Femtosecond photolysis of aqueous HOCI

Article abstract of DOI:10.1063/1.1413964

The photolysis of HOCl was studied using femtosecond transient absorption spectroscopy. Pumping HOCl at 266 nm, unity quantum yield was observed for direct photodissociation into OH and Cl atoms. 45% of the fragments recombined geminately after diffusion.

Full text of DOI:10.1063/1.1413964

Femtosecond photolysis of aqueous HOCl
C. L. Thomsen, D. Madsen, J. Aa. Poulsen, J. Thøgersen, S. J. Knak Jensen, and S. R. Keiding
Citation: The Journal of Chemical Physics 115, 9361 (2001); doi: 10.1063/1.1413964
View online: http://dx.doi.org/10.1063/1.1413964
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/115/20?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Efficient dehalogenation of polyhalomethanes and production of strong acids in aqueous environments: Water-
catalyzed O–H-insertion and HI-elimination reactions of isodiiodomethane ( CH 2 I–I ) with water
J. Chem. Phys. 120, 9017 (2004); 10.1063/1.1701699
Vuv photolysis of hydrazoic acid: Absorption and fluorescence excitation spectra
J. Chem. Phys. 109, 2210 (1998); 10.1063/1.476789
Real-time changes induced by pulsed laser heating in ammonium perchlorate at static high pressures
AIP Conf. Proc. 429, 809 (1998); 10.1063/1.55584
193 nm photolysis of H 2 S in rare-gas matrices: Luminescence spectroscopy of the products
J. Chem. Phys. 108, 5747 (1998); 10.1063/1.475985
Laser-photolysis/time-resolved Fourier-transform absorption spectroscopy: Formation and quenching of HCl (v)
in the chain reaction Cl/Cl 2 /H 2
J. Chem. Phys. 107, 6499 (1997); 10.1063/1.474264
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
158.42.28.33 On: Tue, 25 Nov 2014 09:50:48

JOURNAL OF CHEMICAL PHYSICS
VOLUME 115, NUMBER 20
22 NOVEMBER 2001
Femtosecond photolysis of aqueous HOCl
C. L. Thomsen, D. Madsen, J. Aa. Poulsen, J. Thøgersen, S. J. Knak Jensen,
and S. R. Keiding
Department of Chemistry, University of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
͑Received 19 March 2001; accepted 5 September 2001͒
This paper reports an experimental study of the photolysis of aqueous HOCl using femtosecond
pulses at 266 nm. The formation of photoproducts is monitored by transient absorption spectroscopy
from 230 to 400 nm. The HOCl molecules dissociate with unity quantum yield to form OHϩCl
faster than 1 ps, and as a result of the potential along the HO–Cl reaction coordinate, all excess
energy is given to the fragments as translational energy. After dissociation, and solvent cage escape,
the majority of the Cl and OH fragments recombine after diffusion on a time scale of 50 ps. The
diffusion dynamics is studied using a simple model for diffusive recombination and a more
extensive molecular dynamics simulation. A minor fraction of the Cl atoms ͑ϳ10%͒ reacts with
HOCl in a diffusion limited reaction to form Cl2ϩOH. © 2001 American Institute of Physics.
͓DOI: 10.1063/1.1413964͔
I. INTRODUCTION
recombination͒. If the cage back reaction dominates, it im-
plies that the solvent-assisted transition to the vibrationally
excited electronic ground state is sufficiently fast to compete
with the permanent separation ͑cage escape͒ of the primary
fragments. Strong caging effect are observed in both ClO2
and CS2, where the dissociation channel along the asymmet-
ric stretch is effectively closed in the liquid phase as opposed
to the gas phase where it is fully open.
In this work we propose, and demonstrate, that aqueous
HOCl offers a unique possibility for studying the fundamen-
tal solvent solute interactions taking place during the initial
phases of a chemical reaction. During a chemical reaction, or
a chemical transformation, excess energy is distributed
among the intra- and intermolecular degrees of freedom, rep-
resented by rovibrational excitation or the translational en-
ergy of the products. Each of these degrees of freedom will
subsequently relax through the solvent induced interactions.
Precise quantitative studies of the energy relaxation of the
products are often very difficult, as the precise distribution of
the energy is difficult to obtain both theoretically and experi-
mentally. Systems where the energy is deposited predomi-
nantly in one or a few degrees of freedom are therefore
highly desirable for experimental tests of the different theo-
retical descriptions of solvent–solute interactions. In HOCl
the O–H bond length is very close to the O–H bond length
found in the free hydroxyl radical1,2 and, consequently when
HOCl is photolyzed by UV light to form ClϩOH, the OH
bond is a spectator mode purely in the vibrational ground
state, leaving all the excess energy for the translational en-
ergy of the OH and Cl fragments. Furthermore, but associ-
ated with the lack of vibrational excitation, the potential en-
ergy along the reaction coordinate, the HO–Cl distance, is
barrierless and strongly repulsive as indicated in Fig. 1. This
ensures that the quantum yield for photodissociation is near
unity with negligible cage back recombination,3 and, in ad-
dition, also opens for the possibility of tuning the kinetic
energy of the fragments by changing the energy of the pho-
tolysis pulse.3 This is in sharp contrast to some of the previ-
ously studied molecules like I3,4,5 ClO2, and CS2.6 In these
molecules excitation initially populates a quasi-bound state
that subsequently undergoes one or several solvent curve
crossings before either ending up in a dissociative state from
where the molecule dissociate, or returning to the vibra-
tionally excited electronic ground state ͑geminate cage back
The cage back geminate recombination leads to a fast
regeneration of the parent molecule in a highly excited vi-
brational state followed by vibrational relaxation on a pico-
second time scale. In the case of HOCl, excitation leads di-
rectly to a dissociative state with several eV remaining for
the translational energy of the fragments. This makes HOCl
particularly well-suited for experimental and theoretical
study of solvent-solute interaction, in particular the ‘‘stop-
ping power’’ of the solvent, i.e., the ability to thermalize the
translational energy of the recoiling reaction products.
The theoretical description of solute–solvent interactions
often starts from hydrodynamic continuum theories using
friction to account for the influence of the solvent on the
relevant solute coordinate ͑translation, vibration, or rotation͒.
The evolution of the solute coordinate is then described us-
ing the generalized Langevin equation7,8 ͑GLE͒ where the
finite response time of the solvent is taken into account by
assuming a friction spectrum with high frequency cut off, as
opposed to the Langevin equation ͑LE͒ where here the sol-
vent is assumed to be able to respond instantaneously.
