Resonance Raman intensity analysis of chlorine dioxide dissolved in chloroform: The role of nonpolar solvation

Article abstract of DOI:10.1063/1.1362297

An absolute resonance Raman intensity analysis (RRIA) of OClO dissolved in chloroform is presented. It is shown that solvent invariance is consistent with nonpolar or mechanical solvation dynamics dominating the solvent response to OClO photoexcitation. F

Full text of DOI:10.1063/1.1362297

Resonance Raman intensity analysis of chlorine dioxide dissolved in chloroform: The
role of nonpolar solvation
Catherine E. Foster, Bethany P. Barham, and Philip J. Reid
Citation: The Journal of Chemical Physics 114, 8492 (2001); doi: 10.1063/1.1362297
View online: http://dx.doi.org/10.1063/1.1362297
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 114, NUMBER 19
15 MAY 2001
Resonance Raman intensity analysis of chlorine dioxide dissolved
in chloroform: The role of nonpolar solvation
Catherine E. Foster, Bethany P. Barham, and Philip J. Reida)
Box 351700, Department of Chemistry, University of Washington, Seattle, Washington 98195
͑
Received 28 December 2000; accepted 14 February 2001͒
Absolute resonance Raman cross sections for chlorine dioxide ͑OClO͒ dissolved in chloroform are
2
2
obtained at several excitation wavelengths spanning the photochemically relevant B – A optical
1
2
transition. The absolute scattering cross sections of OClO are determined by reference to the 666
Ϫ1
cm transition of chloroform whose absolute scattering cross sections are reported here. The
time-dependent theory for Raman and absorption are used to develop a mode-specific description of
2
the A excited state surface. This description demonstrates that photoexcitation of OClO leads to
2
significant structural evolution along the symmetric stretch and bend coordinates, with only limited
evolution occurring along the asymmetric stretch. This description is similar to that determined for
OClO dissolved in cyclohexane and water demonstrating that the excited-state structural evolution
of OClO is similar in these solvents. Analysis of the OClO absolute scattering cross sections
Ϫ1
establishes that the homogeneous linewidth is 95Ϯ15 cm in chloroform, essentially identical to
the linewidths in cyclohexane and water. To establish the origin of this linewidth, the fluorescence
cross section for OClO dissolved in cyclohexane is measured and found to be consistent with an
excited-state lifetime of ϳ200 fs. Comparison of this lifetime to the homogeneous linewidth
establishes that the homogeneous broadening is dominated by solvent-induced pure dephasing. It is
proposed that the apparent solvent independence of the homogeneous linewidth reflects the
mechanical response of the solvent to the photoinitiated change in solute geometry. In support of
this hypothesis, the homogeneous linewidth is reproduced using the viscoelastic continuum model
of nonpolar solvation. Finally, it is argued that the restricted evolution along the asymmetric-stretch
coordinate is due to dielectric solvent–solute interactions consistent with the increase in
inhomogeneous linewidth with an increase in solvent polarity. © 2001 American Institute of
Physics. ͓DOI: 10.1063/1.1362297͔
polar and polar solvents, respectively.39 Current interest in
OClO photochemistry involves understanding the factors re-
sponsible for the environment-dependent reactivity of this
compound.
INTRODUCTION
The photochemistry of chlorine dioxide ͑OClO͒ has
been the subject of recent interest due to its participation in
the reactive chlorine reservoir and potential role in strato-
1
–4
Recent solution phase studies of OClO have sought to
spheric ozone layer depletion.
Photoexcitation resonant
2
2
identify the solvent–solute interactions which influence the
with the B – A electronic transition (␭ ϳ360 nm) re-
1
2
max
23,24,27–31,40–48
2
1,5
photoproduct quantum yields.
In particular,
sults in population of the predissociative A state. Internal
conversion from this state to the A state is followed by
2
2
femtosecond transient absorption and time-resolved reso-
nance Raman studies have been performed to monitor the
processes occurring after excited-state internal conversion.
Two main insights have emerged from this work. First, it has
been established that geminate recombination of the ClO and
1
2
internal conversion to the B2 surface from which photo-
product production is believed to occur.6,7 In the gas phase,
OClO photoexcitation results predominately in the formation
of ClO and O, with a modest amount of Cl and O also
2
1
,6–22
O photofragments resulting in OClO formation is extremely
produced.
The production of Cl and O may be pre-
2
efficient in condensed environments.2
8–30,43–46
Second, these
ceded by the formation of the peroxy isomer, ClOO, pro-
duced by OClO photoisomerization. Although Cl produc-
tion is modest in the gas phase, with the quantum yield for
6
studies have shown that Cl is produced through two distinct
pathways.4
7,48
The majority of Cl is formed within 5 ps of
atomic chlorine formation (⌽ ) being р0.04, the produc-
tion of Cl becomes substantial in condensed media with
photoexcitation, with a modest amount of Cl produced on the
hundreds-of-picosecond time scale through the thermal de-
composition of ClOO. This work has provided insight into
the reaction dynamics of OClO following internal conversion
to the ground state, and how these dynamics are modified by
the presence of solvent.
Cl
⌽Clϭ0.1–0.2 in water and methanol, and approaching unity
in low-temperature matrixes.2
3–38
In addition, the mechanism
of Cl formation is dependent on solvent polarity with the
1
3
Ϫ
g
ClϩO ( ⌬ ) and ClϩO ( ⌺ ) channels dominating in non-
2
g
2
In addition to the ground-state reaction dynamics, the
presence of solvent also influences the excited-state reaction
dynamics of OClO. We have explored this issue through
a͒Author to whom correspondence should be addressed. Electronic mail:
preid@chem.washington.edu
0021-9606/2001/114(19)/8492/13/$18.00
8492
© 2001 American Institute of Physics
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1

8493
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Resonance Raman study of OClO in CHCl3
resonance Raman intensity analysis ͑RRIA͒, and have found
the intensity of the 666 cmϪ1 transition of chloroform was
standardized for use as an internal scattering standard. The
absolute scattering cross sections of this transition were mea-
sured at the excitation wavelengths employed in this study,
and analyzed using a standard A-term cross section expres-
sion. Following standardization of the solvent, the absorption
and absolute resonance Raman cross sections for OClO were
obtained and modeled using the time-dependent formalism.
The central result of this analysis is that the excited-state
dynamics of OClO in chloroform are similar to those previ-
ously observed in water and cyclohexane, with excited-state
structural evolution dominated by motion along the symmet-
ric stretch and bend coordinates. Limited evidence is found
for evolution along the asymmetric-stretch coordinate in ac-
cord with previous work. The absolute scattering cross sec-
that the extent of evolution along the asymmetric-stretch co-
ordinate is environment dependent.4
0–42,49
Our first studies
were performed in cyclohexane where we anticipated that
modest solvent–solute coupling would result in excited-state
dynamics similar to those in the gas-phase; however, we
found that the dynamics are substantially perturbed in this
solvent. In the gas-phase, substantial evolution occurs along
the asymmetric-stretch coordinate, but the evolution along
this coordinate is extremely modest in cyclohexane.4
0,41
Ex-
tension of this work to aqueous OClO demonstrated that evo-
lution along the asymmetric stretch is essentially nonexistent
4
2
in this solvent. These observations suggest that in contrast
to the gas phase where substantial evolution along the
asymmetric-stretch results in a reduction in symmetry from
C2v to C , the limited evolution along this coordinate in
tions constrain the homogeneous linewidth in chloroform to
s
Ϫ1
9
5Ϯ15 cm , essentially identical to the values determined
condensed environments results in the preservation of C2v
symmetry. Through comparison with ab initio calculations
and symmetry-defined state-correlation diagrams, we have
proposed that this preservation of symmetry is largely re-
sponsible for enhanced Cl production in condensed environ-
ments.
