Ultrafast Time Resolved Photodissociation ofTrihalide Ions in Solution.

Thesis submitted for the degree

‘‘Doctor of Philosophy”

by

Erez Hai Gershgoren

Submitted to the senate of the Hebrew University, Jerusalem

2002

This work was carried out under the supervision of

Professor Sanford Ruhman

To my dear parents, Ilana and Benzi,

and to my wife, Gitit, who has provided me with unconditional

love and support throughout my graduate years.

ACKNOWLEDGEMENTS

This thesis would not be possible without the help of many people.

I would like to thank my advisor, Professor Sandy Ruhman, for making my graduate

school experience a great one. Apart from being a friend and mentor, and despite the oc-

casional argument settled over a cup of coffee, Sandy not only exposed me to the exciting

world of ultrafast spectroscopy, but more importantly, helped me to respect the rigors of

scientific research. This project is a success mostly due to his advice.

I would also like to thank Professor Ronnie Kosloff for his support and guidance.

Ronnie, always with a smile, taught me more than any class I had ever taken during cof-

fee break or near the copy machine, as well as being responsible for most of my formal

education.

I would like to thank Dr. Jiri Vala for a fruitful collaboration and for introducing me to

the wonders of computer simulation.

Many thanks to DR. Edward Mastov for his magical solution in the machining depart-

ment, and to the electronic shop staff for their daily basis support.

ABSTRACT

In my thesis, advanced ultrafast laser technology is applied to study the dynamics and

kinetics of the triiodide photodissociation reaction in polar solvents. The thesis focus on

three different aspects of the photodissociation reaction, which are all exclusive to the

condense phase chemistry.

The first chapter demonstrates coherent control of triiodide ground state dynamics.

The coherent control scheme relays on the impulsive excitation process that results in the

creation of a dynamical hole. The control goal was to increase the ratio of second to first

harmonic spectral modulations of the symmetric stretching vibrational coherences. An

original theoretical model and complete quantum wavepacket simulation provides insight

on the light/matter interactions that are active in achieving the control goals. A different

subject address in this chapter is a better charactization of the impulsive excitation process.

In the second chapter we demonstrate that the geminate recombination process is com-

pleted in three different time scales, that represent three independent kinetics pathways,

leading to ground-state triiodide. The first route is a direct recombination and vibrational

relaxation on a time scale of a few ps. The second is a long-lived complex that decays in

40 ps. Finally, encounters of geminate pairs, that initially escape the solvent cage, leads

to slow residual component of recombination. Changing the solvent modify the relative

amplitudes of the different pathways, but do not vary the decay rate of complex. The

experimental results farther imply that the fate of the reaction fragments is determined

shortly after the bond fission.

In the last chapter, the pure dephasing rate of the fundamental and its first overtone

of the symmetric stretch mode are measured as a function of temperature, from room

temperature to 100K. The reduction in temperature leads to a 2-fold decrease in the rate of

pure dephasing, where the fundamental/overtone ratio reduces slightly but remains in the

range of 2.7 to 2. These results do not confirm the predictions of either the Kubo line-shape

theory or the Poisson model, assuming reasonable intensities and rates of intermolecular

encounters in the solutions.

The thesis proves the critical role of ultrafast spectroscopy in understanding the con-

dense phase chemical and physical properties.

TABLE OF CONTENTS

CHAPTER

I. Scientific Backgrownd . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Time Domain Investigation of Photodissociation Dynamics in Con-densed Phases. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Femtosecond Spectroscopy . . . . . . . . . . . . . . . . . . . . 21.2.1 Femtosecond vs. Frequency Domain Spectroscopy’s . 3

1.3 Impulsive Excitation and Coherent Control . . . . . . . . . . . . 51.3.1 Impulsive Excitation . . . . . . . . . . . . . . . . . . 51.3.2 Coherent Control . . . . . . . . . . . . . . . . . . . . 7

1.4 Geminate Recombination . . . . . . . . . . . . . . . . . . . . . 81.5 Dephasing Mechanism of molecular vibrations . . . . . . . . . . 10

1.5.1 Kubo Line Shape Theory . . . . . . . . . . . . . . . . 111.5.2 Poisson Model . . . . . . . . . . . . . . . . . . . . . 12

1.6 The Model System . . . . . . . . . . . . . . . . . . . . . . . . . 131.6.1 Spectral Characteristics . . . . . . . . . . . . . . . . . 141.6.2 Symmetry Properties . . . . . . . . . . . . . . . . . . 151.6.3 Experimental Features . . . . . . . . . . . . . . . . . 16

1.7 Previous Results . . . . . . . . . . . . . . . . . . . . . . . . . . 181.8 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . 21

II. The Experimental System and Working Procedures. . . . . . . . . . . 22

2.1 Dye Laser System . . . . . . . . . . . . . . . . . . . . . . . . . 232.2 Solid State Based System . . . . . . . . . . . . . . . . . . . . . 23

2.2.1 Ti:Sapphire Laser . . . . . . . . . . . . . . . . . . . . 252.2.2 Stretcher . . . . . . . . . . . . . . . . . . . . . . . . 272.2.3 Pulse Selector . . . . . . . . . . . . . . . . . . . . . . 292.2.4 Multipass Amplifier . . . . . . . . . . . . . . . . . . 292.2.5 Compressor . . . . . . . . . . . . . . . . . . . . . . . 312.2.6 TOPAS . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.3 The Experimental Setup . . . . . . . . . . . . . . . . . . . . . . 332.3.1 Photoselection Experiments . . . . . . . . . . . . . . 35

2.4 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.5 Ultrafast Pulse Characterization . . . . . . . . . . . . . . . . . . 392.5.1 The Autocorrelation . . . . . . . . . . . . . . . . . . 392.5.2 The Optical Kerr Effect . . . . . . . . . . . . . . . . . 40

2.6 Ultrafast Pulse Propagation . . . . . . . . . . . . . . . . . . . . 402.7 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

III. Impulsive Control of Ground Surface Dynamics of I−

3in Solution . . 50

IV. Caging and Geminate Recombination following Photolysis of Triio-dide in Solution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

V. Investigating pure vibrational dephasing of I−

3in solution; Temper-

ature dependence of T∗

2for the fundamental and first harmonic of

υ1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

VI. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

CHAPTER I

Scientific Backgrownd

1.1 Time Domain Investigation of Photodissociation Dynamics in Con-densed Phases.

Understanding the full course of a chemical reaction in the condensed phase is one of

the most important goals of modern chemistry. The main objective of this research is to

acquire a deep and detailed understanding of all the mechanisms involved in a photodis-

sociation reaction in solution, including intramolecular and intermolecular potentials. In

a photodissociation reaction of an isolated molecule the excess energy is redistributed be-

tween the product degrees of freedom according to the forces unleashed by the absorbed

photon. Consequently, the energy content of the products can be measured long after the

excitation, due to the lack of dissipation. Moving to the condensed phase complicates the

picture considerably. First, the reaction coordinates are often modified significantly for

reactions in liquids. Also, the rapid relaxation process in solution hinders the ability to

determine the transition state structure and its energy. Almost immediately after the pho-

ton is absorbed, random interaction with solvent molecules govern the dynamics. Those

stochastic interactions cause rapid dephasing, energy relaxation, and can even encourage

recombination. The overall result of these processes is a full thermalization and stabiliza-

1

2

tion of the products [1].

The irreversible nature, along with the fast time scale of the relaxation processes,

makes it impossible to retrieve the full course of the reaction using late measurements.

Therefore, in order to be able to record the chronology of the reaction, the necessary ex-

perimental time resolution must be shorter than the typical time scale of both the bond

fission and the intermolecular collisions. Recent advances in time domain spectroscopy

have enabled experimentally to capture the chemical processes in condensed media di-

rectly on the time scale of the fastest elementary step [2, 3]. Consequently, femtosecond

laser spectroscopy is the only tool that enables us to investigate the full course of a con-

densed phase chemical reaction [4].

1.2 Femtosecond Spectroscopy

To date there is no detector that has a short enough response time to enable direct

measurement of a transient signal on a femtosecond time scale. Therefore, a femtosecond

experiment begins with an initiating strong pulse (the pump pulse) that starts the chemi-

cal reaction and defines the zero of time. A second weak pulse (the probe pulse), whose

timing can be controlled precisely with respect to the pump, is used to sample the tran-

sient response of the system. In this type of pump-probe measurement, the time difference

between the pulses can be adjusted with high precision, leaving the pulse duration as the

main limitation on the time resolution of the experiment. For sufficiently short excitation

pulses the Franck-Condon principle forbids significant changes in the reactant geometry

during the excitation process. As an outcome of this impulsive excitation, the ensemble of

the nascent products starts the photoreaction concurrently, in a geometry closely related to

3

the reactant ground state. We define the impulsive limit as an excitation with a pulse that is

substantially shorter than the typical time scale of the molecular motion under study (hun-

dred of femtoseconds for the slowest vibration motion, and up to a psec for slow rotation

motion). This impulsive excitation mechanism results in the creation of a wavepacket on

the exited electronic states [5] as well as generating a coherent superposition on the ground

electronic state . The time evolution of these vibrational wavepackets offers a unique in-

sight into the details of the reaction coordinate, product state distributions and degree of

coherence that is preserved during the chemical reaction. Those unique characteristics

of the impulsive excitation, together with the transient response of the reaction products

to the secondary short pulse, are the heart of the femtochemistry experiments. In this

spirit “Femtochemistry” can be thought as the observation of unstable molecular species,

formed during the transformation from reactant to product. This is the only available

method of retrieving the full course of a chemical reaction in solution. The information

one can get using this approach is exclusive, and cannot be reached fully by any frequency

based methodology.

1.2.1 Femtosecond vs. Frequency Domain Spectroscopy’s

In an effort to understand the advantages of the different spectroscopies, it is necessary

to link between the time-evolution of the nuclear motion to the measured observable for

each of the methods. Resonance Raman spectroscopy (RR), can be formulated in terms

of the overlap between the propagating wavepacket on the excited state to the final vibra-

tional level on the ground electronic surface [6, 7]. The absorption spectrum depends on

the overlap between the ground and the excited state vibrational eigenfunctions. In a fem-

4

tosecond experiment, the impulsive excitation pulse creates a coherent superposition of the

nuclear and electronic levels. It is only after the electronic dephasing occurs, that we can

distinguish between wavepacket on the ground electronic level to the one on the excited

electronic level. However, in the condensed phase the electronic dephasing is very rapid,

so in practice the separation between the electronic to the nuclear excitation is almost in-

stantaneous. Thus information on the nuclear dynamics provided by frequency resolved

spectroscopies is similar to that extracted from femtosecond measurements. However, in

the frequency domain, information is provided just as long as the electronic phase coher-

ence is maintained [5, 6, 7]. In contrast, time domain spectroscopy continues to provide

significant information for as long as the system is probed. As a consequence, time domain

spectroscopy yields information about a much larger region of the potential surfaces.

In this thesis ultrafast spectroscopy was used to study the dynamics of the photodisso-

ciation reaction of I−3 immersed in polar and nonpolar solvents:

I−

3hυ−−−−−→ I

−

2 · + I · recombination−−−−−−−−→ I−

3

The research focuses on three different aspects, which are unique to condensed phase

chemistry. The first, “Impulsive Control of Ground Surface Dynamics of I−

3 in Solution”

(chapter III), studies two related issues. It starts with a detailed description of the impulsive

excitation mechanism, where the relevant time scale is on the order of the laser pulses. The

chapter also demonstrates the ability of exploiting the coherent properties of the excitation

process to achieve control on the chemical system dynamics. The second subject, “Caging

and Geminate Recombination following Photolysis of Triiodide in Solution.” (chapter IV),

deals with the cage effect and geminate recombination mechanisms that start from the

5

very beginning of the photodissociation reaction and end hundreds of psec later. The

last topic, “Investigating pure vibrational dephasing of triiodide in solution; Temperature

dependence of T∗

2 for the fundamental and first harmonic of υ1”, (chapter V) focuses on

vibrational phase relaxation, where the typical time scale is on the order of a few psec.

1.3 Impulsive Excitation and Coherent Control

1.3.1 Impulsive Excitation

The key to real time study of chemical dynamics is the impulsive excitation process.

Despite this evident importance of the excitation process, an accurate theoretical model

for describing the excitation process, as well as the precise influence of the experimental

parameters on it, are still matters of debate. Both simulation and experiments show that

impulsive excitation as defined above vertically promotes a compact wavepacket on the

excited state. Another outcome of the impulsive excitation is the creation of a coherent

superposition on the ground electronic state. Ideal conditions for large amplitude excita-

tion of ground state coherent vibrations are pulses shorter than the vibration period, but

longer than electronic dephasing leading to a pulse spectrum which is broader than the

vibration frequency, but narrower than the electronic spectrum. There are two pictures to

describe the light-matter interaction during the excitation. The first is a vibronic eigenstate

description [8]. The impulsive excitation is described as a three stage two-photon process:

1) At t=0, set by the pump pulse, first interaction with a pump photon transfer ampli-

tude to an excited electronic state.

2) The excited amplitude propagates in time, according to the excited state potential

energy surface topology.

6

3) During the propagation, at a later time ∆t ( ∆t is limited by the pulse length), a

second interaction with a pump photon stimulates emission and transfer portion from

the excited amplitude back to the ground electronic state, creating a nonequilibrium

population (i.e. initiate coherence between different vibrational levels) that evolves

under the ground state hamiltonian.

Within this picture, pulses sorter than the vibration period are required for simultane-

ous excitation of numerous eigenvectors. Pulses longer than the electronic dephasing are

required to enable step two. Interference, due to the phase relation imposed by the in-

teraction with the coherent pulse, results in a preferred depletion (“hole burning”) of the

population at a location that best fits the resonance condition with the pump wavelength.

The term RISRS (Resonance Impulsive Stimulated Raman Scattering), for describing the

result of the impulsive excitation on the ground state, is related to this Raman-like mecha-

nism [9, 10, 11, 12, 13, 14, 15].

The second approach, named coordinate dependent two-level-system, was first intro-

duced by Ruhman and Kosloff [9]. It states the following: The short excitation time does

not allow significant nuclear motion. Consequently, we can think of the molecule as being

composed of a series of frozen subsystems, each at a different intermolecular configura-

tion. For every configuration, we use the Rabi formalism to define a local frequency, in a

way that the overall result of the excitation is the superposition of those subsystems. The

“hole” in this picture is generated because the efficiency of the population transfer is a

strong function of the detuning. In contrast to the eigenvalue approach, the coordinate de-

pendent scheme is not a perturbative one. The scheme inherently incorporates all orders of

7

interaction through the local Rabi cycling. In this picture, the short pulse limit is necessary

to prohibit substantial nuclear motion, while the long pulse limit is needed to conserve the

local nature of the resonance.

1.3.2 Coherent Control

The goal of “coherent control” is to steer a quantum system toward a desired final

state, using its interaction with coherent light, while canceling all the other possible paths.

To demonstrate the concept of coherent control, let’s assume that two different paths can

lead to the reaction product. Quantum mechanics states that the final outcome of the

reaction will be a superposition of those paths [16] . Shaped light fields can manipulate

the interference between all those paths leading to the enhancement or the elimination

of a specific product. Coherent Control techniques have been employed to manipulate

chemical reactions [17], electron dynamics in semiconductors [18] , Rydberg excited

states [19] and cold atoms [20].

Two major approaches to the control of quantum mechanical systems have been pro-

posed and developed, both exploit wave interferences in the quantum mechanical systems.

The first, a purely frequency domain technique, proposed by Brumer and Shapiro [21]

, utilizes the excitation of two pathways that interfere constructively or destructively de-

pending on the relative phase of two CW lasers. The probability of forming a given product

depends on the coherent sum of the two states since they are indistinguishable. Although

this approach has been quite successful [22, 23, 24] , its efficiency was limited because

CW lasers act on a fraction of the thermal distribution of the atoms or the molecules,

while the energy redistribution relies on relatively slow processes (such as collisions) to

8

restore depleted populations.

An alternative, a time domain technique, proposed by Tannor, Kosloff and Rice [25,

26] suggested using pairs of ultra short pulses to manipulate the quantum system. The

scheme, named pump-dump, excites a wave packet on an excited state surface, then a

second pulse “dumps” the excited population back to the ground-state level, or some dis-

sociative product channel. By controlling the time delay between the two pulses, it is

possible to manipulate the time propagation on the excited state, where different time

propagation can, in principle, produce different quantum species. Obviously, a successful

application of coherent control from the second scheme, requires that the pulses be sorter

than the decoherence time of the quantum system, so ultra short pulses are well suited for

the controlling of quantum system.

1.4 Geminate Recombination

The question of the solvent induced recombination processes, named the “cage ef-

fect” [27], has been the subject of many theoretical and experimental studies [28] . The

fact that the stage of recombination can provide valuable information concerning curve

crossings far from the Franck-Condon region, makes the recombination a key tool in con-

struction of the potential surfaces for the photodissociation reaction.

Early experimental studies of the I2 photodissociation reaction interpreted the gemi-

nate recombination yield in terms of atomic diffusion models [29], which led to prediction

on the time scale of the geminate process, after assuming an initial distribution for the

iodide radicals [30] .

A different approach to the recombination process, emphasizing its microscopic as-

9

pect, emerged through the use of direct time resoled measurements. Harris et. al. [31]

measured the transient absorption of the Iodine photodissociation reaction, using a broad

spectrum of probe wavelengths. The measurements clearly indicated very fast dissociation

(or predissociation) followed by recombination onto the ground (or excited) potential sur-

face, or escape into the solvent. These experiments clearly demonstrated the importance

of isolated binary collisions in the vibrational energy transfers, and suggested that the fate

of the excited molecule, as to dissociate or to recombine is determined early in the pho-

todissociation process. Later experiments in rare gas liquids [32] support the assumption

that the photoproduct fate is decided almost immediately after the excitation process. An-

other aspect of this reaction, uncovered by the ultrafast spectroscopy experiment, was the

substantial recombination on a bound excited state.

Barbara et. al. studied the recombination process of the corresponding charged species

I−

2 in polar solvents, and revealed the vast influence of solvent on the photodissociation

dynamics [33]. The strong interactions between the ionic species to the polar solvent,

lead to rapid vibrational relaxation and recombination process, i.e. the I−

2 recombines and

looses approximately two third of the vibrational energy on the ground state within a sin-

gle vibration period, while the entire relaxation process occurred within several picosec-

ond [34]. Moreover, the nonexponential behavior of the energy dissipation was attributed

to a solvent induced charge flow, as latter was confirmed by comparison with MD simu-

lations [35]. Here also (as before) part of the recombining molecules do so on a bound

excited state. Coherent vibrational dynamics on that state were initially erroneously inter-

preted as solvent reverberations.

10

The I2 and the I−

2 studies proved the basics for the dynamical picture describing the

recombination process. Femtochemistry played a crucial role in obtaining this picture.

The extension to the recombination of a tri-atomic species, where the probability of the

recombination process is no longer a function only of the distance between the fragments,

is especially interesting. In the case of triiodide, the relative orientation between the photo-

products, the I−

2 ion and the I atom, can in principle be of major importance in determining

the rate of geminate reformation of triiodide.

1.5 Dephasing Mechanism of molecular vibrations

Chapter V addresses the mechanism of solvent induced pure vibrational dephasing.

Vibrational relaxation has been extensively studied in condensed phase systems [36]. Dis-

sipation of the excess vibrational energy into the bath, as well as the dephasing rate, de-

pends strongly on the nature of the coupling between the relaxing mode to the surround-

ing liquid environment. The qualitative insight provided by the comparison of theoret-

ical models and experimental results provides a probe to the underlying dynamics and

the structural properties of the condensed phase. For a strong and long-range interaction

these process are on the ultrafast time scale, thus time resoled experiments (CARS [37],

ISRS [5, 38, 39, 40, 41, 42, 43], RISRS [9, 10, 11, 12, 13, 14, 15] and OKE [44, 45]) are

ideal tools for testing dephasing theories. Both energy relaxation as well as the loss of

phase correlation contributes to the measured dephasing time, through the relation:

1

T2

=1

2T1

+1

T∗

2

(1.1)

11

where T2 and T ∗

2 represent the measured and the pure dephasing time respectively, and T1

stand for the population life time (energy relaxation time).

1.5.1 Kubo Line Shape Theory

The theoretical model that has been used for decades to analyze vibrational line shapes

is an adaptation of Kubo line shape theory to vibrational dynamics by Oxtoby [46]. In

this quantum stochastic theory, the system transitions frequencies randomly fluctuate due

to interaction with the solvent [47]. The model assumes that the instantaneous frequency

shift is proportional to the instantaneous random force along the vibrational normal mode.

The fluctuation of the transition energy assumed to be a zero average Gaussian, following

the central limit theorem, which states that a stochastic process becomes a Gaussian one in

the limit of infinite uncorrelated small events [48]. Further simplification, assuming that

the frequency-frequency correlation function decays exponentially, results in the following

analytical expression for the vibrational line-shape (omitting the oscillatory part):

Sig(t) = exp(−∆2(τct− τ 2c (1 − exp(− t

τc)))) (1.2)

Where τc is the correlation time between the jumps and ∆ is the frequency jump spread.

The model discriminates between two separate cases:

1) ∆τc >> 1 defining the slow modulation limit. Expanding exp(−t/τc) to the second

order, leads to a Gaussian lineshape:

Sig(t) = exp(−∆2t2

2) (1.3)

2) ∆τc << 1 the fast modulation limit. Replacing exp(−t/τc) by zero, we can write

Sig(t) = exp(−∆2τc t) (1.4)

12

give rise to exponential dephasing and a Laurentzian lineshape.

The slow/fast modulation limits labeled inhomogeneous/homogeneous (life-time) broad-

ening mechanism, respectively. Kubo line shape theory has been successfully used in

determination of ∆ and τc for molecular systems [48, 49].

A related subject, which can also be addressed by the model, is the relative time decay

of different vibrational harmonics. Assuming that the modulation mechanism is indepen-

dent of the harmonic (i.e. τc is a characteristic property of the system understudy), and

that the fluctuation amplitude of the nth vibrational level, is n times larger than that of the

fundamental frequency:

∆ω0↔n = n(∆ω0↔1) (1.5)

consequently, the model predicts that in the fast modulation limit the decay time depends

quadratically on the harmonic, and linearly in the slow modulation limit. Despite the

apparent success of the Kubo line shape theory in the prediction of T ∗

2 , its predictions

regarding the ratio are found to be incorrect [50, 51].

1.5.2 Poisson Model

There are many cases where the quantum system is coupled strongly to a small number

of solvent molecules. In such cases there is no reason to assume that the fluctuations follow

the Gaussian distribution. Among these kind of process is the vibrational dephasing due

to repulsive interaction, originates from the repulsive collisions between liquid molecules

and the under study quantum system. The distribution of the number of the uncorrelated

collisions shows a Poisson distribution [52], not a Gaussian one, where the non-Gaussian

nature is more dominant for the overtones [53, 54]. Accordingly, the dephasing is caused

13

by a mutually uncorrelated phase jump, where the events are taken to be very rare with a

significant influence on the oscillator. The model assumes that the interactions can only

influence the vibration’s phase, i.e. the energy of the oscillator is conserved throughout the

dephasing process. The resulting phase relaxation is predicted to be exponential, where

the dependence of the dephasing rates in the different harmonics range from quadratic for

small phase jumps, to zero dependence when the jumps are large.

