Photofragment angular momentum polarization from dissociation of hydrogen peroxide near 355 nm

Article abstract of DOI:10.1063/1.1557920

The measurements on the dissociation of hydrogen peroxide (H₂O₂) around 355 nm, in the long-wavelength tail of the ultraviolet (UV) absorption spectrum were reported. Measurements of angular momentum polarization give a detailed picture of state-specific dissociation from nonequilibrium configuration of the ground-state parent molecule occurs. In addition, evidence for interference between multiple dissociating electronic states was reported as well.

Full text of DOI:10.1063/1.1557920

Photofragment angular momentum polarization from dissociation of hydrogen peroxide
near 355 nm
Andrew J. Alexander
Citation: The Journal of Chemical Physics 118, 6234 (2003); doi: 10.1063/1.1557920
View online: http://dx.doi.org/10.1063/1.1557920
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/118/14?ver=pdfcov
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 118, NUMBER 14
8 APRIL 2003
Photofragment angular momentum polarization from dissociation
of hydrogen peroxide near 355 nm
Andrew J. Alexandera)
School of Chemistry, University of Edinburgh, West Mains Road, Edinburgh, EH9 3JJ, United Kingdom
͑Received 5 December 2002; accepted 15 January 2003͒
Hydrogen peroxide (H2O2) was photodissociated at around 355 nm, using both linearly and
circularly polarized light. OH(2⌸) rotational distributions, spin–orbit branching ratios, lambda
doublet populations, and angular momentum J polarization in the laboratory and molecule frames
were measured by polarized laser probing of the products using laser induced fluorescence. The
effects of dynamical torsion and parent molecule bending vibrations on product rotational alignment
is discussed, and evidence supporting preferential dissociation of ground-state molecules far from
the equilibrium configuration is presented. Possible mechanisms for orientation of product angular
momentum in the molecule frame are discussed, and evidence is presented that interference occurs
˜
˜
between OH molecules dissociating via the A and B electronic states of H2O2. © 2003 American
Institute of Physics. ͓DOI: 10.1063/1.1557920͔
I. INTRODUCTION
5
1
˜
( ; 38%͒ states. In its ground X( A) state, the H2O2 mol-
ʈ
ecule prefers a twisted conformation with the dihedral angle
between the OH molecules ␾dϷ112°, see Fig. 1. Reinsch
Directional properties of angular momentum, and their
correlations with fragment velocities, have played a key role
in the study of molecular photodissociation.1 Currently there
is a growing interest in molecules that dissociate via more
than one pathway leading to a single product.2,3 This may
happen, for example, as the result of mixed transitions to
excited states, or by nonadiabatic transitions that occur dur-
ing the dissociation. In the limit of diatomic photodissocia-
tion, transition moments may be parallel or perpendicular to
the bond axis. Often, states exhibiting parallel or perpendicu-
lar transitions are overlapped in the dissociation spectrum,
and this can have significant effects on the directions of the
products and their angular momenta. Most of the primary
studies of the photodissociation of small molecules were car-
ried out at the absorption maxima, or at convenient laser
wavelengths.1 However, photodissociation studies at wave-
lengths far from the absorption maximum allow us to inves-
tigate interesting regions that may be rich dynamically, e.g.,
in the low-energy ͑long photolysis wavelength͒ tails of the
absorption spectrum, where a weaker transition is becoming
competitive with a stronger feature.
At 350 nm, the absorption cross section of H2O2 vapor is
4ϫ10Ϫ22 cm2, one order of magnitude lower than at 266
nm, and some 3 orders of magnitude smaller than the cross
section at 193 nm.4 The ultraviolet dissociation of H2O2 has
been studied by a number of groups at different wavelengths:
193,5,6 248,7,8 266,6,9–11 and 355 nm.12 Brouard et al.13 stud-
ied dissociation of H2O2 at 308, 351, 390, and 455 nm to
investigate the long-wavelength near-threshold dynamics. At
193 nm, the angular anisotropy parameter, ␤ϭ0.0Ϯ0.02,
suggesting that the dissociation proceeds via a mixture of
˜
has calculated that the A state transition moment lies along
˜
the C2 axis, and the B state transition moment lies very
nearly parallel to the O–O bond axis.14 Both the A and B
˜
˜
states are strongly repulsive, but in terms of the dihedral
˜
angle, the A state minimum is a trans conformation (␾
d
˜
ϭ180°), and the B state minimum is cis (␾dϭ0°). Such a
change in torsional conformation on accessing the excited
states is believed to be responsible for the observation of a
strong correlation of J
ʈ
at 266 nm, where
is the OH
v
v
velocity.10 Photodissociation of H2O2 becomes almost purely
perpendicular at 266 nm (␤ϭϪ0.71)10 and then shows mix-
ing again by 351 nm (␤ϭϪ0.10).13 Brouard et al. presented
compelling evidence that the long-wavelength (␭
˜
Ͼ310 nm) dissociation of H2O2 again accesses both the A
˜
and B states. Energy requirements dictate that the ground-
state molecules that are dissociated at longer wavelengths are
either thermally excited, or more probably that the Franck–
Condon factor selects a subset of molecules far from their
equilibrium configurations.8,13
In this paper, we report measurements on the dissocia-
tion of hydrogen peroxide (H2O2) around 355 nm, in the
long-wavelength tail of the ultraviolet ͑UV͒ absorption spec-
trum. Measurements of angular momentum polarization give
a detailed picture of state-specific dissociation mechanisms
for this molecule, showing that dissociation from nonequilib-
rium configurations of the ground-state parent molecule oc-
curs. Evidence for interference between multiple dissociating
electronic states is also reported. The experimental apparatus
is briefly described in Sec. II, the polarization parameters are
introduced in Sec. III, laboratory frame and molecule frame
polarization results are presented in Secs. IV and V, respec-
tively, and a final summary is given in Sec. VI.
perpendicular (Ќ) and parallel ( ) transitions, and the disso-
ʈ
1
1
˜
˜
ciation is believed to access the A( A) (Ќ; 62%͒ and B( B)
aElectronic mail: andrew.alexander@ed.ac.uk
0021-9606/2003/118(14)/6234/10/$20.00
6234
© 2003 American Institute of Physics
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J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Polarization from dissociation of HOOH
6235
FIG. 2. Schematic diagram showing experimental geometries used in the
present study, with the direction of the laser beams shown as straight single-
head arrows, and the photolysis ⑀ph and probe ⑀pr laser electric field vectors
as labeled. Geometries 5 and 5 have opposite probe circular polarizations,
Ј
although we did not determine which was left and which was right circularly
polarized. The PMT detector lies above the interaction region in all cases.
1
˜
FIG. 1. Schematic diagram showing an H2O2 twisted ground-state X( A)
conformer. The C2 symmetry axis is shown, along with the directions of the
quarter-wave plates at 308 and 355 nm ͑Coherent, UK͒. Vari-
ous tests for purity of polarization were carried out, includ-
ing measurement of null difference signals for molecules in
rotational states with Jϭ0.5 that should show no alignment.
For OH molecules J refers to the total angular momentum,
parallel (␮ ) and perpendicular (␮Ќ) transition moments, as calculated by
͉͉
Reinsch ͑Ref. 14͒. The dihedral angle ␾ is the angle between the two OH
d
bonds, as shown. The molecule frame used in the present work is also
shown, with the z axis defined by the product OH velocity vector , and the
v
x axis lying along the C2 symmetry axis. Note that the conformer shown is
chiral. A racemic mixture of H2O2 at 300 K would contain equal amounts of
left and right handed conformers.
and N is total J excluding spin: for ⌸3/2(F1) JϭNϩ 12, and
2
⌸
1/2(F2) JϭNϪ 12.