in water or cyclohexane. To ascertain the contribution of
excited-state internal conversion to this linewidth, the fluo-
rescence cross section of OClO dissolved in cyclohexane
was measured and found to be modest (5.7Ϯ2.8
Ϫ9
2
ϫ10 Å ). When combined with an estimate for the radia-
tive decay rate, the fluorescence cross section constrains the
excited-state decay time to ϳ200 fs. This result demonstrates
that the homogeneous linewidth is indeed dominated by
solvent-induced pure dephasing, and that the nature of this
dephasing is similar in all solvents studied to date. We pro-
A second result to emerge from the RRIA studies was
that vibronic dephasing time as reflected by the homoge-
neous linewidth is essentially identical in cyclohexane and
water. Analysis of the absolute scattering intensities estab-
lished that the homogeneous linewidths in cyclohexane and
Ϫ1
Ϫ1
40,42
pose that mechanical or nonpolar solvation dynamics are re-
water were 80Ϯ15 cm and 85Ϯ15 cm , respectively.
sponsible for this dephasing.5
2–62
In support of this proposal,
The apparent absence of fluorescence intensity in cyclohex-
ane implied that the homogeneous linewidth was dominated
by excited-state internal conversion from the optically pre-
we demonstrate that the homogeneous linewidth as deter-
mined by RRIA can be reproduced using a viscoelastic con-
tinuum model for nonpolar solvation, consistent with me-
chanical solvation dynamics dominating the solvent response
to OClO photoexcitation. Finally, comparison of the inhomo-
geneous broadening observed in chloroform to that in cyclo-
hexane and water demonstrates that the extent of inhomoge-
neous broadening increases with solvent polarity. The
contribution of dipolar solvent–solute interactions to slower-
time broadening processes reflects the limited evolution in
the molecular dipole moment of OClO upon photoexcitation.
It is proposed that the restricted evolution along the
asymmetric-stretch coordinate is due to dielectric solvent–
solute interactions that remain roughly at equilibrium follow-
ing photoexcitation.
2
2
pared A state to a nearby state of A symmetry. The en-
2
1
2
2
ergetic proximity of the A state relative to the A state
1
2
was established by analysis of the resonance Raman depolar-
4
1
ization ratios and verified by fluorescence studies of
matrix-isolated OClO.50 However, recent femtosecond tran-
2
sient absorption studies have shown that decay of the A2
state in water and cyclohexane occurs on the ϳ200 fs time
scale suggesting that the homogeneous linewidth is not
2
dominated by decay of the A surface, but is instead due to
2
5
1
solvent-induced pure dephasing. This observation raises
the following question, ‘‘What solvent–solute interactions
are operative following OClO photoexcitation, and why
would these interactions be relatively independent of sol-
vent?’’ The experiments outlined here were performed to
address this question.
MATERIALS AND METHODS
Materials
In this paper, we present an absolute RRIA of OClO
dissolved in chloroform. This work is motivated by the fol-
lowing. The dominant solvent–solute interactions between
OClO and water are expected to be dielectric and intermo-
lecular hydrogen bonding. In contrast, both of these interac-
tions are modest and/or absent in cyclohexane. Polar, aprotic
chloroform represents an intermediate case in which dielec-
tric solvation should be operative, but intermolecular hydro-
gen bonding is not. The absolute resonance Raman cross
sections of OClO are measured at a variety of excitation
The preparation of chlorine dioxide ͑OClO͒ has been
presented elsewhere; therefore, only a brief description is
provided here.4
0,63
Potassium chlorate ͑Aldrich͒ was com-
bined with oxalic acid ͑Baker͒ and 2.3 M sulfuric acid
͑Baker͒. The reagents were heated to ϳ60 °C with continu-
ous stirring resulting in the formation of gaseous OClO. The
gaseous product was passed through a drying tube containing
phosphorous pentoxide ͑Baker͒, and then bubbled through
neat chloroform ͑Fisher, spectrophotometric grade͒ to pro-
duce a OClO in chloroform solution that was refrigerated
until use. Caution must be used in handling this solution in
2
2
wavelengths spanning the B – A optical transition. The
1
2
quantitative determination of these cross sections requires
knowledge of the solvent scattering cross sections; therefore,
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8494
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Foster, Barham, and Reid
that OClO undergoes a slow reaction with chloroform over
the course of a few days resulting in the production of a
noxious gas of unknown composition. To maintain sample
integrity, sample preparation was performed at least every
other day, and the absence of sample decomposition was
verified through measurement of the absorption spectrum,
with the presence of a transition at ϳ230 nm serving as an
indicator of sample decay.
setup, we employed the external method to standardize the
666 cm transition of chloroform. This mode, correspond-
Ϫ1
ing to the C–Cl stretching, was chosen since it is the most
intense transition in the frequency region of interest, and is
well separated from the OClO transitions. The absolute scat-
tering cross section of this transition was determined through
Ϫ1
comparison to the 802 cm line of cyclohexane, a well-
known scattering standard.6
5,67
Both 135° and 90° scattering
geometries were employed, resulting in identical cross sec-
tions within the error of the measurements ͑see below͒.
Measurement of absolute scattering cross sections also
requires knowledge of depolarization ratios, defined as the
intensity of light scattered with polarization perpendicular to
that of the excitation light divided by the intensity of light
scattered with polarization parallel to that of the excitation
light.68 Raman and resonance Raman depolarization ratios
were measured at each excitation wavelength employed in
this study. The excitation beam was passed through a set of
quartz microscope slides oriented at Brewster’s angle to de-
fine the incident polarization resulting in a contrast ratio of
Resonance Raman spectra and depolarization ratios
Resonance Raman spectra of OClO dissolved in chloro-
form were obtained at 282.4 nm, 319.9 nm, 354.7 nm, 368.9
nm, 435.7 nm, and 532.0 nm using the direct or hydrogen-
shifted second and third harmonic outputs from a 30 Hz
Nd:YAG laser ͑Spectra Physics GCR 170͒. Solutions of
OClO were flowed through a glass capillary ͑532.0 nm,
435.7 nm, 368.9 nm, and 354.7 nm͒ or wire-guided jet
͑282.4 nm, 319.9 nm, 354.7 nm, and 368.9 nm͒ at a rate
sufficient to replenish the illuminated sample volume be-
tween excitation pulses. The scattered light was collected
using standard UV-quality refractive optics, and passed
through a polarization scrambler located at the entrance of a
1
000:1. A large aperture Glan–Taylor calcite polarizer was
placed before the polarization scrambler serving to define the
polarization of the scattered light passed to the spectrograph.
Raman spectra were measured for both parallel and perpen-
dicular polarization components, with spectra corresponding
to a given component interleaved. The literature value for the
0.75 m focal length spectrograph ͑Acton͒. The scattered light
was dispersed using either a 1200 groove/mm classically
ruled or a 2400 groove/mm holographic grating. Scattered
light was detected using an 1100ϫ300 pixel, back-thinned,
liquid-nitrogen-cooled CCD detector ͑Princeton Instru-
ments͒. Sample concentrations ͑10–40 mM͒ were monitored
before and after each experiment using a HP diode array
spectrometer, with the concentration change limited to
р10% for a given experiment.
Ϫ1
depolarization ratio for the 666 cm transition of chloro-
form ͑0.02͒69 was verified in this study.
