Vibrational population dynamics of the HgI photofragment in ethanol solution

Article abstract of DOI:10.1063/1.470376

The vibrational population dynamics of HgI fragments in ethanol solution, resulting from the 320 nm photolysis of HgI2, are examined both experimentally and by a simulation.The experiments reveal an HgI population distribution which rapidly relaxes toward equilibrium.At the earliest times, the HgI exhibits vibrational coherent wave-packet motion that dephases with a time constant of ca. 1 ps.These data are used to gain insight into the character of the solvated potential energy curves.The population relaxation was adequately reproduced by master equations which were formulated to incorporate the HgI anharmonicity and a solvent frequency dependent friction.This treatment characterizes the spontaneous vibrational relaxation timescale for the n =1->0 transition to be ca. 3 ps, and is used to identify the relaxation rate constants for all other HgI level pairs.The simulations estimate that the initial excess energy of HgI is centered at n ca. 10 which corresponds to a total excess energy of ca. 1050 cm^-1.

Full text of DOI:10.1063/1.470376

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Vibrational population dynamics of the HgI photofragment in ethanol solution
Nick Pugliano, Arpad Z. Szarka, S. Gnanakaran, Matt Triechel, and Robin M. Hochstrasser
Citation: The Journal of Chemical Physics 103, 6498 (1995); doi: 10.1063/1.470376
View online: http://dx.doi.org/10.1063/1.470376
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Vibrational population dynamics of the HgI photofragment
in ethanol solution
Nick Pugliano, Arpad Z. Szarka, S. Gnanakaran, Matt Triechel,
and Robin M. Hochstrasser
Department of Chemistry, 231 South 34th Street, University of Pennsylvania, Philadelphia,
Pennsylvania 19104
͑Received 8 September 1994; accepted 14 July 1995͒
The vibrational population dynamics of HgI fragments in ethanol solution, resulting from the 320
nm photolysis of HgI2, are examined both experimentally and by a simulation. The experiments
reveal an HgI population distribution which rapidly relaxes toward equilibrium. At the earliest
times, the HgI exhibits vibrational coherent wave-packet motion that dephases with a time constant
of ca. 1 ps. These data are used to gain insight into the character of the solvated potential energy
curves. The population relaxation was adequately reproduced by master equations which were
formulated to incorporate the HgI anharmonicity and a solvent frequency dependent friction. This
treatment characterizes the spontaneous vibrational relaxation timescale for the nЉϭ1→0 transition
to be ca. 3 ps, and is used to identify the relaxation rate constants for all other HgI level pairs. The
simulations estimate that the initial excess energy of HgI is centered at nЉХ10 which corresponds
to a total excess energy of ca. 1050 cmϪ1. © 1995 American Institute of Physics.
dissociated atoms. Vibrationally hot IϪ2 is obtained by photo-
I. INTRODUCTION
dissociating IϪ3 in solution8,9 and hot HgI was detected fol-
lowing the photolysis of HgI2.10,18,19 For the case of I2, the
relaxation dynamics depend greatly on the solvent. Times-
cales in different solvents have been reported and range from
50 to 200 ps.7 The hot ion IϪ2 dissipates its energy on the
timescale of a few ps in ethanol.8,9 The polar HgI also cools
on the timescale of a few ps in ethanol.10,18,19 Each of these
systems presents an opportunity to evaluate the effectiveness
of different types of intermolecular forces related to vibra-
tional relaxation. A systematic study of the mechanism of
vibrational cooling in HgI has not previously been presented
and forms the subject of this paper.
The relaxation of vibrational energy in diatomic mol-
ecules is a fundamental component of chemical reaction dy-
namics in solids,1 liquids,2 and solutions.3 In high pressure
gases and liquids a basic question which remains unresolved,
is the detailed manner by which a vibrationally hot diatomic
molecule approaches equilibrium with its surroundings.4 Ex-
perimental studies of such relaxation can expose the influ-
ence of the external solvent forces acting on a single mode,
free from the complications arising from internal mode cou-
pling, such as occurs in polyatomic molecules.5,6 In liquids,
experiments on highly excited diatomic molecules produced
by photoreactions have begun to appear only recently7–10 and
there is a need for more investigations of this type. In addi-
tion, computer simulations based on classical dynamics have
been employed to predict the nature of the forces involved in
such energy relaxation processes.11–13 The appropriateness of
such simulations in predicting the relaxation of quantum me-
chanical oscillators in model liquids is also being
evaluated14,15 but methods for the prediction of these pro-
cesses in real solutions need considerably more develop-
ment.
