Femtosecond photolysis of HOCl(aq): Dissipation of fragment kinetic energy

Article abstract of DOI:10.1021/jp026968u

In this work, we present an experimental study of the energy dependence of the photolysis of aqueous HOCl and the subsequent recombination of the OH and Cl photofragments. Using femtosecond transient absorption spectroscopy, we follow the time-dependent concentration of the fragments. The excess energy in the photolysis is given to the fragments as kinetic energy, and tuning the wavelength enables a study of the energy-dependent thermalization and geminate recombination of the fragments in the liquid environment. The recombination yield and rate are governed by the initial fragment separation, and we deduce an approximately linear dependence of the fragment separation versus the kinetic energy with a slope of 0.13 nm/eV. Performing a simple MD simulation of the system gives qualitative agreement with the observations, although the calculated slope is only 0.04 nm/eV.

Full text of DOI:10.1021/jp026968u

3606
J. Phys. Chem. A 2003, 107, 3606-3611
Femtosecond Photolysis of HOCl(aq): Dissipation of Fragment Kinetic Energy
D. Madsen, C. L. Thomsen, J. Aa. Poulsen, S. J. Knak Jensen, J. Thøgersen, and
S. R. Keiding*
Department of Chemistry, UniVersity of Aarhus, Langelandsgade 140, DK-8000 Aarhus C, Denmark
E. B. Krissinel
European Bioinformatics Institute Genome Campus, Hinxton Cambridge CB10 1SD, U.K.
ReceiVed: September 11, 2002; In Final Form: NoVember 15, 2002
In this work, we present an experimental study of the energy dependence of the photolysis of aqueous HOCl
and the subsequent recombination of the OH and Cl photofragments. Using femtosecond transient absorption
spectroscopy, we follow the time-dependent concentration of the fragments. The excess energy in the photolysis
is given to the fragments as kinetic energy, and tuning the wavelength enables a study of the energy-dependent
thermalization and geminate recombination of the fragments in the liquid environment. The recombination
yield and rate are governed by the initial fragment separation, and we deduce an approximately linear
dependence of the fragment separation versus the kinetic energy with a slope of 0.13 nm/eV. Performing a
simple MD simulation of the system gives qualitative agreement with the observations, although the calculated
slope is only 0.04 nm/eV.
I. Introduction
bination. Femtosecond studies of the kinetic energy tuning of
the photofragments, as reported here, has to our knowledge been
reported only once before, namely, in OClO.8 In that work, the
increase in cage escape along the O‚‚‚ClO coordinate in OClO
with decreasing photolysis wavelength was investigated. The
cage escape grew approximately linearly with photon energy
when the photolysis wavelength was tuned from 400 to 320
nm. However, the presence of a barrier in the upper electronic
A˜ 2A2 state of OClO and the unknown distribution of energy
among intra- and intermolecular degrees of freedom complicated
the interpretation of the experimental data.
The theoretical work on caging and recombination can be
divided into models using a continuum approach and discrete
(microscopic) models. The continuum models9,10 have their
origin in the classic works of Smoluchowski11 and Noyes12 and
are based on the diffusive motion of fragments in a continuous
solvent, typically described by a friction coefficient. The
continuum descriptions have successfully been applied to
numerous nano- and picosecond experiments13 on the caging
and recombination of iodine. Very efficient and flexible
numerical codes modeling such processes are generally avail-
able.14 The microscopic models of photodissociation in solution
are primarily based on molecular dynamics (MD) simulations,
where fragment trajectories are calculated by classical propaga-
tion on the intermolecular potential describing the solvent-
solute interactions. The most detailed microscopic model has
been developed for systems of dihalogens in rare gas matrices.
In these systems, a mixed quantum-classical description is
formulated for the coupling between the electronic and nuclear
coordinates of the dihalogen solutes and the electronic and
nuclear degrees of freedom of the rare-gas solvent. In this
description, it is possible to monitor simultaneously the trajec-
tories of the caged fragments and the nonadiabatic transitions
among the electronic states of the parent molecule.5 These
methods have not yet been applied to caging-recombination
processes in real room-temperature liquids.