Intensity corrections
Quantitative determination of the OClO resonance Ra-
man cross sections requires knowledge of the chloroform
scattering cross sections at all of the excitation wavelengths
employed; however, absolute scattering cross sections for
this solvent have been reported for only two excitation
Scattered intensities were corrected for the wavelength
sensitivity of the detection apparatus using a standardized
quartz–tungsten–halogen lamp ͑Oriel͒ for 532.0, 435.7,
3
68.9, and 355.0 nm excitation, or a standardized deuterium
lamp ͑Hellma͒ for 319.9 and 282.4 nm excitation. Correction
for self-absorption of the sample was performed as described
elsewhere,42 with this correction resulting in only a modest
6
4
wavelengths. Therefore, a measurement of the solvent ab-
solute scattering cross sections was performed. Several meth-
ods have been used to quantitatively measure the absolute
Raman scattering cross sections of solvents. The integrating
cavity method developed by Trulson and Mathies can be
used to directly measure the total cross section of the solvent
͑р2%͒ modification of the intensities.
Determination of absolute Raman cross sections
6
5
of interest. Asher and co-workers have measured absolute
Absolute Raman cross sections for OClO were deter-
cross sections by comparing the Raman scattering of a sol-
Ϫ1
vent to the scattering from a suspension of barium sulfate.66
mined through comparison to the 666 cm mode of chloro-
form using the following expression:
Experimentally less complex standardization methods have
also been employed, with these techniques generally involv-
ing comparative methods in which scattering intensities for
the solvent of interest are compared to those of a standard-
1
ϩ2␳
IOClOCCHCl3
ͩ
ͪ
1
ϩ␳
OClO
␴OClOϭ
␴CHCl3
,
͑1͒
6
7
1ϩ2␳
1ϩ␳
ized solvent. This can be done in an ‘‘internal’’ arrange-
ment where a mixture of two solvents is studied, or in an
ICHCl3COClO
ͩ
ͪ
CHCl
3
‘‘external’’ arrangement where the Raman spectrum of the
where ␳ is the Raman depolarization ratio for a given tran-
sition, ␴ is the scattering cross section, C is concentration,
and IOClO and ICHCl3 are the experimentally determined scat-
unstandardized solvent is obtained, and then the spectrum of
the standardized solvent is obtained employing the identical
experimental apparatus. The external method has been
shown to be comparable in accuracy to the integrating cavity
tered intensities of OClO and chloroform, respectively.
Given the separation of the solvent and solute transitions,
intensities were determined through measurement of the area
under the transition of interest by trapezoidal integration.
6
7
method. Given the comparability of measurement accuracy
combined with the fact that the external standard method was
much easier to implement with our current experimental
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8495
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Resonance Raman study of OClO in CHCl3
Fluorescence spectra
corresponding to both excited-state population decay and
pure dephasing. Consistent with previous work, a Gaussian
functional form for D(t) was found to best reproduce the
In order to determine the excited-state lifetime of OClO
and the contribution of excited-state internal conversion to
the homogeneous linewidth, the fluorescence quantum yield
of OClO in cyclohexane was determined. The experimental
apparatus used for this study was essentially unchanged from
that described above. The fluorescence generated by photo-
excitation at 435.7 nm was delivered to the 0.75 m spec-
trograph using standard refractive optics, and dispersed using
a 300 groove/mm classically ruled grating. The substantial
Stokes-shift and breadth of the fluorescence spectrum re-
quired the acquisition of four spectral frames with approxi-
mately 10 nm of spectral overlap between adjacent frames.
Total integration times of 30 minutes were used to acquire
each spectral frame. To guard against differences in concen-
tration affecting the observed intensity between adjacent
spectral frames, four sample solutions of identical concentra-
tion were prepared, and a fresh solution employed for each
frame. At a given spectrograph setting, a spectrum of OClO
in solution, a spectrum of the solvent only, and a spectrum
with the incident beam blocked were obtained. The later
spectrum was used to judge the contribution of background
light to the data, but was found to be negligible for all spec-
tral frames. The spectra corresponding to OClO in cyclohex-
ane and cyclohexane only were corrected for the wavelength
sensitivity of the detection apparatus using a standardized
quartz-tungsten-halogen lamp as described above. The spec-
tra were not corrected for the chromatic aberration of the
collection optics.
absorption spectrum, and was employed in this analysis.
2
The optically prepared, A potential-energy surface was
2
modeled in the ground-state dimensionless-coordinate basis
as follows:
2
2
2
1
2
␻
1 ␻
1 ␻
el
e2
e3
2
2
͑q3͒2
͑4͒
Veϭ
͑q1Ϫ⌬1͒ ϩ
͑q2Ϫ⌬2͒ ϩ
␻gl
2 ␻g2
2 ␻g3
1
␻el 3/2
3
ϩ
␹111ͩ ͪ ͑q Ϫ⌬ ͒ .
1
1
6
␻
gl
In the above expression, ␻ and ␻ are the vibrational fre-
quencies of the ground and excited states, and the subscripts
, 2, and 3 refer to the symmetric-stretch, bend, and
e
g
1
asymmetric-stretch coordinates, respectively. Also, q is a
given normal coordinate, ⌬ is the displacement of the
excited-state potential relative to the ground state along a
given coordinate, and ␹ is the cubic anharmonicity term
along the symmetric stretch. We have assumed that there is
no anharmonic coupling between coordinates such that the
absorption ( i͉i(t) ) and Raman ( f͉i(t) ) time correlators
͗ ͘ ͗ ͘
are separable into three independent overlaps along each co-
ordinate:
3
͗
͗
i
f
͉
i t͒ ϭ
͑
͘
͟
͗
i
͉
i t͒ ,
͑
͘
͑5͒
͑6͒
k
k
kϭ1
3
͉
i͑t͒
͘
ϭ
͗
f1
͉
i1͑t͒
͘
͗ ͘
ik͉ik͑t͒ .
͟
kϭ2
Computational analysis
For harmonic modes, the analytic expressions of Mukamel
were used to calculate the time-dependent overlaps along a
The absorption spectrum and Raman cross sections were
modeled using the time-dependent formalism for absorption
and Raman scattering:7
0–72
3
4
4
eg
8
␲E E e M
ϱ
s
l
␴R͑E ͒ϭ
͵
ץE H͑E ͒
00 00
1
ប6c4
9
Ϫϱ
2
ϱ
i͑E ϩE ͒t/ប
l
i
ϫ
͵
͗
f
͉
i͑t͒
͘
e
D͑t͒dt ,
͑2͒
͑3͒
ͯ
ͯ
0
2
2
eg
4
␲e E M
ϱ
l
␴A͑E ͒ϭ
͵
ץE H͑E ͒
l
ប2cn
00
00
6
Ϫϱ
ϱ
i͑E ϩE ͒t/ប
l
i
ϫ
͵
Ϫϱ͗
i
͉
i͑t͒
͘
e
D͑t͒dt.
In the above expressions, M is the transition length, E and
eg
l
E are the incident and scattered frequencies, respectively, n
s
is the refractive index of the solvent, E is the initial vibra-
i
tional energy, and E00 is the energy difference between the
ground vibrational levels of the ground and excited elec-
tronic states. H(E ) represents inhomogeneous broadening
0
0
corresponding to the distribution of E00 energies created by
different solvent environments that are static on the time
scale of Raman scattering. The solvent site distribution was
modeled as Gaussian with reported values for the inhomoge-
neous broadening ͑⌰͒ representing the standard deviation of
this distribution. D(t) is the homogeneous damping function
FIG. 1. Experimental ͑solid͒ and calculated ͑dotted͒ electronic absorption
spectrum of OClO dissolved in chloroform. The parameters used in calcu-
lating this spectrum are presented in Table III.
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1

8496
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Foster, Barham, and Reid
TABLE I. Absolute Raman cross section for the 666 cmϪ1 mode of chlo-
roform.
