( ϭ1). Indeed,
v
͘
47͑5͒
This work
b
10
10
10
10
9
9
5
7
7
7, 9
7
7
5
5
nearly 100% selective bond fission has been demonstrated in
analogous HOD studies, for which the OH versus OD stretch
local mode behavior is now essentially complete.14 These
studies have been extensively corroborated by exact QM dy-
namical calculations,13 resulting in an impressive level of
consensus between theory and experiment.1 It remains an
open question, however, what happens to this spectator para-
digm at lower levels of polyad excitation, e.g., where a local
mode description of the H2O stretch vibrations might begin
to break down. However, such studies require accessing mul-
tiple vibrational states with ‘‘tunable’’ spectator mode char-
9 660
9 910
Ͼ99.5
Ͻ0.5
b
10 070
16 640
18 140
8 010
10 140
14 300
18 320
14 790
18 800
11 000
11 670
Ͼ98
Ͼ90
Ͻ2
Ͻ10
Ͻ10
03Ϫ1
͘
͘
03Ϫ2
Ͼ90
Ϫ
b
04
͘
04
͘
04
͘
04
͘
13
͘
13
͘
Ϫ
Ϫ
Ϫ
Ϫ
Ϫ
266
Ͼ98
99͑1͒
91͑3͒
16͑6͒
6͑5͒
Ͻ2
1͑1͒
9͑3͒
84͑7͒
94͑5͒
Ͻ2
239.5
218.5
239.5
218.5
282
04Ϫ2
Ͼ98
Ͼ98
͘
Ϫ
05
͘
282
Ͻ2
acter, which do not exist for the lowest OHϭ0 and
v
vOH
ϭ1 polyads. It therefore proves particularly interesting to
explore vibrationally mediated photodissociation in the
aA sizable population in ϭ2 has been observed.
v
bOnly OH( ϭ0) product state was examined.
v
vOH
ϭ2 polyad, which permits access to the lowest OH stretch-
Ϫ
ing states ͑e.g.,
͉
02
, ͉ ͉
02 ϩ, and 11 ϩ) with distinguish-
͘ ͘ ͘
Sec. II, followed in Sec. III by quantum state resolved frag-
able local mode quanta in the spectator bond.
mentation results for H O excited to a series of OHϭ2 vi-
v
2
The thrust of the present work is to explore state-
brational levels. These distributions are analyzed and dis-
selected photodissociation of H2O in the OHϭ2 polyad,
v
cussed in Sec. IV, and interpreted in the context of simple
QM models for the fragmentation event. The major conclu-
sions are summarized in Sec. V.
which allows several questions of dynamical interest to be
addressed. First of all, as mentioned earlier, such studies can
Ϫ
directly access several different intermediate levels,
͉
02
͘
,
͉
02 ϩ, and
͉
11 ϩ, whereby photodissociation now has the
͘
͘
II. EXPERIMENT
option of either conserving ͑or destroying͒ vibrational exci-
tation in the uncleaved OH bond. As a secondary motivation,
photolysis of these vibrational states with 193 nm excitation
(EtotalϷ7.3 eV) samples regions on the upper PES quite en-
ergetically similar ͑see Table I͒ to those of Crim and
The essential experimental approach has been described
in previous studies from this laboratory,10,16 and builds on
powerful vibrationally mediated dissociation methods pio-
neered by Andresen and Crim.6,7,17 Water molecules are ex-
cited into specific rovibrational intermediate states with di-
rect overtone pumping and then selectively photolyzed with
193 nm ultraviolet radiation. This excimer photolysis wave-
length is close to optimal for Franck–Condon excitation of
co-workers7 in the classic OHϭ4 studies of H2O. As a re-
v
sult, one can further explore how photolysis dynamics de-
pend on the initial wave function projection on the upper
surface for comparable energies, specifically probing nascent
OH product state distributions. Third, as all three of these
the outermost lobe of the wave function in the H2O A
X
OHϭ2 overtone states are sufficiently bright for vibra-
absorption band, which therefore suppresses UV absorption
by unexcited water molecules present in the expansion by
several orders of magnitude. The translational, vibrational,
and rotational states of OH fragments are probed with laser
induced fluorescence, providing information on the forces
breaking the molecule apart during the photodissociation
process. Experimental details relevant to the current study
are briefly summarized in the following.
v
tionally mediated photofragmentation, the influence of wave
function symmetry ͑gerade versus ungerade͒ on the photo-
dissociation dynamics can be directly tested. Finally, as a
somewhat more practical consideration, these monomer pho-
todissociation results provide essential background for inter-
preting vibrationally mediated spectroscopy and dynamics of
water containing clusters currently under investigation.15
The organization of this paper is as follows: Key experi-
mental details relevant to the present work are discussed in
All experiments utilize a supersonic expansion of 1% of
H2O in a monoatomic carrier gas ͑He or Ar͒ at a total stag-
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10160
J. Chem. Phys., Vol. 119, No. 19, 15 November 2003
Nizkorodov et al.
nation pressure of 50 Torr ͑1 Torrϭ1.333 22 mbar͒ through a
pulsed slit valve ͑4 cmϫ125 ␮m, 10 Hz, 500 ␮s pulse dura-
tion͒. Even under these mild supersonic expansion condi-
tions, H2O cools down almost entirely into the lowest rota-
tional states allowed by the nuclear spin statistics, JK K
studies correspond to fewer than 0.01 collisions of the na-
scent OH species.
The OH fluorescence is collected through an f/1 CaF2
elliptical lens with a photomultiplier tube ͑PMT͒ positioned
at right angles with respect to the supersonic expansion and
collinear laser propagation axis. The pump and probe lasers
propagate collinearly through the slit jet expansion, and are
linearly polarized along the expansion axis. The OH fluores-
cence signal is sampled with a boxcar integrator, with scat-
tered light attenuated by a 295 nm long pass and UV band-
pass ͑UG-5͒ filters positioned in front of the PMT. Overall
photon collection efficiency is a few percent, typically yield-
ing 104 –105 signal photons per laser pulse with all three
lasers present. Laser powers, gas pulse intensities, and refer-
ence photoacoustic spectra are stored for normalization, di-
agnostics, and frequency calibration purposes. The detection
efficiency for OH is estimated from signal-to-noise ͑S/N͒
resulting from 193 nm dissociation of H2O. With the en-
hanced path length, density, and collection volume due to the
slit expansion, detection sensitivities below 5ϫ105 OH mol-
ecules per quantum state are routinely obtained.
a
c
ϭ000 (para) and 101 (ortho), in a 3:1 ratio. The jet-cooled
molecules are intersected 2 cm downstream with an infrared
laser beam ͑5 ns pulse duration, 0.25 cmϪ1 bandwidth͒,
where the partial H2O and total jet densities are 2ϫ1013 and
2ϫ1015 #/cm3, respectively. The IR laser can deliver up to
30 mJ/pulse to the jet region in a 5 mm2 beam area. For a
spectral pulse width of 0.25 cmϪ1, this is sufficient to drive
stronger OHϭ2 water overtone transitions nearly into satu-
v
ration, resulting in vibrationally excited water densities ap-
proaching 1012 #/cm3. The long path length nature and
slower 1/r density drop off of the slit expansion permits laser
excitation, photolysis, and detection to occur efficiently over
a much larger interaction region than would be accessible in
a pinhole supersonic expansion geometry.
The IR laser ͑pump͒ pulse is followed in time by a coun-
terpropagating ArF excimer laser ͑photolysis͒ pulse at 193
nm, delayed by approximately 20 ns from the pump. Typical
photolysis laser energy in the intersection region is 1 mJ/
pulse, with a 10 mm2 cross section in the jet intersection
area. Based on an estimated UV absorption cross section of
Ϸ1.8ϫ10Ϫ21 cm2/#18 for ground state water molecules, a
relative photodissociation probability of 2ϫ10Ϫ5 is pre-
dicted for IR unexcited species. Empirically, we observe that
The relevant spectroscopy for the laser induced fluores-
cence ͑LIF͒ detection of nascent OH product is as follows.