2
Laser induced fluorescence ͑1ϩ1 LIF͒ from the A–X
͑0,0͒ band of OH was collected via a fifth arm of the steel
cell using a pair of f/1.5 fused-silica plano convex lenses and
an interference filter centered at 307.1 nm ͑Coherent, UK͒,
and was focused onto a photomultiplier tube ͑Hamamatsu,
R3896͒. Transitions in the present work are labeled
⌬N⌬JfF(N) where f and F refer to the spin–orbit state of the
OH A and X states, respectively. In the case that ⌬Nϭ⌬J,
and fϭF, only one label is given, e.g., Q1(3) is shorthand
II. EXPERIMENT
The experimental setup was very similar to those de-
scribed in detail previously elsewhere,6,10 and only a brief
description will be given here. A 60% w/v aqueous hydrogen
peroxide solution was gently distilled under vacuum and
stored in a glass bulb. Only polytetrafluoroethene ͑PTFE͒
parts, or stainless steel coated with a film of PTFE, were
used in the gas handling manifold. The vapor was constantly
flowed thorough a stainless steel reaction cell with six or-
thogonal arms that had been internally coated with carbon
paint. Four arms of the cell contained painted baffles, with
four broadband UV anti-reflection coated windows, posi-
tioned normal with respect to the incoming light. During the
experiments, the total pressure in the cell was kept constant
below 100 mTorr.
The photolysis radiation at 355 nm was generated using
third harmonic generation from a Continuum Surelite III-10
YAG laser operating at 10 Hz. The beam was passed through
a 2 mm diameter iris, and loosely focused using a 250 mm
focal length lens. The total power before the lens was on the
order of 7 mJ cmϪ2 pulseϪ1. Second harmonic light ͑532
nm͒ from the same laser was used to pump a Sirah dye laser
͑GS-R-2400͒, which was operated with DCM dye at around
615 nm. The fundamental output from the dye laser was
doubled to ϳ308 nm using a KDP crystal. The quality of
polarization was measured using a Glan Laser polarizer
͑Special Optics, USA͒ and both the resulting 355 nm and the
308 nm laser radiations were found to be highly linearly
polarized (Ͼ99.5%͒. The 308 nm probe radiation was
switched between vertical and horizontal linear polarization
every shot by synchronizing the laser to the stress cycle of a
fused-silica photoelastic modulator ͑Hinds PEM-90D͒. Cir-
cularly polarized light was produced using zero order quartz
Q
for Q11(Nϭ3). The fluorescence was collected without
analysis of polarization. A schematic diagram of the experi-
mental geometries employed is shown in Fig. 2. The fluores-
cence signal was amplified with a home-built fast preamp-
lifier and integrated using a boxcar ͑SRS 250͒ with a gate
width of 50 ns after the probe laser pulse. A photodiode was
used to monitor the probe laser power, and experimental
checks were carried out to ensure that no saturation of the
laser induced fluorescence ͑LIF͒ occurred. Since the photo-
dissociation cross section of H2O2 at 355 nm is very small,
and almost an order of magnitude lower than that at 308 nm,
several tests were made to ensure that photolysis at 308 nm
did not affect the measurements. Data were transferred to a
computer running Labview ͑National Instruments͒ by GPIB
via a computer interface ͑SRS 245͒, and stored according to
the probe polarization.
III. EXTRACTION OF THE POLARIZATION
PARAMETERS
The intensity of the LIF signal in the laboratory frame is
written following Kummel, Sitz, and Zare ͑KSZ15͒
(k) (k)
IϭC det͒n J͒
P
A
,
͑1͒
͑
͑
͚
qϮ qϮ
k,q,J
f
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6236
J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Andrew J. Alexander
TABLE I. Conversion factors between the polarization parameters of Rakitzis et al.,19 the polarization parameters of Vasyutinskii et al.,2,18 and the dynamical
functions of Siebbeles et al.17 The directional interpretations of the aq(k)(p) parameters in the molecule frame are also shown. A full summary of the physical
meaning and directional properties of kϭ1,2 real spherical tensor moments has been tabulated by Miranda et al.20 Note that the conversion factors given in
Refs. 21 and 2 are valid only in the semiclassical limit. The a(01)(Ќ) parameter does not exist for photolysis of an achiral molecule by linearly polarized light,
(1)
1ϩ
(1)
1
, a(1)
ϭϪͱ2 Re a
and for this we have used ␤ appropriate for circularly polarized photolysis radiation. The following equivalences apply a
͓
͔
1Ϫ
(1)
1
(2)
1
(2)
2
, a(12ϩ) ϭϪ
, and a(22ϩ) ϭ
.
͔
ϭϪͱ2 Im a
ͱ2 Re a
ͱ2 Re a
͓
͔
͓
͔
͓
a
Rakitzis ͑Ref. 19͒
Vasyutinskii ͑Refs. 2 and 18͒
Siebbeles ͑Ref. 17͒
1,1͒
When positive
When negative
3␣1
f
͑
1
a(01)(Ќ)
orientation parallel to z
orientation parallel to x
orientation parallel to y
alignment along z
orientation antiparallel to z
orientation antiparallel to x
orientation antiparallel to y
alignment perpendicular to z
alignment perpendicular to z
alignment along xϪz
1ϩ␤
f0 1,1͒
͑
6Re f 1,0͒
͔
͓
͑
(1)
1
ʈ
ʈ
ʈ
,Ќ)
,Ќ)
)
3␥1
a
(
(
(
1ϩ
f0 0,0͒ϩ2f 1,1͒
͑
͑
0
6Im f 1,0͒
͔
͓
͑
(1)
1Ϫ
1
a
3␥Ј
1
f0 0,0͒ϩ2f 1,1͒
͑
͑
0
5 s Ϫ2␣ ͒
1
f 0,0͒
͑
2
͑
2
2
a(02)
1ϩ␤
W J͒ f 0,0͒
͑
͑
0
10 s ϩ␣ ͒
1
f2 1,1͒
͑
͑
2
2
a(02)(Ќ)
alignment along z
2Ϫ␤
W J͒ f 1,1͒
͑ ͑
0
6
Re f 1,0͒
͓ ͑ ͔
2
(2)
5ͱ3␥
alignment along xϩz
a
a
(
ʈ
,Ќ)
2
1ϩ
W J͒ f 0,0͒ϩ2f 1,1͒
͑
͑
͑
0
0
Ϫ5ͱ3␩
2Ϫ␤͒
1
f2͑1,Ϫ1͒
f0͑1,1͒
(2)
2ϩ
2
(Ќ)
alignment along x
alignment along y
Ϫ ͱ2W J͒
͑
͑
aW(J)ϭ J(Jϩ1)/(2Jϩ3)(2JϪ1)
.
͔
1/2
͓
where C(det) is a function of the particular detection appa-
ratus, assumed to be constant for all of our experiments, and
4␲A(02) ␪,␾͒ϭP cos ␪͒ 1ϩ␤͒a(2)
ʈ
͒cos2 ␪
͑
͑
͑
͑
ͫ
2
0
n(J) is the population of the initial rotational state J. The
(k)
qϮ
1
2
sensitivities to angular momentum polarization, P , were
ϩ
2Ϫ␤͒a(2) Ќ͒sin2 ␪
͑
͑
ͬ
0
calculated using the method described by KSZ, and included
known line-strength factors for OH and effects of hyperfine
depolarization.15,16 The laboratory frame ͑also known as
ͱ3 sin2␪ 2Ϫ␤͒a(2) Ќ͒sin2␪
ϩ
Ϫ
͓͑
͑
͔
(k)
qϮ
2ϩ
space-fixed frame͒ polarization moments A can be written
4
in terms of molecule frame ͑also known as body-fixed frame,
or velocity frame͒ polarization parameters. The laboratory
frame zero order moment A(00) can be written
ͱ3 a
(2)
1ϩ
ʈ
,Ќ͒sin22␪,
͑4͒
͑
4
ͱ3 sin2 ␪ cos 2␾ 1ϩ␤͒a(2)
(2)
2ϩ
4␲A(00) ␪,␾͒ϭ1ϩ␤P cos ␪͒.