␴R (ϫ1012 Å )a
2
Excitation wavelength ͑nm͒
5
4
3
3
3
2
32.0
35.7
68.9
55.0
19.9
82.4
0.6Ϯ0.1b
1.6Ϯ0.5
3.7Ϯ0.3
4.3Ϯ0.4
7.5Ϯ0.3
13.0Ϯ4.0
aCross sections were determined by comparison to the 801 cmϪ1 mode of
cyclohexane as described in the text.
b
Errors represent one standard deviation from the mean.
given coordinate.73 For anharmonic modes, we used the ap-
proximate time-propagator method of Feit and Fleck.7
4,75
2
2
i͑⌬t͒“ /4M
eϪ1͑⌬t͒V
i͑⌬t͒“ /4M
3
͉
i͑t͒
͘
ϭe
e
͉
i͑0͒
͘
ϩ␽͑⌬t ͒,
͑7͒
2
FIG. 3. Resonance Raman spectrum of OClO dissolved in chloroform ͑10
mM͒ obtained at 368.9 nm excitation. Transitions due to the solvent are
marked with asterisks. Transitions corresponding to the symmetric-stretch
(v ) and bend (v ) are indicated. The inset shows an enlargement of the
region of the asymmetric-stretch overtone transitions, and demonstrates the
absence of intensity for this transition.
where “ is the Laplacian in position space, V is the poten-
tial of the excited state, and ⌬t is the size of the propagation
time step in femtoseconds. Given that the error in the ap-
proximate time-propagator method scales as the their power
of the time step, a minimum step size of 0.5 fs was em-
ployed. Overlaps were determined for times up to ϳ1 ps.
1
2
RESULTS
broadening observed in water and the modest broadening
observed in cyclohexane. We have assumed that the absorp-
tion cross section at the maximum is 0.042 Å , identical to
Absorption spectrum
2
The absorption spectrum of OClO in chloroform is pre-
the cross sections in water and cyclohexane.
sented in Fig. 1. Similar to the absorption spectra of OClO
dissolved in cyclohexane and water,4
0,42
the spectrum in
chloroform displays vibronic structure arising from progres-
sions involving the symmetric stretch. The broadening evi-
dent in the spectrum is intermediate between the substantial
Absolute Raman cross sections for chloroform
As illustrated by Eq. ͑1͒, measurement of the absolute
scattering cross sections of OClO requires knowledge of the
absolute Raman scattering cross sections of the solvent.
Therefore, absolute scattering cross sections for the 666
Ϫ1
cm mode of chloroform were measured at the excitation
wavelengths employed. The measured scattering cross sec-
tions for this transition are reported in Table I and presented
in Fig. 2. Also presented in Fig. 2 is the best fit to these cross
sections employing an ‘‘A-term’’ expression:6
5–67
2
2
0
2
2
v ϩv
e
3
␴R͑v ͒ϭKv ͑v Ϫv͒
.
͑8͒
0
0
0
ͩ
2
2
ͪ
͑
v Ϫv ͒
e 0
In Eq. ͑8͒, v is the energy of the excited state from which
the preresonant intensity is derived, v is the incident fre-
e
0
quency, v is the frequency of the mode of interest, and K is
the coupling strength. Parameters derived from best fit to the
Ϫ1
A-term expression are v ϭ123 400 cm
and Kϭ1.313
e
Ϫ9
2
ϫ10 Å . The value for v is consistent with the prediction
e
Ϫ1
of several excited states around 110 000 cm , with intensity
likely derived from more than one of these states.76 Cross
sections for this transition have also been measured by Abe
et al. at two excitation wavelengths ͑514.5 and 337.1 nm͒,
and these values are also presented in Fig. 2. Inspection of
the figure demonstrates that the agreement between our re-
sults, previous measurements, and the A-term fit are all quite
reasonable.
FIG. 2. Absolute Raman cross sections for the 666 cmϪ1 transition of chlo-
roform measured in this study ͑circles͒, and the cross sections reported by
Abe et al. ͑squares͒ ͑Ref. 64͒. Absolute cross sections are presented in
Table I. The A-term fit to these cross sections as described in the text is
given by the solid line. Errors represent one standard deviation from the
mean.
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1

8497
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Resonance Raman study of OClO in CHCl3
TABLE II. Absolute Raman cross sections of chlorine dioxide in chloroform.
Excitation
wavelength
␴R v1
␴R 2v1
(ϫ10 Å )
␴R
v
␴R 2v2
(ϫ10 Å )
␴R 2v3
(ϫ10 Å )
2
a
(ϫ10 Å2)b
10
10
2
(ϫ10 Å2)
10
10
2
10
2
͑nm͒
␳(v1)
532.0
435.7
368.9
355.0
319.9
282.4
0.28Ϯ0.07c
0.26Ϯ0.03
0.36Ϯ0.04
0.31Ϯ0.04
0.28Ϯ0.05
0.18Ϯ0.04
0.08Ϯ0.02
2.3Ϯ0.5
7.0Ϯ1.0
8.0Ϯ2.0
7.1Ϯ1.0
2.0Ϯ0.8
1.8Ϯ0.3
6.1Ϯ0.7
9.9Ϯ0.7
4.3Ϯ0.5
0.7Ϯ0.5
1.9Ϯ0.4
0.5Ϯ0.2
р0.18d
aRaman depolarization ratio for the symmetric-stretch fundamental transition. This ratio is defined as the
scattered intensity with polarization perpendicular to that of the incident radiation divided by the scattered
intensity with polarization parallel to the incident radiation.
b
Absolute Raman scattering cross sections. These values were determined by comparison to the 666 cmϪ1 mode
of chloroform as described in the text.
Errors represent one standard deviation from the mean.
The value represents an upper limit for the cross section. This limiting value was determined by comparison to
c
d
the intensity of the symmetric-stretch overtone transition and the signal-to-noise of the measurements.
bonding in water.42 Isotope splitting of the overtone band is
evident with intensities consistent with the natural abundance
Resonance Raman intensity analysis
The resonance Raman spectrum of OClO in chloroform
obtained with 368.9 nm excitation is shown in Fig. 3. The
absolute cross sections for all transitions investigated in this
study at the excitation wavelengths employed are reported in
Table II. Fundamental transitions corresponding to the sym-
3
5
37
of Cl and Cl. Finally, the expanded view of the overtone
region presented in Fig. 3 demonstrates that intensity assign-
able to the overtone transition of the asymmetric-stretch co-
ordinate is not observed. The absence of intensity assignable
to this transition is consistent with limited evolution along
this coordinate as discussed below.
Refinement of the excited-state potential energy surface
parameters ͓Eq. ͑4͔͒ was performed to reproduce the absorp-
tion and resonance Raman cross sections. The best reproduc-
tion of the absorption spectrum is presented in Fig. 1 ͑dotted
line͒, with the excited-state parameters derived from this
analysis presented in Table III. Inspection of Fig. 1 demon-
strates that the agreement between the experimental spec-
trum and the model spectrum is good. Deviation between the
data and model is observed on the red edge of the absorption
spectrum. Similar deviations have been observed for other
Ϫ1
Ϫ1
metric stretch ͑938 cm ͒ and the bend ͑450 cm ͒ coordi-
nates are readily observed, as are overtones and combination
bands involving these coordinates. This pattern of scattered
intensity is similar to that observed for OClO dissolved in
water and cyclohexane demonstrating that the excited-state
structural evolution in all three solvents is similar.4
0,42
In
addition, the transition frequencies observed in chloroform
are consistent with those observed in cyclohexane. For ex-
ample, the frequencies of the symmetric-stretch fundamental
transition in chloroform and cyclohexane are identical ͑938
Ϫ1
cm ͒, but different from the frequency of this transition in
Ϫ1
water ͑945 cm ͒ consistent with intermolecular hydrogen
TABLE III. 2A2 excited-state potential energy surface parameters for chlorine dioxide in chloroform.a
␴R Expt.f
␴R Calc.