Each rovibrational level of the ground electronic state of
OH (2⌸) is split into two spin–orbit components, F1
ϵ2⌸3/2 and F2ϵ2⌸1/2 . Each spin–orbit level is further split
into two closely spaced ⌳-doublets (A and A ), which, in
Ј
Љ
the high-J limit, can be correlated with the unpaired electron
p-orbital lying in or perpendicular to the plane of rotation.
The energy levels are labeled by J ͑total angular momen-
tum͒, overall parity, N ͑total angular momentum excluding
spin͒, symmetry with respect to the reflection through the
plane of rotation (A ϵ⌸ϩ and A ϵ⌸Ϫ), and additionally
for the strongest H O transitions in OHϭ2, the photodisso-
v
2
ciation signal is increased by 102 –103 due to vibrationally
mediated enhancement at 193 nm. Both the vibrationally me-
diated and direct 193 nm photolysis signals scale linearly
with the excimer laser power, indicating that multiphoton
processes and saturation effects are of negligible importance
for the photolysis laser.
Ј
Љ
with spectroscopic e/f labels. For example, in this notation,
ϩ
3/2
2
⌸
(5) refers to a state with Nϭ5 in F1e manifold with A
Ј
reflection symmetry, with rotational branches of the
Fluorescence from the OH fragments is detected on the
A 2⌺( X 2⌸(
)
)
v
Љ
bands labeled using notation
v
Ј
A 2⌺ X 2⌸ ϭ1 0, 0 0 and 1 1 bands of OH. The
v
⌬NF F (N ), e.g., Q (3). To achieve high oversampling in
Љ
21
Ј Љ
probe radiation is produced by a frequency doubled dye laser
͑Ͻ0.1 cmϪ1 bandwidth, Rhodamine 590͒ pumped by a fre-
quency doubled Nd:YAG laser. The probe laser pulse ͑5 ns
duration͒ is delayed by Ϸ20 ns from the photolysis pulse. To
discriminate between vibrationally mediated and direct 193
nm photolysis events, the pump laser is operated at half the
repetition rate, with the laser off and on triggers subtracted to
generate a background-free IR-induced signal. To minimize
saturation effects, the UV probe laser power is maintained
the data set, all 12 rotational branches with the exception of
S21 are used in the data analysis, with each spin–orbit and
⌳-doublet level independently probed on at least two
branches.
III. RESULTS AND ANALYSIS
Figure 1 displays a sample action spectrum of jet-cooled
H2O between 7205 and 7310 cmϪ1, obtained by tuning the
probe laser to the top of the OH Q11(2) probe transition and
scanning the IR pump laser frequency. All features in the
spectrum result from vibrationally mediated dissociation of
quantum state-selected H2O in the jet-cooled expansion. The
lines in this spectral range are therefore due to the transitions
out of the lowest nuclear spin states (JK K ϭ000 and 101) of
well below 25 ␮J/pulse for ϭ0 0/1 1 bands ͑Ͻ90 ␮J/
v
pulse for the ϭ1 0 band͒ in an unfocused beam size of
v
30 mm2 area that overfills both pump and photolysis beams.
This results in partial saturation effects ͑Ͻ20%͒ for the
strongest OH lines, which are explicitly corrected by normal-
izing with respect to a reference spectrum of collisionally
thermalized OH. The thermalized OH sample is obtained un-
der identical probe laser conditions by photolyzing a flowing
1–2 Torr mixture of N2O, CH4 and Ar through the vacuum
chamber. Delays of Ͼ500 ␮s between the photolysis and
probe pulses translate into over 3000 hard-sphere collisions,
which ensures complete thermalization. By way of contrast,
densities and time delays selected for the actual photolysis
a
c
Ϫ
H2O, into rotational levels belonging to the
ϩ␯ in normal mode representation͒ and
͉
02
(ϵ␯
1
͘
͉
02 ϩ (ϵ2␯1) vi-
͘
3
brational modes. Throughout this paper, we will be using the
͉
mnϮk notation9 for H O vibrational states, where m and n
͘
2
represent local mode stretching quanta,19 and k ͑omitted for
kϭ0) represents the quanta in the HOH bend. The strongest
band, ͉
02 Ϫ, is of A-type ͑i.e., ⌬Kaϭ0, ⌬KcϭϮ1) and can
͘
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J. Chem. Phys., Vol. 119, No. 19, 15 November 2003
Dissociation dynamics of H2O
10161
FIG. 1. Sample action spectrum obtained by scanning the IR probe laser
FIG. 2. Sample 2⌺( ϭ1) 2⌸( ϭ0) LIF probe spectra of OH photofrag-
over H2O absorption lines within the OHϭ2 vibrational manifold. The
v
v
v
ϩ
2
probe laser is fixed on the ϭ1 0 Q11(2) line of OH. Transitions from
v
ments. Only the R11 and R21 branches are displayed, probing
⌸3/2(N) lev-
Ϫ
ϩ
JK ϭ000 and 101 states of H2O into rotational levels of ͉02 and ͉02
͘ ͘
els of OH. From top to bottom, the intermediate H2O state systematically
K
a
c
Ϫ
Ϫ
vibrations are observed in the displayed spectral range. The remaining weak
changes from ͑a͒
͉
02
͘
with no rotation, ͑b͒
͉
02
͘
with two quanta of
Ϫ
rotation, and, finally, ͑c͒ two quanta of both rotation and bending excitation.
Note the increase in photofragment rotational excitation, due to projection of
H2O bending and rotational motion onto the asymptotic states of OH.
transitions are due to incompletely cooled rotational levels of
͉02 state
͘
͑such as JK ϭ110). The relative intensities of peaks in the action spectrum
K
a
c
depend on: ͑i͒ relative populations of H2O states; ͑ii͒ state-to-state infrared
absorption cross sections; ͑iii͒ UV photolysis cross sections; ͑iv͒ photodis-
Ϫ
2
sociation quantum yields of OH into the
⌸3/2(Nϭ2) probe state.
particular, we find both qualitative successes and failures of
these spectator model predictions at such low polyad num-
bers.
therefore access 000 , 101 , 202 , and 220 rotational levels ͑the
By fixing the IR pump laser on a specific feature in the
H2O action spectrum and scanning the probe laser, a fluores-
cence excitation spectrum of the OH photofragments is ob-
tained. Figure 2 shows sample portions of such spectra ex-
220 101 transition lies outside the frequency range shown in
ϩ
Fig. 1͒. The corresponding
͉
02
͘
band is of B-type ͑i.e.,
⌬KaϭϮ1, ⌬KcϭϮ1); it is an order of magnitude weaker
and accesses a different subset of rotational levels: 111
000 , 210 101 , and 212 101 . The remaining weak lines
tending over the R11ϩR21 branches in the ϭ1 0 band of
v
ϩ
2
OH. Both branches probe the ⌸3/2(N) rotational manifold
in the action spectrum labeled with asterisks are straightfor-
Ϫ
of OH. The top panel corresponds to photodissociation via
wardly assigned to
͉
02
͘
transitions from incompletely
Ϫ
the rotationless
͉
02 000 intermediate state. The lower two
͘
cooled H2O 110 rotational state ͑e.g., the transition at Ϸ7300
cmϪ1 is 211 110). Such ‘‘hot’’ transitions can be purposely
enhanced by less efficient rotational cooling in pure He di-
luent versus Ar expansions. Approximately 300 cmϪ1 to the
Ϫ
panels, ͉02 202 and ͉
01Ϫ2 202 , correspond to progres-
͘ ͘
sively increasing amounts of rotational and bending excita-
tion, respectively. Note that the relative intensities of indi-
vidual OH rotational transitions are quite different for these
ϩ
Ϫ
red of these
͉
02
͘
and
͉
02
͘
bands, another two weak
three intermediate states of H2O. The ͉
01Ϫ2 2 state of
͘
02
groups of lines can be assigned to combination bands of
symmetric and asymmetric stretch fundamentals with two
quanta of bending excitation, ␯1ϩ2␯ and ␯3ϩ2␯ in nor-
H2O, which has both bending and rotational degrees excited,
clearly results in the most energetic distribution. To verify
that the populations are indeed nascent, the stagnation pres-
sure and the photolysis-probe delay have been increased by
more than an order of magnitude without affecting the rela-
tive intensities in the spectrum. This is fully consistent with
only Ϸ1% probability of hard-sphere collisions between the
OH photolysis fragment (␷OHϷ1.2ϫ105 cm/s) and the car-
rier gas expected for the present experimental conditions.