In this work, we study the energy dependence of the geminate
recombination of OH and Cl following femtosecond photolysis
of aqueous HOCl. We have previously shown that aqueous
HOCl offers a well-suited and simple system for studying the
fundamental solute-solvent interactions taking place during
bond breaking and the subsequent recombination.1 When
photolyzed at wavelengths below 340 nm, the isolated HOCl
molecule dissociates to Cl and OH. The majority of the excess
energy is converted into the kinetic energy of the Cl and OH
fragments with little vibrational excitation of the OH fragment.1-4
When excited at 266 nm, the kinetic energy that is released is
on the order of 2.5 eV (∼240 kJ/mol). This energy is sufficient
for the fragments to escape the aqueous solvent cage, leading
to a negligible quantum yield for geminate recombination within
the first solvation shell. The escaping fragments thermalize
through interaction with the solvent and may subsequently
recombine by diffusive geminate recombination occurring on a
10-100 ps time scale. The quantum yield for diffusive geminate
recombination depends on the initial separation of the fragments,
which for HOCl(aq) becomes an experimentally accessible
parameter through the tuning of the photolysis wavelength. This
makes HOCl particularly well suited for experimental and
theoretical studies of solvent-solute interaction, in particular
the “stopping power” of the solvent (i.e., the ability to thermalize
the translational energy of the recoiling reaction products).
Recently, detailed experimental and theoretical studies of
caging, recombination, and cage escape have intensified, spurred
by advances in ultrashort pulse laser technology. Experimentally,
model systems based on either halogens trapped in rare gas
matrices,5 molecular beams of I2- in CO2 or Ar clusters,6 or I2
in rare gases7 at high pressure have provided valuable insight
into the ultrafast dynamics of caging phenomena and recom-
* Corresponding author. E-mail: keiding@chem.au.dk.
10.1021/jp026968u CCC: $25.00 © 2003 American Chemical Society
Published on Web 04/10/2003

Femtosecond Photolysis of HOCl(aq)
J. Phys. Chem. A, Vol. 107, No. 19, 2003 3607
In this work, we present a detailed experimental and theoreti-
cal investigation of the photodissociation of HOCl and subse-
quent thermalization of the hot fragments by interaction with
the solvent molecules. We follow these processes by monitoring
the femtosecond transient dynamics of the chlorine photofrag-
ments as function of the photolysis wavelength, which in the
present system directly dictates the kinetic energy of the
photofragments. From the experimental data, we extract the
initial fragment separation using a diffusion model. Because
the separation derived from this analysis is very short, on the
order 1 nm, we have, in addition to the classical continuum
model, also modeled the experiment using molecular dynamics
simulations.
The paper is organized as follows: Section II briefly describes
the experimental procedures for synthesizing and characterizing
HOCl and the photolytic products (Cl, OH) and the generation
of the different pump wavelengths. Section III describes the
experimental results obtained whereas section IV contains the
data analysis and discussion.
Figure 1. Gas-phase potential energy curves along the HO-Cl bond
in HOCl from ref 17. The arrows represent different photolysis energies.
II. Experimental Section
to the gas-phase values, indicating a modest solvent perturbation
of the potential energy surfaces in the Franck-Condon region.
Gas-phase photolysis studies of HOCl coupled with ab initio
theoretical studies have given a detailed account of the yield of
the photoproducts and the distribution of the excess energy
among the translational and vibrational degrees of freedom.19
The principal photodissociation products in the wavelength range
from 140 to 440 nm are
An aqueous solution of hypochlorous acid (HOCl) was
synthesized by the method described by Cady.15 The procedure,
described in detail in ref 1, typically resulted in a HOCl(aq)
concentration of ∼1.5 M. The concentration and purity of the
sample were determined by static UV-vis absorption using
previously reported extinction coefficients for HOCl, ClOCl,
and Cl2 in aqueous solution. 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 optical density of the HOCl sample was 1.0 OD/1.8 mm at
the pump wavelength corresponding to a concentration of 0.17
M. Absorption spectra obtained before and after experiments
were identical, demonstrating that no significant sample deg-
radation occurred during the course of the experiment.