1.6 The Model System

Photodissociation reactions of small molecules provide a benchmark for testing many

aspects of rate theories of chemical reactions. In particular, the photodissociation of a

triatomic species allows a detailed study of the excess pulse energy partitioning between

the various degrees of freedom that are created during the chemical reaction. Further more,

a photodissociation reaction of triatomic molecules provides an easy tool to generate non-

thermal diatomic species in gases and in liquid solutions.

The ultraviolet photodissociation of triiodide in polar solvent provides a perfect case

study for the investigation of various aspects of chemical reaction dynamics in the con-

densed phase. The reaction occurs on a variety of times scales reflecting different elemen-

tary processes that make up the overall chemical reaction. Notably, the strong electrostatic

forces characterizing the reactions of an ionic species in a polar solvent cause the energy

transfer in these systems to be dominated by long-range and intense interactions. Both

theory and experimental results suggested that the strong coupling between the solvent

and the solute causes rapid dephasing and efficient energy relaxation.

14

1.6.1 Spectral Characteristics

The absorption spectra of the triiodide is composed of two bands, both having tran-

sition moments orientated parallel to molecular axis. The bands centers are located at

290nm and 360nm. The energy difference between these two bands closely resembles the

spin-orbit splitting of atomic iodine. Therefore, the bands were originally assigned to ex-

cited states of triiodide that correlate with ground state diiodide ions and atomic iodine in

either the spin-orbit ground or excited state.

The diiodide electronic absorption spectrum is built up from two bands as well. The

higher band center at 375 nm and is partially overlapping with the triiodide absorption, a

fact that must be taken into consideration when analyzing the experimental result if the

probe is in the UV spectral range. The second band is centered at 740nm, and is well

separated from the reactant spectrum.

200 300 400 500 600 700 800 900

I3-

I2-

O.D

λnm

Figure 1.1: The absorption spectrum of triiodide and diiodide ions

15

1.6.2 Symmetry Properties

In the gas phase triiodide ions, calculations predict linear and centro-symmetric ge-

ometry. These predictions were verified for triiodide using spectroscopic tools. Placing

the ion in a dilute solution changes the picture substantially. Johnson and Myers were

the first to observe experimentally that although the main feature in the resonance Raman

spectrum of triiodide in ethanol is the symmetric stretch, the spectrum shows some asym-

metric stretch activity [55, 56]. Thus, independently on the presence of a laser pulse, the

typical D∞h symmetry can be lowered to C∞v. The origin of the symmetry break are the

random forces acting between the solute molecules to the solvent, which cause a rapid

change in the solute conformation. Therefore, the issue of symmetry braking becomes

a statistical question, of whether the ensemble average conserves the initial symmetry of

the isolated ion. The solvent induced reduction in symmetry was further supported in

experiments conducted in our lab [57]. We compared the amount of initial vibrational ex-

citation and the degree of vibrational coherence in the photodissociation products. Based

on known Raman spectra as well as the theoretical models, we have chosen to focus on

two solvents with drastically opposite effects on the parent ion: acetonitrile that conserves

the D∞h symmetry of the solute, and ethanol, which favors the broken symmetry energet-

ically. We have shown that I−2 in acetonitrile was formed vibrationally hotter and with less

vibrational coherence than in ethanol.

Trying to understand how the immersion of ions in solvents can lead to the breaking of

the initial symmetry has been the subject of numerous theoretical studies. Sato et. al. [58]

calculated ground state free-energy surface of the triiodide ion in acetonitrile, methanol

16

and aqueous solutions. The simulation concludes that in the condensed phase, the elec-

tronic structure of the solute is strongly affected by the solvent molecules. The most

profound effect was observed for aqueous solutions where the ground-state free-energy

surface becomes practically flat in the vicinity of the gas phase equilibrium geometry. For

acetonitrile solution, the simulation predicts that the free energy surface will not be as

tightly bound as in the gas phase, but the symmetry of the structure is maintained.

Lynden-Bell et. al. took a different approach for studying the symmetry breaking

aspects [59]. Their basic argument is that symmetry breaking will occur only if the de-

crease in the free energy resulting from the solvation process is bigger than the energy

required for polarizing the ion. Given a particular charge distribution and specified bond

lengths of the ion, the solvation structure, solvation free energy, and the mean forces on

the ion were examined. The simulation results predict that in aqueous solution the min-

imum free energy geometry is no longer the centro-symmetric one, where the solvation

process stabilizes a dipole on the ion. On a microscopic level, the simulation shows that

as the dipole increases, the water molecules move towards the negative charge where one

proton is hydrogen-bonded to the ion. The larger the total charge on the end atom, the

more structured the solvent around it. Agreement between the theoretical simulations and

experimental results where verified by comparing calculated and experimental vibrational

line widths for the triiodide ion, these where shown to be in quantitative agreement.

1.6.3 Experimental Features

The specific choice of the triiodide as the model system for the current research stems

from the following considerations:

17

1) Separation of time scales between electronic excitation and nuclear evolution, both

for the reactant and the product - due to large inertia of the heavy nuclei. This allows

us to nearly approach the limit of impulsive excitation. As a consequence ultrafast

spectroscopy provides a means of following the full course of the photodissociation

reaction, including bond fission, energy partition between the product fragments,

relaxation of vibration coherences, energy relaxation, and on a longer time scale -

the recombination process.

2) Though there is some spectral overlap between the reactants and products, there

are discriminate absorption region for the different species. Therefore, changing

the probe wavelength can be used to explore the dynamics of the different species.

Probing in the vis-IR is a suitable range to discover the product dynamics, while

probing in the UV is most sensitive to the reactant.

3) One of the photodissociation products of the reaction is a molecular species, so

vibration and rotation excitation in the product can be investigated as well in addition

to the reactant excitation. Also, all the species involved in the reaction are small

enough to enable sophisticated theoretical modeling, which can be compared to the

experimental result.

4) As already mentioned, one of the main targets of the research is to better understand

the interaction between the solvent and the solute. The ionic nature of the reactant,

and polarity of the solvents ensures dramatic solvent effects.

5) The excited states potential of both the reactant and the product are repulsive. This

18

topology leads the exited wavepacket away from the overlap area with the remaining

ground state population and enables us to probe ground state dynamics exclusively

at later times.

1.7 Previous Results

The spectroscopy and dynamics of triiodide have been studied in great detail in our

lab, prior to my arrival, by Banin and Ruhman. As stated above, when probing in the

vis-IR range, the measured signal is sensitive exclusively to the reaction product. The

rapid excitation process prohibits significant nuclear motion. As a result, the product will

start the dissociation from a joint configuration with a low kinetic but very high poten-

tial energy. Following this picture, Banin and Ruhman were able to demonstrate that in

the photolysis of triiodide at 308 nm, diiodide ions are formed within 400 fsec after the

impulsive optical excitation [1]. The excitation results in an efficient transfer of nuclear

coherence from the initially prepared state into the exit channels leading to diiodide ions

in a coherent superposition and atomic iodine [60]. This coherence stems from the impul-

sive photoexcitation process and is feasible only if both the excitation optical pulses and

the reaction are shorter than the product vibrational period. The spectroscopic signature

of these coherences are modulations in the absorption spectra, at a frequency which is re-

lated to the average vibration energy of the states involved in the superposition [61]. The

dephasing rate of the coherence reflects the dissipative nature of the collisions with the

solvent (elastic and inelastic collisions) as well as the anharmonicity of the potential well

and local inhomogeneities in the solution. Thus, the quality of the coherence superposi-

tion and its decay are of critical importance, because they are controlled by the full course

19

of the reaction, making them very sensitive to the reaction potential surfaces and to the

solvent properties [62].

After full dephasing of the coherences, energy relaxation results in narrowing of the

absorption band (cold I−

2 absorption spectra is much narrower than hot I−

2 spectra). Using

different probe wavelengths, Banin et. al. were able to construct the transient spectrum of

the products. The initial spectrum, as evident by the coherence frequency of the nascent

I−

2 , set the early average vibration energy to be ν = 12. The evolution of the spectrum

predicts vibration relaxation time to be on the order of 4 psec [60]. Photoselective exper-

iments provide a reorientation time of 15 psec for triiodide and 4.8 psec for I−

2 , both in

ethanol [60, 61].

When probing in the UV, the measured signal is mainly sensitive to the reactants. The

RISRS mechanism will immediately initiate ground state coherent motion in Raman ac-

tive modes (in our case, the symmetric stretch vibration), which modulate the transient

absorption of a UV probe pulse [9]. Novel theoretical concepts and full quantum mechan-

ical simulations were formulated in order to better understand the hole burning mechanism

[63, 64], using an empirical LEPS surface for the collinear geometry and a correct func-

tional form for the asymptotic limit when the fragments are separated [62]. Benjamin et.

al. optimized this LEPS potential by fitting the experimental triiodide absorption spectrum

in liquid solution through MD trajectory calculations [65]. The dephasing rate of the mod-

ulation will essentially reflect only the interaction with the solvent and will not be affected

by the anharmonicity, because the superposition is constructed from low-lying vibration

levels where the potential is basically harmonic. All UV/UV experiment suffered from

20

barely achieving the impulsive limit, and a lack of tunability in both the pump and the

probe pulses. These limitations reduced the scope of vibrational excitations possible on

the ground state, and the ability to investigate vibrational dephasing dynamics of ground

state triiodide.

To study the reaction product vibration relaxation dynamics, Banin et. al. develop a

unique three pulse experimental scheme, named TRISRS (transient RISRS) [66]. In this 3-

pulse experiment, transient resonance impulsive excitation is used to impose coherences on

the ground state nascent diiodide, in the same manner that the RISRS impose coherences

between the reactant vibrational levels. The frequency and decay time of the modulations

indicate that the product relax in a few psec [67].

On a longer time scale, the decrease in the overall I−

2 optical density (probing in the

Vis-IR) and the increase in the triiodide absorption (probing in the UV) were assigned

to the recombination process. The recombination process was found to be complete on

(at least) two time scales [60]. In the original study no quantitative investigation of the

recombination dynamics was conducted. Better understanding of the different species

leading to the recombination is the subject of chapter IV in this thesis.

The research conducted by Banin et. al. suggests the following picture for the triio-

dide photodissociation reaction: After the photoexcitation process, the initial propagation

is along the symmetric stretch coordinate of the triiodide. This fast evolution can be ob-

served using wavelength selective probing, where the probe wavelength defines the exact

location of the detection filter, which in turn serves as a window of the coherent wave

packet propagation. Few hundred femtoseconds after the impulsive excitation process,

21

bond breakage as well as coherent product formation takes place. In spite of the ultrafast

nature of these events, the solvent actively interferes in these early stages of the reaction.

Those interferences reveal themselves through the fast dissipation process of most of the

excess energy initially provided by the excitation pulse.

1.8 Thesis Objectives

The main objective of this thesis is to characterize the molecule - bath interaction,

using the triiodide photodissociation reaction as a case study system. The goal is address

via the following steps:

1) Acquire a profound understanding of the solvent effect on the geminate recombina-

tion process, i.e. fully explore the cage effect properties.

2) Achieve a complete understanding of the impulsive excitation mechanism and the

parameters that control the process.

3) Resolve frequencies, dephasing times and relaxation dynamics of higher harmonics

and weak vibrational modes.

4) Explore the effects of pulse Intensity, wavelength, and chirp on the induced dynam-

ics.

5) Measure the dephasing time of the fundamental and higher harmonics as a function

of temperature, and used the experimental result to differentiate between the various

theoretical models.

CHAPTER II

The Experimental System and Working Procedures.

The heart of the ultrafast pulse generation is the phenomena of passive/active mode

locking. A finite number of longitudinal modes, governed by the gain profile of the active

medium, oscillate in the cavity. In CW mode, the relative phases of those modes fluctuate

randomly, leading to random interference effects. Zeroing the relative phases of the modes

in a specific region in the cavity, results in the generation of transform limit pulses, i.e. the

shortest pulses available, limited only by the bandwidth via the uncertainty principle. The

weak pulses coming out of a mode-locked laser are amplified, at a much lower repetition

rate, using Q-switched laser in either a multipass or regenerative configuration. Both of

the methods were used in the current thesis, and will be described bellow.

A typical vibration period is on the order of 10-100 fsec. The time scale for the pho-

todissociation processes, bond fission, and curve crossing are on the order of 50 to 300

fsec. Therefore, the ability to monitor a chemical reaction in real-time fashion, requires an

experimental system that meets the follow requirements:

a) The experimental time resolution must be on the order of a few tens of femtoseconds.

b) Wavelength tunability, both for the pump and the probe is an evident advantage in

22

23

trying to map the properties of both the reactant and the products.

c) Finally, averaging significantly improves signal to noise, making stability and high

repetition rate advantageous.

2.1 Dye Laser System

The laser system used in chapter IV of the thesis is a dye laser system that was con-

structed before my arrival and its full description can be found elsewhere [60]. Briefly,

the source of the femtosecond pulses is a dye laser, based on rhodamine 6G as its lasing

medium and DODCI solution used as a saturable absorber. The dye laser is synchronously

pumped with frequency-doubled output of a mode locked ND:YLF laser. The output of

the dye laser is 82 MHz train of 60 fsec pulses, centered at 616 nm, 0.4 nJ/pulses. The

pulses are amplified in a three-stage dye amplifier pumped by a 1 kHz Nd:YLF regen-

erative amplifier, which is seeded by pulses from a mode locked YLF laser. Use of the

same laser to pump the dye laser and to seed the amplifier results in full synchronization

between the oscillator and the amplifier.

2.2 Solid State Based System

For chapters III and V, we needed to improve the time resolution and pulse intensity as

well as to broaden the wavelength tunability for the pump pulse. To meet our experimental

needs, we constructed a home built solid-state laser system followed by a chirped pulse

amplification scheme. Most high power lasers today rely on solid-state crystals as the

lasing and amplifying medium [68]. By far, the dominant crystal is the Titanium-doped

sapphire, which has numerous advantages that make it ideal as a lasing medium and as

24

high power amplifier material [69]. As a lasing medium Ti:Sapphire has an extremely

broad gain profile [70], ranging from 700 to 1100 nm and very high thermal conductivity.

As a gain medium the crystal has a relatively long upper level lifetime, high saturation

fluence (∼ 1Jcm2), a large gain cross section, high damage thresholds (∼10 Jcm−2) and

a broad absorption at 500 nm, making it perfect for pumping with doubled Nd:YLF/Yag

output.

The amplifier uses chirped pulse amplification (CPA) [71]. The idea behind CPA is to

increase the energy of a short pulse, while avoiding high peak power in the amplification

process. The goal is achieved by lengthening the duration of the pulse being amplified, by

dispersing (or chirping) it in a reversible manner. By lengthening the pulse, energy can

be efficiently extracted from the laser gain medium while maintaining low peak power.

On the contrary, using short pulse to extract the energy will lead to intensities above the

damage threshold of the amplifier material as well as the generation of high order nonlinear

processes (like self phase modulation).

The CPA systems layout works as follows: The ultrafast pulses are generated at low

pulse energy through the use of a Kerr Lens mode locked (KLM) Ti:Sapphire laser. The

output of the laser is then stretched in time (using a dispersive delay line) and amplified.

After the amplification process, a dispersive compressor is used to shorten the pulse back

to the fsec regime, as close as possible to a transform limited pulse. Finally, a TOPAS

(parametric frequency converter) is used, such that the pulse wavelength can be tuned

continuously from the near IR to the near UV. A detailed description of the component is

given below.

25

2.2.1 Ti:Sapphire Laser

This is the fast pulse generator, the starting point for the ultrafast laser system. The os-

cillator is a passively mode locked laser [72], where the mode locking mechanism is based

on the self-focusing effect (Kerr lensing) within the laser material. The effect induces

modification in the resonator that translates to a power dependent loss (or gain), responsi-

ble for the mode locking [73, 74]. The laser is pumped with a continuous Argon ion laser

lasing on all lines. It is capable of generating sub 20-fsec pulses centered at 790nm [75],

at a repetition rate of 85 MHz and spectral bandwidth of 45 nm.

Argon Ion

Ti:Sapphire output:

17 fsec, 85 MHz

Figure 2.1: The Ti:Sa laser

The cavity, based on the Kapteyn Murnane design [76], consists of flat end mirror

(CVI) and output coupler (Newport), two 10 cm radius-of-curvature mirrors in an X con-

figuration (Newport) focusing on a Ti:Sapphire crystal (EKSMA ,4.5 cm optical length,

75% absorption of Argon radiation) and a pair of intracavity quartz prisms, cut at an angle

which ensures Brewster/Brewster incidence, for dispersion compensation.

As mentioned above, mode locking is achieved through the action of the Kerr lens

induced in the laser crystal. Kerr lens phenomena can be describe in the following way.

For sufficiently high intensities of irradiation, the material index of refraction become a

26

-40 -20 0 20 40

FWHM=24 fsec

Double

d fre

quen

cy inte

nsi

ty

Time [fesc]

Figure 2.2: Colinear autocorrelation trace of the Ti:Sa laser

function of the light intensity:

n(t) = n0 + nnon linearI(t) (2.1)

The gaussian radial intensity dependence of the transverse mode of the laser, results in a

concave deformation of the fields phase front. When the laser is operating in the pulsed

mode, the focused intensity inside the crystal is sufficient to induce significant Kerr lens-

ing. If this occurs in a laser cavity which is adjusted for optimum efficiency without this

lens, the self-focusing will contribute to higher losses within the cavity. However, a modest

reduction in the spacing between the focusing mirrors surrounding the Ti:Sapphire crystal

can result in an increase in the mode matching within the cavity, leading to an increase in

the output power when Kerr lensing in present. Thus, the laser can be aligned to be stable

in either a CW or a pulsed mode.

27

2.2.2 Stretcher

The pulse stretcher uses all reflective optics to minimize uncontrolled chirp and unde-

sirable aberrations [77]. It was built from a single gold coated grating (Richardson Grating

Laboratory, 11 cm length, 600 lines/mm), a single gold parabolic mirror of 92 cm focal

length (Edmond, 6 inch diameter), and two gold protected flat mirrors (CVI, 11 cm length,

λ/10) to form an achromatic one to one telescope. The dimension of the optics in the

plane of dispersion must be bigger than the dispersed spectrum dimensions.

To evaluate the total dispersion in the stretcher, we start by calculating the grating

angle for littrow reflection at 790 nm (the central wavelength), using the grating equation

(see fig 2.3):

2d sin(Φ) = λd=1/600−−−−−−→ Φ = 0.239 (2.2)

Next, we calculate the angular dispersion of a 50 nm spectral bandwidth, around 800nm

Grating

f

L

Folding

mirror

Spherical

mirrorInput

Φ∆θ λ=815 h

Figure 2.3: The Stretcher top view layout

28

(the central wavelength, typical parameters of the oscillator):

d(sin(Φ) + sin(Φ + ∆θ)) = λ

∆θλ=815 = 0.016

∆θλ=765 = −0.015

(2.3)

Finally, we use the ABCD law [78] to calculate the optical path difference (OPD) between

the two wavelengths:

Rout

R′

out

=

1 L

0 1

1 0

− 1f

1

1 2f

0 1

1 0

− 1f

1

1 L

0 1

Rin

R′

in

=

−1 2(f − L)

0 −1

Rin

R′

in

=

−Rin + 2(f − L)R′

in

−R′

in

(2.4)

PutRin = 0, and use the calculated ∆θ asR′

in, we can solve for h (the horizontal spectrum

spread):

h = Rout∆θλ=815 +Rout∆θλ=765

= 2(f − L)(R′

in,λ=815 +R′

in,λ=765)

= 2(f − L)(0.015 + 0.016) = 0.062(f − L) (2.5)

Finally, the OPD can be calculated using the relation:

tan Φ = OPD/h 7→ OPD = 0.015(f − L) (2.6)

Experimentally, setting L=67 cm (with f=92 cm) proved to conserve the full spectrum

width of the input pulse. The total delay is 4 times the calculated OPD (twice coming into

the folding mirror, and twice going out), so the stretched pulse is:

τstretched,psec = 4OPDcm

ccm/psec

= 50psec (2.7)

29

2.2.3 Pulse Selector

Pulse selection at a 1KHz repetition rate from the 85 Mhz Ti:Sapphire output is achieved

using a Pockell’s cell (Fast pulse technology), between two crossed glan-laser polarizers

(Special Optics). The ratio between the leakages through the pockells cell, to the transmit-

ted pulse was measured to be 1/3000.

2.2.4 Multipass Amplifier

The amplifier assembled in a multipass configuration, following the design by Backus

et. al. [79], meaning the pulse passes through the gain medium several times without the

use of a cavity. The main advantage of the multi-pass configuration over the regenerative

amplifier [80] is that it accumulates less high order phase distortions. The reasons are

double:

1) The ASE (Amplified Spontaneous Emission) can be suppressed to a grater degree,

since the optical path is not a resonator so the multipass configuration has higher

gain per pass (which means fewer passes through the gain medium).

2) The regenerative configuration needs high index material (Pockells cells and polar-

izers) which add to the phase distortions.

As a result, shorter pulses are easier to produce using the multipass configuration. The

regenerative amplifier, however, is more efficient in extracting the pump energy as well

as resulting in a better beam quality (both related to the better overlap between the short

pulse and the pump in the resonator).

30

The amplifier is pumped with 1Khz, 10 mJ pulses from a frequency-doubled Q-switch

YLF laser (Quantronix 527DP-H-MM). The basic components of the amplifier are two

dichroic spherical mirrors (CVI, f=37.5cm), which transmit the pumping radiation and

reflect the near-IR, and one planar gold reflector (CVI, 11cm,λ/10 surface quality) in

a ring configuration. The amplification medium is a Ti:Sapphire crystal (Casix, 6mm

optical path) positioned at the focus of the spherical mirror. We utilize eight consecutive

passes through the crystal, experimentally shown to be the best compromise between the

desired pulse amplification and the ASE, after which the amplified pulse is ejected from

the cavity. An additional spherical silver mirror (Janos, f=40cm) positioned after the end

dichroic mirror, is used to refocus the remainder of the pump back to the Ti:Sapphire

crystal, effectively doubling the amplification power. A mask of 2.2 mm holes drilled on

centers spanned 3.6 mm is introduced between the planar mirror and one of the spherical

mirrors in order to reduce the effects of both ASE and self-focusing. The overall output of

the amplifier is a 1.3 mJ/pulse ( 7 orders of magnitude as the amplification factor). Aside

YLFPulse

Input AmplifiedPulse

Mask

Figure 2.4: The Amplifier layout

from increasing the pulse energy, the amplification process shapes and shifts the pulse

31

spectrum due to the finite gain bandwidth of the amplifier crystal (though for Ti:Sapphire

its quite large). Since the gain cross section appears in the exponent in the calculation of

the amplification factor, successive passes through the amplifier tend to narrow the band.