(ϫ10 Å )
Transitionb
␻g ͑cm
Ϫ1 c
͒
␻e ͑cmϪ1
͒
⌬d
␹ ͑cm
Ϫ1 e
͒
(ϫ10 Å2)
b10
10
2
v1
v2
v3
938
450
1100
695
267
825
5.62
0.45
0
Ϫ17.5
7.0Ϯ1.0
1.9Ϯ0.4
Ͻ0.1
8.5
1.9
0
2
2
2
v1
v2
v3
6.1Ϯ0.7
0.5Ϯ0.2
р0.18
6.1
0.4
0.18
a
Calculation performed with a Gaussian homogeneous linewidth. Best fit to the experimental cross sections
Ϫ1
Ϫ1
resulted in ⌫ϭ95Ϯ15 cm
ϭ17 940 cm , nϭ1.444.
,
inhomogeneous standard deviationϭ220Ϯ10 cm
, Megϭ0.38 Å, E00
Ϫ1
b
Raman transition for which the calculation is performed. The symbols v , v , and v refer to the symmetric
1
2
3
stretch, bend, and asymmetric stretch, respectively. The first three terms correspond to fundamental transitions
and the latter three terms refer to overtone transitions.
␻g refers to the ground-state harmonic frequency, and ␻e is the excited-state harmonic frequency.
The dimensionless displacement of the excited-state potential energy surface minimum relative to the ground
c
d
state.
e
Anharmonicity prefactor for the cubic term in the series expansion of the potential energy surface. By com-
1.5
0.5
parison to the description of the Morse oscillator, this term is equal to (␻ /2) /De in dimensionless units
e
where ␻ is the excited-state harmonic frequency and De is the Morse dissociation energy given by
e
2
␻e/(4␻ x ) where x is the anharmonicity parameter ͑Ref. 93͒.
e
e
e
f
Experimental Raman cross sections determined using 368.9 nm excitation.
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8498
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Foster, Barham, and Reid
ond attempt to improve agreement between the data and
model involved application of the stochastic model for
broadening developed by Kubo and adapted by Mukamel.79
However, the best agreement was obtained in the slow-
modulation limit of this formalism corresponding to a Gauss-
ian functional form for D(t), identical to the phenomeno-
logical model originally employed.
Figure 4 presents the Raman excitation profiles for the
symmetric-stretch fundamental ͑A͒, symmetric-stretch over-
tone ͑B͒, bend ͑C͒, and asymmetric-stretch overtone transi-
tions ͑D͒. Best reproduction of these intensities is presented
as the solid line corresponding to the excited-state potential-
energy-surface parameters presented in Table III. Absolute
resonance Raman cross sections are dependent on the mag-
nitude of the homogeneous linewidth; therefore, these cross
sections can be used to partition between homogeneous and
inhomogeneous broadening.71 The dotted line presented in
Fig. 4 corresponds to a model in which all broadening is
incorporated as homogeneous. The figure demonstrates that
the symmetric-stretch fundamental and overtone cross sec-
tions are modestly dependent on the homogeneous linewidth.
However, the slower buildup of the Raman time correlator
along the bend results in this fundamental transition along
this coordinate being quite dependent on the extent of homo-
geneous broadening ͓Fig. 4͑C͔͒. The measured cross section
along this coordinate in combination with the symmetric-
stretch fundamental and overtone transitions were used to
Ϫ1
constrain the homogeneous linewidth to 95Ϯ15 cm
.
The ground-state symmetry of OClO is C2v such that
fundamental resonance Raman intensity along the
asymmetric-stretch coordinate is not expected. However,
overtone intensity along this coordinate can be observed if
the excited-state potential-energy surface differs significantly
FIG. 4. Raman excitation profiles for the symmetric stretch fundamental
A͒, the symmetric stretch overtone ͑B͒, the bend ͑C͒, and the asymmetric
80
from that of the ground state. The paucity of asymmetric-
͑
stretch overtone intensity ͑Fig. 3͒ suggests that excited state
evolution along this coordinate is modest. Comparison to the
intensity of the symmetric-stretch overtone transition and the
signal-to-noise of the spectrum places an upper limit on the
stretch overtone ͑D͒ transitions. The points represent the experimental data,
and the error bars represent the standard deviation from the mean. The best
fit to the data ͑solid lines͒ was obtained using the parameters reported in
Table III. The fit using only homogeneous broadening ͑dashed lines͒ is
presented.
Ϫ11
2
cross section of the overtone transition of 1.8ϫ10
Å .
This modest cross section is consistent with a reduction in
excited-state frequency along this coordinate to у825
Ϯ20 cm . As in our previous studies, the gas-phase poten-
tial Richard and Vaida and the ab initio surface of Peterson
systems when an exponential form for D(t) is employed, and
Ϫ1
this has lead to the incorporation of Gaussian and other func-
tional forms for D(t).7
7,78
However, Fig. 1 demonstrates that
were not capable of reproducing the lack of intensity ob-
a Gaussian functional form for D(t) still results in a notice-
able deviations between the experimental spectrum and the
model. Therefore, other functional forms for D(t) were stud-
ied in an attempt to better reproduce the absorption intensity
at lower frequency. Previous studies of rotationally cooled
gaseous OClO have shown that the homogeneous linewidth
increases with excitation along the symmetric stretch.9
Therefore a level-dependent homogeneous linewidth was in-
corporated to reproduce the dependence of the excited-state
decay rate on excitation along the symmetric stretch. In this
approach, a slow Fourier transform of the absorption and
Raman time correlators was performed with the homoge-
neous linewidth increasing as the energy over which the
transformation was performed was increased. Level depen-
dence of the homogeneous linewidth did not significantly
improve the agreement beyond that evident in Fig. 1. A sec-
7
,8
served in the asymmetric stretch in chloroform.
Fluorescence results
Figure 5 shows the emission and absorption spectra of
OClO in cyclohexane. Measurements were also performed
for OClO dissolved in water; however, the fluorescence cross
section in water was found to be essentially identical to that
in cyclohexane such that the results in water are not pre-
sented. Inspection of the figure demonstrates that a broad
background is observed under the sharper Raman features,
with this background corresponding to OClO fluorescence.
The fluorescence intensity appears to be the mirror image of
the absorption intensity consistent with the emission being
relaxed; however, it must be noted that excitation wave-
length dependence of the emission was not investigated to
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8499
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Resonance Raman study of OClO in CHCl3
rate assuming an estimate for the radiative rate is available.
An estimate for this rate is provided by the following:83
9
2
3
Ϫ1
k ϭ2.88ϫ10 n
͗
vf
͘
͵
⑀d ln v,
͑10͒
R
where ⑀ is the extinction coefficient, n is the solvent refrac-
tive index, the term in brackets corresponds to the average
frequency of the emission band, and the integration is done
over the absorption band. For OClO in cyclohexane, we cal-
6
Ϫ1
culated k ϭ5ϫ10 s . Combining the estimate for k with
R
R
␾F , a value for the nonradiative-decay rate of kNRϭ5
1
2 Ϫ1
ϫ10 s is obtained corresponding to an excited-state life-
time of ϳ200 fs. This estimate for the excited-state lifetime
is in remarkable agreement with the ϳ200 fs decay time of
2
the A2 state measured by femtosecond pump–probe
spectroscopy.51
FIG. 5. Fluorescence and absorption spectra of OClO in cyclohexane. The
absorption cross sections are displayed in units of Å , and the fluorescence
DISCUSSION
2
spectra are scaled to approximately the same height in arbitrary intensity
units. The fluorescence emission is the broad background under the sharper
Raman transitions. The excitation wavelength ͑435.7 nm͒ is indicated.