͑2͒
4␲A
␪,␾͒ϭ
ʈ
͑
͑
ͫ
͑
͒cos2 ␪
0
͑
͑
2
2
1
1
ϩ
2Ϫ␤͒a(2) Ќ͒sin2 ␪ ϩ 1ϩcos2 ␪͒
͑
͑
͑
ͬ
The angular variables (␪, ␾) are defined in the laboratory
frame ͑our laboratory frame is identical to Fig. 1 of Ref. 17,
with the photolysis electric field vector along the Z axis͒.
P2(x) is the second Legendre polynomial. The normalization
factor 4␲ ensures that by integration over all angles A(0)
ϭ1. The beta parameter ͑␤͒ takes axial recoil limits ϩ2 for
a pure parallel transition, and Ϫ1 for a pure perpendicular
transition. In the case of photolysis using circularly polarized
light, these limits change to Ϫ1 and ϩ 12, respectively.
For photolysis with circular polarization, the laboratory
frame orientation moment A(01) can be written
0
2
4
ϫcos 2␾ 2Ϫ␤͒a(2) Ќ͒sin2 ␪
͓͑
͑
͔
2ϩ
1
4
(2)
1ϩ
,Ќ͒sin2 2␪ cos 2␾.
͑5͒
͗
͘
0
Ϫ
a
ʈ
͑
The above equations have been obtained by rotating mol-
ecule frame parameters a(qk)(p) to the laboratory frame using
a transformation similar to Eq. ͑16͒ of Bracker et al.18 We
have used the molecule frame notation a(qk)(p) of Rakitzis
et al.19 to distinguish between parameters that originate from
parallel ( ) and perpendicular (Ќ) transitions, and the
ʈ
Hertel–Stoll definitions of real spherical tensor moments
4␲A(01) ␪,␾͒ϭ 1ϩ␤͒a(1) Ќ͒cos2 ␪ϩ 1a(1) ,Ќ͒sin2 ␪. ͑3͒
ʈ
͑
1ϩ
͑
͑
͑
2
0
have been used ͑see Table I͒. We have neglected higher order
(k)
qϮ
moments A
with kϾ2. This is partly justifiable because
(2)
2ϩ
For photolysis with linearly polarized light, the A(02) and A
the sensitivities for these moments were found to be small
for the transitions and geometries used in the present study.
laboratory frame alignment moments can be written
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J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Polarization from dissociation of HOOH
6237
An average estimate of the effect of not including moments
kϾ2 was found to be Ͻ5%: Much less than experimental
uncertainties in the moments kр2. Some parameters vanish
simply as a result of the symmetry of the H2O2 system, see
Fig. 1. The racemic mixture of H2O2 equates to the existence
of three orthogonal reflection planes, with two that include
(2)
(2)
the C2 axis: This causes all a(qkϪ) (p), a
(
ʈ
) and a (Ќ) to
1ϩ
1ϩ
(2)
˜
vanish ͑see Fig. 1͒. The a
(
ʈ
) vanishes, because the B-state
2ϩ
transition moment lies parallel to the O–O bond axis,14 and
the H atom angular positions are not correlated with it. The
resulting equations show that the H2O2 molecule behaves
much like a diatomic molecule, and that the perpendicular
transition moment ␮(Ќ) and the velocity define a specific
v
plane in the molecule frame.
The interpretation of molecule frame parameters
1,2
1,2
a(qk)
( ,Ќ) that arise due to coherence between parallel and
ʈ
FIG. 3. Isotropic I (␯) and anisotropic I
(␯) LIF composite spectra,
iso
aniso
scanned over the Q1 and Q2 branches. The data were taken using linear
polarizations ͑geometries 1 and 2 in Fig. 2͒. The anisotropic spectrum has
been magnified (ϫ4) and vertically displaced for clarity. Some of the J
ϭ0.5 lines that cannot be aligned ͑and should therefore have no anisotropic
signal͒ have been identified with asterisks.
perpendicular transitions is not straightforward in the case of
polyatomic parent species. The electronic transition moment
may not be exactly parallel or perpendicular to the
asymptotic direction of the lysing bond, and the coherent
moments can be observed from incoherent transitions of ei-
ther symmetry. For example, if a linear triatomic happens to
be excited during bending vibration, an observed aq(k)
( ,Ќ)
ʈ
tolysis light, corresponding to geometries 1 and 2 shown in
Fig. 2. In this way it was also possible to obtain the inte-
grated lab frame alignment A(2) as a function of rotation
may originate from parallel and perpendicular projections of
an in-plane transition moment, as discussed by Ahmed et
al.22 for NO2 dissociation, and by Kim et al.23 in the case of
OCS dissociation. Likewise, the a(22ϩ) (Ќ) parameter for a
polyatomic molecule may result from parent bending, rather
͗
͘
0
͑see Sec. IV B below͒. Sum and difference spectra were
formed by taking I1is,o2(␯)ϭI1(␯)ϩ 25I2(␯) and I
(␯)
1,2
aniso
ϭI1(␯)ϪI2(␯). I1is,o2(␯) and I
(␯) isolate population and
1,2
aniso
than coherence between excited
molecule. In the present report, we keep the (
and will develop our interpretation with the above caveat in
mind. The Rakitzis alignment parameters are easily con-
͉
⍀
͉
ϭ1 states of the parent
,Ќ) notation,
alignment contributions, respectively, and were fitted simul-
taneously using line strengths and alignment sensitivity
factors.15,16 Note that the factor of 5/2 in the above expres-
sion for I1is,o2(␯) is J dependent, and is obtained from the ratio
ϪP(02)(geometry1)/P(02)(geometry 2): We have used 5/2 as
an approximate mean of this ratio over the Q branch. The
raw data are shown in Figs. 3 and 8, and the resulting rota-
tional distributions are shown in Fig. 4. The peak in the
rotational distribution around Nϭ3 agrees with previous
work by Crim and co-workers.27 We calculate the average
ʈ
verted to the
␣
parameters of Vasyutinskii and
K
co-workers,2,18 or the dynamical parameters f (q,q ) of
Ј
K
Siebbeles et al.,17 and for convenience these conversions are
summarized in Table I. Equations relating ␣K to the bipolar
moments of Dixon24 have appeared elsewhere.21,25 Monte
Carlo simulations of Doppler line shapes D(␯) were ob-
tained by projecting the total distribution ͓Eq. ͑1͔͒ onto the
Doppler axis, and integrating contributions that shared the
same projection on this axis. The extraction of the polariza-
tion moments are greatly complicated by the two photons of
fraction of available energy going into rotation is
f
͘
rot
͗
ϭ4.5%, with
E
ϭ508 cmϪ1, in good agreement with
͘
rot
͗
Brouard et al.13 Although it is not expected that the rota-
tional distribution should follow a Boltzmann distribution,
the ͑1ϩ1͒ LIF that propagate in different directions. Of
(k)
qϮ
course it would be possible to rewrite the A
laboratory
frame equations in the Doppler frame, however, this would
produce very cumbersome general expressions. Experimen-
tal Doppler line shapes were fitted, by nonlinear least-
squares methods, using a basis set of simulated line shapes
with known values of the molecule frame parameters, as de-
scribed in detail elsewhere.19,26
IV. LABORATORY FRAME RESULTS
A. Rotational distributions
Rotational distributions of the OH molecule were ob-
tained by scanning over the Q1, Q2, R1, and R2 branches of
the LIF spectrum. Spectra were obtained by timing the PEM
to produce light linearly polarized parallel I1(␯) or perpen-
dicular I2(␯) with respect to the horizontally polarized pho-
FIG. 4. Rotational distributions as function of the rotational quantum num-
ber N, obtained from the isotropic spectra shown in Figs. 3 and 8.
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6238
J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Andrew J. Alexander
FIG. 7. Integrated laboratory frame alignment moment A(02) for each of the
OH spin–orbit states as a function of the total angular momentum quantum
number, J. These moments were obtained by fitting the anisotropic rota-
tional spectrum shown in Fig. 3; see text for details.
FIG. 5. Ratios of spin–orbit state populations as a function of the rotational
quantum number, N. The ratio of populations has been scaled by the factor
N/(Nϩ1) to account for rotational J degeneracies in the two OH spin–orbit
states ⌸3/2(F1) and ⌸1/2(F2). The dashed lines are theoretical distributions
at different temperatures, obtained using a Boltzmann distribution.