The details of the ultrafast transient absorption spectrometer
have been presented elsewhere;16 therefore, only a brief descrip-
tion is given here. A regenerative amplified titanium:sapphire
laser producing 90-fs, 750-µJ pulses centered 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 tunable pump
pulses at 290, 310, and 330 nm were obtained by quadrupling
the output from a traveling wave parametric generator (TOPAS)
pumped by 480 µJ at 800 nm. The 266-nm pump pulse was
generated by frequency tripling the 800-nm pulse whereas the
250-nm pulse was achieved by sum-frequency mixing the 800-
nm pulse with the signal pulse from the TOPAS followed by
frequency doubling. We obtained pulse energies on the order
of 5-10 µJ that were tunable from 250 to 340 nm. The probe
pulse was generated at 340 nm using a supercontinuum
generated by focusing residual 800-nm light into a 2-mm
ethylene glycol jet and subsequently frequency doubling a
portion of the supercontinuum selected around 680 nm in a
1-mm BBO crystal. Because of dispersion in the optical setup
and in the 1.8-mm flow cell, the temporal resolution is limited
to ∼700 fs in this work.
HOCl(Xˆ 1A′) + hυ f OH(2Π) + Cl(2P)
(1)
We previously studied in detail the photolysis of HOCl with
266-nm pump pulses and probe pulses in the range from 250
to 340 nm and observed that OH and Cl were formed with a
near-unity quantum yield.1 Since our time resolution is limited
to approximately 0.7 ps, we are unable to confirm the hypothesis
of a unity quantum yield directly. However, both a detailed
analysis of the pump-probe excitation geometry1 and a
normalization of the data at 1 ps yield a near-unity quantum
yield for dissociation, suggesting the absence of fast (<1ps)
direct cage back-recombination Since the OH radical absorbs
below 300 nm and the extinction coefficient of HOCl is very
small (<100 L cm-1/mol) relative to that of Cl, the transient
absorption spectrum above 300 nm is solely due to the chlorine
atoms formed in the photolysis of HOCl.20,21 From the transient
absorption spectrum, we can thus directly obtain the time
dependence of the Cl concentration by selecting a probe
wavelength above 300 nm where only the Cl fragments absorb.
In this work, we have kept the probe wavelength constant at
340 nm and have scanned the photolysis wavelength across the
absorption band of HOCl from 250 to 330 nm to monitor the
dynamics of the photolysis as function of energy. In Figure 2,
we show the time-dependent chlorine concentration for the five
photolysis wavelengths employed in this work. As discussed
in detail in ref 1, the dynamics of the chlorine concentration is
caused by slow diffusive geminate recombination with OH
radicals. For all of the pump wavelengths, the Cl concentration
undergoes a nonexponential decay. At long delays (175 ps),
the Cl concentration corresponds to ∼35-60% of the initial
value, depending on the wavelength. This level directly measures
the fraction of Cl atoms that survives secondary geminate
recombination, although a more precise determination of the
long-time escape would require longer delays.22 The experi-
mental data at long delays obtained at a 266-nm pump
III. Results
The absorption spectrum of HOCl is composed of two
absorption bands with maxima at 235 and 310 nm, respectively.
The maximum at 310 nm is due to the 11A′′ r X1A′′electronic
transition whereas the maximum at 235 nm is caused by the
21A′ r X1A′′ electronic transition.17,18 The two electronic
transitions are only slightly blue-shifted (∆λ ≈ 5 nm) compared

3608 J. Phys. Chem. A, Vol. 107, No. 19, 2003
Madsen et al.
TABLE 1: Thermalization Distance r0 (nm) as a Function
of the Excess Energy ∆Ea
wavelength
(nm)
r0 D (nm)
V ) 0
r0 D (nm)
V ) Morse MD simulation
r0 MD (nm)
∆E (eV)
330
310
290
266
250
1.61
1.85
2.13
2.52
2.81
0.44
0.49
0.53
0.58
0.60
0.49
0.52
0.57
0.60
0.65
0.49
0.51
0.53
a
r0 denotes the peak of a Gaussian distribution function (σ )
D
0.2 nm) derived from the spherically symmetric diffusion model used
to analyze the experimental data. The values of r0 are listed both
D
for the case where the interfragment interaction is governed by a Morse
potential and for the case where the interaction is assumed to be zero.