Through the work of Stratt, Ladanyi, and co-workers,9–12 it
has been shown how the GLE can be directly obtained from
an instantaneous normal mode ͑INM͒ description of the sol-
ute. This result thus enables one to connect the microscopic
molecular dynamics of the solvent to the continuum proper-
ties expressed by the GLE. The photolysis of aqueous HOCl
offers a well-suited system to study the influence of solvent
friction on a well-defined coordinate, the translational mo-
tion of the photofragments.
Another reason to study the details of the photolytic de-
0021-9606/2001/115(20)/9361/9/$18.00
9361
© 2001 American Institute of Physics
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
158.42.28.33 On: Tue, 25 Nov 2014 09:50:48

9362
J. Chem. Phys., Vol. 115, No. 20, 22 November 2001
Thomsen et al.
FIG. 2. The static absorption spectrum of the relaxed photoproducts Cl͑aq͒
and OH͑aq͒. Note that the extinction coefficient of the Cl͑aq͒ absorption
spectrum is reduced by a factor of 5. Also shown is the absorption spectrum
of the HOCl͑aq͒ molecule.
FIG. 1. Potential energy along the HO–Cl bond in HOCl. The arrow rep-
resents the 266 nm photolysis pulse exciting the purely repulsive 1 1A and
Љ
2
1A states.
Ј
spectral dynamics caused by simultaneously induced bleach-
ing of the parent molecules and induced absorption due to
the photoproducts is absent in HOCl.
The paper is organized as follows: Section II describes
the experimental procedures for synthesizing and character-
izing HOCl and the photolytic products ͑Cl, OH͒. Section II
also contains a brief description of femtosecond transient ab-
sorption spectrometer. In Sec. III we describe the experimen-
tal results obtained and Sec. IV contains the data analysis
and the discussion.
composition of HOCl is linked to its importance in atmo-
spheric photochemistry. HOCl has the potential of acting as a
reservoir of atmospheric chlorine13,14 through both homoge-
neous and heterogeneous photochemical processes in the
stratosphere and can thus play a central role in the processes
leading to the catalytic destruction of ozone. Consequently,
numerous theoretical15–18 and experimental19–24 studies of
the gas phase HOCl and HOCl on ice have been published in
recent years. We will use these gas-phase results as a guide
through the description of the results of the photolysis of
aqueous HOCl presented in this paper. In addition, the gas-
phase results, in combination with the work presented here,
provide us with an illustrative example on the differences
between gas-phase and liquid-phase chemistry. In particular,
this emphasizes the similarities at short internuclear dis-
tances and the differences at large internuclear distances,
where the solvent plays a decisive and dominating role in
keeping the photofragments from separating permanently.
Gas-phase photolysis studies of HOCl coupled with ab
initio theoretical studies have given a detailed account for the
yield of the photoproducts and the distribution of the excess
energy among the translational and vibrational degrees of
freedom. The principal photodissociation products in the
wavelength range from 140 to 440 nm are
II. EXPERIMENT
A. Materials
Aqueous solution of hypochlorous acid ͑HOCl͒ was syn-
thesized by the method described by Cady.26 The procedure
involves initial preparation of a solution of Chlorine ͑I͒ oxide
͑ClOCl͒ in carbon tetrachloride, which afterward was shaken
with water to form an aqueous solution of hypochlorous
acid. Briefly, 300 ml of dry carbon tetrachloride ͑99%, anhy-
drous, Aldrich͒ was cooled to ϳ6 °C. The solution was con-
tinuously stirred and chlorine gas ͑Liquid Carbonic, Airbags:
pure Cl2͒ was bubbled into the carbon tetrachloride solution
until a ϳ1.7 M concentration of chlorine was obtained. The
concentration of chlorine was determined by VIS-UV ab-
sorption. The solution was then warmed to 25 °C, and at least
1.1 mol of dry yellow mercury ͑II͒ oxide ͑HgO͒ ͑Baker ana-
lyzed, J. T. Baker͒ per mol of chloride was added and the
mixture was stirred for at least 45 minutes, while the reddish
brown ClOCl is formed. The solution was separated from the
solid by filtration through a coarse sintered-glass funnel with
a typical ClOCl concentration of ϳ0.8 M. The aqueous so-
lution of hypochlorous acid is then obtained by mixing the
filtrated solution of ClOCl in carbon tetrachloride with 300
ml of water ͑distillated water͒ in a separator funnel. The
reaction between ClOCl and water is nearly quantitative and
the aqueous solution of hypochlorous acid obtained after
withdrawal of the carbon tetrachloride phase is essentially
free from chlorine and other impurities. The procedure de-
scribed above typically resulted in a HOCl ͑aq͒ concentra-
2
2
HOCl X 1A ͒ϩh␷→OH ⌸͒ϩCl P͒.
͑1͒
͑
͑
͑
Љ
In this work we study the photolysis of HOCl by light at 266
nm. The photoproduct formation following photoexcitation
is monitored over the entire spectral range from 230 to 400
nm on an absolute optical density scale. In the spectral range
from 230 to 400 nm primarily the Cl-photoproduct and sec-
ondarily the OH-radical contribute to the spectrum.25 An ad-
ditional advantage of the aqueous HOCl system is that the
oscillator strength of the product absorption is significantly
larger than that of the parent HOCl molecule. The static ab-
sorption spectra of the species involved in the photolysis are
shown in Fig. 2. This fact is of great use in the interpretation
of the primary data, as the often encountered complicated
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
158.42.28.33 On: Tue, 25 Nov 2014 09:50:48

J. Chem. Phys., Vol. 115, No. 20, 22 November 2001
Femtosecond photolysis of aqueous HOCL
9363
tion of ϳ1.5 M. The concentration and purity of the sample
was determined by static VIS-UV absorption using previ-
ously reported extinction coefficient values for HOCl,
ClOCl, and Cl2 in aqueous solution.
B. Static absorption spectra of the species involved
In order to interpret the time-dependent absorption sig-
nal the spectral properties of all chemical species involved
in the photolysis are required. The photochemistry of
HOCl in aqueous solution produces the solvated OH radical
and Cl͑aq͒, which have been well-characterized spectro-
scopically,27,28 and are depicted in Fig. 2. We measured the
UV absorption spectrum of HOCl in aqueous solution with a
Cary 219 spectrophotometer with 2 nm resolution. The spec-
trum, also shown in Fig. 2, is in good agreement with that of
previous studies where the extinction coefficient was deter-
mined to be 105 MϪ1 cm at 235 nm. The absorption spec-
trum of HOCl is composed of two absorption bands with
maximum at 235 and 310 nm, respectively. The first absorp-
FIG. 3. Transient absorption following the photolysis of HOCl at 266 nm.