760 780 800 820 840

Ti:Sa pulse Amplified pulse

wavelength [nm]

Figure 2.5: Ti:Sa and Amplifier spectrum

After the amplifier, the pulses are spatially filtered to improve the beam profile. The

fact that the input pulse is positively chirped (the leading edge is red) and blue shifted

relative to the center of the gain spectrum, results in a better amplification to the red part

of the pulse spectrum. As a consequence the output spectrum is red shifted by 8nm.

2.2.5 Compressor

The final stage in the ultra short pulse generator is to recollect the frequency com-

ponents, trying to get as close as possible to a transform limited pulse. In principal, the

compressor setup could be similar to the stretcher, where the grating is placed behind the

focal plane of the parabolic mirror instead of infront it. We chose a simpler and more

flexible alternative where we use double reflections from a grating pair (Richardson Grat-

ing Laboratory, 11cm and 5.8cm length, 600 lines/mm) and a gold reflector (CVI, 11cm

32

length λ/10 surface quality). This affords us with an additional degree of freedom where

we can tune the grating angle thus varying both GVD and TOD in an effort to obtain the

shortest possible pulse. The grating pair must be parallel to each other in order to avoid

spatial chirp (different frequency component in different zones of the beam). The ultimate

GoldReflector

Grating

Grating

Figure 2.6: The Compressor layout

output pulses obtained where 28 fsec FWHM, 0.7mJ/pulse in energy at a 1kHz repetition

rate, centered at 800 nm. Peak to peak instabilities are generally on the order of 1%.

2.2.6 TOPAS

80% of the output is used to pump a commercial parametric converter, capable of

generating 18-22 fsec pulses throughout the whole of the visible spectrum (450-750 nm).

TOPAS operation is based on second order non-linear optics, namely 3-photon interaction,

in a non-centrosymmetric crystal (the second harmonic generation process is a degenerate

example of the same process). A strong pump at a frequency, ω1, can simultaneously

amplify two different frequencies, ω2 and ω3, provided both energy and momentum are

conserved (ω1 = ω2 +ω3 and k1 = k2 +k3). Extension of the frequency range is achieved

via either doubling the IR output, or by mixing with the fundamental 800 nm. Finally, an

additional second harmonic crystal can be inserted so as to generate the desired UV pulses

33

for the experiment.

-200 -100 0 100 200

123 fsec

44 fsec

24 fsec

Time (fsec)

Dye LaserTi:SaTopas, 700 nm

Figure 2.7: Characteristic autocorrelation traces of the dye laser, the Ti:Shapphire laserand the a typical output of the TOPAS. The pulses are 70, 31 and 17fsec,respectively.

2.3 The Experimental Setup

In all pump-probe setups the short pulses are split into two portions and the relative

time difference between them is changed via a computer control translator stage. In the

pump arm, wavelength tunability into the near UV is available by second harmonic gener-

ation of the pulses using a thin nonlinear crystal. The importance of the crystal thickness

is two folded: a thin crystal has less critical phase matching, enabling the generation of a

broader spectrum. Second, group velocity dispersion, which can lead to a significant tem-

poral broadening, is proportional to the crystal thickness. A small reflection from a quartz

window of the frequency-doubled light is sent to an amplified photodiode (EG&G, UV-

4000) and is used to monitor the fluctuation in the pump intensity (the pump photodiode).

For the photoselective experiments (see below), controlling over the relative polarization

34

between the pump and the probe is achieved via a half waveplate, introduced before the

quartz window.

In the probe arm, white light generation, via self phase modulation (SPM), is an effec-

tive method for generating continuous spectra. The origin of the process is a non-linear

interaction that occurs when a short and intense pulse propagates through a transparent

medium. The fast changes in the temporary intensity of the pulse, produces a momentary

change in the material nonlinear index of diffraction (in a similar manner responsible to

the Kerr lens phenomena, Eq 2.1). This variation will modify the instantaneous phase of

the pulse and thus altered the frequency distribution. For a normal medium, the nonlin-

ear index coefficient is positive, so SPM results in lowering of the pulse frequency on the

leading edge of the pulse, while increasing the frequency of the trailing edge. Finally,

whenever a UV probe is needed, a second harmonic crystal is used. Either a quartz win-

dow or 50% beam splitters send part of the probe beam to a second amplified photodiode

(EG&G, UV-4000) that serve as a reference to monitor probe instability (Io photodiode).

A third photodiode collect the beam that passes through the sample (Probe channel).

Preserving nearly transform-limited pulses all the way to the sample cell poses diffi-

culties due to dispersion in the optical elements en-route. To overcome this problem, we

introduce prism pairs both before and after the harmonic generation. Using these prisms

we could control the GVD of the pulses for efficient second harmonic generation and to

maintain the time resolution by pre-compensating for the GVD of all the elements, all the

way to the experimental cell. In addition to the GVD correction, the prism pair placed

before the experimental cell is used for efficient separation between the fundamental and

35

the second harmonic light (any kind of filter will introduce extra dispersion). Finally, we

use the same prism pair to introduce controllable excess GVD as an extra experimental

parameter.

2.3.1 Photoselection Experiments

Femtosecond experiments with control of the relative polarization between the pump

and the probe can be used in order to retrieve the vectorial properties of the photodissoci-

ation reaction. Time resolved polarization experiments have been carried out in order to

explore the dynamics of molecular rotational motion in liquid solution as well as to resolve

the symmetry properties of the potential energy surfaces relevant for bond breaking [81].

Both theoretical and experimental studies imply that the molecular rotational motion in the

condensed phase resembles free rotor dynamics on the short time scales and a Brownian

rotor dynamics on longer time scales [82]. In the case of the photodissociation reaction

where one of the products is a molecular species, this time scale separation implies that

(at least in principle) it is possible to inspect the rotational excitation and reorientational

dynamics of the parent species as well as the product. The decay of the angular align-

ment can be connected to the correlation function of the fluctuating torques exposed on

the system by the surrounding solvent cage.

The anisotropy measures the correlation function of the second Legendre polynomials

of the scalar product between the pump and the probe transition dipoles [83]:

r(t) =1

2〈P2[µpump(0)µprobe(t)]〉 =

2

5〈P2[cos(θ)] (2.8)

where r(t) is the time dependent orientational anisotropy, θ is the angle between the tran-

sition dipole of the pump at zero delay time and that of the probe transition at some later

36

time delay t. For an ensemble of free rotors at temperature T, the equation can be solved

numerically, starting from the Maxwell distribution of rotational velocities [84]:

r(t) =2

5[1

2+

3

4

∫

∞

0

dωP (ω) cos(2ωt)]

P (ω) =ω

kTexp(− Iω2

2kT)

(2.9)

where I is the moment of inertia of the molecule. Thus, the initial part of the anisotropy de-

cays as a Gaussian with the free rotor orientational correlation time that scale as (I/3KT )1/2.

Measuring the signal with a relative polarization of 54.7 degrees between the pulses,

named “Magic Angle” polarization, will result in signals that are not sensitive to the re-

orientation process.

2.4 Data Collection

The experimental observable is the change in the probe transmission as a function of

the time delay between the pulses, where only the ratio between the transmission with and

without the pump is of interest. Usual signals amplitudes are on the order of 1%. There-

fore, obtaining a signal with superior signal to noise forced us to use several strategies in

the data collection routine:

1) Differential Detection: Blocking the pump, we use a variable neutral density filter

to exactly match the intensity of the reference photodiode (Io) to the probe photo-

diode. The change in the probe absorption is then measured directly by feeding the

probe and Io photodiodes to the differential input of a lock-in amplifier.

2) Signal Normalization: Further improvements in signal to noise is achieved by con-

tinuously reading Io and pump intensities using SSH (Simultaneous Sample and

37

Hold), and normalizing the transient signal to the dynamical variation in the pulses

intensity. Actual data points are taken only when both the Pump and Io fluctuations

are smaller than a predetermined fraction.

3) Frequency sensitive detection: Lock-in amplifiers cause gradual smearing of the

signal, resulting from the fact that the signal at a specific time has an exponentially

decaying memory of the earlier points. The influence of the previous points is pro-

portional to the difference between the values of data points. To account for this

effect, the program recollects data points, if the change between two consecutive

data points is bigger than predetermining value.

4) Averaging: Finally, the signal was further improve by averaging number of scans

(up to 50, for the finest details). Before averaging, the quality of the translator,

in term of its ability to reproduce the exact time delay at the different scans was

confirmed.

38

Io

Probe

Probe

Sample

Pump

Signal(t)=Probe(t) I (t)

Pump(t) I (t)

0 Lock in

SSH

Ref. Frequency

From chopper

Lock-in

Amplifier

Beamsplitter

Photodiode

Quartz Window

Lens

Prism

Variable OD

Retro Reflector

Second Harmonic

crystal

Waveplate

Pump

SSH

A to D converter

To translator

stage

0.1 um

resolution

translator

800 nm

Topas

t

0

Figure 2.8: The experimental setup: The pulses are split into two replicas. The relativepump-probe delay is introduced via a computer control translator stage. Inthe pump arm wavelength tunability is achieve using a second harmonic crys-tal. The probe is either the second harmonic or the whitelight generated in aSapphire crystal. Prism pairs are needed only for the shortest pulses exper-iments. For each time delay, the reported signal, Signal(t), is calculated bynormalizing the measured lock-in signal Probe(t)-I0(t) against the product ofthe photodiode amplitudes Pump(t)*I0(t). Each photodiode amplitude is readon the SSH.

39

2.5 Ultrafast Pulse Characterization

The most common methods for ultrashort pulse characterization are the autocorrelation

measurement, using a second harmonic crystal, or crosscorrelation via the optical Kerr

effect [83]. Though the measured signal in the autocorrelation technique is stronger and

easier to achieve, there are no suitable harmonic crystals for UV pulses below 400 nm. As

a result of the above, we use the autocorrelation for measuring the amplified pulse and for

the visible output of the TOPAS, while the cross-correlation was used for the UV pulses or

when the pulses are differ in color. The experimental setup for both of the measurements

will be described below.

2.5.1 The Autocorrelation

The intensity of the second harmonic light from a nonlinear crystal is proportional to

the square of the fundamental harmonic field intensity. Therefore, in a degenerate pump

probe experiment, the measured signal from the non-linear crystal can be written as a

function of the time delay between the pulses:

SH(τ) =

∫

∞

−∞

I1(t)I2(t− τ)dτ (2.10)

Assuming both of the pulses are of Gaussian shape, we can solve the integral to get a

closed expression that correlate between the autocorrelation trace and the pulse length:

σSH =√

σ2pump + σ2

probe =√

2σpulse (2.11)

The autocorrelation trace is inherently symmetric in time, thus it cannot be used to obtain

the exact pulse shape.

40

2.5.2 The Optical Kerr Effect

The Kerr effect is a nonlinear polarization response that occurs in all the transparent

materials. The physical origin of the Kerr effect is a change in the material index of refrac-

tion generated by an electric field. In the Kerr measurement, the probe is detected through

crossed polarizes, while λ/2 wave plate is introduced in the pump arm and rotates its po-

larization by 45 degrees. As an outcome of the setup, the probe pulse can be decomposed

to the parallel and perpendicular to the pump polarization. When both of the pulses are

present in the material, the variation in the refractive index induced by the pump leads to

different retardation between the two components of the probe polarization, effect known

as birefringence. As a result, the probe pulse will develop ellipticity in its polarization,

and will be partly transmitted though the analyzer.

The fact that the induced birefringence is proportional to the pump intensity, leads to

the following equation for the Kerr signal:

Kerr(τ) =

∫

∞

−∞

I2pump(t)Iprobe(t− τ)dτ (2.12)

Using a Gaussian approximation for the pulse shape, one can explicitly carry out the

integration to get the relation between the Kerr trace and the pulse length.

σKerr =

√

σ2pump + 2σ2

probe

2=

√

3

2σpulse (2.13)

2.6 Ultrafast Pulse Propagation

A challenging aspect of working with ultrashort pulses is retaining their duration de-

spite the effects of dispersion. The uncertainty principle states that the time bandwidth

41

product has a minimum value:

∆ω∆t ≥ 2πN (2.14)

where N is a numerical constant of order unity, depending on the exact pulse shape. Thus,

construction of a femtosecond pulse requires ∼ 1000cm−1 of spectral bandwidth. The

broad spectrum forces us to consider the effect of light propagation on the temporal shape

of the pulse [85]. Starting from E(zi, t) as the field at the input to any optical system,

the Fourier transform of E(zi, t) gives the corresponding amplitude and phase of the input

pulse in the frequency domain:

E(zi, ω) = FE(zi, t) (2.15)

When this pulse is transmitted thought a dispersive medium, different spectral components

accumulate different phase. We can use the response of the optical system to propagate

each frequency component:

E(zf , ω) = R(ω) exp−iφ(ω)E(zi, ω) (2.16)

where R(ω) is the amplitude response (accounting for loss/gain) and φ(ω) represent the

phase response (dispersion).

Finally, the time domain field at the output of the optical system is obtained by taking

the inverse Fourier transform:

E(zf , t) = F−1E(zf , ω) (2.17)

42

Material:

φ(ω) =n(ω)ω

cd

n(ω) can be calculate using the sellmeier coefficients, d is the material thickness.

—————

Grating pair:

φ(ω) = Lg2ω

c

√

1 −(

2πc

ωd− sin γ

)2

Lg is the normal grating separation.

—————

Prism Pair:

φ(ω) = ω cosβ(ω)Lp

β(ω) = − arcsinn(ω) sinα(ω) + arcsinnreff (ω) sinα(ωreff )

α(ω) = Apex− arcsin

(

sin(θBrewster)

n(ω)

)

Lp is the prism separation, ωreff is the frequency that travel from apex to apex.

————————————————

The phase response of some optical systems, used in our experimental setup:

material, grating pair [86] and prism pair [87]

One way to account for the effect of the phase accumulated by the different frequen-

cies, is simply to calculate the derivative of the phase with respect to the frequency. The

calculated group delay is the full picture of the frequencies components phase evolution.

A different approach is to expand the phase in a power series assuming that the Taylor’s

expansion of the phase is valid and well behaved (meaning, the effect of each term in the

43

0 1 2 3 4 50

100

200

300

Chi

rped

pul

se F

WH

M [

fsec

]

Quartz Thickness [cm]

15 fsec25 fsec40 fec60 fsec100 fsec

Input pulse:

Figure 2.9: Pulse elongation resulting from propagation through different slabs of quartz.As the pulse gets shorter (meaning, more spectral components) the distortionto the pulse shape is enhanced.

expansion is significantly smaller than the effect of the previous term):

φ(ω) = φ0 +dφ

dω(ω − ω0) +

1

2

d2φ

d2ω(ω − ω0)

2 +1

6

d3φ

d3ω(ω − ω0)

3 (2.18)

where ω0 is the carrier frequency. While the first term is a constant and the second simply

represent an overall time shift of the pulse, the remaining terms represent distortion of the

pulse shape.

For the third term, namely the GVD, the effect on a Gaussian pulse can be calculated

analytically, leading to the following expression for the pulse elongation:

FWHMchirped =

√

ln(16)2GVD2 + σ4

σ2(2.19)

Thus, in the limit when the GVD1/2 is much bigger than the pulse length, the outcome

pulse FWHM is proportional to GVD/σinput.

44

20 40 60 80 100

40

60

80

100

Chi

rped

pul

se F

WH

M [

fsec

]

Input pulse FWHM [fsec]

Figure 2.10: Pulse elongation as a result of one cm of quartz, as a function of the pulselength. Red: full phase calculation Magenta: using just the GVD term (for1cm quartz, GVD=360fsec2)

2.7 Data Analysis

The experimental results consist of probe intensity difference as a function of the time

delay between the pulses. Extracting the experimental parameters is commonly accom-

plished using non-linear least squares fit routines. There are many different algorithms

capable of performing the non-linear fitting (Simplex, Levenberg-Marquardt etc.), all of

them share the same basic problem: as the number of the fitting parameters increases, the

least-squares result ends in a local minimum that is close to the initial guess. For analy-

sis of oscillatory signals, Fourier Transformation (FT) has the advantage of not requiring

initial guesses, however, the uncertainty principle, which is a direct consequence of the

transform, leads to ambiguities when trying to resolve closely spaced frequencies. Mea-

suring longer signals can alleviate this problem, but experimentally this is an expensive

and inefficient solution.

45

We found that using the filter diagonalization (FD) algorithm invented by Prof. Danny

Neuhauser [88, 89, 90] provided us with a technique that did not present any of the prob-

lems of FT or the least square fitting. The method assumes that the experimental signal

can be represented as the time evolution of a system composed of a set of uncoupled

springs in the presence of friction force. The scheme found many applications in physics

and chemistry [91]. For example, it was used as an efficient methodology for extracting

bound eigenstates and eigenvalues, reducing the simulation time in multi-dimension scat-

tering problems and for extracting frequencies from classical trajectories. The algorithm

can also be extended to multi-dimensional signals [92] (2D nuclear magnetic resonance,

2D imaging, etc.). FD is especially suitable for experimental results where the sampling

interval is known to a much higher accuracy than the measured amplitudes. The method

was found to be very efficient in handling signals having a large number of frequencies,

where the eigenvalues outside the desired experimental range are eliminated through the

use of a filter function, while eigenvalues within the range are extracted by diagonaliza-

tion of relatively small matrixes. The key point is that all the unknown matrices can be

constructed solely in terms of the experimental data.

The mathematical foundation of the FD algorithm is as follows: First we assume that

the experimental signal can be represented as a sum of exponentially decaying sinusoidal

functions. Explicitly, we can write:

C(t) =∑

j

aj exp −iωjt− (Γj/2)t (2.20)

Where C(t) is the measured signal, and aj, ωj, andΓj are the desired amplitudes, frequen-

cies, and decay times, respectively.

46

Next, we need to prove that the signal can also be written as a quantum correlation

function, i.e.:

C(t) =(

ψ0 exp−iHt ψ0

)

(2.21)

To begin, we construct an orthogonal basis set, Φn, and a diagonal Hamiltonian with (ωn−

iΓ) as its eigenvalues:

HΦn = (ωn − iΓn)Φn = εnΦn (2.22)

Even though the energies of these eigenfunctions are the desired parameters, their actual

nature, as well as the Hamiltonian’s, is of no importance, as they drop out from the final

results. The fact that the Φn′s are a complete base, means that we can chose ψ0 to fulfill

the following relation:

ψ0 =∑√

anΦn (2.23)

Starting from the correlation function (Eq. 2.21), we substitute for ψ0 remembering that

H is diagonal in the Φn basis leading to:

(

ψ0 exp−iHt ψ0

)

=(

ψ0

∑

n

exp−iHt √an ψ0

)

=

∑

n

an exp−iωnt−Γnt (ΦnΦn) = C(t) (2.24)

which completes the proof of Eq. 2.21.

Next we define a set of approximately energy-resolved vectors, in the range of the

experimental frequencies:

ψl =

∫ T

0

expiElt f(t) expiHt ψ0dt (2.25)

f(t) is the filter function, introduced in order to destroy contribution from far away eigen-

vales. l = 1, 2 . . . L are the number of frequencies to be resolved and T is the length of

47

the signal. Once the number of these functions, L, becomes larger than the number of

eigenstates within the sample range, the functions ψl′s become a complete basis set in the

range. To make sure that L is bigger than the relevant number of the Φn′s, we use the

Fourier spacing as the frequency spacing between consecutive ψl′s functions. The excess

eigenvalues can be eliminated using standard methods (such as Singular Value Decompo-

sition). Make use of the fact that the ψl′s are a complete bases set over the desired area,

1/2T Full Energy

Range

Sample

Range

SVD Diagonalization Φn nψ

E

Filter

Figure 2.11: Schematic representation of the FD routine.

we expand the original eigenvectors Φ in term of the ψl′s:

Φn =∑

Blnψl (2.26)

Operating with(

ψk exp−iHdt)

on both sides of Eq. 2.26, and substituting for Φn, results in

the following expression:

ψk exp−iHdt Φn = ψkΦn exp−iεnt =∑

l

ψkψlBln exp−iεnt =

∑

l

ψk exp−iHdt ψlBln (2.27)

48

In matrix notation, the equation takes the form of the well known generalized eigenvalue

equation:

sBZ = uB (2.28)

Z is a diagonal matrix with the desire exp(ε) as its eigenvalue. Both s and u matrices are

small matrices (LxL), that can be constructed directly from the experimental signal:

skl = (ψk ψl) =

∫ T

0

dt′f(t′)

∫ T

0

f(t)dt expiEkt′ expiEkt(

ψ0 exp−iHt′ exp−iHt ψ0

)

=

∫ T

0

dt′f(t′)

∫ T

0

f(t)dt expiEkt′ expiEktC(t+ t′) (2.29)

ukl =(

ψk exp−iHdt ψl

)

=

∫ T

0

dt′f(t′)

∫ T

0

f(t)dt expiEkt′ expiEkt(

ψ0 exp−iHt′ exp−iHdt exp−iHt ψ0

)

=

∫ T

0

dt′f(t′)

∫ T

0

f(t)dt expiEkt′ expiEktC(t+ t′ + dt) (2.30)

Finally, we solve for the weights. Starting from the ψ0 expansion (Eq. 2.23):

√aj = (Φj ψ0) =

∑

l

Blj (ψl ψ0) =

∑

l

Blj

∫ T

0

f(t)dt expiElt(

ψ0 exp−iHt ψ0

)

=

∑

l

Blj

∫ T

0

f(t)dt expiEltC(t) (2.31)

As an illustration of the FD performance, I compose the following signal:

Sig(t) = 5 sin(106t) exp−t/500 +10 sin(116t) exp−t/1000 +Noise

49

and use it as an input to the FD routine. While the FFT is incapable to distinguish between

the different frequencies, the FD fit perfectly matches the composed signal.

0 1 2 3

Time [psec]

Build Signal FD fit

60 90 120 150

Extracted parameters:ω

1=116 τ

1=1030 d

1=9.85

ω2=106 τ

2=520 d

25.12

FFT FD Spectrum

Frequency [cm ]-1

Figure 2.12: FD and FFT fit to a compose signal.

The spectrum is computed using the standard relation:

F (ω) =∑

n

dn

ω − ωn + i ∗ Cheat(2.32)

where Cheat is an external parameter used to artificially narrower the spectrum lines. In

the example, cheat was chosen to be 0.1, so the lines are spectrally resolved.