Vibrationally hot diatomic molecules resulting from
chemical reactions are readily generated and are often stud-
ied in gases.16 The timescales of the relaxation dynamics are
controllable in such cases by changing the pressure of a
buffer gas. Reactions having these characteristics form the
basis of infrared chemical lasers.17 In solutions, the ‘‘colli-
sional’’ frequency is in excess of 1013 sϪ1 and the corre-
sponding relaxation processes can be extremely fast if the
solute–solvent forces are sufficiently large. Therefore, the
study of vibrational relaxation of hot diatomics in solutions
relies heavily on the recent developments of ultrafast laser
methods. Three systems have been reported on recently. The
most extensively studied is hot neutral I2 ͑Ref. 7͒ which is
created by solvent cage induced recombination of the photo-
The photolysis of HgI2 has been well characterized by a
number of groups and the early work has been reviewed by
Maya.20 Excitation of gas phase HgI2 into its lowest energy
absorption band is known to produce ground state HgI free
radicals with a quantum yield of unity.20 The excitation of
this HgI2 absorption band results in a branching of the I atom
2
2
photofragment between its P3/2 and P1/2 ground and ex-
cited spin–orbit components. The spin–orbit splitting is ca.
7600 cmϪ1 and the pump wavelength dependence of the
branching has been characterized in the gas phase by Hoff-
mann and Leone.21 Finally, the vibrational frequencies for
HgI2 corresponding to the symmetric stretch, the asymmetric
stretch and the bend are 155, 237, and 33 cmϪ1
,
respectively.22 The lowest energy absorption spectrum of
HgI2 in ethanol is very similar to that in the gas phase.23
2
2
The B ⌺ϩ→X ⌺ϩ emission of the HgI free radical
has been carefully studied in the gas phase by a number of
groups.24–27 These experiments have determined that the
equilibrium bond length decreases substantially ͑which is
typical for an ion pair→valence transition͒ from 3.3 to 2.8 Å
when the molecule electronically relaxes from the B to the X
state. This is corroborated by the calculations of Wadt28
which characterize the ionic character, and the dipole mo-
ments in these electronic states of the HgCl and HgBr radi-
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Pugliano et al.: Photolysis of HgI2
6499
cals. The extensive data set has provided an accurate deter-
mination of the potential energy surfaces for both the ground
and excited states, the transition dipole moment function for
the B↔X transition27 and the vibrational frequencies for the
X and B states which are 125 and 110 cmϪ1, respectively.
Ultrafast studies of HgI2 dissociation by Zewail and
co-workers,29 have illustrated isolated molecule dynamics on
the femtosecond timescale. These experiments demonstrated
that a vibrational coherent superposition state of HgI was
created by the reaction, and the wave packets were modeled
using quantum propagation methods.30 The transients also
provided evidence for the branching between the spin–orbit
states of atomic iodine and this has been further verified by
femtosecond time-of-flight techniques.31 This work con-
electric mirrors. Deconvolution of the cross correlation of the
320 nm beam with the 20 fs 620 nm pulse results in a 35–40
fs UV pulsewidth. This represents more than a twofold in-
crease in time resolution over the work presented in Ref. 10.
The second portion of the 620 nm beam is variably delayed
and focused into an ethylene glycol jet to generate a con-
tinuum and this provides tunability from ca. 400 nm into the
near infrared. Spectral selection of a particular probe wave-
length is accomplished with 10 nm wide interference filters.
The probe is split into two equal portions which serve as a
signal and reference beam, each of which is detected with
photodiodes. The photodiode signals are processed with box-
car integration and the results are stored in units of absor-
bance. Averaging ca. 2000–3000 laser shots permits a mini-
2
firmed that the P3/2 atomic I channel resulted in vibra-
mum detectable fractional absorbance change of ca. 5ϫ10Ϫ4
.
2
tionally hot HgI, whereas the P1/2 channel produced rela-
The sample was a 0.5 mm flowing jet of an ethanol
solution containing HgI2 at a concentration of 10 mM. The
HgI2 ͑99.999% purity Aldrich͒ was used as received, without
further purification. For this HgI2 concentration, only 60% of
the pump light was absorbed. UV pump energies were al-
ways maintained at ca. 2 ␮J. Under these conditions, satura-
tion effects were not observed and all signals linearly fol-
lowed the pump intensity. Time zero was found by
conducting a pump–probe experiment on a molecule such as
a stilbene. The estimated uncertainty in t0 is no larger than
ca. Ϯ20 fs. The delay line was scanned linearly from Ϫ1 to
ϩ1 ps with 50 fs steps and logarithmically thereafter.
tively cold HgI product. The dissociation dynamics of high
lying excited states of HgI2 have most recently been investi-
gated by means of multiphoton absorption32 to characterize a
number of dissociative pathways that lead to highly energetic
products.