The transient absorption is shown for a probe wavelength of 300 nm, where
the Cl͑aq͒ absorption dominates. The spike at tϭ0 is the two-photon ab-
sorption ͑1 pumpϩ1 probe͒ of liquid water.25
sample. Both beams were spectrally filtered before they were
detected by two matched photodiodes and boxcar integrators,
and the ratio of the signals from the two boxcar integrators
was sent to a digital lock-in amplifier referenced to the pump
beam modulation. The probe wavelength was measured by a
calibrated spectrometer and the instrument response time
was 0.6 ps ͑FWHM͒.
tion band at 310 nm is due to the 1 1A
X 1A electronic
Љ
Љ
transition, whereas the second peak at 235 nm is caused by
the 2 1A X 1A electronic transition. The two electronic
Ј
Љ
transitions are only slightly blue shifted (⌬␭Ϸ5 nm) com-
pared to the gas-phase values, indicating a modest solvent
perturbation of the potential energy surfaces in the Franck–
Condon region.
The HOCl solution was exchanged frequently during the
series of measurements, and the flow was adjusted to ensure
a fresh sample of HOCl for each laser pulse. The sample
optical density of the HOCl solution was 1.0 OD/2 mm at the
pump wavelength. Absorption spectra obtained before and
after experiments were identical demonstrating that no
sample degradation occurred during the course of the experi-
ment. A series of experiments, in which the power of the
pump pulse was changed by one order of magnitude, showed
that the changes in the transient absorption was proportional
to the pump power and that the reaction dynamics was inde-
pendent of the pump power. Likewise, the observed dynam-
ics was found to be independent of the HOCl sample con-
centration. Unwanted generation of solvated electrons from
the water solvent by two-photon absorption was minimized
by adjusting the pump power until the magnitude of the sig-
nal originating from the water solvent was less than 3% of
the signal from HOCl in the spectral range investigated. The
overall uncertainty of the transient absorption measurements
is estimated to be less than Ϯ15% for the spectral region
from 230 to 400 nm. All measurements were made at room
temperature.
C. Experimental setup
The details of the ultrafast transient absorption spec-
trometer have been presented elsewhere25 and therefore, only
a brief description is given here. A regenerative amplified
Titanium: Sapphire laser producing 90 fs, 750 ␮J pulses cen-
tered at 800 nm with a repetition rate of 1 kHz was employed
in this work. The pump and probe pulses were produced as
follows: The fundamental pulse at 800 nm was frequency
doubled in a 0.5 mm BBO crystal to give the 400 nm pulse
which was then sum-frequency mixed with the residual 800
nm pulse in a 0.2 mm BBO crystal to generate the 266 nm
pump pulse used to excite the HOCl sample. The pump pulse
was sent through a variable delay line, and a zero-order ␭/2
wave plate was used to rotate the polarization of the pump
54.7° relative to that of the probe before it was weakly fo-
cused into a 2 mm thick sample flow cell. The pump pulse
energy was typically 50 ␮J with a spot diameter at the
sample cell of ␻0ϭ0.7 mm. The pump beam was modulated
at 0.5 kHz, phase locked to the 1 kHz repetition rate of the
regenerative amplifier. The probe pulse was generated using
a combination of second-harmonic generation and sum-
frequency mixing of a supercontinuum generated by the re-
sidual 800 nm pulse in a 2 mm ethylene glycol jet. The
spectral range from 400 to 295 nm was covered by frequency
doubling the white light continuum in a 1 mm BBO crystal.
To generate the probe wavelengths from 230 to 317 nm the
white light continuum was sum-frequency mixed with part of
the 400 nm in a 0.2 mm BBO crystal. The probe beam was
separated into signal and reference beams using a beamsplit-
ter. The reference portion of the probe was sent to a detector,
while the remainder of the beam was sent through the
D. Description of transient absorption data and
assignments
The light-induced transient absorption of aqueous HOCl
following photolysis at 266 nm was probed at 16 wave-
lengths in the spectral range from 230 to 400 nm. In Fig. 3͑a͒
representative example is shown with pump wavelength
equal to 266 nm and probe wavelength equal to 300 nm. The
induced absorption exhibit an initial sharp peak resembling
closely that obtained at the same probe wavelength when
pure water is substituted for the aqueous HOCl solution. The
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
158.42.28.33 On: Tue, 25 Nov 2014 09:50:48

9364
J. Chem. Phys., Vol. 115, No. 20, 22 November 2001
Thomsen et al.
FIG. 4. The full transient absorption spectrum following photolysis of aque-
ous HOCl at 266 nm. The steady state spectrum of Cl͑aq͒ is shown in the
wavelength-transient absorption plane, and the spectrally integrated dynam-
ics is shown in the time-transient absorption plane.
peak is due to two-photon absorption25 ͑one pump and one
probe photon͒ in water. Hence, we take the temporal position
and the width of the peak to mark the point of zero delay
(tϭ0) and the experimental response time ͑0.6 ps͒. For
probe wavelength longer than 340 nm, the two-photon peak
vanishes allowing us to estimate a rise time of the induced
absorption close to 1 ps. In Fig. 4 the induced absorption
data are depicted in a 3-D plot showing time, wavelength and
induced absorption. The initial two-photon spike has been
removed from the plot, allowing for a better visualization of
the data. The transient absorption observed after 1 ps is
dominated by the absorption of Cl͑aq͒, which has its maxi-
mum around 310 nm and stretches across the entire investi-
FIG. 5. The dynamics of the excess absorption observed in the UV region.
The excess absorption is obtained by subtracting the transient absorption
contributions from stoichiometric amounts of OH͑aq͒ and Cl͑aq͒ from the
experimental data.