CHAPTER III

Impulsive Control of Ground Surface Dynamics of I−3

inSolution

50

Impulsive Control of Ground Surface Dynamics of I3- in Solution

Erez Gershgoren,† J. Vala,‡ R. Kosloff,‡ and S. Ruhman*,†

Institute of Chemistry, The Hebrew UniVersity, Jerusalem, 91904 Israel

ReceiVed: October 25, 2000; In Final Form: February 14, 2001

Coherent control of I3- ground state dynamics in ethanol and acetonitrile solutions is demonstrated. Themethod is based on impulsive excitation creating a dynamic hole employing sub 30 fsec tunable UV laserpulses. The target of control was to increase the ratio of second to first harmonic spectral modulations of thesymmetric stretching vibrational coherences. Methods demonstrated to achieve this target include alteringpulse intensity when the excitation pulses are tuned to the maximum of the absorption peak, double excitationpulses separated by half a vibrational cycle, and tuning the pumping or probing pulses to a wavelengthsimultaneously resonant with both absorption bands of ground state I3

-. Chirping the probing pulses furtherallows full mapping of the ground state coherence in phase space, pinpointing the position of the dynamicholes not only in coordinate space but also in momentum. A theoretical model reconstructs the results nearlyquantitatively and provides insight into the mechanisms active in achieving the control aims. It furtherdemonstrates how the fundamental suppression serves to precisely characterize the relaxation dynamics ofweak spectral features such as higher harmonics of the symmetric stretching and the antisymmetric stretchingfundamental. In particular, the ratio of dephasing rates of the first two harmonics (∼2.3) deviates considerablyfrom the ratio of 4 predicted by Kubo line shape theory. Possible sources of this discrepancy based uponalternative dephasing models are discussed.

I. Introduction

Impulsive photoexcitation is a key tool in modern applicationsof ultrafast spectroscopy to chemical dynamics.1 It involvesoptical excitation of molecular species with laser pulses shorterthan the time required for the constituent nuclei to movesignificantly in response to the suddenly modified forces actingbetween them. A major result of such optical transitions is thenearly vertical promotion of localized material wave packetsonto the excited potential surface. The subsequent evolution ofthis density, probed with a pulse of similar duration, serves tofully reveal the chronology of the excited ensemble, from theinitial ground-state geometry to the final products.2

An equally important and ubiquitous consequence of impul-sive excitation is the buildup of ground-state vibrationalcoherences. After their generation, the evolution of thesecoherences gives rise to spectral modulations in the ground-state absorption bands and can be followed as before, withdelayed ultrafast probing pulses.1,3-11 No matter whether thisspectroscopic feature is a nuisance, masking a dynamical processof interest, or the main object of the experiment, it is essentialto understand its fundamental nature and omnipresence byprobing its origins and its dependence upon the experimentalparameters.

Initial theoretical descriptions of resonant impulsively inducedground state coherence utilized perturbative expansions of themolecular density matrix, which associated the phenomenonexclusively with the Raman excitation term. This led to itsacronym: resonant impulsive stimulated Raman scattering(RISRS).3,7,9The analysis showed that from the time evolutionof the RISRS spectral modulations, information concerning the

underlying vibrational dynamics could be attained which is akinto the constants obtained from frequency domain Raman spectra.The above holds true also for the theoretical analysis of theRISRS process when cast in the dynamically motivated butotherwise equivalent correlation function formalism.7

Subsequently, more rigorous approaches to describing theRISRS process were introduced.12-14 This included work of ourown groups,5,10,11,15which was dedicated to rationalizing resultsof a femtosecond laser study of triiodide photodissociationdynamics.15-19 On the basis of direct integration of the quantumdynamics which explicitly includes the radiation in the Hamil-tonian, the material density could be followed directly beyondthe range of validity of perturbation theory. When nuclear inertiaprohibits substantial motion during the optical pumping, it isjustifiable to think of the transition dipole as acting locally incoordinate space. Accordingly, a phase space description of thematerial density has real advantages over an eigenstate descrip-tion. Using this approach, an intuitive understanding of theRISRS process can be formulated.10

The pump pulse acts to transfer density to the excited potentialin a coordinate selective fashion, acting most effectively forthe molecular configuration where the potential gap matchesthe frequency of the light. Thus, if the Bohr frequency is a strongfunction of the molecular geometry, the field will drill alocalized coherent hole in the ground state density. This holethen evolves, giving rise to the spectral modulations from which,when followed by delayed probe pulses, the vibrational dynam-ics is deduced. The conceptual framework also explains the finebalancing of pulse duration required for optimizing the RISRSsignal.10,11,15An ideal excitation pulse must be short enough tofulfill the requirements of impulsivity, yet not be so short thatit interacts equally throughout the entire coordinate space,leading to a reduction of the ground-state norm without localerosion of portions of the density.

* To whom correspondence should be addressed.† Also the Farkas Center for Light-Induced Processes.‡ Also the Fritz Haber Research Center for Molecular Dynamics.

5081J. Phys. Chem. A2001,105,5081-5095

10.1021/jp0039518 CCC: $20.00 © 2001 American Chemical SocietyPublished on Web 05/08/2001

I3- is linear and centrosymmetric in its ground and reactive

excited states. Accordingly most of the induced dynamics uponexcitation is along the symmetric stretch mode. It exhibits anear UV absorption spectrum which is dominated by two majorpeaks centered at 34 050 and 27 500 cm-1, which at 300 K are∼3600 cm-1 wide.20-22 The rapid evolution of the excitedpopulation, and the fact that the absorption of the primaryphotoproducts does not strongly overlap with much of thisspectrum, conveniently allows delineation of impulsively in-duced ground-state vibrational dynamics by pumping andprobing in the near UV.

In earlier studies, 70 fs pulses centered at 310 nm wereemployed both as pump and probe in RISRS experiments onI3

-. The same spectroscopic tool was also used in a transientfashion to follow vibrational relaxation of nascent I2

- photo-products.18 Vibrational dephasing dynamics of the symmetricstretching motion was determined in various polar solvents andin glass forming liquids at reduced temperatures.19,75 Coherentvibrations were detected only along the symmetric stretchfundamental. No evidence of antisymmetric stretch fundamentalactivity, known to exist in protic solvents from Ramandata,23,24,70,71or higher vibrational harmonics, were detected.Kuhne and Vo¨hringer25 studied the I3- system with a highertime resolution, interpreting the results to indicate activity ofhigher harmonics and antisymmetric band excitation. A shorterpulse also led to the observation of the second harmonicvibrational coherences in I2.26

The theoretical model was also employed to gain additionalinsights into the process of impulsively induced ground-statevibronic coherence. The purpose was to set guidelines on howexperimental control parameters such as pulse intensity,11

wavelength, and linear chirp27-29 influence the induced dynam-ics and their detection. In the present study, the same molecularsystem is revisited with improved theoretical tools and with alaser source capable of testing theoretical predictions whichexceeded our earlier experimental capabilities. The tunable lasersource producing∼30 fs pulses approaches the impulsive limitto a much greater extent and allows observation of vibrationcoherence in higher frequency modes.

With these sharper tools for experiment and analysis, theobjectives of the present study could be recast in the frameworkof impulsive coherent control.30 The pump pulse parametersconstitute control levers which can be used to selectively sculptthe ground state density. In an analogous fashion, the parametersof the probe pulse serve as selective filters for observing thetransient ground state evolution. These parameters includecentral wavelength, intensity, relative timing, and residual chirp.The objective of the current study is to investigate the degreesof control afforded by these levers over the RISRS process.Through these insights, manipulation of the pump and probestages will be used to selectively observe specific modes ofvibrational motion and follow their evolution at will.

In this paper, nearly quantitative agreement between themodel and experiment is demonstrated. Results show that evenat very moderate excitation intensities the observed behaviordeviates from the range of validity of perturbation theory. Properselection of pump and probe pulse wavelengths provides aneffective suppression of the symmetric stretch fundamental inthe RISRS signal, allowing measurement of the first and secondharmonic dephasing dynamics and of antisymmetric stretchingactivity with enhanced precision. Finally, control of the probepulse chirp was demonstrated to have strong impact on theRISRS spectral signature, serving to fully map motion of thedynamical hole in phase space.

II. Theory

A theoretical framework of understanding is the basis forinterpreting and guiding the experimental studies. This task isachieved by a two tier approach: combining approximateanalytic formulas with more rigorous quantum simulationmethods. Much of the theory has been developed and tested inprevious studies.10,11,15The present account briefly reviews themain conceptual points and the simulation methods. Thesubsection describing the absorption of probe pulse containsnew results and, therefore, is described in more detail.

A. Impulsive Control: Coordinate Dependent Two-LevelPicture. The conceptual framework of controlling the groundsurface dynamics is based on abruptly sculpting the nucleardistribution in phase space. A pulsed optical transition from theground to the excited electronic surface changes the ground statefrom a stationary to a nonstationary distribution. The maincontrol knobs on the process are the central excitation frequencyωL, pulse durationτpump, amplitude ε, and chirp. A morecomplex control scheme involves a multipulse excitationprocedure where the time delayτ12 between pulses is anadditional control parameter.

In the impulsive limit, a time scale separation exists betweenthe electronic excitation process and the nuclear dynamics.Conceptually the theory resembles the Born-Oppenheimerapproximation. Freezing of the nuclear motion during the pulseenables study of the excitation process at each nuclear config-uration separately. This is the basis of the coordinate dependenttwo-level-system approximation.10,15For each internuclear con-figuration X, a local Rabi frequency can be defined:

where 2∆(X) ) Ve(X) - Vg(X) - pωL is the local RWAdetuning andU(X) is the local coupling

ε(X) is the instantaneous pulse amplitude mapped onto thecoordinate using the reflection principle (Cf. Figure 1) andµ(X)

Figure 1. Schematic illustration of the impulsive excitation of thesymmetric stretch mode. The pulse shape in the time domain istransformed into a bandwidth in the frequency domain. The coordinaterange∆X influenced by the pulse is obtained by the reflection principle.Notice that for I3- there are two excited surfacesVe andV′e leading totwo overlapping absorption bands.

Ω(X) ) x∆2(X) + U2(X) (2.1)

U(X) ) ε(X)‚µ(X) (2.2)

5082 J. Phys. Chem. A, Vol. 105, No. 21, 2001 Gershgoren et al.

is the dipole function. The maximum degree of Rabi cyclingis determined by the angleθ(X) defined by cos(θ(X)) )∆(X)/Ω(X).

The position dependent Rabi frequency, eq 2.1, is the key tounderstand the control possibilities. For regions of configurationclose to the resonance pointXL, ∆(XL) , U(XL) which resultsin θ ≈ 90°. The population can therefore fully cycle betweenthe ground and excited electronic surfaces. The degree of cyclingdepends on the area under the pulse profile. For pulse intensitiesless than∫U(XL) dt ) π, the population transferred to the excitedelectronic surface leaves a void in the ground surface positiondistribution. The position of the void or dynamical hole can becontrolled by tuning the carrier laser frequencyωL. For pulseintensities larger thanπ, because of Rabi cycling, the void startsto refill. In the extreme case of a 2π pulse, the void atXL

completely refills. Because of different rates of cycling becauseΩ ) Ω(X), each internuclear position obtains a different phasefrom the field, shifting the final phase space distribution in themomentum direction. Far from the resonance point∆(X) .U(X), the degree of cycling is small, and therefore, almost nopopulation transfer takes place. The large Rabi frequency resultsonly in a small momentum shift to the initial distribution.10,13

Chirping the excitation pulse has two main consequences.First, the chirp has a tendency to correlate the changes in theposition and momentum distribution.27,31,32 Second, at highintensity, the chirp leads to adiabatic transfer.33,34The first effectcan be understood semiclassically as an excitation that followsthe motion of a wave packet. To synchronize with positivemomentum, the pulse has to have a negative chirp (from blueto red). A positive chirp will synchronize with the motion of awave packet with negative momentum. At high intensity, thechirp has an additional effect which leads to adiabatic transfer.33-35

If the chirp rate is slow relative to the Rabi period, adiabatictransfer prevails and all of the population is transferred fromthe ground to the excited surface at the particular range ofposition∆X. As a consequence, the Rabi cycling is eliminated.36

Electronic dephasing has a profound effect on the shape of thedynamical “hole”. The effect diminishes the population transferand diffuses the localization of the hole.10

B. Simulation. The creation of the dynamical hole wassimulated by solving the multisurface time dependent Schro¨d-inger equation for each initial vibrational eigenvalue:

The dynamics were generated by an effective Hamiltonianoperator using the rotating wave approximation:

where-εj(t) is the envelope of the pump field. Extension tomultiple excited electronic states is straightforward. The rotationvector|ψ⟩ is related to the original state by the transformation:|ψ⟩ ) exp(iωLtSz)|ψ⟩, whereSz is a rotation generator. Propaga-tion in time was performed using a Chebychev polynomialexpansion of the evolution operator.37 The propagation wasrealized in discrete steps with a time increment shorter by two-orders of magnitude than the pulse duration. The results of thepropagation for each initial vibrational wave function werecombined with Boltzmann weights to construct the final state:Ff ) Σie-âEi|ψi(tf)⟩⟨ψi(tf)| whereψi(tf) is the wave function onthe ground surface after the pulse is over. The projection ofFf

on the ground surface was the starting point of simulations

including the dissipative dynamics, on the basis of propagatingthe Liouville von Neumann equation.15

The detected signal is proportional only to the dynamical partof the ground surface density. This leads to a definition of thedynamical hole which is orthogonal to the equilibrium state:10

Fd ) Ff - c2Feq, whereFf is the density operator after the pulseFeq is the stationary or initial density operator.c2 is thenormalized scalar productc2 ) trFf‚Feq/trFeq

2, whichrepresents the difference between the final state and the initialequilibrium state. A measure of the coherence induced by thepump has been defined as10 C2 ) trFd

2, which equallyrepresents the depth of the dynamical hole.

A Wigner function38,39 of the final density operator

as well as one for the holeWd(p,x) were generated for visualizingthe state prepared by the pump pulse. Figure 2 shows the Wignerfunction created in this fashion using scalled position andmomentum coordinatesxj ) (mω/p)1/2x andpj ) (1/mωp)1/2p.In these coordinates, the unitary time evolution is simply arotation around the origin in phase space.

The negative density in the Wigner function ofFf (the bluecolor in the upper panel) is evidence for a purely quantummechanical contribution to the distribution in phase spacereflecting interference in the light-induced coherent motion.

ip∂

∂t (ψe

ψg) ) H (ψe

ψg) (2.3)

H ) (He - pωL/2 -εj(t)µ/2-εj(t)µ/2 Hg + pωL/2) (2.4)

Figure 2. Phase space picture of the state created by the pump pulseFf is shown in the upper panel. Below, the initial stateFeq and thedynamical holeFd ) Ff - c2Feq are also shown. In this example, thehole is created by an excitation pulse with a frequency correspondingto the center of the lower absorption band, i.e., 364 nm. The states areshown as Wigner functions in phase space in scalled coordinates, whereblue color represents negative density (see text).

Wf(p,x) ) 12π∫ Ff(x - y/2, x + y/2)eipy dy (2.5)

Ground Surface Dynamics of I3- J. Phys. Chem. A, Vol. 105, No. 21, 20015083

C. Absorption of the Probe Pulse.The total energy absorbedby the probe pulse is linearly related to the change in populationon the ground electronic surface15

The change in population∆Ng can be simulated directly bysolving eq 2.3 with the characteristics of the probe pulse. Theinitial condition is the transient wave function induced by thepump on the ground electronic surface. It is assumed that theexcited part of the wave packet at the probing timetp has alreadydissociated and thus moved out of the observation window.

An approximate alternative to the direct simulation of theprobe signal is obtained by an observable represented by awindow operatorW:

The window operator provides direct insight into the probingprocess as well as reducing the computational effort. Equation2.7 implies that the window operatorW is independent of thestate of the systemF(tp). This statement is true if the intensityof the probe pulse vanishes, which eliminates the contributionof cycling back from the excited electronic surface. Moreover,the observation process is not instantaneous and is completedin a time duration proportional to the probe pulse durationτp.The concept of eq (2.7) is to collapse the observation to a singleinstant of timetp. The collapse assumption for the windowoperator is equivalent to the impulsive condition that the nuclearmotion is frozen during the observation.

Because the static contribution is subtracted from the signal,the probe signal observation can also be viewed as an overlaybetween the density of the holeWd in phase space and a compactWigner-Weyl function38,39Ww(p,x) ) 1/(2π)∫ W(x - y/2, x +y/2)eipy dy, representing the observation window:

Equation 2.8 is the basis of the conceptual insight on theemergence of the transient signal form the overlap in phase spacebetween the dynamical hole and the window operator.

Explicit expressions of the window operator are obtained byconsidering an initial state on the ground electronic surfaceψg(tp - cτp) at a timecτp before the probing timetp. Theconstantc is determined such thatε(t ( cτp) ≈ 0. This initialstate will evolve under the influence of the probe pulse to

Because of the total norm conservation, the change in norm onthe ground surface can be measured on the excited surface:

For a probe which typically has weak intensity, time dependentperturbation theory can be used to obtain the final excited-statewave functionψe(tp + cτp) from the initial ground-state wavefunction ψg(tp - cτp):

Under the impulsive conditions [He, Hg] ≈ 0, eq 2.10 simpli-fies to

whereε(t) ) εj(t) exp(iωLt). The structure of eq 2.11 allows asynchronization of the ground and excited wave function to acommon timetp, leading to

Equation 2.12 relates any arbitrary initial wave function on theground surface to the final wave function on the excited surface,collapsed to a single instant of time. The window operator istherefore constructed from the projection composed from thecurly bracket in eq 2.12.

For a Gaussian shaped probe pulse with the envelope function,εj(t) ) Ae-(t-tp)2/2τp

2, eq 2.12 can be integrated leading to thewindow operator:

This expression is identical to the one obtained by Ungar andCina.14 A similar expression can be obtained for a square pulsewhere the Gaussian is replaced by a sinc function.15

The window operator representing the probe absorption signalcan be interpreted as a finite precision position measurementperformed on the ground surface densityFg. The precision ofthe position measurement is determined by the slope of thedifference potential 2∆(x), at the point of resonance:R ) 2d∆(x)/dx|∆)0, leading to∆X ≈ p/Rτp (see Figure 1). For theI3

- system, with a pulse duration ofτp ) 25 fs, the resolutionin position in the symmetric stretch direction becomes∆X )0.1 Å.

Chirping the probe pulse modifies the window operator.Consider the following chirped pulse:

whereø measures the chirp rate. Because the chirp lengthensthe pulse, the impulsive approximation is corrected by thenext order inτ in the exponent of eq 2.10, i.e., [He,Hg] )2[∆,P2/2M] ≈ ipRP/M. This will lead to the following excited-state wave function:

Comparing eq 2.15 to eq 2.12, one finds that the chirp rateø iscorrelated with the velocityVj ) ⟨P/M⟩. On performing theintegration, the window operator is approximated as

The window operator in eq 2.16 enhances areas in phase spacewhere the velocity is correlated with the chirp rate. Taking the

∆E ) -pωL∆Ng (2.6)

∆E ≈ -pωLtrF(tp)‚W (2.7)

Signal) ∆E ≈ -pωL∫∫ dp dx Wd(p,x)Ww(p,x) (2.8)

(0ψg(tp - cτp) ) f (ψe(tp + cτp)ψg(tp + cτp) ) (2.9)

∆Ng ) -∆Ne ) - ⟨ψe(tp + cτp)|ψe(tp + cτp)⟩

|ψe(tp + cτp)⟩ ) ip∫-cτp

+cτp dτ exp[-i/pHe(cτp-τ)]µε*(τ)

exp[-i/pHg(τ+cτp)]|ψg(tp - cτp)⟩ (2.10)

|ψe(tp + cτp)⟩ )

exp(-i/pHecτp) ip∫tp-cτp

tp+cτp dτ exp(-i/p2∆τ)µεj*(τ)exp(-i/pHgcτp)|ψg(tp - cτp)⟩ (2.11)

|ψe(tp)⟩ ) ip∫tp-cτp

tp+cτp dτ exp(-i/p2∆τ)µεj*(τ)|ψg(tp)⟩ (2.12)

W(x,x′) )π(τpA)2

p2exp( -2∆2(x)

p2τp

2)‚µ2(x)δ(x - x′) (2.13)

ε(t) ) A exp[ -(t - tp)2

2τp2

+ iø2(t - tp)

2 + iωL(t - tp)] (2.14)

|ψe(tp)⟩ ) ip∫-cτp

+cτp dτ exp[- ip2∆τ - τ2

2τp2]

exp[i(ø/2 - R/2p P/M)τ2]µ|ψg(tp)⟩ (2.15)

W(x,x′) ∝ exp[-2∆2(x)

p2τp

2 2

1 + τp4(ø/2 - (R/2p)Vj)2]‚

µ2(x) δ(x - x′) (2.16)

5084 J. Phys. Chem. A, Vol. 105, No. 21, 2001 Gershgoren et al.

next order in the expansion of∆, i.e., R2 ) (d2∆/dx2)∆)0,through the commutator of the ground and excited Hamiltonianwill add the momentum position correlation operatoripR2/M(XP + PX) to eq 2.16. This addition will cause a rotation inphase space of the window operator (see section IV.D). Thepresent approach to a chirped probe is different than thesemiclassical approach of Zadoyan et al.32 where the windowfunction is defined only in coordinate space.

The concept of synchronizing the ground and excited wavefunctions to a common timetp can be used to obtain a numericalrepresentation of the window operator. Each initial eigenfunctionφn on the ground electronic surface at timet ) -cτp evolves toan excited-state wave functionψe(n)(+cτp), where the peak ofthe probe intensity is shifted to timet ) 0. These wave packetsare propagated backward in time under the free evolution onthe excited surface tot ) 0: ψe(n)(0) ) e+i/pHecτpφe(n)(+cτp).The window operator is constructed from the sum of excited-state projections from all of the initial eigenvalues. To completethe synchronization, the window operator is propagated forwardin time for durationcτp generated by free evolution on theground surface Hamiltonian:

The window operators are shown in phase space in Figure 3.The blue color regions representing negative density are an

indication of the failure of the perturbation description, eq 2.15,even for vanishingly small probe intensities. The basic assump-tion in the perturbative expansion is that population movesunidirectionally from the ground to the excited surface or in atwo-level description the light induces only a small fraction ofa Rabi cycle. However, the Rabi frequency for vanishingintensity, Ω(X) ≈ |∆(X)|, is proportional to the detuning.Therefore, even for zero intensity for large detuning, there isconsiderable cycling. These considerations define the range ofvalidity of the perturbation approach as∆(X)‚τp , p. For apulse of 30 fs for the I3- system, this translates to a detuningof ∆(X) , 1500 cm-1.

III. Experimental ProceduresA. Experimental Details. The amplified laser used in this

study removes two major limitations imposed by its predeces-sor: mediocre time resolution and the inability to tune the

excitation pulses. The current homemade system provides a highrepetition rate source of nearly transform limited pulses whichare continuously tunable from the near-IR to the UV. The systemconsists of a KLM Ti;sapphire oscillator and multipass amplifier,coupled to a commercial OPA (TOPAS, Light Conversion). Theoscillator follows the design published by Asaki et al.40 and ispumped with 4 W ofargon ion radiation (Coherent Innova 310).This oscillator, which was built around a crystal purchased fromEKSMA, produces a 300 mW train of 17 fs pulses, with aFWHM spectral band of 45 nm, and an 85 MHz repetition rate.Before amplification, the pulses were stretched in an allreflective stretcher, which preserves the spectral width of theoscillator output, to a duration of 25 ps. The stretcher wasconstructed from a 600 line/mm grating (Richardson GratingLab) and a 6 in. gold parabolic mirror of 91 cm focal length(Edmund Scientific).