˜
have reported calculations that suggest that crossing from A
nevertheless the data can be approximated by the rotational
temperatures Tϭ650Ϯ16 K for the F1 states and Tϭ650
Ϯ32 K for the F2 states.
Spin–orbit branching ratios as a function of N are shown
in Fig. 5, along with the Boltzmann distributions expected at
various temperatures. The experimental ratios are all close to
unity, implying that there is no preference for production of
either spin–orbit state, in agreement with results at other
wavelengths.13
3
to B, as a result of spin–orbit coupling, causes preferential
population of the A state.29 Our ⌳-doublet ratios are very
Љ
similar to the 193 nm photolysis results of Gericke et al.,
˜
consistent with the hypothesis of Brouard et al. that the A
13
˜
and B states are the main states involved at 355 nm.
B. Laboratory frame alignment
The laboratory frame alignment integrated over all trans-
lational directions of the product, A(2) , is plotted as a func-
Lambda-doublet ratios for the A /A ⌸ states are shown
Љ
Ј
͗
͘
0
in Fig. 6. There appears to be a slight preference for the A
Ј
tion of J in Fig. 7. Since the Q branches have the highest
sensitivity to the A(02) , only Q branch data were analyzed.
Rotational transitions that should show zero alignment ͑be-
cause Jϭ0.5) are highlighted in Fig. 3. Integrating Eq. ͑4͒
over all angles ␪,␾, we obtain
⌳-doublet at low J, moving towards more A population at
Љ
high J. In the limit of high J, we can associate the A lambda
Љ
doublet with molecules in which the unpaired electron popu-
lates a p-orbital that is perpendicular to the plane of
rotation.28 Gericke et al. have determined the expected or-
2
1
1
A(2)
ϭ
͘
1ϩ␤͒a(2)
ʈ
͒Ϫ 2Ϫ␤͒a(2) Ќ͒
͑ ͑ ͑ ͑
0 0
˜
bital populations resulting from excitation to the A( A),
͗
ͫ
ͬ
0
15
2
1
1
˜
˜
B( B), and C( A) states using a simple molecular-orbital
picture.10 They concluded that there should be no strong
preference for population of either ⌳-doublet, except for dis-
2
ϩ
Ϫa(2)
ʈ
,Ќ͒ϩ 2Ϫ␤͒a(2) Ќ͒ ,
͑6͒
͓
͑
͑
͑
2ϩ
͔
1ϩ
5ͱ3
˜
˜
sociation via the C state. The C state seems an unlikely
candidate for the dissociation at 355 nm, because it lies much
that is, A(2) ϭϪ2(␣ ϩ␥ ϩ␩ ) in the lab-frame notation
͗ ͘
2 2 2
0
of Vasyutinskii et al.18 The classical limits of alignment in
the laboratory are Ϫ1 to ϩ2. It is clear that the experimental
results are small compared to their limiting values, and actu-
ally appear to decrease slightly with increasing J. Following
the classical arguments of Docker et al.,7 we note that
A(2) ϭ2␤ P (J• ) /5. Given that ␤Ͻ0, we might expect
˜ ˜
higher in energy than the A or B states. Morita and Kato
v
͘
͗
͘
͗
2
0
to find that the positive A(2) that we measure in the labo-
͗
͘
0
ratory frame results from a correlation of JЌ in the mol-
v
ecule frame, i.e., a(02)(p)Ͻ0. Such a conclusion would be
erroneous, and arises because J is not axially symmetric
(2)
(2)
around
when the parameters a
( ,Ќ) and a (Ќ) are
ʈ
v
1ϩ 2ϩ
nonzero, as we shall show in more detail in Sec. V A below.
An interesting feature of Fig. 3 is the alignment observed
for the Q (1) line. A(2) ϭϪ0.18 for F (Jϭ1.5) has twice
͗
͘
1
1
0
the magnitude and has opposite sign to A(2) ϭϩ0.095 for
͗
͘
0
the F2 (Jϭ1.5) state. It is possible that this stems from an
(2)
1ϩ
increased contribution from the coherent a
(
ʈ
,Ќ) param-
FIG. 6. Ratios of lambda doublet populations ⌸(A )/⌸(A ) as a function
Љ
Ј
of the rotational quantum number, N, for each of the OH spin–orbit states.
eter to the overall alignment in Eq. ͑6͒. The low Jϭ1.5 states
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J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Polarization from dissociation of HOOH
6239
differ significantly in the composition of the total angular
momentum, made up from electronic and rotational angular
momentum. In Hund’s case ͑a͒, for F1 (Jϭ1.5), the total J is
purely electronic, being composed of spin and orbital angular
momentum to give a total projection ⍀ϭ1.5 on the bond
axis: The molecule has no nuclear rotation. In contrast,
F2 (Jϭ1.5) is made up of spin ϩ orbital angular momentum
⍀ϭ0.5 with a further unit of rotational angular momentum,
giving total Jϭ1.5. Therefore, the exceptional alignment of
OH F1 (Jϭ1.5) molecules could result from pure electronic
alignment created by the absorption of the photolysis photon,
whereas all of the other J states have an additional alignment
contribution from the rotation of the OH molecule. The ro-
tational alignment is dependent on the shape of the ground-
state potential energy surface, including contributions from
the torsional and bending motions of the parent H2O2 mol-
ecule. The rotational alignment of the OH also depends on
the shape of the excited state potential energy surface, viz.,
5,5
5,5
Ј
Ј
FIG. 8. Isotropic Iiso (␯) and anisotropic Ianiso(␯) LIF composite spectra,
scanned over the R1 and R2 branches. The data were taken using circular
polarizations ͑geometries 5 and 5 in Fig. 2͒ The anisotropic spectrum has
been magnified and vertically displaced for clarity.
Ј
˜
the change in torsional minimum from ␾dϭ112° in the X
maximal ͉ ͉ would be 0.212 at Jϭ0.5, rising to 0.349 at
A(1)
͗ ͘
0
˜ ˜
state to ␾dϭ180° and 0° on accessing the A or B states,
Jϭ9.5. Clearly, the observed
͉ ͉ lie well below these
A(1)
͗ ͘
0
respectively.
limits. The
͉ ͉ appears to peak at around Jϭ4.5 (F1)
A(1)
͗ ͘
0
and Jϭ6.5 (F2), showing decreased orientation at lower and
higher J. Since the racemic H2O2 mixture is achiral, the
C. Laboratory frame orientation
͉
A(1)
͉ in the laboratory frame results from the helicity of
͘
0
Laboratory frame orientation measurements were carried
out using counter-propagating photolysis and probe beams,
both of which were circularly polarized—see geometries 5
͗
the circularly polarized photolysis photon, so that helicity of
the system is conserved in the laboratory frame. On the other
hand, the circularly polarized photon acts upon the electrons
in parent molecule, i.e., the photon has no selectivity over
the helicity of motion of the nuclei. Although
ϭ0.5 ͑F2) is slightly higher than that for Jϭ1.5 (F2), there
and 5 in Fig. 2. Using these geometries, it is possible to
Ј
determine the laboratory frame orientation, integrated over
all product directions,
͉ ͉ for J
A(1)
͗ ͘
0
A(1) ϭ 1 1ϩ␤͒a(1)
͓͑
ʈ
ʈ
͒ϩa
͑
1ϩ
,Ќ͒ ,
͑7͒
(1)
͑
͔
͗
͘
3
0
0
is no variation in at low J as dramatic as was ob-
͉
A(1)
͘
͉
͘
͗
0
that is A(1) ϭ␣ ϩ␥ using the lab-frame notation of
served for the A(2) . This is consistent with the orientation
͗
͘
1
1
͗
0
0
Vasyutinskii et al.2 Transitions with ⌬JϭϮ1 have the high-
est sensitivity to orientation, and therefore spectra of the R1
and R2 branches were taken. Sum and difference spectra
being produced only as electronic orientation over the entire
range of J, in comparison to the electronic and rotational
alignment mechanisms discussed in Sec. IV B. The lower
A(1)
͉ at low J may be due to increasing influence from the
͘
0
5,5
Ј
5,5
Ј
͉
were calculated as Iiso (␯)ϭI5(␯)ϩI5 (␯) and Ianiso(␯)
͗
Ј
(1)
coherent a
( ,Ќ), as we shall discuss in Sec. V B.