OClO excited-state structural evolution
The RRIA of OClO dissolved in chloroform presented
here demonstrates that the excited-state structural evolution
in this solvent is similar to that observed in water and
cyclohexane.4
0,42
The dominant structural change upon pho-
ascertain if this is indeed the case. Etaloning effects from the
back-thinned CCD employed in this study restricted the
spectral region to that depicted in Fig. 5. This limitation
required the generation of an accurate estimate for the fluo-
rescence intensity at lower frequency. This was performed
by fitting the entire emission envelope using the time-
dependent formalism for fluorescence via the following
toexcitation occurs along the symmetric-stretch ͑Table III͒,
with the displacement along this coordinate in chloroform
essentially identical to that in water (⌬ϭ5.62 in CHCl ver-
3
sus 5.63 in water͒. There is also modest evolution along the
bend (⌬ϭ0.45 in CHCl versus 0.4 in water͒, and essentially
3
no evolution along the asymmetric stretch. In our previous
analysis of aqueous OClO, the dimensionless displacements
were determined to reflect geometry changes corresponding
to an increase in Cl–O bond length from 1.47 Å to 1.68 Å
and a decrease in valence angle from 117.4° to 108.8°.42 The
similarity of excited-state displacements observed between
chloroform and water dictates that this evolution must also
describe the excited-state structural relaxation of OClO in
chloroform.
8
1,82
equation:
Iϰv3
͗
i
͉
f͑t͒
͘
,
͑9͒
where v is the emission frequency, and
͗
i
͉
f(t)
͘
is the over-
lap between the initial wave function in the excited state and
the same wave function propagating under the influence of
the ground state Hamiltonian. The parameters reported in our
previous RRIA study of OClO in cyclohexane were used in
4
0,42
this analysis.
Although this approach clearly compro-
Depolarization ratios
mises the quantitative determination of the fluorescence in-
tensity, it does provide a reasonable estimate of the intensity
at lower frequency. The area of the fluorescence band deter-
mined from this analysis was compared to area of the
symmetric-stretch fundamental transition to determine the
fluorescence cross section. This analysis provided a value for
The resonance Raman depolarization ratio can be used to
ascertain if the observed intensity is generated via resonance
with a single electronic excited state.6
8,84
Specifically, a
value of ␳ϭ1/3 indicates that the contribution to the scatter-
ing is from a single state. In our previous studies, the depo-
larization ratio for the symmetric-stretch fundamental transi-
Ϫ9
2
the fluorescence cross section of 5.7Ϯ2.8ϫ10 Å . Two
separate measurements were performed, and the value for the
cross section represents the average of these measurements.
The difference between measurements was only 20%; how-
ever, the error estimate provided here is substantially greater
than this value reflecting the possibility of systematic errors
in the area determination as described above. The fluores-
cence and absorption cross sections were used to calculate
the fluorescence quantum yield (⌽ ϭ␴ /␴ ) resulting in
tion was Ͻ1/3, and we have shown that contributions to the
2
polarizability tensor from the nearby A state were respon-
1
sible for the deviation of ␳ from 1/3.41 In contrast, the depo-
larization ratio of the symmetric stretch fundamental transi-
2
tion in chloroform is essentially 1/3, implying that the A
1
2
state is energetically shifted relative to the A surface in this
2
solvent relative to water or cyclohexane. This hypothesis can
be tested by acquiring and analyzing the resonance Raman
depolarization dispersion curves, and we are currently pursu-
ing such a study. With respect to the current analysis, the
closeness of the ␳ to 1/3 indicates that the single state ap-
proximation employed in this analysis is reasonable.
F
F
A
Ϫ6
␾Fϳ1ϫ10 . Elementary kinetics dictates that the fluores-
cence cross section is equal to k /(k ϩkNR) where kNR is
R
R
the nonradiative-decay rate and kR is the radiative-decay
rate. Given this, ⌽ can be used to calculate the nonradiative
F
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8500
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Foster, Barham, and Reid
Homogeneous and inhomogeneous broadening
general theory and the key equations of VCT have been
presented;5
3,87,88
therefore, only a brief overview describing
Analysis of the absolute scattering intensities demon-
the physics behind this model and the central results of this
theory are presented here. The solute is approximated as a
spherical cavity located within the solvent modeled as a vis-
coelastic continuum. Before excitation, a balance exists be-
tween the force applied by the continuum directed towards
collapse of the solute cavity, and the restoring force applied
to the continuum by the solute opposing cavity collapse.
Photoexcitation of the solute initiates a change in molecular
size, which results in a corresponding change in the force
applied by the solute to the cavity boundary. The size of the
solute cavity will therefore change to restore equilibrium be-
tween the solvent and solute forces. The solvent is modeled
as isotropic, and the solvent response is separated into two
components, one that occurs in the same direction of the
applied force ͑known as the compressive strain͒ and another
that occurs in directions perpendicular to the applied force
strates that the homogeneous linewidth ͑⌫͒ in chloroform is
Ϫ1
95 cm , essentially identical to that determined in water or
cyclohexane. The homogeneous linewidth contains contribu-
tions from both excited-state population decay and solvent-
induced pure dephasing:77
1
1
1
⌫
ϭ
ϭ
ϩ
.
͑11͒
T2 2T1 T*
2
In the above expression, T is the total dephasing time, T is
2
1
the excited-state lifetime, and T* is the time scale for pure
2
dephasing. The solvent independence of ⌫ could mean either
that the contributions from T and T* are equal in all sol-
1
2
vents studied to date, or that the solvent-dependent differ-
ences between T and T* cancel each such that the homo-
1
2
geneous linewidth simply appears to be solvent invariant.
The fluorescence cross section of OClO in cyclohexane and
recent femtosecond pump–probe work51 establishes that T1
͑known as the shear strain͒. Correspondingly, the response of
the solvent is described by the compressive and shear moduli
denoted as K and G, respectively. For a force resulting in
deformation of the material only in the same direction as the
applied force, the ratio of the stress to the strain in that di-
rection is called the wave modulus, M, and is given by
is ϳ200 fs. Given a T time of ϳ200 fs and the homoge-
1
Ϫ1
neous linewidth of 85 cm corresponding to T ϳ60 fs, Eq.
2
͑
10͒ dictates that T* is ϳ64 fs such that solvent-induced
2
pure-dephasing processes must make the dominant contribu-
tion to the homogeneous linewidth.
4
3
MϭKϩ G.