After a single pulse was selected from the stretched pulsetrain at a frequency of 1 kHz (Pockells cell; Fast PulseTechnology), the pulse was injected into a multipass amplifierpumped with 10 mJ pulses from an intracavity doubled YLFlaser (527 Quantronix DP-H). The amplifier is based on thedesign of Backus et al.,41 with some modifications. Pumpingwas achieved axially by focusing the YLF output into a 6 mmoptical path length brewster cut sapphire crystal (Casix). Thisis achieved using 2 in. diameter dichroic end mirrors with 75cm radii of curvature (CVI), which transmit the pumpingradiation and reflect the near-IR. A mask of 2.2 mm holes on3.6 mm centers is introduced between the planar gold reflectorand one of the end mirrors to reduce effects of ASE, and self-focusing. 8 round trips in the amplifier produce a 1.3 mJ pulse(13% conversion of the pump energy). The amplified pulseswere spatially filtered and temporally compressed with a gratingpair to produce the ultimate output of 28 fs (FWHM) pulsescontaining 700µJ of energy, at 1 kHz. The spectrum of theoutput is centered at 800 nm. 80% of this output is used topump the OPA, generating 18-22 fs pulses throughout thevisible range (450-750 nm) via frequency doubling the IRoutput or nonlinear mixing with the 800 nm fundamental.

The UV pulses were generated by quadrupling the OPAoutput in sub-100 micron BBO crystals which minimize pulsebroadening because of group velocity mismatch. Prism pairswere used to control linear chirp both before and after the BBOdoubling crystals, to obtain the highest time resolution. In someexperiments linear chirp was intentionally introduced byincreasing or decreasing the depth of prism insertion in the samecompensating pairs.

I3- solutions were prepared by mixing iodine and iodide salt

(KI for ethanol or (CH3)4NI for acetonitrile) with a 10% excessof iodide. The concentration of the solution changed fromexperiment to experiment to provide 50% absorption of pumpenergy. The integrity of the solution was monitored by measur-ing the UV-vis absorption spectrum before and after theexperiments, and demonstrated to be unchanged by the irradia-tion. The sample was circulated through a 200µm path lengthcell equipped with 150µm quartz windows, using an all Teflonperistaltic pump (Cole Parmer), at a rate which refreshed thesample irradiated between shots.

Pump and probe pulses were focused through a 25 cm quartzsinglet into the sample. Intensity of the pump and probe pulses,as well as the transmitted probe, were collected by amplifiedphotodiodes and digitized on a fast A/D converter. Thetransmitted probe was subtracted from the reference pulse in alock-in amplifier (EG&G, 7260) and the pump beam choppedat 500 Hz. The resulting signal detected at this frequency was

Figure 3. Window operator in phase space. (a) Top: a probe centeredat 364 nm. Bottom: a probe centered at 400 nm. (b) The influence ofthe chirp on a window function centered at 400 nm. The( signsrepresent the positive and negative chirp of 500 fs2. Notice that thephase space in panel b is rotated by 90° with respect to panel a.

W ) -exp[-i/pHgcτp](∑n

|ψe(n)(0)⟩⟨ψe(n)(0)|)

exp[+i/pHgcτp] (2.17)

Ground Surface Dynamics of I3- J. Phys. Chem. A, Vol. 105, No. 21, 20015085

digitized and dynamically normalized to changes in pump andprobe reference intensities. The time delay between pump andprobe was controlled by a high-resolution DC motor actuatedtranslation stage (Newport, PM500). Computer control of thedata collection as well as the subsequent data analysis to bedescribed below were programmed in Labview.42

B. Experimental Analysis.The outcome of the experimentwas a time series, composed of the absorption of the probe pulseat incremental time delays:Sex(n∆t). The time series reflectsthe ground-state nuclear motions induced by the pump andviewed by the probe. The ultimate goal of the analysis is abreakup of the spectral modulations into contributions fromindividual active vibrational modes and to extract accurate valuesfor their frequencies and decay dynamics.

A powerful tool employed for this purpose is the filterdiagonalization technique.43-45 The method is based on theassumption that the time signal can be represented as a sum ofcomplex exponentials:

whereΩj ) Re(ωj) is the desired frequency,τj ) 1/Im(ωj) isthe life time, anddj is the complex amplitude of thejthcomponent. 4K is the number of fitting parameters. Theassumption of exponential vibrational dephasing of each com-ponent is by no means assured in view of contrary examples inthe literature.46 Implications of this assumption will be addressesin section V.

The analysis method employs only a small frequency windowinside the physically relevant range. In this range, the frequen-cies are extracted by diagonalization of a small matrix. Thematrix elements are evaluated directly from a stroboscopicsampling of the signalS(n∆t) where∆t is the sampling interval.The method is particularly suited for pump-probe ultrafastexperiments where∆t is determined to a very high precision(( 0.3 fs).

The experimental background of the signal was eliminatedeither by the subtraction of a low order polynomial fit to thedata (order 2-3) or by letting the Filter-Diagonalizationprocedure fit the background. The relevant frequencies above100 cm-1 were not sensitive to the background subtractionmethod.

The advantage of the method is the ability to extract thedesired parameters, with high fidelity, using only a limitednumber of data points. The validity of the output parameterswas checked in the time and frequency domains. In the timedomain, the results were checked by eq 3.1. The experimentalsignal was reconstructed starting with the frequencies with thelargest amplitudes|dj|. For each additional frequency,ωj thatwas added to the sum, the signal was compared to theexperimental output. When the agreement with the experimentaldata was satisfactory the procedure was stopped. This constitutesthe minimum set of amplitudes and frequencies which recon-struct of the experimental signal. Adding frequencies beyondthe minimum set increasedø2, whereø2 ) Σn)1

N (Sex(n∆t) -S(n ∆t))2/(N - 4K). In the frequency domain, the spectrum wasreconstructed using the relation

TheF(ω) function was reconstructed with the minimum set offrequencies and compared to the Fourier transform of the

experimental signal. In the analyzed signals, aside from veryrapidly decaying or very low-frequency components, the leadingamplitudes could be assigned to the known molecular modes,their harmonics and combination bands.

There were cases where the analysis resulted in a group ofclose-lying frequencies. The possibility of regrouping thesefrequencies was checked by using a nonlinear fit procedure torefit the experiment with only one representative frequency. Anonlinear fit procedure was also used to check the possibilityof non exponential decay. Theø2 criteria was used to determineif this procedure was valid.

The filter-diagonalization (FD) fitting procedure can becompared to the linear prediction singular value decomposition(LP-SVD)47 procedure because both methods fit the data to asimilar functional form. The advantage of the FD is that thestroboscopic structure of the data is incorporated in the method.Typically in pump probe spectroscopy the time delay isdetermined very accurately compared to the amplitude of thesignal which is affected by noise. The FD method is ideallysuited for such situations.48

IV. Case Studies

Once the target of control was defined as suppression of thesymmetric stretch fundamental and the enhancement of theremaining frequencies, a number of distinct strategies werestudied. Each subsection describes a specific strategy, itsexperimental implementation, and theoretical foundation.

After the concept of both the dynamical hole and the probingwindow function are described, the general approach forsuppressing the first harmonic component of the symmetricalstretching in the RISRS signal is straightforward. The completesignal cycle involves both the generation of the hole by thepump and its observation through the coordinate dependent maskdefined by the probe. We concentrate on a two-dimensionalrepresentation of vibrational phase space in terms of thesymmetrical stretching mode and disregard the possibility of achirped probe. All that is required for first harmonic suppressionis to prepare a dynamical hole and/or to devise a probe windowfunction withC2 symmetry in phase space, assuming the rotationaxis is perpendicular to the (p,x) plane and centered at its origin.Either or both of these will ensure that one period of phasespace rotation (one period of vibration) will produce a signalwith two repeated and identical time sections, excluding a firstharmonic component at the fundamental frequency by definition.The following case studies will examine specific strategies forobtaining this goal and describe their limitations and fortitudeswith respect to the control objective.

A. Drilling a Hole in the Middle of the Absorption Band.By tuning the pump frequencyωL to the center of the absorptionband, the dynamical hole in coordinate space is produced withreflection symmetry with respect to the minimum point of thepotential well. If inversion symmetry is also imposed withrespect to zero momentum, the desiredC2 symmetry is obtained.A momentum kick induced by the pump will break thissymmetry leading to the appearance of a first harmoniccomponent in the signal. A measure of the degree of symmetrybreaking of the dynamical hole is defined as the momentumchange on the ground surface normalized to the depth of thedynamical hole:

whereC is the coherence measure (cf. subsection II.B).

S(t) ) ∑j)1

K

dj exp(-iωjt) (3.1)

F(ω) ) ∑j

dj

ω - ωj

(3.2)Ph )

⟨P⟩C

)trPFd

C(4.1)

5086 J. Phys. Chem. A, Vol. 105, No. 21, 2001 Gershgoren et al.

The source of the momentum kick is quite subtle. We foundby simulation that our previous semiclassical estimations10,15

were misleading. Figure 4 shows the buildup of the momentumkick during the pulse. At small fractions of the Rabi cycle, i.e.,Ut , π, a universal buildup of a negative momentum kickPh isobserved. In this region of intensity, the momentum⟨P⟩, thecoherence measureC, and the population transfer∆Ng all scalelinearly with the fluence (ε2). This phenomena can be rational-ized by first decomposing the zero momentum initial stationarystate to a superposition of pairs of wave packets with positiveand negative momentum. The absorption process has a bias tothe promotion of the positive momentum wave packet, thusleaving behind a negative momentum contribution. This phe-nomena is related to the different absorption of a positive ornegatively chirped pulse.27,36 The zero intensity negativemomentum kick means that a residual symmetry breaking,causing a first harmonic signal, will occur even at very smallfluence values. The broken symmetry in the dynamical holefor low fluence is clearly observed in panel 1 of Figure 5 whichshows a phase space picture of the dynamical holeFd.

Upon increasing intensity thePh increases nearly linearly withfluence and eventually changes sign (cf. Figure 4). This effectis purely quantal because it results from interference betweenthe ground state wave function and the wave transferred backfrom the excited state by the optical cycling, see Figure 5. Thepopulation transfer which accompanies the change of sign ofPhis moderate∆Ng ∼ 13%. This point represents a peak ratio insecond to first harmonic amplitude. This maximum is clearlyobserved in the experimental signal (cf. Figure 6). Furtherincrease in intensity was found to reduce this ratio, which isconsistent with an increase of the positive momentum kick.

For even higher pump intensities the momentum distributionchanges shape almost completely loosing theC2 symmetry. Thisis the result of additional interference causing an oscillation inthe momentum kick as a function of fluence (cf. Figure 5).Figure 5 confirms the analysis that theC2 symmetry breakingis in the momentum direction. This fact means that the peak ofthe first harmonic components will coincide with half thetransmission peaks of the second harmonic component. As aresult, one of the peaks of the second harmonic componentwill be enhanced, creating a sawtooth like signal with adifferent direction for negative and positive momentum kick(cf. Figure 6).

The insight gained by this analysis leads to the possibility ofcontrolling the relative phase between the first and secondharmonic components using intensity and detuning as controlknobs. A phase shift ofπ/2 (with respect to the fundamentalfrequency) between the first and second harmonic componentscan be obtained by symmetry breaking in the coordinatedirection. This operation is easily obtained by detuning theexcitation frequency slightly off the center of the absorptionband. A combination of intensity and detuning enables controlof the amplitude ratio as well as control of the relative phase ofthe first and second harmonic components of the signal.Alternatively, observing the transient signal allows a directdetermination of the initial shape in phase space of thedynamical hole.

Figure 6 displays the measured pump probe signal fordifferent intensities corresponding to the simulation presentedin Figure 5. The transition from a signal with a significant firstharmonic component for low intensity to a signal dominatedby a second harmonic component at higher intensity and adecrease of the second harmonic component for even higherintensity is evident in the time domain, where the main periodof oscillation doubles. This is born out in the spectral analysis

Figure 4. The buildup of the momentum kickPh as a function of timefor different intensities. The duration of the pulse is indicated. Afterthe pulse is over the momentum kickPh oscillates with the period ofthe fundamental frequency. The insert shows the final momentum kickPh determined after the pulse is over as a function of fluence, showingthe transition from negative to positive momentum.

Figure 5. Intensity effect on a holeFd drilled in the middle of theband (364 nm) showing the breaking of theC2 symmetry. The intensitiesare in units of fluence, where panel 1, 0.017 mJ/cm2 (∆Ng ) 0.02);panel 2, 0.14 mJ/cm2 (0.13)Ph ) 0; panel 3, 0.24 mJ/cm2 (0.19); panel4, 0.66 mJ/cm2 (0.23); panel 5, 2.63 mJ/cm2 (0.30). The ellipse in panel1 represents the probe windowWw located at 400 nm. The white pointrepresents the origin of rotation in phase space which is the zero positionmomentum point. The left panels show a top view, whereas the rightpanel shows a stereoscopic perspective.

Ground Surface Dynamics of I3- J. Phys. Chem. A, Vol. 105, No. 21, 20015087

shown in the right panel of Figure 6. The other significantfrequency in the data is the antisymmetric stretchω ) 145 cm-1,indicating a breaking of symmetry of the I3

- molecule by thesolvent.23,24,50

A series of experiments were performed where both the pumpand probe were in the middle of the absorption band either at364/364 or, for the upper band, at 290/290. With a carefulselection of the wavelength and chirp, the first harmonic signalwas suppressed almost completely because ofC2 symmetry ofthe probing window function in phase space.

B. Drilling Two Holes Simultaneously. Pump 325 nmProbe 400/325 nm.The absorption spectrum of I3

- is composedof two overlapping absorption bands. By choosing an excitationfrequency where the two absorptions are equal, two holes arecreated (see Figure 1). Because the two holes are positionednearly symmetrically around the zero point in phase space, thedesiredC2 symmetry is approximately obtained. Panel b inFigure 8 shows the phase space distribution after the pump.The excitation removes amplitude from both sides of the initialdistribution, creating a state which is narrower than its uncer-tainty width in the ground state. Such a nonclassical distributionindicated by its negative components (blue) resembles a“squeezed state” in quantum optics.51,52The distribution of thehole shows that a probe far from the center will experience morefirst harmonic character than a probe close to the center of theabsorption band. This is evident in Figure 7, where a probe at400 nm shows dominant first harmonic dynamics. A probe at325 nm shows dominant second harmonic dynamics due to afiltering effect of the double probing window. At first sight thepump probe signals in the two solvents look very similar. Amore careful examination, in particular by filter-diagonalizationanalysis, reveals an antisymmetric contribution in I3

- in ethanolwhich will be absent from the acetonitrile data.

The 325/325 trace in the acetonitrile data has the typicalcharacteristics of aπ/2 phase shift between the first and secondharmonic components. This means that the symmetry breakingis along the momentum direction which could be interpreted asan intensity effect. Other traces with the similar pump probe

wavelength combinations (not shown) display a sawtooth likesignal indicating symmetry breaking in the coordinate direction.

C. Multipulse Excitation. Pump 400/400 nm Probe 400nm. A generally applicable method for ensuring theC2

symmetry in phase space is the introduction of a doubleexcitation pulse delayed by half a fundamental period. A similarmethod was previously used for studying interference effectsin impulsive Brillouin scattering.49 The holes created havesimilarities to the ones created by the simultaneous drilling oftwo holes.

From an eigenstate viewpoint, the double excitation createsa constructive interference for the even eigenstates and adestructive interference for the odd eigenstates. This processcan be observed in Figure 9. As an indication of a coherentprocess, the amplitude of theV ) 2 component after the secondpulse is enhanced by a factor of∼5 relative to its amplitudeafter the first pulse.

From the phase space viewpoint, one can imagine the effectof the pulse as first shaving one side of the distribution andthen using the dynamics to rotate the distribution by 180° andshaving the other side of the distribution. This effect can alsobe utilized to make higher order harmonics by using three pulsesseparated by1/3 of a period etc. The shape of the dynamicalhole created by this method is shown in the top panel of Figure

Figure 6. Pump probe signal of I3- in ethanol for four different pump

intensities. The spectrum of the pump and probe pulses is indicated inthe insert superimposed on the absorption spectra of I3

-. The right panelshows the Fourier transform of the signal together with the filter-diagonalization fit to the data shown as histograms indicating the mainfrequencies and amplitudes in the data. The top label indicates theposition of the fundamental frequency 111 cm-1 and its secondharmonic. The insert shows the spectrum of the pump and probe pulsessuperimposed on the absorption spectrum of I3

-.

Figure 7. Pump probe signal for I3- in ethanol (top) and acetonitrile

(bottom). The pump wavelength is at 325 nm. The top trace shows aprobe at 325 nm and the bottom trace shows a probe at 400 nm. Theright panel displays the filter-diagonalization fit to the dominantfrequencies superimposed on the Fourier transform of the data.

5088 J. Phys. Chem. A, Vol. 105, No. 21, 2001 Gershgoren et al.

8. Again the phase space distribution has a nonclassicalcomponent resembling a squeezed state. The symmetric shapeof the hole will lead to a dominant second harmonic componentirrespective of the detection scheme. This effect can be seen inthe experimental results of Figure 10.

D. Chirping the Probe Pulse. Pump 400 nm, ChirpedProbe at 325 nm.As stated in section II.C, residual chirp inthe probe radiation will break the symmetry of the windowfunction with respect to the zero of momentum and, accordingly,

will corrupt the intendedC2 symmetry. In this case study, wewill demonstrate this effect and highlight the utility which itprovides for pinpointing the coordinates of an evolving ground-state density in phase space. The effective suppression offundamental modulations as expected for 325 nm probing isdemonstrated in the no-chirp trace of Figure 11.

A positive chirp of the probe pulse moves the detectionwindow in the direction of negative momentum (see sectionII.C and Figure 3). The breaking of theC2 symmetry will causethe appearance of the first harmonic component in the signal.The same should be true for a negatively chirped probe withthe difference that the detection window is shifted to positivemomentum. This difference in the direction of the symmetrybreaking should cause exactly aπ shift in the phase of the firstharmonic component irrespective of the amount of chirp. Thisfact is clearly observed in Figure 11 where, because of the fasterrelaxation of the second harmonic component, the signal, aftersufficient time (∼1500 fs), is almost exclusively composed fromthe first harmonic component. The positive and negative chirpedmodulations are exactly out of phase. The influence of chirpingthe probe on the phase of the second harmonic component isgradual and is caused by the shift in the window position to

Figure 8. Comparison of final densityWf (left panel) and dynamicaldensityWd (right panel), created by (a) sequential drilling of two holesby half a period delay (excitation at 400/400 nm) to (b) simultaneousdrilling of two holes (excitation at 325 nm) and to (c) an intermediateintensity hole drilled in the center of the band. (excitation at 364 nm).

Figure 9. Creation of a hole by a double pulse. The two pulses arecentered att ) 0 andt ) 0.5 in units of the vibrational period (300 fs).The change in population on the different eigenvalues is shown as afunction of time.

Figure 10. Pump probe signal for I3- in ethanol. The figure compares

a pump at 400 nm (bottom trace) to a multipump pulse with a timedelay of half a period (top trace). The probe is also at 400 nm.

Figure 11. Pump probe signal for I3- in acetonitrile for different chirps.

The figure compares a pump at 400 nm and a probe at 325 nm withdifferent chirp rates. The vertical line emphasizes the correlationbetween the phase shift of the signal and the chirp.

Ground Surface Dynamics of I3- J. Phys. Chem. A, Vol. 105, No. 21, 20015089

earlier or later times depending on whether the chirp is positiveor negative, cf. Figures 11 and 12.

The lower panel of Figure 12 shows a signal directlysimulated for a positive, zero, and negative chirped probe. Thesimulation was carried out by a direct integration of theSchrodinger equation including the pump and probe fieldsexplicitly. The signal was calculated by adding the Boltzmannweighted signal from each initial ground surface eigenstate. Theexactπ phase shift between the first harmonic components isclearly evident. The two peaks in the signal are due to thedetection by the two observation windows. Their lack ofequivalence is the result of a different slope of the differencepotential in the right and left observation windows.

Another effect of the chirped probe is to reduce the signal ofthe late detection in the positively chirped probe and the earlydetection in the negatively chirped probe. This phenomena iscaused by a correlation between momentum and position whichtilts the observation windows, cf. Figure 12 and subsection II.C.The tilting means that the probe can follow the motion of thewave packet for a longer time when it is contracting from theouter turning point and that a positive chirp will shift theobservation to negative momentum. The tilt in the observationwindow is the result of a quadratic term (d2∆/dx2)∆)0 in thedifference potential which causes position momentum correla-tion. When the simulated signal is compared to the observedone, it is evident that the second derivative of the differencepotential is larger in the simulation than in the real I3

- potentials.Chirping a probe with a frequency of 364 nm and a pump at

364 also showed a suppression of the second harmoniccomponent. The 364 nm chirped signal differs from the 325nm chirped signal in that the fundamental component was notenhanced, probably because of its absence from the initial state.

V. Spectral Analysis

The control insight demonstrated in the case studies, inparticular the ability to suppress the strongest spectral feature,the fundamental symmetric stretch signal, enables the study ofthe transient spectroscopy on the ground electronic surface ofI3

- with enhanced precision. With these tools at hand thedephasing dynamics of the different harmonic componentscomposing the signal can be unraveled for different solvents.Moreover weak spectral features such as the antisymmetricstretch and combination band can also be observed. The casestudies presented in the previous section are only a small fractionof the data sets which were studied experimentally for I3

- inethanol and acetonitrile. Detailed analysis of all of the collecteddata is presented below in tabulated form.

A. Dephasing Dynamics of the Fundamental and SecondHarmonic Symmetric Stretch. Table 1 summarizes the resultof the filter-diagonalization analysis of the symmetric stretchdynamics which fit the formula

The amplitude in the table represents the fraction of a particularFourier component in the total transient signal after thebackground has been subtracted. A small amplitude of aparticular component degraded the reliability of the extractedparameters. When the decay of the second harmonic dynamicswas analyzed, the possibility of an inertial effect was checked.A Gaussian fit model was tried for the decay curves but wasinferior to the exponential fit.

The main observations in the table concerning the funda-mental frequency of the symmetric stretch are the following:

(1) The frequency of the motion is 112( 1 cm-1 irrespectiveof the solvent.

(2) The decay is exponential with a decay lifetime of1030( 20 ps for acetonitrile and 950( 20 ps for ethanol.

The fundamental frequency in gas phase is very similar,112 ( 1 cm-1,67 and fits well the ab initio result 114 cm-1.85

The decay rate is independent of the pump and probe charac-teristics except when the pump and probe wavelength is closeto the middle of the absorption band (∼364 and∼290 nm)where a very fast decay time is observed. Under these conditionsthe first harmonic component is suppressed though not entirely.The experiment at 290 nm at the peak of the higher absorptionband was done to prove that the RISRS signal is a true ground-state property independent of the excitation frequency. Thesimilarities of the observations at 364 and 390 nm rule outexcited-state dynamics and chemical modulation of the nascentproduct I2- as a source of the transient signal. The mainobservations concerning the second harmonic are as follows:

(1) The frequency of the motion is 224( 2 cm-1 irrespectiveof the solvent.