ʈ
ϭI5(␯)ϪI5 (␯), although we were unable to determine the
1ϩ
Ј
absolute handedness of circularly polarized light: We only
know that geometries 5 and 5 have opposite circular probe
Ј
polarizations. The spectra are shown in Fig. 8. The ‘‘isotro-
5,5
Ј
pic’’ spectrum Iiso (␯) retains a residual contribution from
lab frame alignment A(02). However, the R branch sensitivi-
ties to alignment in geometry 5 are very small, e.g., P0(2)
ϭ0.249 for R1͑5͒ compared with P(01)ϭ1.421. Lower sensi-
tivity to alignment, combined with the very low integrated
A(2) as determined above, mean that effects of alignment
͗
͘
0
on the measured A(1) are minimized. Also, there are no
͗
͘
0
higher integrated A(k) moments in the laboratory frame.17
͗
͘
q
Since we were unable to determine the absolute handed-
ness of our circularly polarized light, the sign of A(1) can-
͗
͘
0
not be determined. The magnitude of laboratory frame orien-
tation , is plotted as a function of J in Fig. 9. Results
͉
A(1)
͉
͘
͗
0
derived from R1͑1͒ were unreliable due to blending of lines
in the spectrum, and so the value derived from the P1͑1͒
transition has been plotted instead. The values from P1͑2͒
and R2͑2͒ show good agreement within uncertainties. The
FIG. 9. Integrated laboratory frame orientation moment
͉ ͉ for each of
A(1)
͗ ͘
0
the spin–orbit states as a function of the total angular momentum quantum
number, J. These moments were obtained by fitting the anisotropic rota-
tional spectrum shown in Fig. 3; see text for details. Error bars represent
single standard deviations from multiple measurements.
maximal a(01)
Assuming the coherent
(Ќ)ϭͱJ/Jϩ1.
(1)
a
( ,Ќ)ϭ0, and ␤ϭ0.1, we estimate from Eq. ͑7͒ that the
ʈ
1ϩ
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6240
J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Andrew J. Alexander
TABLE II. Beta parameters determined from Doppler line shapes for se-
lected lines; see text for details.
Transition
Angular momentum J
Beta parameter ␤
PQ12(1)
R2(1)
P1(5)
P2(5)
P2(8)
0.5
0.5
5.5
4.5
7.5
Ϫ0.13Ϯ0.05
Ϫ0.10Ϯ0.07 ͑Ref.13͒
Ϫ0.21Ϯ0.04
Ϫ0.18Ϯ0.05
Ϫ0.04Ϯ0.05
V. DOPPLER MEASUREMENTS
In Sec. III, the laboratory polarization moments Aq(k)
were given in terms of molecule frame polarization param-
eters a(qkϮ) (p). The molecule frame parameters can be ob-
tained from measurements using different geometries and
transitions in the laboratory frame, and by resolving product
velocity. The directional part of the product velocity be-
comes especially important in the case of dissociations in-
FIG. 10. P1(5) composite anisotropic doppler line shapes ͑thin solid lines͒
and corresponding fits ͑thick solid lines͒. The data were taken at the pho-
3,4
aniso
tolysis wavelength 355 nm. ͑a͒ D1an,2iso(␯), ͑b͒ D
(␯). The ordinate scales
shown are relative to the respective Diso(␯), normalized to unit area. Note
that ͑b͒ has a visibly large contribution from ␤, but contains significant
polarization information.
volving transitions of mixed ( ,Ќ) symmetry since the frag-
ʈ
ments travel in different directions, even if they have similar
speeds.
(2)
good fit to the data, therefore, a
( ,Ќ)ϭ0 within uncertain-
ʈ
1ϩ
ties. We found that omitting any of the three fitted parameters
led to a very poor fit. Fitted composite anisotropic line
shapes are shown in Fig. 10. The fitted parameters a(q2)(p)
are tabulated in Table III, along with their J-dependent lim-
iting values.
A. Alignment
Fitting of Doppler line shapes to obtain polarization pa-
rameters requires the translational anisotropy parameter ␤.
The ␤ parameter was determined by making measurements
P
The results in Table III clearly show two important mol-
ecule frame alignment effects. The first effect is alignment
along the velocity ͑i.e., the molecule frame z axis͒, repre-
using geometries 3 and 4 for the Q12(1), P1(5), P2(5),
and P2(8) transitions. The photolysis electric field vector
was parallel ͑geometry 3͒ or perpendicular ͑geometry 4͒ to
the Doppler axis ͑the probe laser propagation direction͒, see
Fig. 2. Approximately isotropic and anisotropic composite
Doppler line shapes were formed D3is,o4(␯)ϭD3(␯)
ϩ2D4(␯), D3an,4iso(␯)ϭD3(␯)ϪD4(␯). These composite line
shapes are not ideal, because they include residual contribu-
tions from the alignment A(q2) . Since the integrated align-
ment moments A(2) determined in Sec. IV B are relatively
sented by the positive a(02) ) and a0(2)(Ќ) moments. The
(
ʈ
second effect is alignment along the x axis, indicated by the
positive a(2) (Ќ). The alignment of J along can be ascribed
v
2ϩ
to torsion of the OH bond around the O–O axis.5–11 When
˜
˜
the molecule is excited to the A and B states, the OH frag-
˜
ments will twist towards either the trans A conformation
˜
͗
͘
(␾dϭ180°), or the cis B conformation (␾dϭ0°), resulting
in the observed alignment of J along . The potential wells
for the excited states are much steeper compared with the
0
small, the approximation holds quite reasonably. Further-
v
P
more, the Q12(1) transition originates from Jϭ0.5, and
cannot exhibit alignment. The experimental composite line
shapes were fitted using a basis set of simulated line shapes
that include only the zeroth-order moment A(00)(␪,␾). The
results are shown in Table II. The ␤ obtained are in excellent
agreement with the results of Brouard et al.13 Using ␤
˜
ground X state, and so the generated torque will be
sizeable.29 Comparison of the relative magnitudes of the
a(02)(p) moments shows that a(02)
( ) is slightly larger than
ʈ
a(02)(Ќ). This greater degree of alignment from the B state
implies a greater torque, and is in qualitative agreement
with quantum mechanical simulations by Zhang and
co-workers.31
˜
P
ϭϪ0.13 for Q12͑1͒, we estimate that the fraction of prod-
ucts produced by perpendicular transition to be 71%.
To determine molecule frame alignment parameters, we
made repeated Doppler line shape measurements for the
P1͑5͒ line using geometries 1 to 4. Composite line shapes
were formed for pairs of geometries ͑1,2͒: D1is,o2(␯)ϭD1(␯)
ϩ2D2(␯), D1an,2iso(␯)ϭD1(␯)ϪD2(␯), and ͑3,4͒: Di3s,o4(␯)
ϭD3(␯)ϩ2D4(␯), D3an,4iso(␯)ϭD3(␯)ϪD4(␯). The four
composite line shapes were fitted using an appropriate basis
TABLE III. Molecule frame alignment and orientation moments determined
P
from Doppler line shapes for the P1(5) and Q12(1) transitions. Note that
the absolute sign of the aq(1)
( ,Ќ) were not determined; see text for details.