r0
denotes the separation obtained from an MD simulation of the
MD
fragment dynamics.
in liquid water, and finally (4) the initial separation of the
fragments at t ) 0, r0 . The diffusion coefficient of OH in water
is well known experimentally and is equal to 2.0 × 10-3 nm2/
ps.23 In contrast, the diffusion coefficient of Cl(aq) has, to our
knowledge, not been measured. However, using the self-
diffusion coefficient of water and the estimated radius for Cl-
(aq), the diffusion coefficient has been estimated by Parson et
al.:24 DCl ≈ 1.0 × 10-3 nm2/ps. The relative diffusion constant
thus becomes DCl-OH ) 3.0 × 10-3 nm2/ps. To estimate the
reaction radius, we use the potential energy surface for the
X1A′′ground state of HOCl obtained from the ab initio calcula-
tions by Peterson et al.18 We define the reaction radius as the
internuclear distance (RCl-OH) where the potential energy is
approximately equal to kT. For HOCl in the electronic ground
state, the reaction radius is estimated to be Rc ≈ 0.35 nm. When
the Cl and OH fragments are separated by a distance equal to
or less than Rc, they are assumed to recombine with unity yield,
corresponding to the absorption boundary condition in the
diffusion problem. The X1A′′potential is well approximated by
a 1D Morse potential along the RCl-OH coordinate,25 and we
use this as the interfragment potential energy in the simulation.
This is similar to a recent simulation published by Bradforth
on recombination in aqueous I-.26 As will be shown later, the
choice of the intermolecular potential has only a weak influence
on the parameters obtained, which is why we have chosen a
simpler gas-phase potential instead of a mean-force potential
that better takes into account the dynamic structure of the liquid
solvent. Because of the high concentration of HOCl employed
in this work, there is a small probability for secondary reactions
between Cl and HOCl that could account for the additional loss
of Cl atoms and the weak excess absorption due to the OH
radical previously observed.1 We have added a small sink term
describing the slow loss of Cl atoms due to secondary reactions
between Cl and HOCl. We describe the reaction as a pseudo-
first-order reaction because of the high HOCl concentration and
obtain a rate constant on the order 5 × 108 s-1. The only
remaining parameter in the SSDP model is thus the desired
initial separation, which may be extracted by comparing the
model with the experimental data shown in Figure 2. Because
of the statistical nature of the thermalization process, a distribu-
tion of distances is expected rather than just a single value, and
we therefore use a Gaussian distribution function defined by
the peak position of the initial separation r0 and the width σ
of the distribution.
Figure 2. Time-dependent chlorine concentration shown for the
different photolysis energies. The legend lists the photolysis wavelength
and the derived excess kinetic energy. The partition between escape
and recombination is approximately given by the concentration at 150
ps delay.
wavelength differs slightly from the other data sets, but given
the low signal levels (∆A < 10 m OD) and the fact the 266-nm
pump pulse was obtained using third-harmonic generation of
the fundamental 800-nm pulse, we refrain from analyzing this
deviation in greater detail. For high excitation energy, the kinetic
energy imparted to the OH and Cl photofragments is high,
leading to a large initial separation of the fragments and a low
recombination yield. For low excitation energy, less energy is
given to the fragments that, consequently, have a shorter initial
separation, leading to a higher recombination yield.
IV. Analysis and Discussion
The large amount of excess energy available to the fragments
following the photolysis of HOCl results in a large initial
separation of the fragments and consequently a slow geminate
recombination, as the photofragments must await diffusional
encounters. The recombination dynamics reflected by the time-
dependent Cl concentration therefore allows us to follow the
solvent-solute interactions responsible for the thermalization
of the hot fragments and the subsequent diffusion dynamics. In
particular, the initial fragment separation r0 and its dependence
on the excess energy may be extracted from the Cl transient
absorption using a model for the diffusive recombination. Thus,
determining the initial fragment separation r0 as a function of
excess energy provides a measure of the solvent’s stopping
power.