4 is nearly accounted for. However, a small signal, close to
the noise level, but clearly reproducible persists. This signal
appears between 230 and 280 nm and is depicted in Fig. 5,
showing a small absorption hump reaching a maximum
around 10 ps followed by a slow decay to zero. The residual
absorption constitutes less than 10%͑Ϯ15%͒ of the total sig-
nal in the lower spectral region from 230 to 280 nm and
exhibits the same decay dynamics. We here consider two
possible sources to this residual absorption. One possibility
is to assign the residual absorption to vibrational relaxation
of HOCl following delayed recombination. As Cl and OH
recombine, the HOCl molecule formed initially contains
most of the ground-state binding energy in the HO–Cl bond
as vibrational excitation. However, the amplitude of the re-
sidual absorption is large in comparison with the small ab-
sorption cross sections of HOCl. Using the number of ex-
cited molecules, to be determined later, and the amplitude of
the signal leads to an estimated absorption coefficient for
27
gated spectral range. The static spectrum of Cl͑aq͒ is also
shown in Fig. 4 for comparison. The induced absorption due
to Cl͑aq͒ undergoes a nonexponential decay to reveal a
nearly constant absorption that persists out to the longest
delays investigated ͑up to 350 ps for selected probe wave-
lengths͒. The decay of the transient absorption is illustrated
in Fig. 4 by the time evolution of the spectrally integrated
signal shown in the time- induced absorption plane. At long
delays, the induced absorption, and thus the concentration of
the Cl atoms, has decayed to ϳ55% of the initial value. The
nearly constant spectral behavior, i.e., very little change in
the shape of the absorption curve, and the nonexponential
decay of the transient absorption, suggest that the decay of
the induced absorption is due to diffusive geminate recombi-
nation between Cl and OH.29–31 This will be further investi-
gated below by comparing the transient absorption data with
diffusion limited recombination models. Careful inspection
of the induced absorption data recorded below 300 nm indi-
cates a slightly different decay as compared to the data re-
corded above 300 nm, and in addition there is also a slight
deviation from the static Cl͑aq͒ spectrum. Part of this is
caused by the weak contributions from the bleaching of
HOCl and the red wing of the induced absorption from OH.
By subtracting the known stoichiometric contributions from
these photoproducts, the transient absorption depicted in Fig.
vibrationally excited HOCl of at least ␧Ϸ300 MϪ1 cmϪ1
which is three times the theoretical prediction,15
Ӷ100 MϪ1 cmϪ1
,
␧
.
Alternatively the residual absorption in the spectral re-
gion from 230 to 280 nm could be caused by temporary
excess concentration of OH radicals, which absorb in the
same spectral region. In Fig. 6 the average residual transient
absorption obtained after 10 ps is compared to the static ab-
sorption spectrum of the OH. Good agreement is observed
and this, together with observation of one common decay
rate of the residual absorption strongly indicates that excess
OH radicals are the source of the residual absorption. Ac-
cordingly, the data indicate that excess OH radicals are
formed on a few picosecond time scale and subsequently
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
158.42.28.33 On: Tue, 25 Nov 2014 09:50:48

J. Chem. Phys., Vol. 115, No. 20, 22 November 2001
Femtosecond photolysis of aqueous HOCL
9365
III. DISCUSSION
The recombination of HOϩCl is in striking contrast to
the standard prototype for fast recombination reactions, like
I2, OClO, and CS2, where prompt recombination within the
first picosecond is the dominating recombination process.
The absence of prompt recombination combined with a high
yield of delayed recombination might be due to a barrier for
recombination on the ground-state surface. However, there is
no theoretical or experimental evidence that an electronically
imposed barrier exists for HOCl. Another example of slow
recombination has recently been observed by Barbara and
co-workers34 in the photolysis of aqueous OϪ3 where 50% of
the photoexcited molecules returned to the ground state
within the first 10 ps due to delayed recombination, whereas
prompt recombination was absent. The absence of prompt
recombination was assigned to extraordinary strong solva-
tion effects of the fragments resulting in a solvent induced
barrier for recombination. Thus OϪ is one of the most
strongly solvated species in water, and dynamic evolution of
the solute-solvent structure during the photo dissociation
may be responsible for the lack of prompt recombination. It
is not obvious that an extraordinary strong solvation of the
fragments in the case of HOCl also explains the delayed
recombination observed, since the fragments OH and Cl are
not nearly as strongly solvated as OϪ. Instead we suggest
that the delayed recombination could be a result of the large
amount of excess energy available to the fragments follow-
ing the photolysis of HOCl. This results in a large initial
separation of the fragments and consequently a delay of the
recombination as the photofragments are awaiting diffusional
encounters. This situation is equivalent to the well-studied
process of photolysis of liquid water, where the hydrated
electron geminately recombines with either OH or H3Oϩ as a
result of diffusion.25,31 The transient data thus provides a
direct measurement of the time-dependent quantum yield,
⌽(t), for photodissociation, and in particular, it allows us to
follow the dynamics of the solvent-solute interactions re-
sponsible for both the thermalization of the hot fragments
and the subsequent recombination. This will be investigated
below, where we, after first discussing the quantum yield,
compare the transient absorption data with a simple recom-
bination model based on diffusive geminate recombination.
FIG. 6. The spectral distribution of the excess absorption ͑points͒ from Fig.
5 compared to the steady state spectrum of the OH radical ͑full line͒. Good
agreement is observed, indicating that the residual absorption is caused by a
nonstoichiometric contribution from OH.
decays within 100 ps. Based on the stoichiometry of the
reaction and the known extinction coefficients of OH, we
estimate that of the order of 20% ͑Ϯ10%͒ excess OH are
formed.
The origin of the excess concentration of OH radicals is
the high concentration of HOCl used in these experiments.
At concentrations approaching 1 M the distance between
HOCl molecules is of the order of 10 Å and we must there-
fore also consider reactions between the chlorine atom and
HOCl molecules
ClϩHOCl→OHϩCl2.
͑2͒
This reaction could be a candidate for the excess OH tran-
sient absorption observed and could also explain the 10 ps
rise time as being result of the diffusive encounter of Cl and
HOCl. The extinction coefficient of Cl2 in the probe wave-
length region is very low, and consequently Cl2 cannot be
detected. Reaction ͑4͒ is well known from the gas phase32,33
and, with ⌬G0ϳϬ10 kJ/mol, the reaction is likely to be dif-
fusion limited. Initial measurements of the concentration de-
pendence of the photolysis dynamics did not reveal any sig-
nificant dependence of the concentration of HOCl. However,
due to the low extinction of the HOCl molecule, the concen-
tration could only be varied over a limited range, and the
expected change in the OH dynamics was at the limit of the
experimental sensitivity.
In summary we observe a resolution limited rise of the
absorption of Cl͑aq͒ following the photolysis of HOCl. Sub-
sequently Cl͑aq͒ decays as the Cl and OH fragments undergo
diffusive geminate recombination. Approximately 55% of
the Cl atoms, to be discussed below, escapes the geminate
recombination and will, on a much longer timescale, depen-
dent on concentration, recombine with OH fragments. In ad-
dition, we observe indications that there is a moderate excess
concentration of OH radicals of the order of 20% ͑Ϯ10%͒
corresponding to a reaction where 10% of the Cl fragments
react with HOCl to form OHϩCl2.
A. Quantum yield for cage escape
In order to be able to evaluate the quantum yield for
recombination and dissociation, it is necessary to known the
initial concentration of Cl atoms. By normalizing the tran-
sient absorption data at 340 nm after 1 ps and assuming that
the amplitude is directly proportional to the concentration of
the Cl atoms, we obtain a survival probability of 0.55
Ϯ0.05. The same value is obtained if we instead follow the
time dependence of the signal integrated over the spectral
profile of the Cl͑aq͒ absorption curve. Hence the obtained
quantum yield is given by:
⌬OD tϭ150 ps͒
͑
⌽ Cl͒ϭ
͑
.