(2) The decay is exponential, with a decay lifetime of 480(50 fs for acetonitrile. Ethanol is slightly slower, 500( 50 fs,but it is within the experimental error bars.

(3) Within the experimental error, the decay rate was foundto be independent of the initial conditions induced by the pumpcharacteristics.

(4) An exponential decay describes the results well.

Figure 12. Top: schematic view in phase space of the position of ahole located at the outer turning point and of the observation widows.A positive chirp of the probe shifts the window to the negativemomentum direction and also correlates the position and momentumwhich is observed as a tilt to the window. The opposite is true for thenegative chirp. The lower panel shows a simulated pump-probe signalwithout dissipation. A positive chirp (red) delays the observation ofthe first window and advances the observation of the second windowlocated at the inner turning point. The tilting causes additionalasymmetry between the two observation windows. The negative chirpedcase is shown in blue and the zero chirp in black.

S(t) ) ∑j

|dj| sin(φj - ωjt)e-t/τj (5.1)

5090 J. Phys. Chem. A, Vol. 105, No. 21, 2001 Gershgoren et al.

B. Dephasing Dynamics of the Antisymmetric Stretch andthe Combination Band. Table 2 shows the result of filter-diagonalization analysis for the antisymmetric stretch andcombination band dynamics. A significant signal could onlybe detected in ethanol. Suppressing the fundamental frequencyunravels the weak signals of other frequencies.

(1) The frequency of the antisymmetric stretch is 143( 2cm-1.

(2) The decay is exponential, with a decay lifetime of 640(50 fs.

(3) The frequency of the combination band is 253( 2 cm-1.

(4) The decay is exponential, with a decay lifetime of 480(70 fs.

(5) The decay of the combination band is slower than theexpected decay corresponding to the sum of the rates of thesymmetric and antisymmetric stretch (400 fs).

An antisymmetric stretch frequency of 140 cm-1 for I3- in

ethanol was inferred by Ku¨hne et al.53 Ab initio calculationsindicate a frequency of 147 cm-1 (see ref 85).

VI. Discussion

Impulsive coherent control of molecular dynamics hinges ona separation of time scales between the light induced transitionsand the intramolecular vibrational motions when impulsiveconditions prevail. It is particularly attractive for general controlof ground electronic surface dynamics in condensed phases. Thebrevity of the control process allows initiation of particularmodes of motion before dissipative forces take over.

One may ask whether this process is coherent control? Theaccepted criterion is that coherent control is aninterferenceeffect with at least two pathways leading to the final result.30,55,56

Reconsidering the process that creates the dynamical hole, it isclear that cycling of the amplitude through the excited electronic

TABLE 1: Filter-Diagonalization Fit to the Symmetric Stretch Frequency and Its Second Harmonic

pump [nm] probe [nm] solvent frequencyω [cm-1] decayτ [fs] amplitude|d| phaseφ [rad]

290 289 acetonitrile 111( 1 620( 100 0.4( 0.1 1.8( 0.2229( 1 420( 50 0.6( 0.1 2.3( 0.2

287 291 acetonitrile 112( 1 650( 100 0.6( 0.1 2.0( 0.2227( 1 500( 50 0.4( 0.1 2.4( 0.2

ethanol 112( 5 770( 40 0.16( 0.04 2.1( 0.2364 364 225( 5 500( 50 0.5( 0.1 1.9( 0.2

acetonitrile 113( 1 680( 100 0.3( 0.1 1.7( 0.4227( 1 450( 50 0.7( 0.1 1.( 0.2

364 ethanol 113( 3 1200( 80 0.1( 0.1 0.( 0.3low 400 224( 1 500( 20 0.5( 0.1 -1.0( 0.1intensity acetonitrile 112( 2 850( 50 0.2( 0.1 2.5( 0.1

226( 2 460( 50 0.8( 0.1 -1.1( 0.3

364 ethanol 112( 1 1050( 30 0.39( 0.02 -0.4( 0.3medium 400 222( 1 420( 70 0.44( 0.02 -0.4( 0.3intensity 400 acetonitrile 113( 1 1100( 60 0.32( 0.06 -0.3( 0.3

225( 3 400( 80 0.68( 0.06 -0.8( 0.3

364 ethanol 111( 1 1100( 80 0.60( 0.1 0.( 0.3high 400 224( 2 520( 70 0.3( 0.1 -0.6( 0.3intensity acetonitrile 113( 1 1060( 30 0.85( 0.02 0.5( 0.1

227( 2 540( 60 0.15( 0.02 -0.2( 0.1

ethanol 112( 1 1000( 200 0.3( 0.1 1.7( 0.4325 325 224( 1 530( 80 0.5( 0.1 2.3( 0.4

acetonitrile 113( 1 850( 100 0.3( 0.1 0.2( 0.2225( 1 490( 30 0.7( 0.1 1.0( 0.2

ethanol 112( 1 1040( 10 0.7( 0.1325 400 226( 2 430( 40 0.14( 0.02

acetonitrile 113( 1 1040( 20 0.7( 0.1226( 2 510( 20 0.2( 0.1

325 112( 1 1300( 200 0.2( 0.1 -0.2( 0.1no chirp 226( 3 490( 50 0.8( 0.1 -3.3( 0.1

400 325 acetonitrile 112( 1 1000( 200 0.8( 0.1 -0.3( 0.02+ chirp 225( 2 600( 50 0.2( 0.1 -1.4( 0.2325 112( 1 1100( 100 0.6( 0.1 2.5( 0.3- chirp 226( 2 470( 50 0.4( 0.1 2.4( 0.3

ethanol 112( 1 1030( 30 0.7( 0.1 1.1( 0.1400 400 225( 1 480( 100 0.2( 0.1 1.2( 0.2

acetonitrile 112( 1 1100( 50 0.6( 0.1 1.0( 0.2225( 2 360( 50 0.4( 0.1 1.1( 0.2

ethanol 111( 3 1100( 100 0.1( 0.1 0.0( 0.2400/400 400 226( 1 480( 50 0.6( 0.1 0.9( 0.2

acetonitrile 113( 2 1040( 60 0.1( 0.1 1.9( 0.2226( 2 410( 50 0.9( 0.1 0.6( 0.2

TABLE 2: Filter-Diagonalization Fit to the AntisymmetricStretch Frequency and Combination Band

pump[nm]

probe[nm]

solvent frequencyω[cm-1]

decayτ[fs]

amplitude|d|

364H 400 ethanol 142( 5 720( 70 0.15( 0.02325 325 ethanol 148( 5 650( 300 0.13( 0.07400 325 ethanol 147( 2 670( 50 0.08( 0.03400 325 ethanol 263( 2 364( 50 0.1( 0.03400 325C ethanol 144( 2 680( 50 0.11( 0.03400 325C ethanol 253( 2 870( 50 0.11( 0.03400/400 400 ethanol 143( 3 700( 100 0.12( 0.03400/400 400 ethanol 255( 3 350( 100 0.2( 0.03

Ground Surface Dynamics of I3- J. Phys. Chem. A, Vol. 105, No. 21, 20015091

surface and itsinterferencewith the initial ground-state wavefunction is the main source of control. The basic mechanism ofcoherent control is supplemented by multipulsing which allowsfurther interference pathways.

Many goals have been envisioned for coherent control, fromthe photosynthesis of exotic molecules to precisely timedswitching of currents in mini-scale electronic devices. Here weseek more fundamental insights. On the one hand, to understandhow parameters of the excitation field influence the induceddynamics in the triiodide ground state; on the other hand, toemploy the degrees of control provided by the exploredparameters to learn more about the mechanisms governingvibrational relaxation of triiodide in various solvents.

Impulsive optical excitation, our vehicle of control, is by nomeans a new topic.1,7,9,13,15,57,58However, as demonstrated inthe present study, new insights concerning this process, bothof fundamental and applied importance, are still being uncov-ered. The widespread application of impulsive photoexcitation,with femtosecond lasers in recent years, underlines the impor-tance of understanding its finer details, even in the limited scopeof induced ground state dynamics. Indeed, the material systemsof relevance extend beyond the molecular, identified in theIntroduction. Phonons which dress optical transitions in solids,54

acoustical phonons in nanoclusters,59 charge transfer reactions,60

or photoassociation of cold atoms61 can replace the vibrationalcoordinates in this scenario. Although the frequencies of theinduced coherences may vary widely, the underlying principlesare essentially the same.

One fundamentally significant finding in the present studyis the striking demonstration of the inadequacy of a perturbativeapproach for describing impulsively induced ground statevibrational dynamics and its spectroscopic signature. The lowestpower in field intensity for a ground state variation should bequadratic. Yet, here it was demonstrated that the asymptoticdependence of the momentum change on intensity was linear.Equally significant is the nearly perfect agreement, both in formand in the levels of excitation, between the experiments andthe theoretical approach chosen here. In this study, an alternativeapproach is used to simulate the material response to irradiation,using direct propagation methods of the molecular densitymatrix. A similar approach has recently been suggested forsimulating signals of CARS experiments and of other four-wavemixing spectroscopies.62-65 These points are particularly sig-nificant because many of the alternative theoretical descriptionsdealing with this process are cast in terms of the perturbationtheory, and must therefore be suspected of glossing over thelimitations of this approach as demonstrated in the currentresults.

One of the main sources of insight is the phase space pictureof the dynamical hole. With this tool we are able to rationalizethe control manipulations. Creating a state withC2 symmetryin phase space will completely eliminate the fundamentalfrequency from the signal. Three different techniques weredemonstrated in the case studies to induce such a symmetry.Breaking this symmetry is the agent of control. It can be doneeither in the momentum direction by varying the intensity or inthe coordinate direction by tuning the pump wavelength. Acombination of these two control levers can induce dynamicswith a controlled combination of amplitude and phase of thefirst and second harmonics of the signal. Chirping the pump,which was not demonstrated explicitly, would add the abilityto move in the diagonal direction in phase space. There existother sources of uncontrolled symmetry breaking such asanharmonicity. These can be included or neutralized by the

active control knobs. The symmetry in phase space is also thekey to understanding the probe manipulation. We have elabo-rated on the concept of a window function. The window functioncan be thought of as a shaped porthole limiting the views ofphase space. By constructing a window withC2 symmetryproperties only patterns with such a symmetry are observed inthe signal.

The effects of spectral chirp in the pump and probe pulsesare intriguing. Although up to this point we have related to thisparameter on equal footing with the others tested, in reality,the effects of pump and probe chirp were stumbled over morethan they were intentionally recorded. For 400 pump and 325probe data, we found it hard to reproduce results, until full chirpscans were conducted! This fact, more than any other, exempli-fies just how sensitive the reported results are to slight residualspectral chirp in the pump and probe pulses. In other words,residual chirp which had negligible effects in other wavelengthcombinations strongly influenced the results of these pump probeschemes. In retrospect, this effect can be rationalized and evenused to our advantage in understanding the underlying dynamics.Accordingly, the quantum motion of the induced hole isfollowed in phase space in analogy with the scheme suggestedby Zadoyan et al.32 for following excited state wave packetevolution. Nonetheless, our results serve as a reminder of justhow strongly residual chirp can effect the RISRS signals underspecific conditions when short and therefore broadband pulsesare being employed.

Our results are also illuminating from an applied point ofview. RISRS has been previously used as a spectroscopicmethod, both by ourselves10,18 and by others.6,25,52,59,66-68 Itsnatural aptness for recovering vibrational dynamics of lowfrequency modes stems from the fact that it is a time resolvedmethod. Here we have not only recovered accurate vibrationaldynamics pertaining to first-order coherences but also obtainedsimilar data for one higher harmonic. Furthermore, the pos-sibility of first harmonic suppression by the various methodsdescribed allows the determination of decay dynamics for thesecond harmonic and for weaker bands such as the antisym-metric stretch fundamental in ethanol with much higher preci-sion.

Whereas all of the observed modulations have been ad-equately modeled assuming exponential dephasing, it is impor-tant to point out that any deviations from exponential decays,as in cases of intermediate to slow modulation limits in a Kuboline shape scenario, could be detected using this spectroscopyas well. However, the methods discussed above do not requireany assumptions or functional representations of the prominentfundamental modulation decay in order to implement its veryeffective suppression, allowing reliable and much closer scrutinyof the weaker modulation features. In contrast, an arithmeticsubtraction for achieving the same result would require repre-sentation of the fundamental frequency component, perhaps, asa Lorentzian peak in frequency, or an exponentially decayingoscillation in time. Although it might fit the real feature verywell near its center, it could equally deviate substantially onthe wings distorting the structure of the low intensity featureswhose extraction was the objective in the first place. This is aunique capability of impulsive Raman, and no counterpart existsfor equivalent frequency domain spectroscopies. Accordingly,it might find applications even in cases where the inherent timeresolution of this method is of no consequence.

The triiodide ion is a prime example for the utility of RISRSas an applied spectroscopic method. Above, the informationprovided by this spectroscopy concerning the ground state

5092 J. Phys. Chem. A, Vol. 105, No. 21, 2001 Gershgoren et al.

vibrational dynamics of I3- in solution has been outlined. Otherspectroscopic methods that provide similar relaxation parametersare the resonance Raman and CARS methods. The later isirrelevant in the triiodide case, because the dephasing times andthe vibrational period are of the same order of magnitude.Resonance Raman spectra of triiodide have been collected andanalyzed by Myers and co-workers.23,24,69 However, the linewidths which best fit the data are nearly two times broader thanpredicted by the dephasing times extracted from our data. Apriori this discrepancy does not necessarily identify whichmethod is providing the more accurate result. However, thedephasing times measured match up favorably with line widthsappearing in preresonant Raman spectra. An exception in theRISRS data was found when the pump and probe werepositioned at the peak of the absorption band the first harmonicwas found to decay more rapidly. This may indicate a possiblesensitivity of the decay time to the shape of the dynamical hole.Further investigation in this direction is in progress. In view ofthe close agreement of our data with the preresonant Ramanline widths, we conclude that it provides a more precise measureof ground-state vibrational dynamics of fundamentals and higherharmonics of I3-.

Along with the advantages elaborated upon above, the RISRStechnique also suffers from substantial limitations. As in thecase of resonance Raman spectroscopy, spectral interferencefrom long-lived excited state populations can mask the groundstate dynamics, or at least superimpose spectral modulationsfrom ground state coherences with others related to wave packetmotions in the excited state.78,79 Even in the I3- case, wheredissociation rapidly dissipates the excited-state density, thereexists the possibility of interference from spectral modulationsin the I2- product, because of its UV absorption band which iscentered at∼364 nm in relaxed diiodide. To test this possibility,we duplicated a number of experiments which were originallyconducted using the lower excited state (λmax ) 364 nm), onthe intense absorption band centered at 292 nm. The lack ofsignificant differences in the results proves that contribution tothe signal from chemical modulations caused by coherentvibrations of the product I2

-, which partly overlaps the lowerabsorption band, are absent.

The analysis of the RISRS signals corroborates previousmeasurements of the fundamental frequencies of I3

- in thesolvents tested.10,23,24,70-72 Compared to isolated gas-phase I3

-,very small solvent shifts are observed for the symmetric stretchmode.66 The measured frequencies agree very well with ab initiocalculations on isolated50 I3

-, which again indicates smallsolvent shifts. The weak influence of the solvent is remarkablein view of the strong interactions existing between the negativelycharged molecular ion and the surrounding solvent. The centralfrequencies of the electronic transitions are also negligiblyinfluenced by solvation. Indeed a recent study by Choi et al.22

shows that the central frequencies in the gas phase are identicalto the ones in polar solvents.

The results related above not only scrutinize the process ofimpulsive excitation itself but reveal the mechanisms ofvibrational relaxation active in the triiodide ground state. In aprevious RISRS study of I3

- in cooled ethanol solutions,dephasing dynamics were analyzed using the Kubo line shapetheory.73-75 To do so, the dephasing contribution made bypopulation relaxation is estimated. In ethanol solutions, bothour own results76 and those of others77 demonstrated thatT1(vib) for the symmetric stretch at low excess vibrationalenergies is between 3 and 4 ps at room temperature, and remainsin that range all of the way down to 100 K. A similar time

scale was also found for acetonitrile solutions at room temper-ature. Given these values for the rate of population relaxation,and that 1/T2 ) 1/T2

/ + 1/2T1(vib), with T2/ representing the

pure dephasing time, we find that theT1 process makes only aminor contribution to the dephasing of the symmetric stretchingmode of I3- in either solvent. Thus, pure dephasing must bethe primary mechanism leading to the loss of coherence in thismode of vibration.

As stated above, an exponential model fits the dephasingdynamics of both the fundamental and the second harmonic ofthe symmetric stretching motions observed in ethanol andacetonitrile. The second harmonic decays about 2.3 times fasterthan the fundamental. Within the Kubo line shape formalism,the exponential dephasing dynamics indicates that the mediuminduced spectral modulations are in the fast modulation limit.Accordingly, the inverse spread of momentary frequencies,1/∆ω, must be substantially longer than the time scale forstochastic changes of the frequencyτc. In terms of theseparameters, Kubo line shape theory80 provides the followingvalue of the dephasing time of the fundamental-T2

/ )1/(∆ω2τc). The same stochastic frequency fluctuations whichgive rise to dephasing of the fundamental must also be thosewhich kill the phase memory in the second harmonic as well;thus, τc is identical for both. In contrast, the spread of thefrequencies for the second harmonic is twice as broad, andwithin this framework, it is expected that the dephasing timefor the second harmonic would be four times as rapid. Withinthis analysis, a subquadraticν dependence of dephasing timesis possible, but only in the intermediate to slow modulationregimes, where the phase memory is markedly nonexponential,contrary to our result.

Nonquadraticν dependence of dephasing rates such as thatobserved here is not limited to the triiodide ion and has beenobserved using other methods in a variety of molecular systemsin solution.81 These observations have led to active recenttheoretical debate concerning the underlying mechanisms fordephasing.80

The exponential decay of the signals suggests that a semi-group memoryless approach is sufficient to describe theobservations. In the past, a quantum Gaussian semigroup modelhas been used to describe the dephasing.10 The model is analternative description of the fast modulation limit of the Kuboline shape theory where the dephasing is caused by fast andabundant frequency modulation induced by the solvent. TheGaussian semigroup model also predicts quadraticν dependencewhich is inconsistent with the observations. Latter we havesuggested an alternative Poisson dephasing mechanism,15 whichcarries the view of isolated abrupt disruptions to the vibrationaldynamics. If the disruption causes a large phase shift, the modelcan explain subquadraticν dependence. This viewpoint isconsistent with a recent study by Yamaguchi, who suggesteddescribing the dephasing dynamics by a binary collision model.82

The model originated in describing gas phase dephasing causedby isolated elastic collisions from other gas particles.83 The basicassumption is that each collision event is random and uncor-related; therefore, the process is the quantum analogue of aPoisson process.84 Yamagauchi applies the model to thecondensed phase environment on the basis of an analysis of alarge set of data from different molecules and solvents showingthat subquadraticν dependence is quite universal. A directsimulation for the dissipative dynamics of the I3

- system bysolving the Liouville von Neumann equation with a Poissondephasing model is in progress. We are currently investigatingthe appropriate model for describing the dephasing dynamics

Ground Surface Dynamics of I3- J. Phys. Chem. A, Vol. 105, No. 21, 20015093

of I3- by measuring the decay of high harmonics at reduced

temperatures. Thus, finally our combined efforts in experimentand theory have come full cycle: starting out to characterizeelementary light induced processes and ultimately opening thedoor for appreciating fundamental aspect of vibrational dephas-ing dynamics in polar solvents.

VII. Conclusions

The comprehensive study of the RISRS process for the I3-

molecular ion has resulted in a wealth of insight into elementarylight-matter interactions in condensed phases. The main pointsare highlighted as follows:

(1) Experimental demonstration of coherent control of ground-state dynamics which enables suppression of the fundamentalcomponent or control of the amplitude and phase of the firstand second harmonic components in the transient signal.

(2) Theoretical analysis in phase space, in particular theidentification of the importance ofC2 symmetry of the densityin phase space is able to rationalize the control manipulations.

(3) Experimental sensitivity to intensity and chirp necessitatea theoretical foundation which goes beyond perturbation theory.The nonperturbative coordinate dependent two-level systemsupplies a conceptual picture verified by experiment andsimulation.

(4) The suppression of the first harmonic provides for thefirst time an accurate measure of dephasing dynamics for thesecond harmonic symmetric stretching and other weak spectralfeatures in I3-.

(5) The dynamics and decay times of dephasing for the firstand second symmetric stretching harmonics contradict thepredictions of Kubo line shape theory. This is significant notonly because it points to shortcomings of a formalism which iswidely accepted for describing vibrational phase relaxation butalso because similar cumulant expansions of correlation func-tions are fundamental components in universally acceptedframeworks for analysis of nonlinear optical spectroscopies.

Our accumulated knowledge concerning the I3- reactant in

solution, has been a crucial ingredient in appreciating thecapabilities of the RISRS technique as a useful alternative tofrequency domain vibrational spectroscopies. It has served todemonstrate that this molecule is taking its place as a valuablemodel liquid-phase reactive system.

Acknowledgment. We thank H. C. Kapteyn, M. Murnane,R. M. Hochstrasser and K. Wynne, for helpful suggestionsconcerning the laser system. E. Mastov has given valuabletechnical assistance. We thank D. Neuhauser and V. Mandelsh-tam for helping to implement the filter diagonalization analysis.We thank D. Neumark for fruitful discussions and the sharingof unpublished data. This research was supported by the IsraelScience Foundation (Moked) administered by the Israel Acad-emy of Science. The Fritz Haber and Farkas Research Centersare supported by the Minerva Gesellschaft fu¨r die Forschung,GmbH Munchen, FRG.

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1996, 258, 523.(67) Zanni, M. T.; Taylor, Greenblatt, B. J.; Soep, B.; Neumark, D. M.

J. Chem. Phys.1996, 107, 7613.(68) Rosca, F. A. T.; Kumar, N.; Ye, X.; Sjodin, T.; Demidov, A. A.;

Champion, P. M.J. Phys. Chem.2000, A 104, 4280.(69) Ashkenazi, G.; Kosloff, R.; Ruhman, S.; Tal-Ezer, H.J. Chem.

Phys.1995, 103, 10005.(70) Kiefer, W.; Bernstein, H. J.Chem. Phys. Lett.1972, 16, 5.(71) Kaya, K.; Mikami, N.; Ito, M.Chem. Phys. Lett.1972, 16, 151.(72) Zanni, M. T.; Davis, A. V.; Frischkom, C.; Elhanine, M.; Neumark,

D. M. J. Chem. Phys.2000, 112, 88847.(73) Kubo, R.Math J. Phys.1963, 4, 174.

(74) Oxtoby, D. W.AdV. Chem. Phys.1979, 40, 1.(75) Wang, Z. H.; Wasserman, T.; Gershgoren, F.; Ruhman, S.J. Mol.