From probe scans extending over 11 branches character-
istic of the OH A 2⌺ X 2⌸ vibrational bands ͑all possible
branches except S21), the relative populations of all rota-
tional, spin–orbit, and ⌳-doublet states of OH can be ob-
tained for a given rovibrational intermediate state. Complete
2
2
mal mode notation, and referred to in local mode notation as
͉
01Ϫ2 and
in intensity by 400 compared to
͉
01ϩ2 . Finally, an extremely weak band ͑down
͘
͘
ϩ
͉
02 Ϫ) due to
͉
11 is ob-
͘
͘
served at around 7400 cmϪ1, corresponding to the overtone
of the asymmetric OH stretch (2 3), but still accessible with
v
quite respectable S/NϷ10 in the slit jet apparatus.
Access to this broad range of intermediate states permits
one to investigate photodissociation dynamics from a family
of energetically similar but physically quite distinct vibra-
tional intermediates. For example, one might expect photo-
dissociation of H2O via excited bending states (␯2Ͼ0) to
produce hotter OH rotational excitation.5,9 Similarly, the
ϩ
OH fluorescence excitation spectra have been recorded for
͉
11 state has its OH stretch excitation more equally dis-
͘
Ϫ
strong
͉
02
,
͉
02 ϩ, and
͉
01Ϫ2 intermediate vibrational
͘
͘
͘
tributed between the two equivalent OH bonds; based on the
levels of H2O, for each of several rotational states accessible
spectator model, therefore, one might predict significantly
out of JK K ϭ000 , 101 . Due to the 200-fold weaker20 IR
ϩ
more OH( ϭ1) vibrational excitation from
͉
11 photodis-
v
͘
a
c
02 Ϫ, only a limited set of popu-
ϩ
Ϫ
sociation compared to either
͉
02
͘
or
͉
02
͘
states. These
cross sections relative to ͉
lations in ⌸3/2 OH manifolds have been examined for exci-
͘
Ϯ
2
effects will be discussed in more detail in the following. In
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10162
J. Chem. Phys., Vol. 119, No. 19, 15 November 2003
Nizkorodov et al.
TABLE II. Percent OH rotational, spin–orbit, and lambda-doublet state populations from vibrationally mediated 193 nm photolysis of H2O. Uncertainties ͑in
parentheses͒ represent 2 standard deviations, evaluated from multiple independent data runs.
Ϫ
Ϫ
Ϫ
Ϫ
ϩ
ϩ
ϩ
͉
02
͉
02
͉
02
͉
02
͉
02
͉
02
͉
02
͉
01Ϫ2
000
͉
01Ϫ2
101
͉
01Ϫ2
202
͘
͘
͘
͘
͘
͘
͘
͘
͘
͘
OH state
N
000
101
202
220
110
111
212
ϩ
3/2
2
1
2
3
4
5
6
7
8
9
19.5͑6͒
2.82͑15͒
0.57͑5͒
0.88͑9͒
0.061͑9͒
0.12͑3͒
0.04͑1͒
11.2͑2͒
4.29͑35͒
9.0͑5͒
12.8͑16͒
3.5͑4͒
9.6͑11͒
2.8͑9͒
0.19͑5͒
0.37͑14͒
0.15͑8͒
0.05͑3͒
0.46͑14͒
12.7͑9͒
2.2͑5͒
0.71͑9͒
0.58͑2͒
0.08͑2͒
0.15͑3͒
6.93͑28͒ 15.0͑13͒
6.66͑31͒
0.63͑6͒
0.35͑4͒
2.44͑3͒
0.32͑4͒
1.48͑11͒
0.64͑8͒
0.15͑3͒
0.16͑5͒
0.021͑5͒
3.20͑12͒
2.13͑26͒
0.78͑6͒
1.17͑4͒
0.89͑14͒
0.61͑2͒
0.44͑2͒
0.19͑2͒
1.47͑29͒
3.87͑12͒
1.76͑3͒
0.98͑4͒
2.15͑33͒
0.78͑9͒
0.77͑6͒
0.48͑2͒
0.20͑5͒
0.20͑2͒
⌸
6.48͑29͒
1.13͑33͒
0.71͑4͒
0.27͑3͒
0.074͑10͒
0.069͑8͒
7.7͑9͒
2.45͑10͒
3.5͑4͒
2.58͑14͒
0.61͑4͒
0.61͑2͒
0.072͑2͒
0.072͑7͒
0.032͑5͒
2.26͑8͒
0.74͑5͒
0.48͑2͒
0.22͑3͒
1.03͑14͒
0.29͑7͒
0.28͑3͒
10
Ϫ
3/2
2
1
2
3
4
5
6
7
8
9
2.01͑19͒
17.3͑4͒
11.0͑4͒
1.65͑7͒
5.0͑4͒
0.30͑2͒
0.93͑13͒
0.34͑3͒
0.047͑9͒
0.064͑4͒
6.94͑34͒
11.4͑1͒
11.2͑3͒
3.84͑17͒
4.64͑18͒
1.05͑25͒
0.73͑4͒
0.47͑3͒
0.061͑5͒
0.041͑5͒
12.6͑9͒
6.63͑36͒
10.6͑6͒
7.1͑6͒
2.17͑11͒
1.80͑25͒
0.61͑3͒
0.62͑3͒
0.20͑3͒
0.046͑6͒
0.035͑5͒
5.9͑5͒
15.4͑3͒
10.2͑11͒
4.3͑1͒
21.3͑19͒
4.5͑6͒
10.7͑23͒
7.0͑10͒
1.80͑11͒
0.81͑28͒
0.095͑10͒
0.77͑17͒
0.14͑3͒
11.0͑5͒
9.7͑17͒
6.9͑19͒
6.4͑13͒
2.52͑6͒
0.78͑45͒
0.78͑4͒
0.61͑17͒
0.32͑9͒
2.4͑6͒
14.3͑8͒
6.4͑5͒
6.7͑6͒
3.90͑7͒
0.46͑6͒
0.59͑13͒
5.6͑7͒
1.99͑15͒
1.65͑16͒
17.7͑13͒
1.48͑40͒
3.03͑8͒
2.14͑18͒
1.98͑3͒
4.89͑40͒
11.2͑6͒
8.30͑8͒
7.5͑8͒
6.69͑43͒
1.3͑7͒
1.28͑21͒
4.0͑10͒
0.95͑6͒
1.86͑42͒
6.6͑7͒
4.19͑8͒
11.8͑5͒
5.17͑20͒
6.20͑30͒
2.85͑46͒
0.35͑8͒
⌸
5.9͑4͒
0.47͑9͒
0.74͑2͒
0.21͑9͒
0.07͑2͒
0.047͑8͒
2.10͑37͒ 10.5͑13͒
0.19͑10͒
0.55͑20͒
0.09͑3͒
6.1͑16͒
0.78͑5͒
1.23͑9͒
10
11
Ϫ
1/2
2
1
2
3
4
5
6
7
8
9
0.76͑7͒
10.7͑8͒
5.83͑26͒
1.18͑4͒
3.34͑33͒
0.60͑7͒
0.63͑7͒
0.31͑8͒
0.038͑2͒
0.037͑4͒
3.23͑23͒
7.95͑60͒
7.71͑12͒
2.32͑16͒
3.00͑12͒
1.25͑10͒
0.55͑2͒
0.43͑3͒
0.065͑3͒
0.055͑4͒
5.6͑5͒
3.94͑20͒
6.3͑5͒
0.77͑14͒
5.4͑7͒
3.80͑15͒
2.63͑22͒
2.6͑4͒
0.44͑5͒
0.44͑5͒
0.24͑9͒
0.068͑5͒
0.074͑5͒
8.6͑5͒
1.92͑24͒
6.5͑8͒
4.01͑30͒
0.72͑5͒
2.1͑5͒
0.17͑4͒
0.54͑29͒
0.11͑4͒
7.2͑19͒
7.3͑14͒
5.8͑5͒
6.11͑31͒
1.51͑36͒
1.81͑4͒
0.60͑8͒
0.50͑7͒
0.23͑5͒
1.45͑16͒
10.6͑21͒
3.8͑6͒
4.2͑6͒
2.4͑5͒
0.98͑11͒
1.67͑33͒
0.20͑4͒
0.48͑15͒
0.18͑6͒
2.6͑8͒
1.29͑19͒
1.46͑2͒
1.25͑6͒
4.26͑39͒
7.4͑5͒
1.85͑36͒
0.85͑3͒
1.32͑1͒
5.3͑6͒
2.1͑8͒
9.1͑8͒
3.83͑4͒
5.2͑5͒
3.1͑9͒
0.48͑2͒
0.75͑7͒
0.13͑5͒
⌸
0.89͑20͒
0.88͑11͒
9.7͑12͒
1.40͑11͒
9.3͑27͒
3.83͑26͒
0.39͑7͒