͑12͒
Nonpolar solvation dynamics and solvent-induced
dephasing
The moduli G, K, and M describing the viscoelastic re-
sponse of the medium are in general time dependent. How-
ever, the dynamics of interest here occur on a relatively short
time scale such that we consider only the short-time, solid
like response of the medium, and only the high frequency
moduli (G , K , and M ) are employed. By solving the
The question remains as to which solvent–solute inter-
actions give rise to dephasing on the ϳ60 fs time scale, and
why these interactions are apparently similar in all solvents
studied to date. We propose that the origin of this dephasing
is nonpolar or mechanical solvation in response to the sub-
stantial geometry changes accompanying OClO photoexcita-
tion. The motivation behind this hypothesis is as follows. Ab
initio studies predict that the dipole moment ͑␮͒ of OClO
changes very little upon photoexcitation with ␮ϭ1.71 D and
ϱ
ϱ
ϱ
appropriate viscoelastic equations of motion, Berg has used
these moduli to calculate the solvent response, R(t):5
2,53
t
t
R͑t͒ϭ͑1Ϫf ͒eϪt/␶
ϩfeϪt/␶st
cosͩ ͪϪ␤ sinͩ ͪͪ
ph
ͩ
␤
␶
␤␶
ph
ph
2
2
1
.85 D in the excited ( A ) and ground ( B ) states,
͑13͒
2
1
8
5
respectively. Furthermore, the direction of the dipole mo-
ment is relatively unchanged. Without a large change in the
electronic distribution of the solute, one would expect the
dielectric response of the solvent to be modest. In contrast,
significant evolution occurs along the symmetric stretch and
bend coordinates such that it is reasonable to assume that
mechanical or nonpolar solvation dynamics dominate the
solvent response to OClO photoexcitation.
with
␤2
M ϩ͑K ϪK ͒
ϱ
s
ϱ
ϭ3
,
͑14͒
͑15͒
͑16͒
͑17͒
͑18͒
M Ϫ3͑K ϪK ͒
ϱ
s
ϱ
4
/3Gϱ
fϭ
,
Ksϩ4/3Gϱ
1ϩ␤2͒
͑
Assuming that nonpolar solvation dynamics dominate
the solvent response, do these dynamics occur on a similar
time scale for the three substantially different solvents ͑wa-
ter, cyclohexane, and chloroform͒? Furthermore, is the time
scale over which these interactions are operative sufficient to
be responsible for dephasing on the ϳ60 fs time scale? There
are several current theories describing nonpolar
␶ph
ϭ
␶l ,
2
␤2
␳
␶lϭrc
ͱ
,
Mϱ
␩
/G
ϱ
␶ ϭ
st
.
1
Ϫf
5
2–62
solvation;
however, we have focused our attention on
the viscoelastic continuum theory ͑VCT͒ developed by
In the above equations, ␶ is the time for longitudinal sound
1
5
2–54
Berg.
This focus is largely motivated by the analytic
waves to travel a distance of one cavity radius, K is the
s
nature of this theory, and by recent three-pulse photon echo
studies of Fleming and co-workers which have demonstrated
the ability of this theory to model nonpolar solvation.86 The
effective compressive modulus of the solute, ␳ is the solvent
density, and r is the cavity radius taken to be 3 Å. Equation
c
͑13͒ is valid in the limit where phonon-induced solvation is
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8501
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Resonance Raman study of OClO in CHCl3
TABLE IV. Solvent-dependent parameters used in viscoelastic calculations.
Gϱ
Kϱ
Ks
␳a
␩a
␶ph
␶st
͑fs͒
(ϫ10Ϫ10 dyn/cm2) (ϫ10Ϫ10 dyn/cm2) (ϫ10Ϫ10 dyn/cm2) ͑g/cm ͒ ͑cP͒ ͑fs͒
3
Solvent
b
4.4b
11.4
4.2e
3.9b
11.4
2.5e
0.778c 1.02c
0.997c 0.89c
Cyclohexane
Water
Chloroform
0.8
8.5
85 1500
d
e
d
d
40
200
670
1.5
1.483c 0.56c 130
a
All values are interpolated for 25 °C.
Values are the average for benzene and toluene reported in Ref. 86.
Values are taken from Ref. 94.
Values are taken from Ref. 52.
b
c
d
e
Values are those reported for CCl in Ref. 86.
4
␦2
␶
2
ph
rapid compared to the structural relaxation of the solvent
such that the solvent response can be partitioned into a
phonon-induced term ͓the term with the (1Ϫf ) prefactor in
Eq. ͑13͔͒ and a structural relaxation term. The validity of this
limit for the solvents studied here deserves some comment.
The time constants for phonon (␶ ) and structural (␶ ) re-
laxation can be determined using Eqs. ͑16͒ and ͑18͒, respec-
tively. With the viscoelastic parameters presented in Table
IV, the predicted phonon relaxation times vary from 40 fs in
water to 130 fs in chloroform while the structural relaxation
time constants vary from 200 fs in water to 1500 fs in cy-
clohexane. These times are sufficiently different such that the
separation of the solvent response into two separate compo-
nents is assumed to be valid.
g͑t͒ϭ͑1Ϫf ͒
1
␤2
ប2 1ϩ
ͩ
ͪ
t
t
ϫ
ͩ
1Ϫet/␶
ͩ
cosͩ ͪϩ␤ sinͩ ͪͪͪ
ph
ph
st
␤
␶
␤␶
ph
ph
2
␦ ␶2
t
st
Ϫt/␶
st
ϩf
ͩ
ϩe
Ϫ1
ͪ
.
͑21͒
ប2 ␶st
The above expression was employed using only ␦ as an ad-
justable parameter in an attempt to reproduce the Gaussian
function form of D(t) as determined in our RRIA studies. A
comparison between D(t) as determined by our RRIA of
OCIO dissolved in cyclohexane40 and the VCT model is pre-
sented in Fig. 6͑A͒. Specifically, the Gaussian form for D(t)
In the limit of linear response, R(t) can be equated to
C(t), the normalized correlation function that describes the
solvent-induced fluctuations in the energy gap between
ground and excited state of the solute:
Ϫ1
with ⌫ϭ80 cm is given by the solid line and the short-
dashed line is the VCT result with ␦ϭ145 cm . The corre-
Ϫ1
sponding solvent response function, R(t), is given by the
short-dashed line in Fig. 6͑B͒. The viscoelastic parameters
used to calculate the VCT result correspond to the average
values determined for benzene and toluene by three-pulse
photon echo ͑Table IV͒.86 The values for ␶ph and ␦ are in
reasonable agreement with the photon echo results where in
benzene and toluene, a ϳ100 fs component of the solvent
͗
␦U͑t͒␦U͑0͒
͘
C͑t͒ϭ
.
͑19͒
␦U2
͗
͘
In the above expression, U is the energy gap between ground
and excited states, and ␦U(t)ϭUϪ is the fluctuation of
͗ ͘
U
the energy gap from its equilibrium value. The assumption of
linear response dictates that the post-perturbation relaxation
of the system towards equilibrium is determined by the fluc-
tuations that characterize the system at equilibrium.89 As-
suming linear response holds, then R(t) as described by
VCT can be used to describe C(t). This term can subse-
quently be used to determine the functional form for homo-
geneous dephasing, D(t). The determination of D(t) follows
Ϫ1
response having a reorganization energy of ϳ50 cm was
found to make a substantial contribution to the solvent
86
response. Inspection of Fig. 6͑A͒ demonstrates that VCT is
capable of reproducing the D(t) in cyclohexane consistent
with mechanical solvation dynamics dominating the solvent
response to OClO photoexcitation in this solvent.
A more stringent test of the VCT model involves its
ability to reproduce the solvent invariance of D(t). Figure
closely the Brownian oscillator development presented by
6
͑C͒ presents the comparison of D(t) determined in our
Mukamel and co-workers7
7,79
in which solvent-induced
Ϫ1
RRIA study of OClO dissolved in water (⌫ϭ85 cm ͒ to the
prediction of VCT with ␦ϭ160 cm and other viscoelastic
parameters as compiled by Berg ͑Table IV͒. The corre-
dephasing is incorporated into the expression for Raman or
absorption cross section by D(t)ϭe
Ϫ1
Ϫg(t)
where
52
sponding solvent response function for water using identical
t
␶
1
parameters is presented in Fig. 6͑D͒. Figure 6͑E͒ presents the
g͑t͒ϭ
͵
d␶1
͵
d␶2
͗
␦U͑␶ ͒␦U͑0͒
͘
.