͑3͒
⌬OD tϭ1 ps
͒
͑
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
158.42.28.33 On: Tue, 25 Nov 2014 09:50:48

9366
J. Chem. Phys., Vol. 115, No. 20, 22 November 2001
Thomsen et al.
The quantum yield defined in Eq. ͑3͒ may, however, not
reflect the real probability for cage escape, since a large frac-
tion of the photolyzed HOCl molecules may geminately re-
combine within the first few hundredths of femtosecond.
This type of direct geminate recombination, perhaps better
described as a large asymmetric distortion of the molecule,
has previously been observed in I2, CS2, and ClO2. In addi-
tion both the bleaching of the HOCl absorption, and the two-
photon spike from water contribute to the signal at very short
delay and, consequently, masks the amplitude of the transient
absorption from Cl. Consequently, it is uncertain whether the
initial concentration of Cl is truly represented by the induced
absorption at 1 ps.
Alternatively, one can estimate the total concentration of
photoexcited HOCl at tϭ0, and thereby the quantum yield,
from the geometry of the transient absorption spectrometer
and the number of pump photons absorbed. By determining
the spot diameter at the sample cell accurately for both the
pump and probe beams and the total pump energy, the quan-
tum yield can be calculated, following the method introduced
by Wallhout et al.34 This method takes into account the spa-
tial nonuniformity of the pump intensity in the region
probed, using the measured width of the assumed Gaussian
beams, ⌫pu and ⌫pr for the pump and probe beams, respec-
tively. The absorption of the probe pulse, without the pump,
is given by Lambert–Beers law as
molecules dissociate, we now proceed by analyzing the re-
combination of Cl and OH and, thus, the decay of the tran-
sient absorption caused by Cl͑aq͒.
B. Modeling the geminate recombination
of Cl and OH
In this part we focus on the dynamics of the recombina-
tion between OH and Cl resulting in the decay of the ob-
served Cl͑aq͒ spectrum. Experimentally, as discussed above,
we observed that at long delays, 45% of the Cl͑aq͒ have
recombined with OH and, thus, that 55% escaped recombi-
nation. The theoretical description of the cage, and cage es-
cape processes in liquid constitutes a very active field of
research fueled both by the central importance of these pro-
cesses in condensed phase chemistry, and by the advances in
molecular dynamics simulation techniques.35–37 In this con-
text it is interesting to reflect a little about the nature of the
reactive encounter between OH and Cl. It is known from
theoretical and experimental low temperature matrix
studies36,38,39 of HCl and F2 that bound, metastable, and re-
pulsive states are all populated following collisional encoun-
ters, depending on the orientation of the angular momentum
of the halogen atom along the axis of the recombining part-
ner. In the present case of recombination between OH and
Cl, we must therefore also expect that both the orientation of
the OH internuclear axis and the angular momentum of the
Cl atoms give rise to recombination via ground state and
excited states. If an excited, repulsive state is populated, the
molecule will immediately dissociate, but not necessarily, as
a result of low kinetic energy, break the solvent cage. Instead
the caged fragments may perform a nonadiabatic transition
to the bound ground-state potential-energy surface. Thus the
diffusion-limited recombination could be viewed as first a
cage break-in collision followed by several in-cage collisions
ending when a nonadiabatic transition brings the molecule to
the ground potential surface.
1
r2
2⌫2pr
ϱ
A0ϭ
dr 2␲r exp Ϫ
Ϫc0␧HOClz ,
͑4͒
͵
ͩ
ͪ
2
⌫
0
pr
where c0 and ␧ are the concentration and extinction coeffi-
0
cients of HOCl and z is the path length through the sample.
With the pump pulse present the probe absorption becomes
1
r2
2⌫2pr
ϱ
Apϭ
dr 2␲r exp Ϫ
Ϫ ␧HOCLc0
͑
͵
ͩ
2
⌫
0
pr
Ϫ␧
¯
HOCLcp r͒ϩ␧
¯
Clcp r͒͒z ,
͑5͒
͑
͑
ͪ
We approach the problem using the classical theory for
diffusion limited reactions based on the work of
Smoluchowski.29,40 The rate for diffusional recombination,
which according to the considerations above perhaps is bet-
ter described as the rate of cage break-in collisions, depends
on the mobility and reactivity of the fragments, and in addi-
tion, and very central to this work, the initial separation of
the thermalized fragments. In the continuum description
of the recombination, the time-dependent survival probabil-
ity of Cl͑aq͒, escaping the recombination reaction
ClϩOH→HOCl, can be expressed as a function of the initial
distance r0 between OH and Cl as41
where the pump-induced concentration of photoexcited
HOCl molecules in the area 2␲r dr is denoted
¯cp and given
by
exp Ϫr2/2⌫2 ͒
͑
Np
pr
¯
cp r͒ϭ
,
͑6͒
͑
2␲⌫2puz
NA
where Np is the number of absorbed pump photons per pulse
and NA is Avogadros number. Using A0 and Ap the quantum
yield becomes
⌬OD tϭ150 ps͒
͑
⌽ Cl͒ϭ
͑
.
͑7͒
log A ͒Ϫlog A ͒
͑
͑
⍀
r ,t͒ϭ1ϪW W t͒,
͑8͒
͑
Cl
͑
0
p
0
ϱ
*
This method leads to a quantum yield of ⌽(Cl)ϭ0.5Ϯ0.1,
in excellent agreement with the yield determined from the
ratio of initial and final amplitude from the transient data
⌽(Cl)ϭ0.55Ϯ0.05 . This strongly indicates that a negli-
gible part of the photo dissociated HOCl molecules gemi-
nately recombines within the first picosecond, in contrast to
what has been previously observed for a number of small
molecules in solutions. Assuming that all photoexcited HOCl
where Wϱ is the probability of ultimate reaction, Wϱϭ1
Ϫ⍀Cl(r0 ,t→ϱ) and W is the time-dependent dynamics of
*
the reaction probability switching from 0 at tϭ0 to 1 at t
͓
͔
→ϱ. Since both OH and Cl are highly reactive in aqueous
environments, we start by assuming that the rate of the re-
combination reaction is purely diffusive, i.e., as soon as the
reactants Cl and OH are separated by less than a given reac-
tion distance R, the probability of recombination is unity and
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
158.42.28.33 On: Tue, 25 Nov 2014 09:50:48

J. Chem. Phys., Vol. 115, No. 20, 22 November 2001
Femtosecond photolysis of aqueous HOCL
9367
the survival probability is 0. The rate constant for diffusion-
limited reaction is given by the Smoluchowski equation40
k
diffϭNA4␲RDCl–OHϫ103,
͑9͒
where DCl–OH is the relative diffusion coefficient of the re-
actants given by DCl–OHϭDClϩDOH . The diffusion coeffi-
cient for OH is well-known from previous studies and its
value is DOHϭ2•10Ϫ3 nm2/ps. In contrast, the diffusion co-
efficient of Cl͑aq͒ is unknown. However, using the self-
diffusion coefficient of water and the radius for Cl͑aq͒, the
diffusion coefficient has been estimated by Parson et al.42
using the Stokes–Einstein relation43 DϭkbT/C␲␩rs to be
DClϷ1.0ϫ10Ϫ3 nm2/ps, where the numerical constant C is
determined by the hydrodynamic boundary condition, being
6 for the stick and 4 for the slip boundary condition.43 ␩ is
the viscosity and rs is the radius of the species, while kb and
T is Boltzmann’s constant and the temperature, respectively.