1.6͑6͒
5.0͑5͒
1.59͑11͒
2.42͑6͒
0.47͑4͒
0.58͑5͒
0.17͑1͒
0.042͑7͒
6.6͑5͒
4.92͑19͒
4.9͑20͒
0.82͑19͒
1.18͑37͒
0.25͑8͒
10
11
12
ϩ
1/2
2
1
2
3
4
5
6
7
8
9
9.25͑41͒
1.45͑14͒
1.44͑21͒
1.21͑15͒
0.18͑2͒
0.26͑3͒
0.077͑19͒
0.029͑5͒
6.1͑4͒
2.33͑24͒
7.5͑7͒
2.11͑29͒
1.16͑15͒
0.75͑5͒
0.15͑1͒
0.18͑2͒
0.058͑11͒
0.025͑5͒
0.017͑5͒
3.35͑19͒
1.52͑11͒
3.28͑13͒
2.03͑26͒
0.25͑7͒
0.32͑4͒
0.12͑1͒
0.059͑13͒
0.04͑1͒
0.40͑19͒
7.4͑18͒
1.30͑26͒
1.22͑36͒
0.71͑16͒
0.16͑6͒
0.27͑2͒
3.28͑5͒
5.08͑20͒
1.85͑5͒
0.79͑6͒
0.59͑20͒
7.4͑13͒
1.61͑10͒
3.4͑12͒
0.95͑11͒
0.52͑13͒
0.38͑9͒
0.11͑5͒
0.10͑5͒
4.3͑8͒
2.44͑17͒
1.92͑2͒
0.40͑11͒
0.60͑6͒
0.68͑5͒
0.70͑4͒
0.60͑7͒
0.48͑8͒
0.22͑2͒
1.2͑7͒
⌸
3.97͑14͒
1.51͑9͒
1.02͑8͒
0.29͑2͒
0.25͑1͒
0.095͑6͒
0.0087͑5͒
0.39͑3͒
0.56͑21͒
1.11͑4͒
0.26͑5͒
1.03͑24͒
0.32͑5͒
0.45͑8͒
0.34͑5͒
2.30͑24͒
0.92͑6͒
0.66͑19͒
1.47͑20͒
0.77͑2͒
1.13͑15͒
0.57͑17͒
0.32͑2͒
0.073͑6͒
10
ϩ
tation into
͉
11 state. To enhance the statistics, each spec-
resolution of the probe laser reduce such overlaps to a mini-
mum. The linewidths in the recorded spectra are limited by
the Doppler broadening with full width at half maximum
Ϸ0.3 cmϪ1, i.e., consistent with the expected OH transla-
͘
trum is collected two to five times and analyzed
independently. Lines in all spectra are integrated and the re-
sulting areas least-square fitted using OH populations as ad-
justable parameters. The required individual rotational tran-
sition strengths are taken from Chidsey and Crosley
database21 and small saturation correction factors are explic-
itly determined from the reference room-temperature OH
spectra on a line-by-line basis. Since all populations are sta-
tistically quite overdetermined ͑each level is probed by up to
three independent branches͒, the least-squares fitting is ex-
tremely robust. Although accidental line overlaps do occur
͓e.g., R22(3) line is blended with the Q11(1)ϩQ21(1) dou-
tional energy release. The fitted populations for OH( ϭ0)
v
are summarized in Table II, wherein the results and uncer-
tainties are obtained as a weighted average of populations
from several independent data runs. OH( ϭ1) populations
v
are not listed because they were recorded only for a limited
subset of states within 2⌸3Ϯ/2 OH manifolds to verify that OH
rotational and vibrational distributions are decoupled form
each other ͑see the following͒.
Of particular interest in this work is the fractional
blet in the ϭ1 0 band͔, the low power and relatively high
branching into OH( ϭ1) and OH( ϭ0) products as a func-
v v
v
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J. Chem. Phys., Vol. 119, No. 19, 15 November 2003
Dissociation dynamics of H2O
10163
FIG. 4. Effect of initial H2O(͉
02 Ϫ) rotation on the observed OH distribu-
͘
tions. The distributions are plotted as a function of N for each spin–orbit and
⌳-doublet rotational manifolds. The oscillations of populations vs N are
pronounced even on the logarithmic scale. Notice that there is little differ-
2
Ϯ
3/2
2
ence in the populations of the two spin–orbit components (2⌸1/2 vs
⌸
)
3/2
FIG. 3. A subset of relative OH( ϭ1) and OH( ϭ0) populations in
⌸
v
v
ϩ
ϩ
but an appreciable difference between the A and A ⌳-doublets. The rota-
Ј Љ
manifolds resulting from UV photolysis of ͉02 110 and ͉11 110 states of
͘ ͘
tional state of H2O(͉
02 Ϫ) changes from 000 to 101 to 202 from left to right,
͘
H2O. Strong similarities in the observed distributions support the assump-
tion of decoupling between vibrational and rotational degrees of freedom in
OH photofragments ͑this assumption is used to derive relative final vibra-
tional populations of OH listed in Table I͒.
which has the effect of slightly increasing the average rotational energy of
OH fragments.
tion of H2O rovibrational intermediate states, which are ex-
amined in a separate experiment by comparing repeated
a function of rotational state. Such oscillations in the nascent
OH distributions are also quite evident in the present study
Ϫ
2
scans over the Q11(3) line, which probes the ⌸3/2(3) level
in OH, for the ϭ1 1 and ϭ0 0 subbands, for a series
of the ϭ2 polyad ͑Table II͒. By way of example, Fig. 4
v
v
v
displays experimental OH populations versus N for each
spin–orbit and ⌳-doublet manifolds for photodissociation of
of intermediate states and range of IR pump powers. Relative
H2O(͉
02 Ϫ) in a series of intermediate rotational states,
transition probabilities for these ϭ1 1 and ϭ0 0 sub-
v
v
͘
bands are taken from Ref. 21. This ratio could in principle be
which indicate clear oscillations even on a logarithmic scale.