ʈ
Transition
Parameter
Experimental value
Limits
set consisting of three moments a(02) ), a0(2)(Ќ), and
(
ʈ
a(01)
P1(5)
Ϫ0.920•••ϩ0.920
Ϫ1.000•••ϩ1.538
Ϫ1.000•••ϩ1.538
Ϫ1.487•••ϩ1.487
Ϫ0.577•••ϩ0.577
Ϫ0.577•••ϩ0.577
0.077Ϯ0.020
0.45Ϯ0.27
0.34Ϯ0.20
0.18Ϯ0.08
Ϫ0.046Ϯ0.019
0.075Ϯ0.032
a(02)
(
ʈ
)
a(22ϩ) (Ќ) for each of the four geometries ͑i.e., nine basis line
shapes in total͒. For fitting we used nonlinear least-squares
minimization employing both simulated annealing and
a(02)(Ќ)
a(22ϩ) (Ќ)
a(01)
PQ12(1)
Levenberg–Marquardt methods.30 We found that it was not
(1)
1ϩ
a
(2)
1ϩ
necessary to include the a
ʈ
( ,Ќ) parameter to get a very
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J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Polarization from dissociation of HOOH
6241
The observed alignment of J along the molecule x axis
˜
for molecules excited to the A state can be explained by the
symmetric ␯2ϭ1394 cmϪ1 and antisymmetric ␯6ϭ1265
cmϪ1 bending modes of H–OO–H.32 The bending modes
result in rotation of the OH fragments with J perpendicular
both to
and to the breaking O–O bond axis. Ab initio
v
calculations show that the H–OO–H bending potential for
˜
the A state in the Franck–Condon region is much flatter than
˜
the X state, with a minimum that is vertically above the
29,33
˜
minimum of the X state,
and so bending energy in the
␯2 , ␯ co-ordinates is effectively channelled into rotation as
6
the molecule dissociates. The a(22ϩ) (Ќ) represents a preferen-
tial alignment along the x axis compared with y, and the
projection of the bending angular momentum onto the x and
5,5
Ј
FIG. 11. Composite anisotropic Doppler line shapes D
(␯). Results in ͑a͒
aniso
P
y axes depends on ␾
d
are for OH(Jϭ5.5) P1(5), the results in ͑b͒ are for OH(Jϭ0.5) Q12(1).
The ordinate scales shown are relative to the respective Diso(␯), normalized
to unit area.
2
2
Jx
Jy
(2)
2ϩ
Ќ͒ϭͱ3
͑
ϭϪͱ3 cos ␾
,
͗ ͘
a
Ϫ
͑8͒
ͩ ͪ ͩ ͪ
ͳ
ʹ
d
J
J
where we have treated J classically. This means that for large
␾dϾ90°, J will be aligned preferentially along the molecule
x axis. With a(22ϩ) (Ќ)ϭ0.18Ϯ0.08, we find that ␾ ϭ96°
The P1(5) results indicate a small orientation a(01)(Ќ) in
(1)
the molecule frame, and we find a
( ,Ќ)ϭ0 within the
ʈ
͗
͘
d
1ϩ
Ϯ2.6°, which is lower than the ground-state equilibrium
value ␾dϭ112°. To satisfy energy requirements, Brouard
et al. noted that the dissociation of H2O2 at longer wave-
lengths must either involve thermally populated vibrational
limits of our signal to noise. In terms of the electronic co-
herence between parallel and perpendicular states, the
(1)
1ϩ
a
ʈ
( ,Ќ) parameter contains phase and amplitude informa-
tion
˜
(1)
levels of the X state, or preferential excitation of molecules
a
ʈ
,Ќ͒ϰN
ʈ
,Ќ͒cos ⌬␸͒.
͑9͒
͑
͑
͑
1ϩ
far from equilibrium geometries.13 Since they did not ob-
serve significant differences in their experiments on cooling
by gaseous expansion with Ar or He, they tended to prefer
the latter explanation.8,13 Indeed, the average available ther-
mal energy kTϭ204 cmϪ1 at 293 K is much smaller than the
fundamental vibrational frequencies of H2O2 , with the ex-
ception of the lowest-lying torsional state (␯4ϭ254 cmϪ1).34
In Eq. ͑9͒, cos(⌬␸)ϭcos(␸ЌϪ␸ʈ) is the cosine of the
asymptotic phase difference between the radial parts of the
outgoing wave functions from parallel and perpendicu-
lar transitions. N(
parallel and perpendicular states, where N(
ʈ
,Ќ) represents the relative mixture of
ʈ
,Ќ)
ϭͱ(1ϩ␤)(1Ϫ␤/2) for photolysis by linearly polarized
,Ќ)ϭͱ(1Ϫ2␤)(1ϩ␤) for photolysis by circu-
light, or N(
ʈ
Brouard et al. proposed that the mean torsional angle ␾
͗
͘
d
(1)
1ϩ
larly polarized light. Note that a
there is an equal mixture of parallel and perpendicular states,
and the asymptotic phase difference ⌬␸ϭ0. The coherent
alignment parameter a
( ,Ќ) is maximal when
ʈ
˜
of X state molecules that absorb radiation would decrease at
longer photolysis wavelengths as these molecules are in-
creasingly displaced from the equilibrium ␾dϭ112°.13 Our
experimental estimate of a decreased mean torsional angle
(2)
1ϩ
ʈ
( ,Ќ) also varies with cos ⌬␸, and
(1)
1ϩ
finding a
( ,Ќ)ϭ0 for P1͑5͒ is consistent with our finding
ʈ
␾
ϭ96° shows remarkable evidence in support of this
͘
͗
d
(2)
1ϩ
that a
ʈ
( ,Ќ)ϭ0, above.
mechanism.
(1)
1ϩ
Comparing the directional properties of a
( ,Ќ) and
ʈ
a(22ϩ) (Ќ), we see that the OH(Jϭ5.5) are aligned but not
oriented along x. In Sec. V A, we suggested that the a(22ϩ) (Ќ)
resulted from ␯ and ␯ bending of the H2O2 parent mol-
B. Orientation
Molecule frame orientation parameters were determined
2
6
ecule. At any given time, there will be as many OH bonds
bending clockwise or anti-clockwise, and it seems reason-
able that the circularly polarized photolysis photon has no
selectivity upon the phase of this bending motion. Following
from the discussion of electronic alignment in Sec. IV C, we
suggest that the circular polarization of the photolysis photon
causes electronic helicity in the molecule frame. The a(01)(Ќ)
can be written35
using geometries 5 and 5 , by scanning over individual
Ј
Doppler line shapes. Isotropic and anisotropic composite
5,5
Ј
line shapes were calculated Diso (␯)ϭD5(␯)ϩD5 (␯),
Ј
5,5
Ј
D
(␯)ϭD5(␯)ϪD5 (␯). Basis line shapes were simu-
Ј
aniso
lated using Eqs. ͑2͒ and ͑3͒, and these basis line shapes were
used to fit the experimental composite Doppler line shapes.
The ␤ values obtained in Sec. V A were multiplied by
Ϫ1/2 to account for the circular polarization of the photoly-
sis laser. Raw data and fits for the P1(5) and PQ12(1) aniso-
mJ
a(01) Ќ͒ϭ
,
͑10͒
͑
tropic line shapes are shown in Fig. 11, and the resulting
ͱ
J Jϩ1͒
͑
(1)
a(01)(Ќ) and a
( ,Ќ) parameters are given in Table III.
ʈ
1ϩ
Note that the absolute sign of the aq(1)
( ,Ќ) were not deter-
ʈ
mined, although the sign of a
where m is the projection of J onto the z axis ( ). If we
v
J
(1)
(
ʈ
,Ќ) relative to a(01)(Ќ) was
assume that the projection (1ប) of the angular momentum of
1ϩ
determined in the case of OH(Jϭ0.5).
the circularly polarized photon on the breaking O–O bond is
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6242
J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Andrew J. Alexander
(1)
1Ϫ
a
ʈ
,Ќ͒ϰN
ʈ
,Ќ͒sin ⌬␸͒.
͑11͒
͑
͑
͑
For a given parent molecule and photofragment, oscillations
(1)
in a
( ,Ќ) will be shifted in photolysis energy relative to
ʈ
ʈ
1Ϫ
(1)
the a
( ,Ќ) as a consequence of the 90° phase between
1ϩ
cos(⌬␸) and sin(⌬␸). Put simply, the interference would be
(1)
minimum for a
a
(
ʈ
,Ќ) when it was a maximum for
ʈ
( ,Ќ). In the present case, we compare the photolysis of
1ϩ
1Ϫ
(1)
(1)
two different systems, and yet the a
( ,Ќ) qualitatively
ʈ
1Ϯ
appear to be ϳ90° out of phase.