Liq. 2000, 86, 229.(76) Wang, Z.; Wasserman, T.; Gershgoren, E.; Vala, J.; Kosloff, R.;

Ruhman, S.Chem. Phys. Lett.1999, 313, 155-161.(77) Hess, S. S.; Bursing, H. H.; Vo¨hringer, P.J. Chem. Phys.1999,

111, 5461.(78) Scherer, N. F.; Jonas, D. M.; Fleming, G. R.J. Chem. Phys.1993,

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Weidenmann, E.; Gerber, G.J. Phys. Chem.1991, 95, 8103.(80) Gayathri, N.; Bagchi, B.Phys. ReV. Lett. 1999, 82, 4851.(81) Tominaga, K.; Yoshihara, K.J. Phys. Chem.1998, A 102, 4222.(82) Yamaguchi, T.J. Chem. Phys.2000, 112, 8530.(83) Levine, R. D.Quantum mechanics of molecular rate processes;

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Ground Surface Dynamics of I3- J. Phys. Chem. A, Vol. 105, No. 21, 20015095

CHAPTER IV

Caging and Geminate Recombination following Photolysisof Triiodide in Solution.

51

Caging and Geminate Recombination following Photolysis of Triiodide in Solution

Erez Gershgoren, Uri Banin, and Sanford Ruhman*

Department of Physical Chemistry, and the Farkas Center for Light Induced Processes,The Hebrew UniVersity, Jerusalem 91904, Israel

ReceiVed: July 2, 1997; In Final Form: September 24, 1997X

A survey of caging and geminate recombination dynamics following the UV photolysis of I3- in a series of

polar solvents is presented. Transient absorption in both the near-IR and UV was measured out to delays of0.4 ns, probing evolution of the nascent product and recombined reactants, respectively. The fate of photolysisfragments is suggested to be determined shortly after the act of bond fission. Kinetic analysis shows cagedfragments either recombine directly and vibrationally relax within a few picoseconds or produce long-livedcomplexes of unknown structure that decay exponentially in∼40 ps, and both routes lead to ground-stateI3-. The persistent complex exhibits a near-IR absorption spectrum that is broadened and red-shifted relativeto free I2-. A very shallow and slow residual component of recombination may be associated with encountersof geminate pairs that initially escape the solvent cage. The choice of solvent strongly effects the probabilityand dynamics of caging, but not the decay rate of complex caged pairs. This is not altered by varying thetemperature of an isobutyl alcohol solution from 5 to 45°C. The results are discussed in an effort to illuminatethe role played by the solvent in triiodide recombination in solution.

I. Introduction

Geminate recombination of photolysis fragments in condensedphases is the subject of active theoretical and experimental study.The driving force for this scrutiny stems from this processesfundamental nature, the accumulating efforts already investedin its elucidation, and the importance of solvent caging as amajor limiting factor of practical photochemical transformation.Early efforts at representing this process are based upondiffusion-limited descriptions1-3 and despite their tenure havenot lost their intuitive appeal.4,5 More recent real time studiesof small molecule photolysis show that mutual diffusion ofseparated fragments is only a secondary route to solvent-inducedgeminate recombination.In molecular liquids iodine predissociation plays an active

role in the dephasing of impulsively excited coherent B statewave packets,6-8 and subsequent recombination onto variousbound potential surfaces takes place within less than 2 ps.9

Dynamical models used to explain these results show that mostgeminate recombination takes place within the confines of theinitial solvent cage and not by cage escape followed by diffusiveencounters in the solvent. The nonadiabatic processes that allowthese transitions have been further scrutinized through spectro-scopic probing of iodine photophysics in rare gas solids.10-12

Similar experiments in high-density rare gas fluids againhighlight the prominent and distinct part played by direct cagereformation of the reactants.13

For I2- in polar liquids, despite marked differences in therange and intensity of solute-solvent forces, the act ofrecombination and loss of excess vibrational energy followingphotodissociation are also extremely rapid. Experiments bothin gas-phase clusters and in solution show that curve crossingto the ground state and most of the vibrational relaxation are

achieved by the recombining molecules very rapidly, and inliquid solutions this takes place in a fraction of a picosecond.14-19

The residual separated population in solutions persists for theduration of the experiments, with no convincing indication ofa diffusive recombination component. Thus in both systems,despite their differences, cage-induced repopulation of theground state is not separated in time scale from the bond fissionitself, rendering both a single unified dynamic process.The photodissociation of triiodide and more recently I2Br-

has been studied by impulsive femtosecond laser photolysis ina variety of polar molecular solvents20-24

All studies conducted in our lab involved photoexcitation oftriiodide ions at 308 nm, just to the red of the more energeticand intense near-UV band centered at∼295 nm. The strongnear-IR spectrum of the diiodide has been used to follow theemerging fragment ions, while probing at the excitationfrequency mapped out dynamical changes in the I3

- remainingin the ground state.Reports have focused on the dynamics of bond fission and

the generation of coherently vibrating diiodide molecularfragments. Spectral modulations in the near-IR transienttransmission signals indicate that the compact coherence inducedby the impulsive photoexcitation transcends bond fission andevolves continuously into compact coherent motion in theproduct. This finding was supported by quantum and classicalMD simulations that demonstrate how preservation of phasecoherent nuclear motions throughout dissociation might takeplace, despite the presence of solvent surrounding the reactingmolecule.25-27 Simulations were conducted employing a LEPSform reactive potential that was not the result of detailedcalculation of electronic structure, and in particular, no routesX Abstract published inAdVance ACS Abstracts,December 1, 1997.

I3- + hν f I2

•- + I•

9J. Phys. Chem. A1998,102,9-16

S1089-5639(97)02138-5 CCC: $15.00 © 1998 American Chemical SocietyPublished on Web 01/01/1998

for nonadiabatic relaxation back to the ground state wereconsidered. Recently, the role of symmetry breaking inpreservation of coherence in photofragment vibrational motionhas also been addressed, by comparing the triiodide reactiondynamics with those of asymmetric I2Br-.24

Nonetheless, experimental probing at longer delays did showobvious signs of solvent-dependent geminate recombinationfollowing trihalide photolysis.21 Nonexponential multiphasedregeneration of reactant absorption along with a concurrentdisappearance of product OD was the key observation. Theabsorption kinetics were followed for less than 100 ps.While delayed recombination mechanisms were not deter-

mined, possible recombination routes were considered.21,22,25

Since I3- is routinely synthesized by reacting I- with I2, it isplausible that geometrical or energetic restrictions might limitthe rate of recombination from the I2

-/I channel. Furthermore,the excess photon energy suffices for producing either of thefragments in low-lying excited electronic states.18 Therefore,electronic relaxation or electron transfer might be required toopen the way to recombination, and such pairs would constituteseparate kinetic routes to the ground state.More recently, an ultrafast laser study of triiodide photolysis

and geminate recombination dynamics was conducted withsuperior time resolution, exciting into the lower of the near-UV bands with∼395 nm excitation pulses.28 At this wave-length both relaxed I2- and I3- absorb considerably, makingprobing at that frequency of limited utility in covering theprocess of recombination. I3

- kinetics were reconstructeddirectly from the IR data. Despite the close resemblance torecombination results following excitation with 308 nm pulses,it has been interpreted in a very different light, in terms of adiffusion-limited geminate recombination model, producingkinetics with stretched exponential appearance. Absorptionkinetics were covered only for a limited delay range.The present study is intended to broaden our understanding

of the mechanisms underlying triiodide caging and recombina-tion following 308 nm photolysis, by recording pump-probedata with high time resolution, extending out to long probedelays, including measurement of signal dependence uponvariation of solvent and its temperature. Given a conceptualframework whereby the crucial electronic and vibrationalrelaxations redirecting excited density back to the bound statesof the reactant take place hand in hand with the process of bondfission, it is impossible to comprehend one without the other.Therefore, a full understanding of the generation of phasecoherent motion in fragments due to impulsive photodissociationof the parent ion requires both processes to be studied as a wholeand incorporated into a refined theoretical model of this reaction.Results reported in this paper demonstrate that the multiple

components of I3- recombination following 308 nm photolysisare most likely due to distinct pathways, none of which isobviously controlled or limited in rate by mutual diffusion ofthe fragments. As in the case of the similar diiodide system,data are interpreted to indicate that most recombining I3

- neverescapes the solvent cage, and the division into recombinant anddissociating populations, which takes place at the initial stagesof dissociation, is strongly dependent upon the nature of thesolvent.The paper is organized as follows: Section II provides a

brief description of the experimental system and methods.Section III is dedicated to a detailed account of the experimentalresults. In section IV these results are discussed, and a simplekinetic model is proposed for their interpretation. Conclusions

of the present study and a summary of remaining undeterminedissues are presented in section V.

II. Experimental Section

The laser system and general methods of sample preparationhave been discussed in detail elsewhere.21 The homemadesynchronously pumped and amplified dye laser system providesa kilohertz train of∼65 fs pulses, centered at 615 nm, containing∼40 µJ of energy. These were used to generate pump pulsesby frequency doubling in1/2 mm of KDP, and probe pulseswere derived either in an identical fashion for UV/UV experi-ments or by white light generation in a sapphire flat followedby interference filtering for visible and near-IR probes. Trans-mission was detected by amplified photodiodes (EG&G UV-4000) and measured with a lock-in amplifier (SRS 530). Allsolvents used were either spectroscopic or HPLC quality, andtriiodide was produced using resublimed iodine crystals andhigh-purity KI.The long scans of probe delay required extra care that results

are free of sample concentration, laser power, and pump-probeoverlap walk-off dependence. Each scan was first run at a pumppower 2-3 times higher than that ultimately used whencollecting data, and linearity of the results with power wasdemonstrated. Trial runs were recorded using solutions nearly10 times more concentrated than those actually employed tocollect data (in a thinner circulating sample cell), and the resultswere virtually superposable with those obtained at lowerconcentrations. Data presented here were collected fromsolutions of∼0.25 mM concentration, with a mild excess ofiodide, which were circulated through a 2 mmcell using aperistaltic pumping station. The UV-vis absorption spectrumof the solutions was monitored both prior to the experimentsand after, with no observable deterioration of the sample in anyof the solutions employed. Flow rates ensured replenishmentof fresh sample for each pulse.Fine alignment of the beams ensured that their transmission

through a 100µm pinhole at the sample position was indepen-dent of the pump-probe delay throughout the range studied.Without this precaution substantial artifactual decays in the dataresulted for delays beyond a few tens of picoseconds. Theexperiments aimed at testing the temperature dependence ofrecombination kinetics in isobutyl alcohol solutions wereconducted by submerging the sealed sample reservoir in acontrolled temperature bath. The temperatures at the cell weredetermined by a thermometer and found to differ by no morethan 2-3 deg from that of the bath.

III. Results

Data obtained for ethanol solutions, which were mostthoroughly studied, will be presented first. A UV transienttransmission scan spanning delays from 0 to 400 ps is depictedin Figure 1. To facilitate the presentation of rapid transmissionchanges taking place at early delay times, an inset of the first8 ps of delay is presented on an expanded time scale. Thepositive going signal here relates negative changes in OD,indicating that photolysis induces a bleach in the triiodideabsorption. The rapid component of decay, which is completein less than 6 ps, is superimposed with periodical oscillationsthat have been reported in detail and stem from impulsiveresonant Raman excitation of the symmetric stretch of thetriiodide ion.28-30 This portion of the data is fit to anexponential decay summed with a damped harmonic oscillation.Following this initial rapid stage of UV bleach recovery, a

continued but slower decrease in transmittance commences

10 J. Phys. Chem. A, Vol. 102, No. 1, 1998 Gershgoren et al.

which takes place in two stages, the first of which is completedin ∼100 ps gives way to a very gradual and shallow decaycomponent. The later portions of transmission decay beyond11 ps are presented along with a fit to a biexponential functionalform

The constants used for this fitting will be discussed in detaillater.Along with UV transmission measurements, transient OD

scans throughout the near-IR were also recorded. Transientabsorption at 700 nm extending up to 400 ps, following UVexcitation att ) 0, is presented in Figure 2. This wavelengthis near the center of the relaxed diiodide band. The inset depictsthe first 2 ps of absorption evolution, exhibiting an initial phaseof absorbance attributed to the dissociative excited state, whichdecays as the bond fission occurs (collected in a 0.2 mm cell

for obtaining high time resolution). The spectral modulationsthat are observed following this stage were the focus of previousstudies and attributed to coherent vibrations of fragment ions.They are superimposed upon an increase of signal associatedwith vibrational relaxation of hot fragment ions and partly toabsorption of cooling recombinant triiodide. At 700 nm thesemodulations are particularly weak since this wavelength is nearthe center of the product band and are more pronounced bothto the red and to the blue.After ∼10 ps, a gradual nonexponential decay in absorbance

commences, which is similar in appearance with that of the laterstages of bleach recovery in the UV. This similarity isdemonstrated in Figure 3, which depicts UV bleach kineticstogether with the decay of 700 nm absorption in adjusted unitsthat achieve normalization of both signals at a 400 ps delay.The signals effectively match each other continuously after aninitial delay of∼10 ps. A similar scan was presented in theinitial report of the ultrafast study of this reaction, as a consistentmeasure of the recombination dynamics of dissociated I3

-. Therationale behind this assertion was that, following an initial stageof solvation and vibrational relaxation, absorption in the near-IR is due solely to I2- radicals, while that in the near-UV isindigenous to the triiodide. Thus, recombination would con-tribute linearly to the disappearance of the first and reappearanceof the later.To investigate this further, a series of transient absorption

scans at various near-IR probing frequencies were collected andare depicted in Figure 4. In the first panel the absorption scansare plotted on a vertical scale that shows the relative intensitiesof absorption at the various wavelengths. The second paneldepicts the same data after arbitrary vertical scaling in order tonormalize all scans to the same intensity at long delay times.From 130 to 400 ps the scans overlap remarkably well. But atearlier times that are yet much later than the duration ofvibrational relaxation, there is no agreement between the variouscurves. The mismatch is systematic, showing larger relativeintensities for the more red-shifted spectral components. Thistrend was also obtained for a less complete series of IR datacollected in isobutyl alcohol solution.In view of the roughly complementary nature of the UV

bleach and IR absorption, and in accordance with a kineticmodel to be outlined in the following section, the IR data inethanol for delays beyond 11 ps were also fit using eq 1 with

Figure 1. Transient transmission scans of triiodide in ethanol solutionwith both UV pump and probe pulses. The inset depicts the first 8 psof probe delays, exhibiting a rapid decay of the initial bleachsuperimposed by impulsive Raman-induced spectral modulations. Seetext for details.

Figure 2. Transient absorption scan at 700 nm following 308 nmphotolysis of triiodide in ethanol solution. The inset shows the first 2ps of probe delay within which spectral modulations due to vibrationalcoherence in photoproducts is observed.

T(t) ) A+ B exp(-t/τ1) + C exp(-t/τ2) (1)

Figure 3. Comparison of bleach kinetics at 308 nm with transientabsorption at 700 nm following triiodide photolysis in ethanol. Bothsignals have virtually the same decay after the initial 10 ps of pump-probe delay.

Photolysis of Triiodide in Solution J. Phys. Chem. A, Vol. 102, No. 1, 199811

the same decay constants that optimally fit the UV/UV data.This portion of the data, on offset and expanded scales, is plottedalong with the fit in Figure 5. As demonstrated, a single pairof constants provides a good rendition of the data at the variousfrequencies.In an effort to further identify the mechanisms for various

stages of trihalide recombination after dissociation, UV trans-mission scans were conducted for triiodide solutions in ethanol,water, acetonitrile, and isobutyl alcohol, also to be augmentedby previous data in methanol and 1-propanol solutions. Resultsare summarized in Figures 6 and 7 for the first four solventsmentioned. Figure 6 presents the earlier portion of the signalsalong with a fit of the modulation to a damped harmonicoscillation riding atop a rapid exponential decay. In the caseof isobutyl alcohol a deviation from exponentiality requiredfitting the underlying decay to a third-order polynomial function.The best fitting parameters are summarized in Table 1.Figure 7 shows similar scans which include delays from 0 to

400 ps for the first four solvents. The vertical scales have beennormalized to rise from 0 to 1 between the signal at negativetimes to the peak of the underlying signal minus the oscillatingcomponent which is associated with the impulsive Raman

mechanism. A number of trends are observable. The initialvery prompt decay of the bleach is most prominent in waterand isobutyl alcohol and weaker in ethanol and acetonitrile. Inall these solutions the decay of the bleach is again wellreproduced by a biexponential decay which does not return tozero, where the smallest absorption recovery is observed foracetonitrile and the highest in water and isobutyl alcohol.The same two decay constants employed for fitting the UV

bleach decay in Figure 1 are employed for delays larger than11 ps, albeit with varying amplitudes, to provide satisfactoryfits to the UV data in Figure 7. The amplitudes of the variouscomponents required for fitting are summarized in Table 2, alongwith the amplitude of the prompt decays required to sum the

Figure 4. Transient absorption at various near-IR wavelengths plottedon two scales. The first frame depicts the scans on a correct relativescale, while the second has normalized all scans to the same intensityat 400 ps.

Figure 5. Demonstration of the quality of fit rendered by an offsetbiexponential described in eq 1 to the near-IR data at various probingwavelengths. All fits employ the same decay constants with varyingrelative amplitudes.

Figure 6. Evolution of the fast component of UV bleach in foursolvents, along with fits that reproduce the decay of the bleach as wellas the periodic modulations. Details of the constants used are sum-marized in Table 1. The bleaches are normalized to the same peakintensity and offset to facilitate their demonstration.

Figure 7. Solvent dependence of the later stages of UV bleach in foursolvents, along with the fit to eq 1 using the same two decay constantsthat best fit near-IR decays in ethanol solutions.

TABLE 1: Fitting Constants for Fast Component

solvent τphase(ps) ω (cm-1) τdecay(ps)

water 0.53 112.5 1.3CH3CN 0.89 114 1.5ethanol 1.2 112 2.6isobutyl alcohola 1.0 112 ∼4aNonexponential decay.

12 J. Phys. Chem. A, Vol. 102, No. 1, 1998 Gershgoren et al.

signal to 1, designated as 1- (A + B + C) ≡ “fast”. Thetable also gives a partial analysis for data not plotted here,obtained in other solvents.Finally, to test the dynamics of geminate recombination in a

single solvent at various temperatures, the UV transmission wasrecorded for a solution of triiodide in isobutyl alcohol attemperatures between 5 and 50°C. Since the results wereexactly superposable with the data in Figure 7 for this solventthroughout this temperature range, data are not presented here.

IV. Discussion

(a) Criteria for Kinetics of Recombination. The goal ofthis study is to follow the process of geminate recombinationfollowing the UV photolysis of I3- in polar solvents. Accord-ingly, data were collected for delays that temporally span thegap between femtosecond studies and earlier conventional flashphotolysis experiments on this system. Analysis of these datamust include a review of the assumptions used previously tointerpret our results, i.e., (1) that near-IR absorption recordedin the data is due solely to free diiodide fragments at all timedelays and (2) that the transient UV absorption at 308 nmmonitors the concentration of relaxed I3

- selectively andquantitatively.In both the red and UV, rapid changes of absorption have all

but leveled off at the far limit of our observation window,indicating that∼0.5 ns is a sufficient delay for covering all thestages of geminate reformation of the reactants. Accordingly,the asymptotic transient IR spectrum must match that of I2

-

from the literature,31-33 which is the sole primary near-IR-absorbing product following nanosecond flash photolysis oftriiodide solutions. For comparison, the data in Figure 4 areemployed to reconstruct the asymptotic absorption spectrum ata delay of 400 ps and displayed along with one from theliterature in Figure 8, showing that the spectra agree well withinerror (determined by repeatability of pump/probe overlappingat different probing frequencies). Thus, the assumption that atthe longest delays covered diiodide remains the sole stable IR-absorbing photofragment to escape geminate recombination isconsistent with the data. Furthermore, in view of the secondpanel in Figure 4, the transient absorption matches that of freeI2- already at a delay of∼150 ps, since all probing frequenciesproduce identical decay kinetics from that delay onward.Now one can apply the conclusion above to test assumption

2, concerning the UV absorption as a quantitative measure ofthe I3- concentration. If the UV absorption at 308 nm is duesolely to the strongly absorbing I3

- throughout the scans,34 theultimate escape probability of nascent I2

-/I fragments can beobtained directly as the ratio of the asymptotic UV OD bleach(proportional to the concentration of nonrecombined triiodideat the end of the geminate reformation) to its initial value. Thiscan be further tested by comparing escape probabilities soobtained with ones measured by nanosecond flash photolysis.Reviewing the data in Figure 7, and the constants in Table

2, lead to an escape probability of nearly 50% in acetonitrile,one of about 33% in ethanol solution, and even smaller yields

in water and in isobutyl alcohol. In a related study, flashphotolysis experiments using 1 ns N2 laser pulses recorded atransient absorption spectrum following the photoexcitation inboth ethanol and acetonitrile.35 From absolute measurement ofthe excitation pulse flux and the instantaneous∆OD atλmax(I2-),the escape probability was measured to be between 40 and 50%in acetonitrile and 30 and 40% in ethanol. In view of the largemargin of error in the nanosecond experiments, the small changein excitation photon energies used for the two experiments isignored. These results agree remarkably well with the valuesderived from the UV transmission data described above. Inlight of this, the assumption that the 308 nm transients serve todirectly monitor relaxed triiodide concentrations will be adopted.Assumption 1 has not yet been verified for all delays, however.

(b) Kinetic Schemes for Recombination.We turn now tounraveling the dynamics at intermediate times. The appearanceof the UV data suggests that distinct temporal phases character-ize the regeneration of the reactants, starting with an ultrashortinitial phase of a few picoseconds, which is attributed to a directrecombination mechanism, the duration of which is stronglysolvent dependent, as demonstrated by the fitting constants inTable 1. Since the duration of this phase must include boththe time required for repopulation of the ground state and theduration of vibrational relaxation, it is not surprising to findthat it is shortest in water and most prolonged in isobutylalcohol. Water should be the most efficient solvent in extractingexcess vibrational energy from highly excited recombinanttriiodide ions, with the heavier alcohols being least effective inthis respect.

As can be observed from Table 1, a similar trend is also foundin rates of dephasing of the vibronic coherences. It is importantto stress that the overall replenishment of the reactant absorptionmust deal with recombination and vibrational relaxation fromvery high-lying vibrational levels of triiodide down to thethermally occupied region of phase space. In contrast, thespectral modulations reflect coherences built up from low-lyingvibronic states of ions that ultimately remain on the groundelectronic surface, as demonstrated in earlier simulations.21,30

As for the nonexponential behavior of bleach decay in the caseof the heavy alcohol, since we are not dealing with a two-levelsystem but rather replenishment from a whole manifold of states,this would be expected to be the rule and not the exception. In

TABLE 2: Amplitudes of F/M/S UV Decay Components

solvent “fast” B C A

water 0.62 0.2 0.0 0.18CH3CN 0.29 0.19 0.084 0.44ethanol 0.34 0.23 0.14 0.27isobutyl alcohol 0.42 0.27 0.04 0.18methanola 0.15

a From earlier study (U. Banin).