Interestingly, these trends are remarkably similar for the two
further corrected for fractional ϭ1 versus ϭ0 population
v
v
Ϫ
2
2
spin–orbit components (2⌸1/2 and ⌸3/2) for each lambda-
in the initial ⌸3/2 manifold level. In practice, however, the
rotational, spin–orbit, and lambda-doublet distributions ap-
doublet manifold, whereas appreciably larger differences are
pear to be strongly uncoupled from the OH( ) vibrational
v
apparent between the A versus A ⌳ doublets. It is worth
Ј
Љ
state, despite a clear sensitivity to different intermediate ro-
tational states. For example, Fig. 3 shows a comparison be-
noting that the population data for different spin–orbit mani-
folds are obtained from entirely independent rotational
branches; the systematic agreement between 2⌸1/2 and 2⌸3/2
traces, therefore, provides additional support for the high
S/N and reproducibility of our data.
tween relative OH( ϭ1) and OH( ϭ0) populations in
v
v
Ϯ
3/2
2
ϩ
⌸
manifolds resulting from UV photolysis of ͉02 110
and ͉11 110 states of H2O. The lambda-doublet and rota-
͘
͘
ϩ
tional populations are the same within the experimental pre-
cision. Therefore, the nascent vibrational populations of OH
integrated over each manifold can be reliably estimated from
The
origin
of
these
oscillations
in
OH
population1,3,5,8,10,12,22 has been thoroughly discussed, and it
arises from quantum mechanical interference between the
various OH outgoing spin–orbit and lambda-doublet product
channels. As a simple zeroth-order prediction, this would
suggest a much smoother distribution when summed over all
interfering channels. This prediction is tested in Fig. 5, which
Ϫ
2
comparison of a single rotational line in the ⌸3/2 manifold
for ϭ1 1 and ϭ0 0 OH transitions ͑as long as the
v
v
same rotational state of H2O is photolyzed͒. The results of
these measurements are listed in Table I, put explicitly into
context with OH( ϭ1)/OH( ϭ0) branching ratios ob-
v
v
displays OH photofragment distributions resulting from pho-
Ϫ
tained from all vibrationally mediated dissociation studies to
date.
todissociation of H2O via
͉
02 JK K ϭ202 , nicely confirm-
͘
a
c
ing the interference nature of the photodissociation process.
Specifically, while populations within a given individual
spin–orbit/⌳-doublet manifold ͓Fig. 5͑a͔͒ are highly non-
monotonic functions of JOH , the sum over these manifolds
͓Fig. 5͑b͔͒ is much more consistent with a smooth rotational
distribution, arising from largely complete cancellation be-
tween the ⌳ϩ and ⌳Ϫ doublets contributions. This behavior
is echoed in distributions for each of the intermediate rota-
IV. DISCUSSION
A. Nascent OH rotational populations
A particularly striking observation from previous vibra-
tionally mediated dissociation studies5–7,9,10 has been the
presence of strong oscillations in OH nascent populations as
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10164
J. Chem. Phys., Vol. 119, No. 19, 15 November 2003
Nizkorodov et al.
FIG. 6. Populations of 2⌸3ϩ/2 ͑open circles͒ and 2⌸3Ϫ/2 ͑closed squares͒ states
of OH in photodissociation of different vibrational states ( OHϭ1 to 5͒ of
v
H2O in JK ϭ000 . Although the photodissociation is probed at very dif-
K
a
c
ferent excess energies ͑see Table I͒, the gross features of the rotational
distributions are strikingly similar, due to the good separability of vibra-
tional and rotational time-scales for the motion.
FIG. 5. OH photofragment distributions resulting from photodissociation of
H2O(
02 Ϫ) in 202 rotational state plotted as a function of JOH . While the
͉
͘
populations within the individual spin–orbit and ⌳-doublet manifolds ͑top
panel͒ strongly oscillate with JOH , the total population ͑bottom panel͒ is
much smoother reflecting the interference nature of the photodissociation.
states, with the latter clearly resulting in a much more rota-
tionally energetic OH distribution. However, in spite of large
differences in populations, a more detailed inspection reveals
clear similarities in the oscillatory structure. For example,
tional states of water from this study, as can be verified from
a detailed investigation of Table II.
2
Ϫ
the ⌸Ϫ distributions for 01Ϫ2 0 interme-
͉02 000 and ͉
͘ ͘
00
diate states ͑Fig. 7, lower panels͒ exhibit local maxima ͑at
Nϭ2, 5, 7͒ and minima ͑at Nϭ1, 4, 6, 9͒, despite quite clear
differences in the overall smoother trend. Such behavior is in
fact consistent with a Franck–Condon picture, reflecting the
approximate separability of the rotational-bending wave
function for the H2O intermediate state. Specifically, the ro-
tational wave function is predominantly responsible for the
fast oscillations, while the bending wave function dictates
the overall shape of the OH distribution.
The theoretical framework developed by Balint-Kurti,
Schinke, and others1,3,5,8,10,12,22 to explain such trends is that
the OH nascent state distribution reflects a Franck–Condon-
type projection of the intermediate state wave function on the
upper potential surface, followed by wave packet evolution
in the exit channel out toward asymptotic products. Based on
this picture, one would expect a relatively strong dependence
of OH( ) populations on H O intermediate vibrational state,
v
2
and, conversely, OH rotational state populations relatively
insensitive to intermediate state vibrations of the same local
mode character. Striking support for the former assertion is
evident in Fig. 6, which shows nascent populations for the
Ϯ
3/2
2
⌸
manifolds, obtained for a progression of increasingly
OH stretch excited polyad states ͑e.g.,
of JK K ϭ000 . Although the excess energies for the H2O
͉
0n Ϫ, nϭ1–5) out
͘
a
c
states in Fig. 6 vary by more than a factor of 2 ͑Table I͒, the
N dependence of the distributions within a given spin–orbit
and ⌳-doublet manifold remains nearly identical. Photodis-
sociation of H2O from a series of vibrational states with
nonzero angular momenta yields results that follow similar
trends, although subtle differences between the OH distribu-
tions start to appear already at Jϭ1.10
In the context of such a Franck–Condon picture, one
would expect overall rotation of the H2O prior to photodis-
sociation to result in warmer OH rotational state distribu-
tions, as is indeed clearly evident in Fig. 4. Vibrational pre-
excitation of HOH bending states would imply even stronger
overlap on final OH rotation wave functions, and thus a
Franck–Condon picture for photolysis would predict a much
hotter rotational distribution. This prediction is directly con-
FIG. 7. Effect of H2O bending excitation on the OH rotational distribution.
The distributions are plotted as a function of N for each spin–orbit and
⌳-doublet rotational manifold. The panels on the left and right show data for
Ϫ
͉
02 and
͉
01Ϫ2 , respectively. Although the bending excitation of H O
͘
͘
2
significantly increases the OH rotation, the nonmonotonic structure on top of
the distributions is quite similar. The solid curves in the bottom panels
correspond to the Franck–Condon projections of the H2O bending wave
functions on the OH rotational states ͑Ref. 9͒.
firmed in Fig. 7, which compares rotational populations re-
Ϫ
sulting from the photolysis of H2O in
͉
02
͘
and ͉
01Ϫ2
͘
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J. Chem. Phys., Vol. 119, No. 19, 15 November 2003
Dissociation dynamics of H2O
10165
FIG. 9. Relative populations of OH ⌳-doublets in photodissociation of
H2O. The top three panels are for 000 , 101 , and 202 rotational states of
H2O(
H2O(
⌸
͉
͉
02 Ϫ) and the bottom panels are for the same rotational states of
͘
01Ϫ2 ).