Continuum Model: Spherical Symmetric Diffusion. Quan-
titatively, we model the slow recombination dynamics using
numerical simulations of the spherical symmetric diffusion
problem (SSDP). A simple and versatile software package,
developed by N. Agmon and E. B. Krissinel, is available for
solving the SSPD for a wide range of reaction types and
boundary conditions.14 Four parameters are needed in the
simplest case to describe the dynamics of diffusive recombina-
tion between the Cl and OH radicals: (1) the relative diffusion
coefficient of the Cl-OH fragments, DCl-OH ) DCl + DOH, (2)
the reaction radius Rc where the recombination takes place, (3)
the interaction potential V(r) between the OH and Cl fragments
The simulated decay of the chlorine concentration obtained
from the diffusion model is shown in Figure 2 together with
the experimental data, and the parameters r0 and σ are collected
in Table 1. We obtain good agreement between experiment and
simulation with the selected parameters, but it is possible to

Femtosecond Photolysis of HOCl(aq)
J. Phys. Chem. A, Vol. 107, No. 19, 2003 3609
obtain almost as good an agreement using a model with the
interfragment potential set to zero. This gives a slightly smaller
value of the initial fragment separation but the same dependence
on the excess energy. The gas-phase value of the dissociation
energy along the O-Cl coordinate is measured to be D0 ) 2.39
eV.27,28 By taking into account the solvent from the estimated
solvation energies for HOCl (0.3 eV),29 OH (0.44 eV),23 and
Cl (0.1 eV),30 we estimate a dissociation energy of 2.15 eV
along the O-Cl coordinate of HOCl in aqueous solution.
Subtracting 2.15 eV from the photon energy of the photolysis
pulse gives the kinetic energy to be distributed among the OH
and Cl photofragments.31 We assume, on the basis of experi-
mental evidence in the gas phase, that no excitation energy is
used to excite the OH fragment vibrationally. In HOCl, the OH
bond distance is very close to the O-H bond length found in
the free hydroxyl radical and merely serves as a spectator mode
remaining in the vibrational ground state.2-4 The fragments
rapidly lose this excess energy as a result of solvent-solute
interactions. When the kinetic energy is on the order of kT, the
fragments have thermalized, and thermal diffusion will deter-
mine their motion in the solvent. The diffusion model assumes
that the fragments are in equilibrium with the surrounding
solvent, and the good agreement with experimental data after 1
ps therefore suggests that r0 of the diffusion model may be
interpreted as the thermalization distance. The experimental data
shown in Figure 2 therefore represents the ability of the solvent
(H2O) to thermalize the high-energy fragments. The experiments
described here are thus similar to the classical stopping power
measurements where the ability of solids and liquids to
thermalize MeV particles were investigated.32,33 The values of
r0 can be compared with the radius of the first and second
solvation shells in pure liquid water.34,35 These are approximately
located at 0.28 and 0.5 nm, indicating that only two water
molecules separate the fully thermalized fragments. This clearly
demonstrates the efficiency by which the solvent, in the present
case, water, is able to act as a sink for the excess energy released
after the photodissociation. However, the short thermalization
distances observed also suggest that a continuum description
of the dissociation and recombination dynamics is likely to be
an oversimplification.
simulation is primarily concerned with the separation of the
fragments in the liquid solvent, this approximation is justified
as the HOCl potential energy surface exhibited a strong θ
dependence at the internuclear distances probed. If, however,
we had included recombination in the model (i.e., included the
ground-state potential surface and the nonadiabatic transition
to the ground state), then the θ dependence would have been
very important. Neglecting both vibrational and rotational
excitation in the OH fragment means that all the excess energy
is deposited into the kinetic energy of the fragments. On the
basis of the dissociation and hydration energies discussed in
the previous section, we subtract 2.15 eV from the photon
energy of the photolysis pulse to obtain the kinetic energy to
be distributed among the OH and Cl photofragments.
The water-water interaction was described by adopting the
SPC-flexible model.36 To model the electrostatic interactions
between one HOCl and one H2O molecule, a simple restricted
Hartree-Fock calculation,37 carried out at the experimental
equilibrium geometry of HOCl, was used to assign Mulliken
point charges to the atoms of HOCl. In the calculation, we used
the cc-pVDZ basis set. The charges on H, O, and Cl were found
to 0.40e, -0.43e, and 0.03e, respectively. In the simulation,
we adopted the charges 0.43e, -0.43e, and 0e, respectively.