For H2O2 dissociation with linearly polarized light
Brouard et al. found that ␤ϭϪ0.76Ϯ0.19 at 308 nm, and
␤ϭϩ0.83Ϯ0.19 at 390 nm, indicating that the transition
moves from being 92% perpendicular at 308 nm to being
(1)
39% perpendicular at 390 nm.13 The a
ʈ
( ,Ќ) results for
FIG. 12. Dependence of orientation parameter on photolysis wavelength.
1ϩ
(1)
Solid line: a
Dashed lines: a
(
ʈ
,Ќ) for OH(2⌸1/2 , Jϭ0.5) from dissociation of H2O2.
1ϩ
OH(Jϭ0.5) are consistent with the measurements of ␤: The
interference drops to near zero at short wavelengths ͑320
nm͒ where the transition is nearly pure perpendicular, and
rises to a maximum at longer wavelengths where the transi-
tion is mixed. At much longer wavelengths 440–465 nm,
Brouard et al. found that ␤ϭ1.7Ϯ0.2. In the 440–465 nm
region, the dissociation becomes very close to the energetic
threshold for dissociation, and we would expect oscillations
in cos(⌬␸) to be more frequent as the total available energy
becomes comparable to the difference in potential energy
(1)
(
ʈ
,Ќ) for Cl*(2P1/2) following dissociation of Cl2 ͑Ref.
1Ϫ
36͒. Solid squares are results for 35Cl*, solid triangles for 37Cl*. Note that
the OH and Cl* results are real and imaginary parts of a1(1)
( ,Ќ), respec-
ʈ
tively; see text for details. The H2O2 results have been scaled to the 37Cl* at
370 nm by multiplying by 1.52. The overlap of points at 355 nm is coinci-
(1)
1ϩ
dental. Note that the absolute sign of a
ʈ
( ,Ќ) for OH was not determined.
shared equally between two OH molecules, for OH (J
ϭ5.5) we find a(01)(Ќ)ϭ0.084, which is very close to the
experimental value a0(1)(Ќ)ϭ0.077 that we measure.
In Sec. IV B we showed that laboratory alignment A(2)
between
ʈ
and Ќ dissociating states.37 Therefore, the mea-
(1)
surement of a
( ,Ќ) at wavelengths Ͼ370 nm would be
ʈ
1ϩ
͗
͘
0
very interesting for a future study.
of Jϭ1.5 molecules was substantially different for
OH(2⌸3/2) compared with OH(2⌸1/2) molecules. Signifi-
cantly, these molecules differ in the amount of rotational
versus electronic angular momentum. Molecule frame orien-
That we measure interference for the H2O2 photodisso-
ciation is, perhaps, remarkable in itself. The Cl* atom results
of Kim et al., and previous measurements of coherence in
atomic polarization, were all carried out on cooled gaseous
expansions.2,36 The present results were obtained from a
flowing room temperature sample. One would expect that the
increased number of degrees of freedom for the potential
energy surface, and thermal averaging over the initial con-
P
tation parameters for Q12͑1͒, given in Table III show both
(1)
an incoherent a(01)(Ќ), and a coherent a
( ,Ќ). Similarly
ʈ
1ϩ
to the OH(2⌸3/2 , Jϭ1.5), the angular momentum of the OH
(2⌸1/2 , Jϭ0.5) molecules is purely electronic. Since
(1)
(2)
1ϩ
a
(
ʈ
,Ќ) and a
( ,Ќ) parameter both vary with cos(⌬␸),
ʈ
1ϩ
figurations of the molecule would lead to a blurring of the
˜
it is very likely that interference between the A(Ќ) and
(1)
1ϩ
phase, and a decreased a
ʈ
( ,Ќ). However, the energy re-
˜
B( ) states is responsible for both the anomalous alignment
ʈ
quirements of the dissociation around 355 nm, supported by
the alignment results presented here, do suggest that a very
selective subset of ground state H2O2 molecules are excited
and go on to dissociate. It seems plausible that this selection
process would narrow the dissociating wave packet produced
on the excited states, leading to the observed interference.
of F1 (Jϭ1.5) molecules and the coherent orientation of
F2 (Jϭ0.5).
An important aspect of the relationship between
( ,Ќ) and cos(⌬␸) in Eq. ͑9͒ is that ⌬␸ depends implic-
ʈ
(1)
1ϩ
a
itly on the total energy available to the photofragment, and
the potential energy landscapes V(R) encountered for mol-
ecules dissociating via parallel and perpendicular states,
where R represents the set of nuclear coordinates.36 To test
VI. CONCLUSIONS
(1)
1ϩ
this dependence, we made measurements of a
ʈ
( ,Ќ) in the
Angular momentum polarization of OH(2⌸) products
following photodissociation of H2O2 near 355 nm has been
studied in detail. Rotational distributions, spin–orbit branch-
ing ratios and lambda-doublet population ratios have been
presented. The fraction of available energy going into rota-
wavelength region 330–370 nm. Due to constraints of our
laser system we were unable to make measurements at wave-
lengths longer than 370 nm. The results are shown in Fig. 12,
along with results from photolysis of Cl2 across the same
wavelength region.36 Kim et al. photolyzed Cl2 using lin-
early polarized light, and detected the Cl*(2P1/2) product
atoms using circularly polarized light. The orientation pa-
tion was small: peaking at NϷ3, f ϭ4.5%, with no pref-
͗
͘
rot
erence for either spin–orbit state. Lambda-doublet formation
rameter that they measured was imaginary Im a(1)
(
ʈ
,Ќ)
͓
͔
showed that ⌸(A ) was more populated than ⌸(A ) at
Ј
Љ
1
(1)
ͱ
ϭϪ 2a1Ϫ( ,Ќ). The results for H2O2 in the present
ʈ
Nϭ3.
(1)
work are real, where Re a(1)
(
ʈ
Integrated laboratory alignment for OH products was
,Ќ) ϭϪͱ2a
( ,Ќ). The
ʈ
1ϩ
͓
͔
1
(1)
a
(
ʈ
,Ќ) parameter depends on the sine of the asymptotic
small A(2) Ͻ0.15, and was roughly independent of J, ex-
͗
͘
0
1Ϫ
phase difference
cept for OH(2⌸3/2) at Jϭ1.5 where electronic alignment
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J. Chem. Phys., Vol. 118, No. 14, 8 April 2003
Polarization from dissociation of HOOH
6243
was found to dominate over rotational alignment. The sym-
metry of the H2O2 molecule is pseudo-diatomic, and simple
expressions were derived for the angular momentum polar-
ization in the molecule frame. Molecule frame alignment
C. J. Howard, A. R. Ravishankara, C. E. Kolb, and M. Molina, JPL Publ.
97-4, 157 ͑1997͒.
5 A. U. Grunewald, K.-H. Gericke, and F. J. Comes, J. Chem. Phys. 87,
5709 ͑1987͒.
6 F. J. Comes, K.-H. Gericke, A. U. Grunewald, and S. Klee, Ber. Bunsen-
ges. Phys. Chem. 92, 273 ͑1988͒.
a(02) )ϭ0.45Ϯ0.27, a0(2)(Ќ)ϭ0.34Ϯ0.20 for OH(2⌸3/2 , J
(
ʈ
7 M. P. Docker, A. Hodgson, and J. P. Simons, Faraday Discuss. Chem. Soc.
82, 25 ͑1986͒.
ϭ5.5) indicated strong alignment of J along for transitions
v
˜
˜
to both the A(Ќ) and B(
ʈ
) states, resulting from change in
8 J. August, M. Brouard, M. P. Docker, A. Hodgson, C. J. Milne, and J. P.
Simons, Ber. Bunsenges. Phys. Chem. 92, 264 ͑1988͒.