Closed circles and open triangles represent
͘
Ϫ
Ϫ
3/2(N)/2⌸3ϩ/2(N) and
⌸
1/2(N)/2⌸1ϩ/2(N), respectively. The ratios are
2
2
quite similar for the two vibrational states but are sensitive to H2O angular
momentum. Faster water rotation results in a smaller difference between the
positive and negative OH ⌳-doublets.
where the N/(Nϩ1) coefficient includes the 2Jϩ1
FIG. 8. Relative populations of OH spin–orbit states in photodissociation of
space
degeneracy.
In
the
(N) / ⌸ (N) N/(Nϩ1), should eventually reach
͔ ͓
1/2
statistical
regime,
H2O(
͉
02 Ϫ). Triangles and closed circles represent the ratios
2
2
͘
*
͔
⌸
͓
3/2
2
2
*
⌸
(N) /
͔ ͓
⌸
(N) N/(Nϩ1) for A and A ⌳-doublets, respectively.
͓
͔
Љ
Ј
3/2
1/2
unity for high N. Indeed, this statistical limit is what was
The N/(Nϩ1) multiplier accounts for the 2Jϩ1 space degeneracy; the
high-temperature statistical limit would correspond to N/(Nϩ1)ϭ1.
observed in early 157 nm photolysis of room temperature
H2O11 as well as 193 nm photolysis of H2O in 000
͉01
͘
Ϫ
state.6,8 However, as shown in Fig. 8, this is not in good
agreement with the current 193 nm photolysis study of H2O
More quantitatively, one can model this second contri-
bution by projecting the HOH bending wave function onto
the asymptotic OH rotational states.1,5,9 This leads to a dis-
tribution proportional to
in the ϭ2 polyad, where sizable N-dependent deviations
v
from unity are evident out at high rotational levels with high
S/N. Supporting results were also observed in previous pho-
todissociation studies of H O in the OHϭ3 polyad, which
v
2
␲
j
revealed sizable deviations from the statistical limit.10 At the
2
k
sin2 j␥ ϩ Ϫ1͒
␾
,
͑
ͩ
ͪ ͩ
ͪ
e
k
¯
m␻
HOH
4
present time, there is no theoretical understanding for the
predominance of ⌸3/2 states in the asymmetric (A ) mani-
Љ
where ␾ is the HOH bending wave function for k quanta of
excitation, j is the rotational angular momentum of OH frag-
k
fold and ⌸1/2 states in the symmetric (A ) manifold. In fact,
Ј
the data might suggest a trend away from statistical behavior
in nascent spin–orbit distributions as a function of H2O
polyad number, though this issue awaits more detailed theo-
retical investigation.
ment, ␥e is the equilibrium bond angle in H2O, ␻
is
HOH
¯
harmonic frequency for the bending motion, and m is the
effective reduced mass for the bending motion.9 Figure 7
shows the nonoscillatory part of the Franck–Condon distri-
bution for kϭ2 compared with the experimental data ob-
The ⌳-doublet ratio of asymmetric (A ) to symmetric
Љ
tained for the ͉
01Ϫ2 state of H O. The data are in excellent
͘
2
(A ) OH product states has been of special dynamical inter-
Ј
est. In the limit of zero spin–orbit interaction ͑which is valid
for sufficiently high OH rotational levels͒, the electronic
transition symmetry in H2O should strongly favor production
agreement with this simple model, especially in reproducing
the slow nodal structure around Nϭ3 and a secondary maxi-
mum at Nϭ7.
of
A
states of OH.
͔ ͓
A
rapid increase in the
Љ
Љ
OH(A ) / OH(A ) ratio with N has indeed been observed
͓
͔
Ј
B. Nascent OH spin–orbit and lambda-doublet
distributions
in several previous studies of photodissociation of H2O and
its general shape is now reasonably well understood, at least
in the absence of the parent rotation.11,16 The ⌳-doublet ra-
As shown above, spin–orbit and lambda-doublet states
have already proven important in generating quantum inter-
ference effects between outgoing exit channels. However,
they also provide additional dynamical information on the
photolysis event. Figure 8 shows the population ratio of the
tios from the present study for two intermediate vibrational
Ϫ
states (
͉
02
͘
and ͉
01Ϫ2 ) and several rotational states of
͘
H2O are shown in Fig. 9 ͑note the logarithmic axis͒. In in-
teresting contrast to the OH rotational energy distribution,
which strongly depends on the parent bending state, the
2
2
*
(N) / ⌸ (N) N/(N
͔ ͓ ͔
1/2
two spin–orbit components,
⌸
͓
3/2
ϩ1), and its variation with N and ⌳-doublet symmetry,
OH(A ) / OH(A ) ratio appears to be remarkably insen-
͔ ͓
͓
͔
Ј
Љ
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10166
J. Chem. Phys., Vol. 119, No. 19, 15 November 2003
Nizkorodov et al.
ϩ
͉
02 states produces substantially more vibrational excita-
͘
sitive to the vibrational state of H2O. The magnitudes and
Ϫ
tion in OH compared to that of the ungerade
Specifically, one finds significant levels of vibrational exci-
tation from both
͉02 state.
͘
phases of oscillations in this ratio are now in very close
Ϫ
agreement for
͉
02 and
͉
01Ϫ2 , as well as for all pairs of
͘
͘
ϩ
ϩ
͉
02
͘
and
͉
11
͘
,
with OH(
͓ v
H2O rotational states considered. This is again consistent
with a simple Franck–Condon separability of bending and
rotational wave functions; the bending wave function influ-
ences only the N dependent features of the OH distribution
and not preferential formation of specific parity levels.
As a final note, these results make for interesting com-
parison with previous 157 nm photolysis studies of room
temperature H2O,11 which exhibit a surprising absence of
any ⌳-doublet inversion ratio. It has been previously argued
that this ‘‘smearing out’’ of the ⌳-doublet population inver-
sion for room temperature samples may be the result of or-
bital mixing caused preferentially by out-of-plane rotational
motion of H2O.11,16 Indeed, the data in Fig. 9 show clear
ϭ0) : OH( ϭ1) ϭ0.63(3):0.37(3) and 0.47͑5͒:0.53͑5͒,
͔ ͓
respectively; these results are in clear contrast to nearly
quantitative 98% yield of OH( ϭ0) from
02 Ϫ. This ob-
v
͔
͉
v
͘
servation is consistent with time-dependent wave-packet
simulations,23,24 which predict significant differences in the
photodissociation dynamics of ungerade and gerade states of
H2O. Specifically, wave packets prepared from ungerade
states are predicted to evolve initially along the asymmetric
stretch coordinate, whereas gerade state wave packets have
an appreciable initial component along the symmetric
stretch. This difference shows up as a 19 fs recurrence in the
wave-packet autocorrelation function, which is found for all
gerade states but does not occur for ungerade ones.24 Physi-
cally, displacement on the upper surface along the symmetric
stretching coordinate corresponds to motion perpendicular to
the minimum energy path. Such motion would predict en-
hanced vibrational excitation of the surviving OH bond, in
good agreement with the current experimental observations.
A second, more subtle observation is that the OH vibra-
⌳-doublet inversion for the series of JK K ϭ000 , 101
,
a
c
2
02 H2O rotational states, which would correspond classi-
cally to increasing in-plane versus out-of-plane rotational
versus motion. However, close examination of Table II indi-
cates that similar ⌳-doublet inversion behavior is observed
for photolysis from both 202 and 220 levels ͑i.e., the two
classical extremes of in-plane and out-of-plane rotational
motion͒, suggesting that such an orbital mixing effect is not
important, at least for small angular momentum values.