To model the dispersion interaction between Cl in HOCl and
the atoms in H2O, Lennard-Jones parameters for H-Cl and
O-Cl interactions were found by applying standard Lorentz-
Berthelot mixing rules.38 A molecular dynamics simulation with
a fixed number of molecules and a fixed volume and energy
(NVE) employing 511 SPC water molecules and 1 HOCl
molecule was performed using a box length of 24.89 Å
corresponding to a density of 0.997 g/cm3. A half-box-length
spherical cutoff together with standard periodic boundary
conditions was applied. The average temperature was set to 298
K through an equilibration run. In this run, the geometry of the
HOCl molecule was kept fixed at the calculated geometry of
Nanbu and co-workers17 by adopting the SHAKE routine by
Ryckaert et al.39 After equilibration, the program was run for
130 ps using a time step of 1 fs. For every 2.5 ps, the positions
and momenta of all the molecules were stored for later use in
the analysis of the dissociation dynamics of HOCl. During
dissociation, the value of the RO-Cl coordinate was recorded
for every 0.125 fs. In none of the trajectories did the separation
between the fragments exceed the half box length, and only a
slight temperature increase of less than 5° was observed.
Because we are far from a phase transition, we do not expect
that such a small temperature increase will influence our results.
A total of 51 trajectories were carried out for each of the pump
wavelengths: 330, 290, and 250 nm, chosen to match the
experimental pump wavelengths.
Discrete Model: MD Simulation. To investigate the validity
of the continuum approach and to assess the value of the
parameters obtained, we performed a classical MD simulation
of the HOCl(aq) system. The dissociation of electronically
excited aqueous HOCl was investigated by applying classical
molecular dynamics simulations to a system of 511 water
molecules and 1 HOCl molecule. The weak absorption band of
HOCl, peaking at 240 nm with a pronounced shoulder 300 nm,
is caused by transition from the X1A′′ground state to the purely
repulsive 11A′′ and 21A′ states. For the photolysis wavelengths
used in this work, the exact contributions of the 11A′′ and 21A′
states are unknown. Since the upper repulsive states are quite
similar, we used the 11A′′ state to describe the dynamics of the
dissociating HOCl molecule. The 1A′′ state is known from the
ab initio calculations of Nanbu and Iwata.17 The initial geometry
of the photolyzed molecule is assumed to be that of the ground-
state equilibrium geometry, and the O-H bond length is kept
fixed in agreement with the assumption that no vibrational
excitation is expected in OH fragments. Additionally, we also
choose to neglect the orientation of the OH fragment, defined
through the angle θ between the OH bond and the relative
velocity vector of the OH and Cl fragments. We use the potential
energy of the repulsive state corresponding to the ground-state
value of the HO-Cl angle equal to 102.45°. Because the
In Figure 3, we show the time-dependent fragment velocity
and distance (RHO-Cl) as a function of time. During the first 20
fs after photodissociation, the fragments separate ballistically
to a distance of 0.3 nm before interaction with the solvent slows
down the fragments, resulting in an outer turning point at RHO-Cl
≈ 0.53-0.60 nm depending on the photolysis wavelength. The
impact of the dissociating fragments leads to a compression of
the surrounding solvent, which forces the fragments back to a
thermalization distance of ∼0.49 to 0.53 nm, measured after
0.5 ps. The thermalization distances derived from experiments
and MD simulation are compared in Figure 4. The magnitudes
of the thermalization distances obtained are in reasonable
agreement, both resulting in a thermalization distance corre-
sponding to two to three water molecules. Moreover, both
models yield an increasing fragment separation with photolysis

3610 J. Phys. Chem. A, Vol. 107, No. 19, 2003
Madsen et al.
overestimate the stopping power of liquid water. For the chlorine
fragment, the interaction with the solvent is quite weak and thus
relatively insensitive to the detailed nature of the MD simulation.