A study of the vibrational energy cooling of solvated HgI
therefore presents an opportunity to evaluate a number of
important parameters of relaxation dynamics for a reaction
which has been well characterized in the gas phase. The
present work is aimed at characterizing the dynamics of en-
ergy flow from HgI to ethanol solvent after the photodisso-
ciation of HgI2. The HgI generated in the photoreaction is
highly vibrationally excited. This permits an opportunity to
explore solute–solvent interactions over much of the poten-
tial surface and thereby examine the effects of anharmonicity
on vibrational energy relaxation. This system is particularly
unique for a number of reasons. The fact that the dipole
moment decreases as the HgI bond stretches is a novel char-
acteristic which presents challenges to condensed phase
theory. The lower energy potential surfaces of HgI are well
known in the isolated molecule and this will allow an evalu-
ation of the effective potential functions in solution. Further-
more, the similarity of the HgI vibrational frequency to those
of I2 and IϪ2 should permit meaningful comparisons with
these systems.
III. RESULTS AND ASSIGNMENTS
The lowest energy absorption band of HgI2 in ethanol
peaks at 273 nm and apart from the spectral maximum shift-
ing approximately 1400 cmϪ1 to lower energy relative to the
gas phase absorption band, the shape is essentially
unchanged.23,34 Therefore, the shapes of the HgI2 surfaces in
the Franck–Condon region and the initial internal dynamics
along the dissociative coordinate are probably similar to
those for the isolated molecule. Furthermore, the primary
photoproducts should be HgI and I ͑2P3/2͒ when the solvated
molecule is photolyzed at 320 nm. The time and frequency
resolved data support this expectation.
A. Gas phase potential surfaces
II. EXPERIMENT
The gas phase potentials are well characterized from the
results of B→X emission experiments.24–27 For simplicity
the ground and excited state potential surfaces were fit to
Morse functions of the form,
The femtosecond spectrometer used to conduct these ex-
periments is based on the 20 Hz Nd:YAG amplification of a
CPM laser. The CPM is first preamplified in two stages up to
an energy of ca. 10 ␮J and the output is recompressed to ca.
100 fs with a grating pair. The light is variably attenuated
and imaged into a short piece of optical fiber. The output of
the fiber extends from 570 nm to beyond 700 nm. This beam
is collimated and used to seed a three stage amplifier for
which the medium is a mixture of DCM and Rhodamine 590
dye. After Nd:YAG amplification up to the 500 ␮J level, the
40 nm wide spectral profile centered at 620 nm is double
passed through a grating compressor and a prism compressor
to achieve 20 fs pulses.33 This beam is separated into two
parts. One portion is frequency doubled in a 50 ␮m slice of
BBO and the transmitted 320 nm beam is collimated and
separated from the residual 620 nm light with reflective di-
2
U r͒ϭT ϩD 1Ϫexp Ϫ␤ rϪr ͒/r ͒
͔
e
͑1a͒
͑
͓
͑
͑
e
0
e
and the X state vibrational energies are described by
2
En
1
1
2
Љ
ϭ␻ nϩ Ϫx ␻ nϩ
.
͑1b͒
ͩ
ͪ
ͩ
ͪ
e
e
e
hc
2
The parameters for the HgI X ⌺ϩ/B ⌺ϩ states in Eq. ͑1a͒
are Teϭ0/24 072 cmϪ1, D0ϭ2800/18 850 cmϪ1, ␤ϭ7.1/
2.86, and reϭ2.8/3.3 Å. These potentials are illustrated in
Fig. 1 by the dashed curves. Open and solid arrows are used
to depict transitions which originate from low and high en-
ergy regions of the X state, respectively. It is apparent from
this drawing that higher frequency probes mainly sample the
2
2
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6500 Pugliano et al.: Photolysis of HgI2
separations and the results used to calculate the solvent in-
duced forces along the internuclear axis. These forces were
then added to those known for isolated HgI to obtain a mean
force potential. The convergence error was estimated42 to be
Ϯ35 cmϪ1. This new surface was very similar to that of
isolated HgI, and showed an increase in well depth of only
3%. These results tell us that if the nuclei of HgI were to
move slowly enough in comparison to the energy changes
resulting from solvent reorganization, the mean potential ex-
perienced would not be much altered from that of the iso-
lated molecule. A less physically relevant limit is when the
solvent response is very slow and there is no reorganization
energy. In this case there will be an inhomogeneous distribu-
tion of surfaces governing the faster HgI motion. The mean
well depth can be estimated from the simulation as the aver-
age of the solute–solvent interaction energy at the minimum
compared with the separated atom configuration. For HgI(X)
this energy was found to be 1800 cmϪ1. At present the true
situation is not known but these calculations suggest that the
shape of the effective HgI potential will be a reasonable
starting point for the analysis. The results presented in sub-
sections D and E below further confirm the reasonableness of
this assumption and at the same time permit a fuller charac-
terization of a solvent perturbed surface. First, the nature of
the signals observed in the experiments are described in sub-
section C.