The diffusion coefficient estimated by Parson et al.42 for
Cl͑aq͒ is obtained using a radius for the complex of rs
Ϸ0.4 nm.
FIG. 7. The time dependence of the Cl͑aq͒ concentration compared to the
simple model for diffusive recombination. Two sets of parameters were used
to model the experimental data: The full line is the recombination dynamics
calculated with the parameters obtained from a MD-simulation of the
ClϩOH recombination process, and the dotted line is obtained by adjusting
the parameters to fit the experimental data.
bination model using Eqs. ͑8͒, ͑10͒, and ͑11͒, with two dif-
ferent choices of R, r ,␦r . In the first case ͑dotted line͒,
The reaction radius, also sometimes known as the con-
tact distance or the absorbing boundary condition, R, can be
estimated from the gas-phase potential surfaces for HOCl.
Taking the distance where the attractive part of the potential
surface is equal to or larger than kT gives a value of a
Ϸ0.3 nm. However, since the Cl atoms are solvated in aque-
ous solution, the contact distance is higher, and probably
closer, to the sum of the radii of the two species. With the
known radius of the OH radical of 0.22 nm and the estimated
value for Cl͑aq͒, rsϷ0.4 nm, we estimate the reaction radius
to be around RϷ0.6 nm.
͗
͘
0
0
the value of the contact radius, R was fixed at 0.6 nm and the
diffusion coefficient at DCl–OHϭ3.0ϫ10Ϫ3 nm2/ps in accor-
dance with the estimate given above, and the values of r
͗
͘
0
and ␦r0 were adjusted to obtain the best agreement with the
data. Good agreement is observed between experiment and
model using r ϭ1.0 nm and a ␦r ϭ0.31 nm. The second
͗
͘
0
0
theoretical curve ͑full line͒, in Fig. 7 represents a choice of
parameters inspired by a preliminary theoretical investiga-
tion using MD-simulations of the dynamics of the Cl and OH
fragments. The MD-simulation was performed with 511 wa-
ter molecules and 1 HOCl molecule at 298 K, using a box of
length 24.86 Å, corresponding to a density of 1 g/cm3. The
SPC-potential was used to model the water properties and
the OH and Cl fragments were modeled using the Lennard-
Jones parameters obtained using the Lorentz–Berthelot mix-
ing rules.45 The simulation, averaging over 50 trajectories,
indicated a thermalization distance between the fragments of
the order of 0.6 nm. The distance was defined as the distance
where the relative velocity of the Cl and OH fragments be-
came similar to the thermal velocity. From the simulations
we also obtain an estimate of the width of the distribution:
␦r0Ϸ0.3 nm. The second curve is thus obtained by adjusting
With the assumption that the reaction is diffusion-
limited, the probability of ultimate reaction is simply given
by the ratio of the reaction radius ͑R͒ and the initial equili-
brated fragment separation (r0)41
R
Wϱϭ
͑10͒
r0
and the corresponding time-dependent reaction probability is
given by
r0ϪR
W ϭerfc
.
͑11͒
ͭ
ͮ
*
ͱ
4DCl–OH
t
In order to compare the expression for the survival probabil-
ity ͓Eqs. ͑8͒, ͑10͒, and ͑11͔͒, we must assume a distribution
function, f(r0) for the initial distance between the Cl and
OH fragments. As discussed earlier31,44 the choice initial dis-
tribution is not critical in reproducing the experimental data,
except for the case where a delta function, f(r0)ϭ␦(r0
the contact distance R while keeping
r ϭ0.6 nm, ␦r
͗ ͘
0 0
ϭ0.3 nm and DCl–OH as previously. This curve gives a some-
what poorer representation of the experimental data, but still
captures the main features. Although both theoretical curves
are able to account more or less for the dynamics of the
recombination, the fits to the experimental data are still far
from perfect and, consequently, we cannot determine the
thermalization distance very accurately using this approach.
Depending on the value of the contact distance, we obtain a
Ϫ r ) was chosen. We have used a simple Gaussian distri-
͗
͘
0
bution function centered at r with a FWHM of ␦r0 . The
͗
͘
0
model can now be compared with the experimental results.
Figure 7 shows the concentration of Cl͑aq͒ ͑points͒ as a
function of time for the 266 nm photolysis of HOCl. The
time-dependent Cl͑aq͒ concentration is obtained from the ex-
perimental data in Fig. 4 by integration over the spectral
profile of Cl͑aq͒ absorption. The drawn curves represents the
concentration of Cl͑aq͒ calculated from the diffusive recom-
value r ϭbetween 0.6 and 1.0 nm. Changing the value of
͗
͘
0
the diffusion coefficient or the FWHM of the distribution
does not dramatically improve the agreement between the
data and the model. The values of r can be compared with
͗
͘
0
the radius of the first and second solvation shell in pure liq-
uid water.46,47 These are approximately located at 0.28 nm
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
158.42.28.33 On: Tue, 25 Nov 2014 09:50:48

9368
J. Chem. Phys., Vol. 115, No. 20, 22 November 2001
Thomsen et al.
and 0.5 nm indicating that the fully thermalized fragments
are only separated by two or three water molecules. This
clearly demonstrates the efficiency by which the liquid sol-
vent, in the present case water, is able to act as a sink of the
excess energy released after the photodissociation. The short
thermalization distances observed also suggests that a con-
tinuum description of the dissociation and recombination dy-
namics is likely to be an over simplification. A more correct,
and unified treatment of dissociation, caging and recombina-
tion would be based on the nonadiabatic molecular dynamics
surface-hopping techniques36,38 previously used to study
halogens in noble-gas matrices. In the following, we will
briefly discuss a simple model that describes the efficient
solvent-solute interaction observed.