For the OH fragment, however, we expect a strong interaction
with the solvent, in particular through hydrogen bonding. The
SPC model gives a poor representation of the hydrogen bond
network41 and is therefore expected to underestimate the
solvent’s ability to thermalize the energetic hydroxyl radicals,
in contrast to the observed overestimation. However, the validity
of such arguments is based on the assumption of weak coupling
between the solvent and solute degrees of freedom. Given the
large value of the kinetic energy, Ekin≈ 2.5 eV, the short
thermalization distances, and the correspondingly short ther-
malization time, the weak-coupling assumption is highly
questionable, and a more elaborate theoretical treatment of the
problem is desirable. Alternatively, one could view the process
as a caging of the fragments between the first and second
solvation shells. The thermalization distances obtained are
approximately located at the second solvation shell. In this
picture, the (weak) increase in thermalization distance with
photolysis energy could be interpreted as a temporary expansion
of the solvent shell caused by the impact of the energetic
fragments. There is some support for this picture in the MD
simulations shown in Figure 3, where the fragment separation
actually decreases slightly following the maximum at 200 fs as
a result of the elastic properties of the solvent shell. However,
the time scale for relaxation of this perturbation of the second
solvent shell is expected to be very fast, less than 1 ps, according
to the MD simulation. It is therefore unlikely to contribute to
the long-time recombination dynamics and in particular to the
observed energy dependence. Again, a more elaborate theoretical
treatment would be desirable; in particular, an MD simulation
utilizing a much larger box size and longer times would be of
interest to determine if the equilibrium diffusive properties of
the OH and Cl fragments would appear before recombination,
as the apparent success of the continuum model seems to
indicate.
Figure 3. Results from the MD simulation giving the separation of
the fragments and the relative velocity. The thermal velocity is given
as the dotted line. The first 20 fs is the ballistic phase after which the
influence of the solvent appears. After roughly150 fs, the fragments
reach thermal velocities.
In conclusion, we have performed an experimental study of
the photolysis of aqueous HOCl. From an earlier study, it is
known that HOCl dissociates with a near-unity quantum yield
into OH and Cl, which subsequently recombine geminately in
a diffusion-limited process. Using femtosecond transient absorp-
tion spectroscopy, we have followed the changes in the
dynamics of the geminate recombination as the photolysis
wavelength was gradually blue shifted, thereby imposing more
kinetic energy to the photofragments, enabling them to separate
more before they thermalize and recombine. The kinetic energy
of the fragments ranges from approximately 1.5 to 3 eV, and
the fragments are observed to have thermalized when they are
separated by r0 ) 0.4 to 0.7 nm, corresponding to two to three
water molecules. r0 increases with fragment energy with a
slope of approximately 0.13 nm/eV. In a simple MD simulation,
we have obtained qualitative agreement with the experimental
data, although the calculated stopping power of the solvent
appears more effective compared to that inferred from the
experimental data.
Figure 4. Excess energy dependence of the initial separation of the
fragments, r0 obtained from the experimental data when analyzed
D
by the spherically symmetric diffusion model and the initial separation
obtained from the MD simulations.
energy, but the slope resulting from the MD simulations is a
factor of 3.3 smaller than that extracted from the experiment.
Thus, the thermalization distances obtained from experiment
may be fitted to a straight line with a slope of 0.13 nm/eV
whereas the MD simulation gives a straight line with a
significantly smaller slope of 0.04 nm/eV.
The thermalization of the photofragment kinetic energy is
caused by the interaction between the solvent and the solute
and can qualitatively be linked to the presence and strength of
the intermolecular forces of the solvent. The process of kinetic
energy relaxation is related to the process of vibrational
relaxation since the solvent degrees of freedom are similar.40
Our experimental data seem to suggest that the solvent, liquid
water, is less capable of dissipating the fragment kinetic energy
as compared to the discrete model based on the properties of
pure (SPC) water. In other words, SPC water seems to
References and Notes
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S. J. K.; Keiding, S. R. J. Chem. Phys. 2001, 115, 9361-9369.
(2) Hickman, C. G.; Brickell, A.; Frey, J. G. Chem. Phys. Lett. 1991,
185, 101-104.
(3) Hickman, C. G.; Shaw, N.; Crawford, M. J.; Bell, A. J.; Frey, J.
G. J. Chem. Soc., Faraday Trans. 1993, 89, 1623-1630.
(4) Bell, A. J.; Pardon, P. R.; Hickman, C. G.; Frey, J. G. J. Chem.
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Femtosecond Photolysis of HOCl(aq)
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