2
2
FIG. 1. The gas phase potentials for the X ⌺ϩ ground state and the B ⌺ϩ
excited state of HgI are shown as heavily dashed lines. The X ⌺ϩ state
2
dissociates to atoms whereas the B ⌺ϩ asymptotically approaches an ion
2
pair. The equilibrium separation of the B state is shifted to 3.3 Å relative to
that of the X state in which the minimum is 2.8 Å. The thin X state corre-
sponds to the potential of mean force. The data points describe the experi-
mentally determined portion of the effective B state as described in Sec.
III E, and the line through the points is the best fit Morse potential. Only the
solid portion of the line is determined by the analysis. The lightly dashed
line is the transition dipole moment function of Ref. 27 used in the analysis.
bottom of the X-state potential, whereas lower frequency
probes sample mainly the higher energy portions of the sur-
face.
The observed energies for the vibrational eigenstates in
the X state, agree well with those obtained from Eq. ͑1b͒,
with ␻eϭ125 cmϪ1 and xe␻eϭ1.38 cmϪ1. The B↔X tran-
sition dipole moment of Ref. 27 was used. Using this func-
tional form for ␮(r) an absorption spectrum for the B→X
transition was calculated. Each vibrational wave function
was calculated using a Numerov–Cooley algorithm35 and the
C. The wavelength dependence of the probe signal
The population decay measurements reported below deal
with time delays, ␶, in excess of ca. 1 ps. It follows that the
pump–probe signal can be calculated from a single time or-
dering of pump and probe fields corresponding to the case in
which the pump fields are first absorbed followed by a cou-
pling to the weak probe field. The probe signal, S͑␶͒ mea-
sured under magic angle conditions, can be expressed by a
first-order interaction of the evolving system with probe
field:
transition moment matrix elements, B
͉␮(r)͉Xn were de-
͘
n
Ј Љ
͗
termined over the range of excited and ground state vibra-
tional levels from 200ϽnЈϽ0 and 42ϽnЉϽ0, respectively.
For these surfaces the transition matrix elements
B
͉␮(r)͉Xn in the probe wavelength region used in our
͘
n
Ј Љ
͗
ϱ
4␲
2
experiments have significant magnitude at HgI bond lengths
corresponding to the attractive region of the X state and the
repulsive region of the B state. The shapes of the potentials
are expected to be least affected by solvent in the region
probed because the B state is least polar there. In the B state,
HgI asymptotically correlates to separated ions ͑HgϩϩIϪ͒
while it correlates to atoms in the X state. For simulations of
the solution spectrum each vibronic transition was broadened
by 80 cmϪ1. This corresponds to an electronic dephasing
time of at most 125 fs which is slightly faster than the
dephasing time reported for I2.36
S ␶͒ϭRe
␻
͉
␮
͉
dt ⑀ tϪ␶͒
͑
͑
͵
͚
n n
Љ Ј
ͭ
3បc0
Ϫϱ
n ,n
Ј Љ
t
ϫ
dt ⑀ t Ϫ␶͒␳ t ͒exp ⍀
t Ϫt͒͒ .
Ј
͑
͑
͑
͑
Ј
Ј
Ј
͵
n
n n
Љ Ј
Љ
ͮ
Ϫϱ
͑2͒
In Eq. ͑2͒ ⑀͑␶͒ is the real probe pulse field envelope, ␮
the transition dipole connecting vibrational states ͉X,nЉ͘ and
͉B,nЈ͘, ␳ (t) is the population of state nЉ at time t,
is
n n
Љ Ј
n
Љ
⍀
␻
⌫
ϭi⌬n n ϩ⌫n n such that ⌬n n ϭ␻
ϭ ␻ Ϫ ␻ being the transition angular frequency,
ϩ ␻ with
n n
n n
Љ Ј
0
Љ Ј
Љ Ј
Љ
Љ Ј
Ј
Љ Ј
n n
Љ Ј
n
n
B. Equilibrium simulations of the X surface
is the electronic dephasing for the (B,nЈ)←(X,nЉ)
n n
Љ Ј
Molecular dynamics simulations of HgI in ethanol using
Charmm37 were used to calculate the potential of mean force
for the HgI, X state. The dipole moment was first calculated
for each internuclear separation by means of the ab initio
effective core potentials38–40 as implemented in GAUSSIAN
92.41 With the dipole represented by point charges at the
atomic centers, 50 ps simulations were run at ten internuclear
transition and ␻ is the center frequency of the femtosecond
probe. Equation ͑2͒ is the time domain version of the overlap
of the pulse spectrum with the spectrum of the B←X transi-
tion of HgI. The integral over t accounts for the detector
being too slow to follow the field envelope or the free induc-
tion decay of the sample. The detector integrates the square
of the fields incident upon it.
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