ϩ
Ϫ
tional distributions from
͉
11
͘
and
͉
02
͘
cannot be fully
explained by adiabatic conservation of the vibrational nodal
pattern in the undissociated H2O bond. Indeed, this is the
essence of the simple spectator model, which worked so
Ϫ
Ϫ
C. OH vibrational distributions
beautifully for photodissociation of the higher
͉
04
͘
,
͉
13
͘
,
03 Ϫ, and 12 states of H2O.1,7,10 Such a model assumes
͉
Ϫ
͉
͘ ͘
A particularly relevant aspect of this study is the ability
to investigate vibrational state symmetry effects on H2O
photodissociation dynamics, as well as the potential break-
down of the spectator model in vibrationally mediated pho-
tolysis events. First of all, as noted in Sec. II, previous stud-
ies have focused on a subset of high overtone vibrations,
specifically antisymmetric ͑i.e., ungerade͒ states and typi-
cally with strongly local mode character due to anharmonic
that the region of the excited PES sampled by the photolysis
is characterized by weak interactions between the two OH
bonds. Although the excess energies utilized in the current
study fall in the expected range of validity of the spectator
model,24 the level of agreement with observed product OH
vibrational excitation is clearly mixed. On one hand, the
fractional yield of OH( ϭ1) from dissociation of
v
͉
͉
11 ϩ(53Ϯ5%) is significantly higher than that from
͘
͘
limitations on vibrational overtone intensities. At the
vOH
02 Ϫ(2Ϯ1%), in qualitative agreement with expectation.
ϭ2 overtone level, these anharmonic effects are less impor-
However, there is only a minimal difference ͑Ϸ1.4-fold͒ be-
tant, yielding sufficient oscillator strength for probing pho-
ϩ
tween OH( ϭ1) / OH( ϭ0) product ratios resulting
͓
v
͔ ͓
v
͔
tolysis events from each member of the polyad,
͉
02
,
͘
ϩ
ϩ
͉
11 ϩ, and
͉
02 Ϫ, including both gerade and ungerade
from photolysis of
contrast with the
exhibited an order of magnitude more OH( ϭ1) than
͉11 and ͉02 states. This is in striking
13 state behavior, which at 218.5 nm
͘
͘ ͘
͘
͘
v
Ϫ
͉
states. Second, OHϭ2 is the lowest polyad with sufficient
v
rearrangements of vibrational quanta to distinguish between
cleaved and surviving bonds in the photolyzed H2O. This
offers a unique opportunity to test the spectator paradigm
down at low levels of vibrational excitation. It is worth not-
ing that predictive understanding of such effects at low vi-
brational quanta on chemical reaction dynamics is particu-
larly relevant, for example, in thermal models of combustion
phenomena. Finally, despite the 50% weaker initial vibra-
tional excitation in the H2O intermediate state, 193 nm pho-
͉
04 Ϫ.7 Even more to the point, there is an order of magni-
͘
tude difference in OH( ϭ1,0) photolysis behavior between
v
ϩ
Ϫ
͉
02
and
͉
02
͘
states, which is in clear contradiction to
͘
predictions from the spectator model.
To help identify the physical origin of these discrepan-
cies, we have explicitly calculated two-dimensional ͑2D͒
wave functions for the bound and continuum OH (R1 ,R2)
stretching states of H2O. Specifically, the ground state wave
functions are obtained from matrix diagonalization of a 2D
distributed Gaussian basis set on the Sorbie–Murrell poten-
tial energy surface,25 with the HOH bend angle fixed at
104.5° and eigenvalues converged by successively increasing
basis set size. Similarly, the excited state wave functions are
obtained by matrix diagonalization on the Staemmler–Palma
potential surface,26 for a uniformly distributed grid of Gauss-
ian basis functions over the Franck–Condon region and ex-
ϩ
Ϫ
tolysis of these first overtone
͉
02
, ͉ ͉02 levels
11 ϩ, and
͘ ͘ ͘
sample comparable upper state energies as previous studies
of ͉04 and ͉
13 states by Vanderwal et al.7 As a result,
͘ ͘
Ϫ
Ϫ
this allows the present study to focus selectively on the in-
fluence of symmetry and intramolecular nodal distribution on
the photolysis dynamics.
Inspection of Table I reveals two important facts. First
ϩ
observation is that photodissociation of gerade
͉
11
͘
and
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J. Chem. Phys., Vol. 119, No. 19, 15 November 2003
Dissociation dynamics of H2O
10167
correlating with OH( ϭ1) overlap well with the outer two
v
ϩ
lobes for the ͉02 state. Conversely, the upper state wave
͘
function correlating with OH( ϭ0) has only one lobe in the
v
symmetric stretch direction, and furthermore, by virtue of
lower asymptotic OH stretch energy, reaches further inward
along the symmetric stretch coordinate. This moves the
single upper state lobe over the oppositely signed lower state
lobes of
Franck–Condon overlap. The result is a net decrease and
increase in photolysis efficiency for formation of OH(
͉
02 ϩ, yielding destructive interference of the
͘
v
ϭ0) and OH( ϭ1), respectively, as experimentally ob-
v
ϩ
served for the ͉02 lower state. The situation for the pho-
͘
Ϫ
tolysis of
lobes of the
the upper state wave function correlating with OH( ϭ0).
͉
02
is precisely reversed, with the outer two
͘
Ϫ
͉
02 wave function now overlapping well with
͘
v
Ϫ
Additionally, ͉02 overlap with the upper state wave func-
͘
tion correlating with OH( ϭ1) is much less efficient, due
v
both to a node in the asymmetric stretch direction and a
larger displacement between lobe centers in the upper state.
The net effect is now an increase and decrease in photolysis
efficiency for formation of OH( ϭ0) and OH( ϭ1), re-
v
v
spectively, again in good agreement with experimental obser-
Ϫ
ϩ
and ͉
02 Ϫ) and excited state symmetric/
͘
vation for the ͉02 lower state.
͘
FIG. 10. Ground state (
͉
02
͘
This qualitative picture suggests that the success of the
spectator model at higher quanta of excitation arises from
anharmonic elongation of the lower state eigenfunctions
along the dissociation coordinate. Since both lower and up-
per state potential surfaces have overlapping wells in the
spectator OH stretch, this leads to relatively tight ͑i.e., par-
allel͒ registry of the upper and lower wave functions on the
way toward dissociation. The spectator model then follows
immediately from an effective one-dimensional Franck–
Condon overlap in these elongated geometries, which is
therefore quasidiagonal in vibrational quanta along the spec-
tator bond. On the other hand, these elongation effects be-
come less important for lower quanta of excitation, and par-
ticularly so for the pure symmetric stretch overtone, i.e.,
antisymmetric wave functions correlating with OH( ϭ0,1) and accessed
via excitation near 193 nm. Bold lines surround the energetically accessible
v
Franck–Condon region for 193 nm excitation out of OHϭ2 H2O states.
v
Contours corresponding to positive and negative wave function values are
shown in solid and dashed lines, respectively.
tending (rmaxϷ10 a0) out into the entrance ͑HOϩH͒ and exit
͑HϩOH͒ channels. Out at rmax , the upper state eigenfunc-
tions approximate the behavior of true continuum wave func-
tions, whose asymptotic OH( ) state can be readily identi-
v
fied by the nodal pattern. Such variational matrix procedures
necessarily yield a discrete representation for the upper
states, which makes it challenging to obtain quantitative
Franck–Condon factors for transitions from symmetric and
asymmetric states of water molecule at exactly the same en-
ergy. However, this does permit estimation of Franck–
Condon factors appropriate to a finite bin of photolysis en-
ergies, and for wave functions correlating asymptotically
͉
02 ϩ. In this regime, Franck–Condon factors depend in de-
͘
tail on the energy dependent shift in registry between the
upper and lower state wave functions along the symmetric
stretch coordinate, which, as evidenced in this work, can lead
to dramatic deviations from simple spectator model predic-
tions.
with a specified OH( ). In particular, this provides an excel-
v
lent qualitative basis for interpretation of experimental obser-
An alternative interpretation of such nonspectator model
predictions arises from the degree of localization in the H2O
vibrational modes. According to the calculations of Lawton
and Child,27 the stretching vibrations in H2O are represented
vations, as demonstrated in the following.