libration component to solvation,55 an intermediate time
scale
(␶Ϸ0.2–1 ps)
and
a
slow
time
scale
(␶Ϸ1–10 ps).56–58 For the slower time scale, a range of
times is given to represent the observation of the relaxation
of different tensorial components ͑dipole, polarizability͒. The
slow and intermediate time scale are, at least by some au-
thors, considered to be a slow structural relaxation time, cor-
responding to the relaxation of a low density icelike struc-
ture, followed by an intermediate time scale relaxation of a
single water molecule. As indicated this is a very active area
of research with many differing views of the water reorien-
tation. Librational/inertial motion is characterized by small
and fast angular displacements, whereas the reorientation
processes are characterized by large and slower angular dis-
placements where the hydrogen bonds are broken. The relax-
ation time used to fit the data, ␶FϷ1 ps, thus indicates that
the solvent motion responsible for stopping the recoiling
fragments is related to the large displacements of the water
molecules. Since the solvated HOCl molecule will perturb
the local water structure, we expect a faster dynamics than
for pure water. As the solute HOCl is likely to lower the
hydrogen bond coordination of the water molecules, equiva-
lent to raising the temperature,59 the relaxation time obtained
is most likely to be related to the slow relaxation time, de-
scribing the structural relaxation of the hydrogen bond net-
work.
As mentioned in the beginning of this paper, we take the
value of
r
as a direct consequence of the ‘‘stopping
͘
͗
0
power’’ of the solvent, i.e., the distance the fragments travel
in the liquid before their kinetic energies are reduced to
ϳkT. In order to investigate the energy dissipation during
the recoil of the fragments in solution, information about the
potential-energy surface along the reaction path is needed.
The gas-phase value of the dissociation energy along the
asymmetric stretch is measured to D0ϭ2.39 eV.48,49 We take
into account the solvent from the estimated solvation ener-
51
52
gies for HOCl ͑0.3 eV͒,50 OH ͑0.44 eV͒ and Cl ͑0.1 eV͒
and obtain a dissociation energy of 2.15 eV along the asym-
metric stretch of HOCl in aqueous solution. This leaves 2.5
eV to be distributed among the intra and intermolecular de-
grees of freedom of the fragments, and, as discussed above,
this energy solely goes into the kinetic energy of the recoil-
In conclusion we have used femtosecond transient ab-
sorption spectroscopy to study the photolysis of HOCl.
Pumping HOCl at 266 nm, we observed unity quantum yield
for direct photodissociation into OH and Cl atoms. 45% of
the fragments recombine geminately after diffusion. 55% of
the fragment escapes recombination and we see indications
of a secondary reaction between escaped Cl and unexcited
HOCl molecules, causing a small excess of OH radicals. Ini-
tially the photofragments have a substantial amount of ki-
netic energy ͑ϳ2.5 eV͒, but they are quickly thermalized in
the aqueous solvent. A preliminary molecular dynamics
simulation indicates a thermalization distance of ͑ϳ0.6 nm͒,
corresponding to a complete thermalization of the hot frag-
ments within the first two solvation shells. Consequently, we
do not expect continuum models, based on bulk water prop-
erties to give a precise representation of the recombination
dynamics. Nevertheless, estimates of the thermalization dis-
tance, based on the generalized Langevin equation, and the
recombination dynamics, based on the Smoluchowski diffu-
sion equation, give result that are qualitatively in agreement
with the experimental observation.
ing Cl and OH fragments. The distance r is thus a mea-
͗
͘
0
sure of how far the two fragments travel in the solution be-
fore the 2.5 eV are dissipated into the solvent. In the simplest
description of the thermalization process, one can apply the
Langevin equation, using a frequency independent friction of
the solvent, to calculate the thermalization distances.53 This
approach results in a thermalization distance much shorter
than the contact radius, R and is consequently not in agree-
ment with the observation of complete dissociation. Extend-
ing the description to the GLE, by assuming a frequency-
dependent solvent friction,54 gives a better description of the
thermalization process. Assuming a time-dependent friction
of the form,
␩ t͒ϭ␩ exp Ϫt/␶͒,
͑12͒
͑
͑
0
where ␩ is the static friction of liquid water and ␶ as re-
0
sponse time of the order of 1 ps, we obtain thermalization
distances in qualitative agreement with both the experimental
data and the MD-simulation.
1 K. A. Peterson, S. Skokov, and J. M. Bowman, J. Chem. Phys. 111, 7446
͑1999͒.
When the recoiling fragments separate, they have to dis-
place the surrounding water molecules in order to escape the
solvent cage. In doing so, the fragments will rupture the
hydrogen bonds in water and angularly displace the water
molecules, and we thus expect to find, that ␶ is of the same
order as the reorientation time constant determined for single
water molecules. The relaxation time needed to model the
experimental data is of the order of 1 ps. Fast relaxation
processes in water occurs generally on three time scales. A
very fast time scale (␶Ͻ50 fs) representing the inertial/
2 M. Ortiz-Repiso, R. Escribano, and P. C. Gomez, J. Phys. Chem. A 104,
600 ͑2000͒.
3 J. Thøgersen, C. L. Thomsen, J.-Aa. Poulsen, and S. R. Keiding, J. Phys.
Chem. A 102, 4186 ͑1998͒.
4 T. Kuhne and P. Vohringer, J. Chem. Phys. 105, 10788 ͑1996͒.
5 E. Gershgoren, U. Banin, and S. Ruhman, J. Phys. Chem. A 102, 9 ͑1998͒.
6 C. L. Thomsen, D. Madsen, J. Thøgersen, and S. R. Keiding, J. Chem.
Phys. 111, 703 ͑1999͒.
7 D. W. Oxtoby, J. Chem. Phys. 70, 2605 ͑1979͒.
8 R. F. Grote and J. T. Hynes, J. Chem. Phys. 73, 2715 ͑1980͒.
9 B. M. Ladanyi and R. M. Stratt, J. Chem. Phys. 111, 2008 ͑1999͒.
10 G. Goodyear and R. M. Stratt, J. Chem. Phys. 105, 10050 ͑1996͒.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
158.42.28.33 On: Tue, 25 Nov 2014 09:50:48

J. Chem. Phys., Vol. 115, No. 20, 22 November 2001
Femtosecond photolysis of aqueous HOCL
9369
11 J. Jang and R. M. Stratt, J. Chem. Phys. 112, 7524 ͑2000͒.
12 J. Jang and R. M. Stratt, J. Chem. Phys. 112, 7538 ͑2000͒.
13 F. S. Rowland and M. J. Molina, Rev. Geophys. Space Phys. 13, 1 ͑1975͒.
14 H. Fujiwara and T. Ishiwata, J. Phys. Chem. A 102, 3856 ͑1998͒.
15 A. R. Offer and G. G. Balant-Kurti, J. Chem. Phys. 101, 10416 ͑1994͒.
16 S. Nanbu and S. Iwata, J. Phys. Chem. 96, 2103 ͑1992͒.
17 J. Weiss, J. Hauschildt, S. Y. Grebenshchikov, R. Duren, R. Schinke, J.
Koput, S. Stamatiadis, and S. C. Farantos, J. Chem. Phys. 112, 77 ͑2000͒.