9 S. Klee, K.-H. Gericke, and F. J. Comes, J. Chem. Phys. 85, 40 ͑1986͒.
10 K.-H. Gericke, S. Klee, F. J. Comes, J. Chem. Phys. 85, 4463 ͑1986͒.
11 S. Klee, K.-H. Gericke, and F. J. Comes, Ber. Bunsenges. Phys. Chem. 92,
429 ͑1988͒.
torsional conformation on accessing the excited states. The
alignment of OH was found to be noncylindrically symmet-
ric about , and this was related to the mean dihedral angle
v
between the OH bonds in the H O molecule ␾ ϭ96°,
͗ ͘
2
2
d
12 M. D. Likar, J. E. Baggott, A. Sinha, T. M. Ticich, R. L. Vander Wal, and
F. F. Crim, J. Chem. Soc., Faraday Trans. 2 84, 1483 ͑1988͒.
13 M. Brouard, M. T. Martinez, C. J. Milne, J. P. Simons, and J.-X. Wang,
Chem. Phys. Lett. 165, 423 ͑1990͒.
which is less than the equilibrium value ␾dϭ112° of the
ground state. The low experimental estimate of ␾ sup-
͗
͘
d
ports the theory of Brouard et al. that nonequilibrium ground
state H2O2 molecules are dissociated.13
14 E.-A. Reinsch, Chem. Phys. Lett. 141, 369 ͑1987͒.
15 A. C. Kummel, G. O. Sitz, and R. N. Zare, J. Chem. Phys. 88, 7357
͑1988͒. Note that E10 for Case A in Table III of this paper should read
(1/ͱ2)sin 2␤.
Molecule frame orientation of OH(⌸3/2 , Jϭ5.5) was
found to be a(01)(Ќ)ϭ0.077Ϯ0.020, which we believe to be
due to electronic orientation. Orientation of OH(⌸1/2 , J
ϭ0.5) was found to be a(01)(Ќ)ϭϪ0.046Ϯ0.019 and
16 J. Luque and D. R. Crosley, LIFBASE: Database and Spectral Simulation
Program ͑Version 1.6͒, SRI International Report MP 99-009 ͑1999͒.
17 L. D. A. Siebbeles, M. Glass-Maujean, O. S. Vasyutinskii, J. A. Beswick,
and O. Roncero, J. Chem. Phys. 100, 3610 ͑1994͒.
(1)
1ϩ
(1)
1ϩ
a
(
ʈ
,Ќ)ϭ0.075Ϯ0.032. The a
ʈ
( ,Ќ) represents elec-
tronic orientation due to interference between dissociating
18 A. S. Bracker, E. R. Wouters, A. G. Suits, and O. S. Vasyutinskii, J. Chem.
Phys. 110, 6749 ͑1999͒.
states from parallel and perpendicular transitions. Measure-
(1)
ments of a
( ,Ќ) as a function of photolysis wavelength
ʈ
1ϩ
19 T. P. Rakitzis and R. N. Zare, J. Chem. Phys. 110, 3341 ͑1999͒.
(1)
were directly compared with measurements of a
( ,Ќ) for
ʈ
1Ϫ
20
˜
´
´
M. P. de Miranda, F. J. Aoiz, L. Banares, and V. Saez Rabanos, J. Chem.
Phys. 111, 5368 ͑1999͒. Note that Eq. ͑A7͒ of this reference can be used to
convert the polarization parameters of Miranda et al. to the A(qk) and aq(k)
Cl*(2P1/2) following dissociation of Cl2 across the same
wavelength range. Despite the polyatomic nature of H2O2,
with increased degrees of freedom, and implicit averaging
over room temperature configurations of the parent, the elec-
tronic coherence is not washed out. This may be due to en-
hanced dissociation cross section of a small subset of the
ground-state molecules, which are displaced from equilib-
rium, and therefore, satisfy more restrictive energy require-
ments at longer photolysis wavelengths.
used in the present work.
21
T. P. Rakitzis, G. E. Hall, M. L. Costen, and R. N. Zare, J. Chem. Phys.
111, 8751 ͑1999͒. Note that this paper deals with the semiclassical formal-
ism of Dixon, and some of the equations may not be appropriate at low J.
22 M. Ahmed, D. S. Peterka, A. S. Bracker, O. S. Vasyutinskii, and A. G.
Suits, J. Chem. Phys. 110, 4115 ͑1999͒.
23 Z. H. Kim, A. J. Alexander, and R. N. Zare, J. Phys. Chem. A 103, 10144
͑1999͒.
24 R. N. Dixon, J. Chem. Phys. 85, 1866 ͑1986͒.
25 B. V. Picheyev, A. G. Smolin, and O. S. Vasyutinskii, J. Phys. Chem. A
101, 7614 ͑1997͒.
ACKNOWLEDGMENTS
26 T. P. Rakitzis, S. A. Kandel, A. J. Alexander, Z. H. Kim, and R. N. Zare,
J. Chem. Phys. 110, 3351 ͑1999͒.
The author wants to thank Professor John Brown ͑Ox-
ford, UK͒, Dr. Mark Brouard ͑Oxford, UK͒, Dr. Marcelo de
Miranda ͑Leeds, UK͒, and Dr. Peter Rakitzis ͑FORTH IESL,
Greece͒ for useful discussions. I am grateful to Dr. Jorge
Luque ͑SRI, USA͒ for providing a version of the LIFBASE
program that deals with lambda doubling. The loan of a YAG
and dye laser system from the UK EPSRC central laser fa-
cility loan pool is gratefully acknowledged. Finally, I wish to
thank the Royal Society for the award of a University Re-
search Fellowship.
27 M. D. Likar, J. E. Baggot, A. Sinha, T. M. Ticich, R. L. Vander Wal, and
F. F. Crim, J. Chem. Soc., Faraday Trans. 2 84, 1483 ͑1988͒.
28 M. H. Alexander and P. J. Dagdigian, J. Chem. Phys. 80, 4325 ͑1984͒.
29 A. Morita and S. Kato, J. Phys. Chem. 92, 1067 ͑1992͒.
30 W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Nu-
merical Recipes in Fortran, 2nd ed. ͑Cambridge University Press, Cam-
bridge, 1992͒.
31 Z. T. Cai, D. H. Zhang, and J. Z. H. Zhang, J. Chem. Phys. 100, 5631
͑1994͒.
32 P. J. Linstrom and W. G. Mallard, editors, NIST Chemistry WebBook,
NIST Standard Reference Database Number 69, July 2001, National
Institute of Standards and Technology, Gaithersburg, MD 20899 ͑http://
webbook.nist.gov͒.
1 H. Sato, Chem. Rev. 101, 2687 ͑2001͒.
2 E. R. Wouters, M. Ahmed, D. S. Peterka, A. S. Bracker, A. G. Suits, and
O. S. Vasyutinskii, in Imaging in Chemical Dynamics, edited by A. G.
Suits and R. E. Continetti, ACS Symposium Series, Vol. 770 ͑American
Chemical Society, Washington D.C., 2000͒. Conversion factors for a(qk)(p)
33 K. Takeshita and P. K. Mukherjee, Chem. Phys. 182, 195 ͑1994͒.
34 J. Koput, S. Carter, and N. C. Handy, J. Phys. Chem. A 102, 6325 ͑1998͒.
35 R. N. Zare, Angular Momentum: Understanding Spatial Aspects in Chem-
istry and Physics ͑Wiley, New York, 1988͒.
36 Z. H. Kim, A. J. Alexander, S. A. Kandel, T. P. Rakitzis, and R. N. Zare,
Faraday Discuss. Chem. Soc. 113, 27 ͑1999͒.
in Table III of this reference are taken from Ref. 21, and may not be
appropriate at low J.
37 T. P. Rakitzis, S. A. Kandel, A. J. Alexander, Z. H. Kim, and R. N. Zare,
Science 281, 1347 ͑1998͒.
3 A. J. Alexander and R. N. Zare, Acc. Chem. Res. 33, 199 ͑2000͒.
4 W. B. DeMore, S. P. Sander, D. M. Golden, R. F. Hampson, M. J. Kurylo,
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