ϩ
The resulting lower state wave functions for
͉
02 and
͘
Ϫ
͉
02 states of H2O are shown in Fig. 10. Also shown are
͘
sample symmetric and antisymmetric upper state wave func-
tions correlating asymptotically with OH( ϭ0) and OH(
ϭ1), respectively. As anticipated, the upper state wave func-
with the local mode basis set, ␺(Ϯ)ϭ2Ϫ1/2 ␹ (R )␹ (R )
͓
v
v
m
1
n
2
mn
Ϯ␹ (R )␹ (R ) , where ␹ (R) are Morse eigenfunctions
͔
n
1
m
2
n
for the individual OH bonds in H2O. Most relevantly, Law-
tions are confined to the saddle region on the upper PES
ton and Child showed that the H2O vibrational Hamiltonian
energetically accessible via 193 nm excitation from
vOH
(Ϯ)
can be highly diagonal in this ␺
basis, at least for high
ϭ2; for the purposes of visualization, this area is enclosed in
Fig. 10 by bold lines. From the Franck–Condon principle,
the photodissociation dynamics will be dominated by wave
function overlap in this classically accessible region.
mn
Ϫ
Ϫ
vibrational levels. For example, H2O states
͉
04
,
͉
13
,
͘
͘
(Ϫ) (94.9%),
Ϫ
and
͉
02
͘
are heavily dominated by
␺
04
␺
(Ϫ) (94.7%), and ␺(Ϫ) (99.9%), respectively ͑percent val-
13
02
Figure 10 offers a good zeroth-order picture for inter-
preting the observed trends. Specifically, due to a strong out-
ward shift of the wave function along the symmetric stretch
direction, the two lobes of the upper state wave function
ues in parentheses represent the squares of the coefficients in
front of the respective basis functions͒. In fact, the majority
of ungerade H2O vibrational states can be well described by
just one local mode basis function with only minor contami-
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10168
J. Chem. Phys., Vol. 119, No. 19, 15 November 2003
Nizkorodov et al.
nation from other members of the basis. On the contrary,
ordinate for gerade state photolysis. This results in a greater
departure from the minimum energy photolysis path and
therefore enhanced vibrational excitation in the asympototic
OH.
ϩ
gerade states (͉02 and ͉
11 ϩ), although still dominated by
͘ ͘
the respective local mode basis functions, tend to have much
smaller degree of localization ͑79.7% and 79.6%,
respectively͒.27 The most important mixing terms have the
ACKNOWLEDGMENTS
form nϮ1,mϯ1͉H͉n,m reflecting interactions between
͘
͗
basis states differing by one vibrational quantum within the
same polyad. Such increased coupling between the two
bonds can therefore lead to one quantum changes in the vi-
This work has been funded by support from the National
Science Foundation and the Air Force Office of Scientific
Research.
brational state of the surviving OH bond. This is of course
1 V. Engel, V. Staemmler, R. L. Vanderwal, et al., J. Phys. Chem. 96, 3201
͑1992͒.
ϩ
consistent with present observations that photolysis of
͉
02
͘
(ϩ)
(ϩ)
ϩ
and
͉
11
states, which each contain both ␺
and ␺
͘
2 S. A. Harich, D. W. H. Hwang, X. F. Yang, J. J. Lin, X. M. Yang, and R.
N. Dixon, J. Chem. Phys. 113, 10073 ͑2000͒.
02
11
basis functions, produce more and less OH( ϭ1), respec-
v
3 R. Schinke, V. Engel, and V. Staemmler, J. Chem. Phys. 83, 4522 ͑1985͒.
4 R. N. Dixon, Chem. Soc. Rev. 23, 375 ͑1994͒.
5 M. Brouard, S. R. Langford, and D. E. Manolopoulos, J. Chem. Phys. 101,
7458 ͑1994͒.
tively, than predicted from a pure spectator model. In view of
this, it would be interesting to examine photodissociation
ϩ
ϩ
dynamics of vibrational states such as
͉
22
͘
and
͉
13
͘
,
6 P. Andresen, V. Beushausen, D. Hausler, H. W. Lulf, and E. W. Rothe, J.
Chem. Phys. 83, 1429 ͑1985͒.
which are even more poorly described by the local mode
picture. Based on the present analysis, one would predict
7 R. L. Vanderwal, J. L. Scott, and F. F. Crim, J. Chem. Phys. 94, 1859
͑1991͒.
photolysis to produce a significant spread in OH( ) levels,
v
mirroring the broader local mode content of the initial wave
function. Although such states cannot be accessed from the
ground state via a direct overtone excitation, they may be
populated by means of two photon transitions as demon-
strated in Ref. 28.
8 R. Schinke, V. Engle, P. Andresen, D. Hausler, and G. G. Balintkurti,
Phys. Rev. Lett. 55, 1180 ͑1985͒.
9 R. Schinke, R. L. Vanderwal, J. L. Scott, and F. F. Crim, J. Chem. Phys.
94, 283 ͑1991͒.
10 O. Votava, D. F. Plusquellic, and D. J. Nesbitt, J. Chem. Phys. 110, 8564
͑1999͒.
11 P. Andresen, G. S. Ondrey, B. Titze, and E. W. Rothe, J. Chem. Phys. 80,
2548 ͑1984͒.
V. SUMMARY
12 G. G. Balintkurti, J. Chem. Phys. 84, 4443 ͑1986͒.
13 R. L. Vanderwal, J. L. Scott, F. F. Crim, K. Weide, and R. Schinke, J.
Chem. Phys. 94, 3548 ͑1991͒.
193 nm photodissociation dynamics of gas-phase H2O
molecules has been examined from selected rotational and
14 M. Brouard and S. R. Langford, J. Chem. Phys. 106, 6354 ͑1997͒; I. Bar,
Y. Cohen, D. David, T. Arusiparpar, S. Rosenwaks, and J. J. Valentini,
ibid. 95, 3341 ͑1991͒; R. L. Vanderwal, J. L. Scott, and F. F. Crim, ibid.
92, 803 ͑1990͒; D. F. Plusquellic, O. Votava, and D. J. Nesbitt, ibid. 109,
6631 ͑1998͒.
vibrational quantum states within the OHϭ2 polyad. Rota-
v
tional, spin–orbit, and lambda-doublet quantum state distri-
butions of the OH photofragments can be well described in
the framework of previous theoretical and experimental stud-
ies at both higher and lower polyad numbers. However, the
OH vibrational distributions deviate considerably from con-
ventional spectator model predictions, which are based on
assuming adiabatic conservation of vibrational quanta in the
surviving OH bond. Instead, the data suggest a somewhat
more restricted regime of applicability for the spectator
model, specifically for vibrational states of H2O at relatively
high levels of local mode excitation. This breakdown of the
15 S. A. Nizkorodov, A. E. W. Knight, M. Ziemkiewicz, and D. J. Nesbitt
͑unpublished͒.
16 D. F. Plusquellic, O. Votava, and D. J. Nesbitt, J. Chem. Phys. 107, 6123
͑1997͒.
17 R. L. Vanderwal and F. F. Crim, J. Phys. Chem. 93, 5331 ͑1989͒.
18 C. A. Cantrell, A. Zimmer, and G. S. Tyndall, Geophys. Res. Lett. 24,
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spectator model is seen to be particularly strong for gerade
ϩ
states of the OHϭ2 polyad such as
͉
11 and
͉
02 ϩ, both of
v
͘
͘
which yield comparable photolysis branching into OH(
v
ϭ0) and OH( ϭ1). This is in good agreement with theo-
v
retical wave-packet studies and can be rationalized by higher
initial momentum projection along the symmetric stretch co-
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