͑20͒
2
Ϫ1
0
0
corresponding comparison for chloroform with ⌫ϭ95 cm
Ϫ1
and ␦ϭ150 cm , and Fig. 6͑F͒ shows the corresponding
Thus, by knowing C(t) and equating the variance of the
fluctuations to ␦ , a functional form for g(t) and subse-
quently D(t) can be obtained. Using the R(t) provided in
Eq. ͑13͒ and performing the integration prescribed by Eq.
solvent response function. In these calculations, the vis-
2
coelastic parameters employed are those for CCl reported
4
by Fleming and co-workers.86 As illustrated by Table IV, the
viscoelastic parameters for these three solvents are markedly
different; however, Fig. 6 demonstrates that the VCT model
͑20͒, we arrive at the following functional form for g(t):
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8502
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Foster, Barham, and Reid
dielectric solvation dynamics are modest as is the case here.
One final question concerns the nature of the solvent–
solute interactions responsible for restricting evolution along
the asymmetric-stretch coordinate. Previously, we had sug-
gested that dielectric solvent–solute interactions were re-
sponsible for this behavior since the largest change in mo-
lecular dipole moment occurs with displacement along the
asymmetric stretch.4
0,42
However, the discussion presented
above indicates that nonpolar solvation dynamics dominate
the initial solvent response to OClO photoexcitation. This
apparent discrepancy can be resolved if one assumes that
dipolar solvent–solute interactions are operative on a time
scale longer than that dictated by the homogeneous line-
width, an assumption that is supported by the increase in
inhomogeneous linewidth accompanying an increase in sol-
vent polarity. The contribution of these interactions to
slower-time dynamics can be understood by considering the
essential invariance of the molecular dipole moment to pho-
toexcitation. We envision OClO as a dipole located at center
of an Onsager cavity, with the surrounding solvent described
as a uniform dielectric. Reorientation of the molecular dipole
FIG. 6. ͑A͒ Comparison between the Gaussian functional form for D(t) and
the viscoelastic continuum theory ͑VCT͒ prediction ͓Eq. ͑21͔͒ of D(t) for
Ϫ1
cyclohexane. The Gaussian form corresponds to ⌫ϭ80 cm ͑solid line͒,
Ϫ1
and the VCT result ͑dashed line͒ corresponds to ␦ϭ145 cm and other
viscoelastic parameters as provided in Table IV. ͑B͒ The solvent response
function ͓Eq. ͑13͔͒ predicted using VCT employing parameters identical to
those used in part ͑A͒. ͑C͒ Comparison between the Gaussian functional
form for D(t) and the VCT result for water. The Gaussian form corresponds
moment will be accompanied by response of the surrounding
90,91
Ϫ1
dielectric, referred to as the solvent frictional force.
In
to ⌫ϭ85 cm ͑solid line͒, and the VCT result ͑dashed line͒ corresponds to
Ϫ1
general, the dielectric relaxation will be frequency depen-
dent, and related to the velocity of charge motion ͑i.e., dipole
rearrangement͒ within the cavity. Optical methods have pro-
vided much insight into frequency dependent dielectric
response,92 and these measurements typically employ probe
molecules whose molecular dipole moment undergoes a sub-
stantial change in direction and/or magnitude upon photoex-
citation. Rapid reorientation of the molecular dipole is ex-
pected to preferentially couple to high-frequency
components of the dielectric response. OClO represents the
opposite extreme in which neither the magnitude nor direc-
tion of the molecular dipole moment changes significantly
upon photoexcitation ͑see above͒. Correspondingly, one
would expect significant coupling to lower-frequency com-
ponents of the dielectric response. Both the presence of in-
homogeneous broadening and the increase in inhomoge-
neous linewidth with an increase in solvent polarity are
consistent with this conceptual picture, and suggest that di-
polar interactions between OClO and the solvent are largely
responsible for the restricted evolution along the
asymmetric-stretch coordinate in condensed media.
␦
ϭ160 cm and other parameters as provided in Table IV. ͑D͒ The solvent
response function predicted using VCT employing identical parameters to
those used in part ͑C͒. ͑E͒ Comparison between the Gaussian functional
form for D(t) and the VCT result for chloroform. The Gaussian form cor-
Ϫ1
responds to ⌫ϭ95 cm ͑solid line͒, and the VCT result ͑dashed line͒ cor-
Ϫ1
responds to ␦ϭ150 cm and other parameters as provided in Table IV. ͑F͒
The solvent response function predicted from VCT employing parameters
identical to those used in part ͑E͒.
is capable of reproducing D(t) in each case. It should be
noted that this agreement is accomplished using a ␦ that is
essentially solvent independent, a result that is consistent
with the similarity of the OClO geometry change that occurs
upon photoexcitation in these solvents.
The discussion presented above suggests that VCT de-
scription of the solvent response is consistent with both the
functional form of the dephasing as well as the solvent in-
variance of homogeneous linewidth. However, the success of
this approach is tempered by whether the assumptions made
here are valid, most notably the continuum treatment of the
solvent and the applicability of linear response. MD simula-
tions of nonpolar solvation dynamics have shown that the
mechanical response of the solvent is dominated by a subset
of the molecules in the first solvent shell.5
7,61,62
This effect is
CONCLUSIONS
directly related to the short-ranged nature of the repulsive
interactions that dominate the mechanical response of the
solvent. Clearly, the molecular aspects of nonpolar solvation
are not reflected in the continuum treatment. Regarding lin-
ear response, Schwartz and co-workers have recently dis-
cussed the breakdown of linear response for several different
changes in the solute upon electronic excitation and found
substantial differences relative to the dynamics predicted by
linear response. However, despite the lack of agreement
between the equilibrium and nonequilibrium calculations, the
end result of this study was that for spectroscopic applica-
tions, equilibrium approximations are still reasonable in the
calculation of line shapes, especially for systems in which
We have presented an absolute resonance Raman inten-
sity analysis ͑RRIA͒ of OClO dissolved in chloroform. Simi-
lar to our previous RRIA results in water and cyclohexane,
the excited-state structural evolution in chloroform is domi-
nated by motion along the symmetric stretch and bend coor-
dinates, with little evolution occurring along the asymmetric
stretch. This pattern of excited-state structural relaxation is
consistent with the preservation of C2v symmetry in the ex-
cited state, with this preservation of symmetry leading to
enhanced Cl production in condensed environments. The ho-
mogeneous broadening determined in this study is similar in
magnitude to that previously determined in cyclohexane and
water suggesting that the vibronic-dephasing time for OClO
6
2
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8503
J. Chem. Phys., Vol. 114, No. 19, 15 May 2001
Resonance Raman study of OClO in CHCl3
2
3
9
0
in solution is solvent independent. We have shown that this
apparent solvent invariance is consistent with nonpolar or
mechanical solvation dynamics dominating the solvent re-
sponse to OClO photoexcitation. Finally, we have proposed
that the limited evolution along the asymmetric-stretch coor-
dinate in condensed environments is due to dielectric
solvent–solute interactions as evidenced by the increase in
inhomogeneous linewidth with an increase in solvent polar-
ity.
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ACKNOWLEDGMENTS
3
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This paper is dedicated to the memory of Professor L.
Slutsky. We would like to thank Kirk Peterson ͑Washington
State University and Pacific Northwest National Laboratory͒
for information regarding the dipole moment of OClO, and
Mickey Schurr ͑University of Washington͒ and Mark Berg
40
4
1
͑
University of South Carolina͒ for discussions concerning
viscoelastic response theory. We also thank Jeanne McHale
University of Idaho͒ for reading of the paper. The National
4
2
͑
43
Science Foundation is acknowledged for its support of this
work through the CAREER program ͑CHE-9701717 and
CHE-0091320͒. Acknowledgment is also made to the donors
of the Petroleum Research Fund, administered by the Ameri-
can Chemical Society ͑P.J.R.͒. P.J.R. is an Alfred P. Sloan
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