18 B. F. Minaev, J. Phys. Chem. A 103, 7294 ͑1999͒.
37 H. Kim, S. Shin, S. Lee, and K. J. Shin, J. Chem. Phys. 105, 7705 ͑1996͒.
38 V. A. Apkarian and N. Schwentner, Chem. Rev. 99, 1481 ͑1999͒.
39 M. Y. Niv, M. Bargheer, and R. B. Gerber, J. Chem. Phys. 113, 6660
͑2000͒.
40 M. V. Smoluchowski, Z. Phys. Chem., Stoechiom. Verwandtschaftsl. 92,
129 ͑1917͒.
41 N. J. B. Green, M. J. Pilling, S. M. Pimblott, and P. Clifford, J. Phys.
Chem. 94, 251 ͑1990͒.
42 R. Parsons, Handbook of Electrochemical Constants ͑Butterworths, Lon-
don, 1959͒
19 R. J. Barnes and A. Sinha, J. Chem. Phys. 107, 3730 ͑1997͒.
20 A. Callegari, J. Rebstein, R. Jost, and T. R. Rizzo, J. Chem. Phys. 111,
7359 ͑1999͒.
43 G. R. Flemming, Chemical Applications of Ultrafast Spectroscopy ͑Ox-
ford University Press, Oxford, 1986͒.
21 R. J. Barnes, G. Dutton, and A. Sinha, J. Phys. Chem. A 101, 8374 ͑1997͒.
22 Y. Tanaka, M. Kawasaki, Y. Matsumi, H. Fujiwara, T. Ishiwata, L. J.
Rogers, R. N. Dixon, and M. N. R. Ashfold, J. Chem. Phys. 109, 1315
͑1998͒.
44 T. Goulet and J.-P. Jay-Gerrin, J. Chem. Phys. 96, 5076 ͑1992͒.
45 M. P. Allen and D. J. Tildersly, Computer Simulations of Liquids ͑Oxford
University Press, Oxford, 1987͒.
46 N. Agmon, J. Phys. Chem. 100, 1072 ͑1996͒.
47 A. H. Narten and H. A. Levy, J. Chem. Phys. 55, 2263 ͑1971͒.
48 R. J. Barnes, G. Dutton, and A. Sinha, Barnes, J. Phys. Chem. 101, 8374
͑1997͒.
23 A. B. Horn, J. R. Sodeau, T. B. Roddis, and N. A. Williams, J. Phys.
Chem. A 102, 6107 ͑1998͒.
24 T. E. Caldwell, K. L. Foster, T. Benter, S. Langer, J. C. Hemminger, and B.
J. Finlayson-Pitts, J. Phys. Chem. A 103, 8231 ͑1999͒.
49 M. R. Wedlock, R. Jost, and T. R. Rizzo, J. Chem. Phys. 107, 10344
͑1997͒.
25 C. L. Thomsen, D. Madsen, S. R. Keiding, O. Christensen, and J.
Thøgersen, J. Chem. Phys. 110, 3453 ͑1999͒.
50 F. M. Geiger, J. M. Hicks, and A. C. d. Dios, J. Phys. Chem. 102, 1514
͑1998͒.
26 G. H. Cady, Inorg. Synth. 5, 156 ͑1957͒.
27
U. K. Klaning and T. Wolff, Ber. Bunsenges. Phys. Chem. 89, 243 ͑1985͒.
51 G. V. Buxton, C. L. Greenstrock, W. P. Helman, and A. B. Ross, J. Phys.
Chem. Ref. Data 17, 513 ͑1988͒.
¨
28 P. Pagsberg, H. Christensen, J. Rabini, G. Nielsson, J. Fenger, and S. O.
Nielsen, J. Phys. Chem. 73, 1029 ͑1969͒.
52 M. D. Sevilla, S. Summerfield, I. Eliezer, J. Rak, and M. C. R. Symons, J.
29 M. Tachiya, Radiat. Phys. Chem. 21, 167 ͑1983͒.
30 H. Kim, S. Shin, S. Lee, and K. J. Shin, J. Chem. Phys. 105, 7705 ͑1996͒.
31 S. M. Pimblott, J. Phys. Chem. 95, 6946 ͑1991͒.
32 J. E. L. Cook, C. A. Ennis, T. J. Leck, and J. W. Birks, J. Chem. Phys. 74,
545 ͑1981͒.
Phys. Chem. 101, 2910 ͑1997͒.
53
¨
¨
T. Kuhne and P. Vohringer, J. Chem. Phys. 105, 10788 ͑1996͒.
54 D. A. McQuarrie, Statistical Mechanics ͑Harper and Row, New York,
1973͒.
55 R. Jimenez, G. R. Flemming, P. V. Kumar, and M. Maroncelli, Nature
͑London͒ 369, 471 ͑1994͒.
33 J. E. L. Cook, C. A. Ennis, T. J. Leck, and J. W. Birks, J. Chem. Phys. 75,
497 ͑1981͒.
56
˚
C. Rønne, P.-O. Astrand, and S. R. Keiding, Phys. Rev. Lett. 82, 2888
34 P. K. Walhout, C. Silva, and P. F. Barbara, J. Phys. Chem. 100, 5188
͑1996͒.
͑1999͒.
57
¨
¨
K. Winkler, J. Lindner, H. Bursing, and P. Vohringer, J. Chem. Phys. 113,
4674 ͑2000͒.
35 H. Van Beijeren, W. Dong, and L. Boucqet, J. Chem. Phys. 114, 6265
͑2001͒.
58 S. Woutersen, U. Emmerichs, and H. J. Bakker, Science 278, 658 ͑1997͒.
59 W. Marbach, A. N. Asaad, and P. Krebs, J. Phys. Chem. 103, 29 ͑1999͒.
36 A. I. Krylov and R. B. Gerber, J. Chem. Phys. 106, 6574 ͑1997͒.
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:
158.42.28.33 On: Tue, 25 Nov 2014 09:50:48