Figure 8. Coarse-grained transient spectrum in the IR 400 ps after308 nm excitation of triiodide in ethanol, along with that of diiodidefrom the literature.

Photolysis of Triiodide in Solution J. Phys. Chem. A, Vol. 102, No. 1, 199813

the case of the more rapidly relaxing solvents it is remarkablethat a single exponential does such a good job of fitting thekinetics.The most complex phase of recombination dynamics follows

this initial prompt component, leading up to the asymptotic stageat the latest observation times. The nonexponential reformationkinetics following the initial “direct” phase of recombinationmight be characterized by the simple scheme

Here the geminate recombination which extends beyond thedirect reformation requires diffusive encounters of separatedfragment pairs as described by Kuhne and Vohringer28 and isexpected to produce nonexponential kinetics. According to thisscheme, absorbance changes both in the UV and throughoutthe near-IR would exhibit identical kinetics (including not onlydecay constants but also identical relative amplitudes) since itentails disappearance of one absorbing species solely responsiblefor near-IR absorption, diiodide, and reappearance of anotherexclusively absorbing in the 300-350 nm region, relaxedtriiodide (with a negligible delay effect caused by the vibrationalrelaxation of the most recently recombined reactants). Thisrequirement is obviously violated in the scans depicted in Figure4, where the IR absorption kinetics demonstrate a strongwavelength dependence well beyond the first 20 ps of delay.Furthermore, had a simple diffusive geminate recombination

mechanism been responsible for reconstitution of triiodide, asignificant change in the rate of this process would be expectedupon changing the viscosity of the solvent, either by variationof the solvent altogether or by altering the solutions temperatureas described above. This is not observed and must indicatethat an alternative mechanism underlies the recorded kinetics.A biexponential functional form was initially utilized for

fitting data in both the IR and UV without reference to anyspecific kinetic model. Furthermore, in view of the slowevolution and incomplete coverage of the shallow decay, thesecond exponent (τ2 ) 350 ps) is poorly determined andeffectively provides a very gradual tapering of the data at longdelays. While in practice kinetics produced by diffusion-controlled models can resemble a biexponent over limitedtemporal ranges, the observation that spectral evolution in thenear-IR is limited to the intermediate phase of reformation istelltale, suggesting that in fact the mechanisms leading to thestrong recombination in the 10-100 ps regime is separate anddistinct.The simplest kinetic scheme capable of reproducing the

observed transient transmission kinetics might be constructedas follows:

According to Scheme 2, aside from the directly caged andrecombined reactants, two independent reactive channels exist,one leading to separated I2

- and I radicals and the other toproduce an as yet unidentified intermediate that ultimately re-forms the triiodide reactant on a time scale of a few tens ofpicoseconds. Since all of the recombination processes thatsupersede the direct portion are much slower than vibrational

relaxation of molecular ions in polar solvents, the near-IRspectrum at delays beyond 10 ps will be a superposition of thatof X and that of I2-, weighted by their instantaneous concentra-tions. Furthermore, if the kinetics of each of these channels isreasonably represented as exponential, the transient absorptionwill follow a biexponential decay characterized by the sametwo decay constants, but with changes in the relative amplitudesaccording to the extinction coefficients of X and diiodide atthe specific wavelength. Finally, since both components ofdecay in IR absorption are due to recombination to produceI3-, the same constants will also adequately characterize thekinetics of replenishment in absorbance of the reactant.The above simplistic scheme explains why, despite the fact

that individual scans might be best fit to somewhat variedconstants, we sought out a single combination that producedvery good fits to all the collected data in both the UV and near-IR for ethanol solutions. These were found to be 45 ps forτ1,the intermediate decay associated with X, and 350 ps forτ2,the shallow long-term decay. The fact that these constants alsoadequately describe the kinetics of recombination in othersolvents will be considered later.(c) Dynamics of Recombination, and Possible Identity of

X. Having outlined a kinetic scheme that can reproduce thedata, the identity of X and the dynamics of its generation anddecay remain to be determined. It is useful to compare ourcurrent results with a closely analogous system, the photodis-sociation and geminate recombination of the I2

- ion in similarsolvents.17-19 As stated briefly in the Introduction, Barbara andco-workers found that practically all the caging and recombina-tion take place directly, whereas the residual diffusive portionof geminate recombination contributes mildly to restoration ofthe reactants, giving rise to a shallow tapering of the data after10 ps, in analogy with delays beyond 150 ps in our results.The similarity extends also to the escape probabilities, whichare highest in acetonitrile solutions and smallest in water fordiiodide photolysis as well. Despite the overall similarities, theX component of geminate recombination is not evident in thediiodide photolysis data.The disappearance of X is accompanied by a simultaneous

reappearance of I3- and does not require mass diffusion to takeplace. Had that been the case, no match of time scales wouldbe expected for both the intermediate phase of I3

- bleach decayand that of diiodide absorption. Accordingly, the X componentmust be due to an intermediate that already contains thenecessary components for reconstitution of triiodide in closeproximity. This could be a complex of diiodide and iodine thatis formed through solvent caging but does not directly crossback to the ground potential surface, either because of theelectronic state of the nascent fragments or because of geo-metrical restrictions characteristic of atom-diatom potentials.According to Scheme 2, a simple spectral decomposition can

provide a transient spectrum of X alone. In terms of eq 1 thisis B(λ) and is plotted in Figure 9, which includes the totalabsorption spectrum at a delay of 11 ps, along with thecomponent due to the free diiodide which is subtracted to obtainB(λ). The resulting spectrum is broader and red-shifted withrespect to the I2- absorbance. It would also appear to besomewhat higher in oscillator strength, although the spectralrange is not sufficient in order to determine to what degree thisis true.Pending a definite identification of X, it is useful to outline

possible triatomic complexes that might match the behaviorobserved. The∼4 eV photon energy is enough to create iodinein the J ) 1/2 or 3/2 states, and previous analysis has assumed

SCHEME 1

I3- + hν T I2

•- + I•

SCHEME 2

I3– + hν

[X]

[I3–]* I2

•– I• I3–

I3–

+

14 J. Phys. Chem. A, Vol. 102, No. 1, 1998 Gershgoren et al.

production of that higher in energy. Assuming that bothenergetically allowed spin states are in fact generated, it ispossible that relaxation of I* is required before recombinationcan take place with an adjacent diiodide ion. It is not trivialthat recombination itself following electronic relaxation shouldbe immediate, nor that such a spin flip should be activationless.Solvent relaxation would however have a limited effect uponits rate, possibly explaining the solvent independent decay times.Other possibilities such as electronic relaxation of an excited

diiodide ion or a stage of electron transfer (I2----I f I2---I-)

might be invoked, but at least for the latter of these both atemperature and solvent dependence of the rate would beexpected. As one may observe, the broad spectrum of X mightalso be suspected to stem from solvated electrons generatedpossibly through an ionization process which competes withphotodissociation following 308 nm excitation. This can beruled out since decay of solvated electrons would not be ableto directly generate I3-. Furthermore, the differences inabsorption spectrum and relaxation rates of solvated electronsin the various alcohols studied would be expected to givesignificant kinetic variations between data collected in ethanoland in isobutyl alcohol, which are not observed.36 In both casesthe onset of the biexponentially fit data commences after∼10ps in both the UV and IR probing, whereas the evolution of afree electron spectrum in these two solvents should be verydifferent.But regardless of the identity of X, the fact that this spectral

component is present from the outset of recombination suggestsa dynamical picture that is analogous with that outlined for I2

-

photolysis, whereby almost all solvent caging takes place duringthe initial stages of dissociation. Photoexcitation of the triiodideat 308 nm leads to a rapid stage of bond fission and cagingwhich determines the ultimate destiny of the reactants. In thiscase, due to the structural complexity of the products, geminatelycaged fragments do not all recombine directly but bifurcate intotwo populations: those which cross over to the ground statedirectly and the X population that creates a long-lived inter-mediate within the cage, which requires longer delays to crossover to the reactant ground state. Thus, the two populationstogether are the counterparts in this process of the directrecombination component in diiodide photodissociation. Fi-nally, the fact that the X absorption was not observed by Kuhneet al. may be due to the fact that there is a fundamentaldifference in the dynamics of triiodide dissociation when

excitation is conducted at 390 nm and not 308 nm, especiallyin light of our speculation that this species might result fromcaging of electronically excited nascent fragments in stateswhich might not be accessible to the less energetic reactants.To clear up these uncertainties, an ongoing Raman study of theevolving X/I2- is underway, as well as a study of reformationdynamics at various excitation photon energies and recombina-tion of triiodide in highly viscous organic solvents.(d) Solvent Effects. In view of the above scenario, it is

worthwhile to consider the source of the strong solvent effectson this process. The effect of solvent on the vibrationalrelaxation of recombined triiodide and dephasing of the ground-state coherence which is observed during the fast portion ofthe regeneration of relaxed reactants has already been discussed.But one also observes that the solvent influences the overallescape probability and the relative amplitudes of the “fast” andX recombination components, as well as that of the residualslow taper.Within the series of alcohols studied (methanol, ethanol,

propanol, isobutyl alcohol) the escape probability decreases withan increase in size of the alcohol monomers. A similar effecthas been reported for the capabilities of rare gas atoms to cagedissociating iodine molecules in clusters and fluid solutions.5,13,17

One possible explanation for this is that the mass of the solventmolecule is instrumental in changing the momentum of separat-ing fragments in solutionswith the larger solvent being moreeffective at forcing a massive iodine fragment to crash backinto its geminate partner. This however does not carry over tothe case of water as solvent, possibly because of an increasedeffective mass for water due to its hypernetted character. Thebehavior in acetonitrile solutions, where the solvent moleculeis also of smaller mass, does agree qualitatively with this trend.Yet none of these considerations can explain the substantial

differences in the partitioning of the recombinant populationinto the three components. Even though the escape probabilityis identical for water and isobutyl alcohol, the direct or “fast”component in water is more the 40% higher than in the largeralcohol. These differences must stem from solvent variationsof the reaction dynamics during the act of bond fission and curvecrossings at the early stages of photolysis. Until more precisepotentials are available for this system it will be difficult tomake sense of these numbers.The solvent is known to effect other aspects of the reaction

dynamics. In a Raman study of triiodide ions in polar solvents,Johnson et al. have demonstrated that the choice of solventeffects the degree of centrosymmetry of I3

-, leading to almostperfect symmetry in acetonitrile and a fluctional displacementalong the asymmetric stretch in ethanol solutions.38 Thisbreaking of symmetry is most likely the cause of the variationin the depth of the Raman excited spectral modulations observedin Figure 6, which are most pronounced in acetonitrile. Thesolvent-induced symmetry breaking was also demonstrated toeffect the degree of compact coherence in the nascent I2

-

fragments following impulsive photolysis in this laboratory.24

It is possible that this same mechanism is responsible for alteringthe relative contributions of the various recombination routes.

V. Conclusions

The caging and geminate recombination dynamics followingthe 308 nm photolysis of I3- in a series of polar solvents hasbeen presented. The time resolution used has been ample toobserve three temporal phases of reactant reformation, charac-terized by time scales of∼2 ps, 45 ps, and one very long and

Figure 9. Coarse-grained spectrum of the X component in the range700-1000 nm, from a spectral decomposition according to Scheme 2.See text for details.

Photolysis of Triiodide in Solution J. Phys. Chem. A, Vol. 102, No. 1, 199815

shallow component>350 ps in duration. The span of delaytimes studies has been shown to close the gap betweenfemtosecond experiments and nanosecond studies of this reac-tion. The three components of geminate recombination aredemonstrated to arise from independent kinetic pathways. Thefate of photolysis fragments is interpreted to be determinedshortly after the act of bond fission. According to a simplekinetic model used to analyze the data, caged fragments eitherrecombine directly and vibrationally relax within a few pico-seconds or produce long-lived complexes of unknown structure,which we have coined X in our discussion and which give riseto the∼40 ps component which decays exponentially. All threeroutes lead to ground-state I3

-.The persistent complex exhibits a near-IR absorption spectrum

that is broadened and red-shifted relative to free I2-. The

extremely shallow and slow residual component of recombina-tion may be associated with encounters of geminate pairs thatinitially escape the solvent cage. Finally, choice of solventstrongly effects the probability and dynamics of caging, but notthe rate of the decay of the complex caged pairs. This is notaltered by varying the temperature of an isobutyl alcohol solutionfrom 5 to 45 °C. The efficiency of caging in the varioussolvents suggests that the mass of solvent molecules may governthe probability of geminate recombination. Further experimentswill be required for a definite identification of the X intermediateand to explain why it produces ground-state triiodide with arate that is insensitive to both solvent viscosity and temperature.In any case, the existence of such an intermediate will needconsideration in the continued 308 nm study of trihalidephotochemistry on the ultrafast time scale.

Acknowledgment. We are indebted to Prof. Ronnie Kosloff,Prof. Noam Agmon, Mr. Guy Ashkenazi, Prof. P. F. Barbara,and Dr. P. K. Walhout for fruitful discussions and Prof. AnneB. Myers for sharing results prior to publication. We thank Dr.E. Mastov for technical assistance. This work was supportedby the Israel Science Foundation. The Farkas Center is supportedby the Bundesministerium fur die Forschung and the MinervaGesellschaft fur die Forschung.

References and Notes

(1) Rabinovitch, E.; Wood, W. C.Trans. Faraday Soc. 1936, 32, 546.(2) Noyes, R. M.Prog. React. Kinet.1950, 1, 547.(3) Otto, B.; Schroeder, J.; Troe, J.J. Chem. Phys.1981, 81, 202.(4) Bultmann, T.; Ernsting, N. P.J. Phys. Chem.1996,100, 19417.

(5) Lienau, C.; Zewail, A. H.J. Phys. Chem.1996,100, 18629.(6) Scherer, N. F.; Ziegler, L. D.; Fleming, G. R.J. Chem. Phys. 1992,

96, 5544.(7) Scherer, N. F.; Jonas, D. M.; Fleming, G. R.J. Chem. Phys. 1993,

99, 153.(8) Ben Nun, M.; Levine, R. D.; Fleming, G. R.J. Chem. Phys. 1996,

105, 3035.(9) Harris, A. L.; Brown, J. K.; Harris, C. B.Annu. ReV. Chem. Phys.

1988, 39, 341.(10) Zadoyan, R.; Li, Z.; Ashjian, P.; Martens, C. C.; Apkarian, V. A.

Chem. Phys. Lett.1994, 218, 504.(11) Zadoyan, R.; Sterling, M.; Apkarian, V. A.J. Chem. Soc., Faraday

Trans.1996, 92, 1821.(12) Batista, V. S.; Coker, D. F.J. Chem. Phys. 1996, 105, 4033.(13) Materny, A.; Lienau, C.; Zewail, A. H.J. Phys. Chem.1996,100,

18650.(14) Papanikolas, J. M.; Vorsa, V.; Nadal, M. E.; Campagnola, P. J.;

Lineberger, W. C.J. Chem. Phys. 1992, 97, 7002.(15) Perera, L.; Amar, F.J. Chem. Phys. 1989, 90, 7354.(16) Papanikolas, J. M.; Maslen, P. E.; Parson,J. Chem. Phys. 1995,

102, 2452.(17) Alfano, J. C.; Kimura, Y.; Walhout, P. K.; Barbara, P. F.Chem.

Phys. 1993, 175, 147.(18) Walhout, P. K.; Alfano, J. C.; Thakur, K. A. M.; Barbara, P. F.J.

Phys. Chem.1995,99, 7568.(19) Benjamin, I.; Barbara, P. F.; Gertner, B. J.; Hynes, J. T.J. Phys.

Chem.1995,99, 7557.(20) Banin, U.; Waldman, A.; Ruhman, S.J. Chem. Phys.1992, 96,

2416.(21) Banin, U.; Ruhman, S.J. Chem. Phys.1993, 98, 4391.(22) Banin, U.; Kosloff, R.; Ruhman, S.Isr. J. Chem.1993, 33, 141.(23) Banin, U.; Kosloff, R.; Ruhman, S.Chem. Phys.1994, 183, 289.(24) Gershgoren, E.; Gordon, E.; Ruhman, S.J. Chem. Phys.1997, 106,

4806.(25) Benjamin, I.; Banin U.; Ruhman, S.J. Chem. Phys.1993, 98, 8337.(26) Ashkenazi, G.; Kosloff, R.; Ruhman, S.; Tal-Ezer, H.J. Chem.

Phys.1995, 103, 5547.(27) Ashkenazi, G.; Banin, U.; Bartana, A.; Kosloff, R.; Ruhman, S.

AdV. Chem. Phys.1997, 100, 229.(28) Kuhne, T.; Vohringer, P.J. Chem. Phys.1996, 105, 10788.(29) Chesnoy, J.; Mokhtari, A.Phys. ReV. A 1988, 38, 3566.(30) Banin, U.; Bartana, A.; Ruhman, S.; Kosloff, R.J. Chem. Phys.

1994, 101, 8461.(31) Fournier De Violet, P.; Bonneau, R.; Joussot-Dubien, J.Chem. Phys.

Lett. 1974, 28, 569.(32) Kliner, D. A. V.; Alfano, J. C.; Barbara, P. F.J. Chem. Phys.1993,

98, 5375.(33) Baxendale, J. H.; Sharpe, P.; Ward, M. D.Int. J. Radiat. Phys.

Chem.1975, 7, 587.(34) Kaya, K.; Mikami, M.; Udagawa, Y.; Ito, M.Chem. Phys. Lett.

1972, 16, 151.(35) Gordon, E. M.Sc. Thesis, Jerusalem, 1997.(36) Kenney-Wallace, G. A.AdV. Chem. Phys.1981, 47, 535.(37) Wan, C.; Gupta, M.; Baskin, J. S.; Kim, Z. H.; Zewail, A. H.J.

Chem. Phys.1997, 106, 4353.(38) Johnson, A. E.; Myers, A. B.J. Phys. Chem.. 1996, 100, 7778.

16 J. Phys. Chem. A, Vol. 102, No. 1, 1998 Gershgoren et al.

CHAPTER V

Investigating pure vibrational dephasing of I−3

in solution;Temperature dependence of T

∗2

for the fundamental andfirst harmonic of υ1.

52

JOURNAL OF CHEMICAL PHYSICS VOLUME 118, NUMBER 8 22 FEBRUARY 2003

Investigating pure vibrational dephasing of I 3À in solution: Temperature

dependence of T2* for the fundamental and first harmonic of n1

Erez Gershgoren, Zhaohui Wang, and Sanford Ruhmana)

Department of Physical Chemistry and the Farkas Center for Light Induced Processes,The Hebrew University, Jerusalem 91904, Israel

Jiri Vala and Ronnie Kosloffa)

Department of Physical Chemistry, and The Fritz Haber Center for Chemical Dynamics, The HebrewUniversity, Jerusalem 91904, Israel University, 91904, Israel

~Received 2 August 2002; accepted 27 November 2002!

Pure n1 vibrational dephasing of triiodide is recorded in ethanol and methyl-tetrahydrofuranesolutions from 300 to 100 K, for the vibrational fundamental and its first overtone. Using impulsiveRaman spectroscopy, dephasing is demonstrated to be homogeneous throughout the temperaturerange studied. Independent measures ofT1 prove that population relaxation contributes negligiblyto the dephasing rates. The reduction in temperature gradually leads to a;2-fold decrease in the rateof pure dephasing. With cooling the ratio ofT2(n51)* /T2(n52)* reduces slightly but remains in therange of 2.7 to 2. These results are discussed in terms of Kubo lineshape and Poisson dephasingtheories. Neither of these consistently explains the experimental observations assuming reasonableintensities and rates of intermolecular encounters in the solutions. ©2003 American Institute ofPhysics. @DOI: 10.1063/1.1539844#

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I. INTRODUCTION

Vibrational relaxation is a subject of both practical aconceptual importance. It is the key to vital stages of checal reactivity, such as thermal activation of transitions btween stable ground state molecular structures, and thesequent dispersal of excess energy and stabilization ofreactants.1 Conceptually, it provides a critical testing grounfor theoretical models for intermolecular interactions in codensed phases.2 Accordingly, IR and Raman lineshapes,3 aswell as ultrafast laser spectroscopy,4,5 have been applied torecord vibrational energy and phase relaxation of molecsolutes. Even in the limited context of relaxation involvinthe lowest rungs of a vibrational ladder, analysis of expemental results can prove challenging. To begin with, eneand phase relaxation are intertwined, through the wknown relation

1/T251/2T111/T2* , ~1!

where T2 and T2* represent observed and pure dephastimes, respectively, andT1 is the inverse rate of populatiodecay. It is therefore almost always necessary to investiboth processes in order to delineate the various contributto the linewidth or equivalently to the dephasing time whmeasured directly.

In liquids, pure dephasing often dominates the decayvibrational coherence. It is almost universally describedterms of a stochastic model, assuming that solvent-indushifts in the vibrational frequencyvv cause the oscillators tolose step with each other. The distribution of local solvearrangements is envisioned to generate a Gaussian spre

a!Authors to whom correspondence should be addressed. Electronicsandy@fh.huji.ac.il

3660021-9606/2003/118(8)/3660/8/$20.00

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instantaneous frequencies, characterized by a rms width oD.The solvent motions induce spectral diffusion that effectivrandomizes the oscillator frequency on a characteristic aage time scaletc . After assuming that the spectral modultion is a Gaussian process, the results of the analysis arfollows: When the spectral diffusion is much slower than 1D(Dtc@1), the coherence decay is Gaussian, dictatedstatic inhomogeneous broadening according to Eq.~2!,

^Q~ t !Q~0!&;exp~2t2D2/2! ~2!

~whereQ is the displacement coordinate!. At the other ex-treme, whenDtc!1, extensive spectral diffusion is going obefore the phase is washed out, the vibrational coherewill be erased exponentially~Lorentzian lineshape!, accord-ing to

^Q~ t !Q~0!&;exp~2D2t tc!. ~3!

This is the ‘‘motional narrowing,’’ or ‘‘fast modulation’’ limitof the model, originally formulated by Kubo6 to explainmagnetic resonance data, and later adapted to vibrationalaxation by Oxtoby.2 In the midrange between the two,hybrid dynamics of dephasing is predicted starting oGaussian, and reverting to an exponential tail at londelays.7 When the autocorrelation of the frequency is asumed to decay exponentially (Cv;e2t/tc), this range canbe described analytically:

^Q~ t !Q~ t !&5exp$2D2@tc2~e2t/tc21!1ttc#%, ~4!

consistently breaching the limits of inhomogeneous andmogeneous broadening.il:

0 © 2003 American Institute of Physics

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3661J. Chem. Phys., Vol. 118, No. 8, 22 February 2003 Vibrational dephasing of I32 in solution

The model described above has proven most valuablrationalizing the microscopic mechanisms that undesolvent-induced pure dephasing. Within its context predtions have been made concerning the changes ofT2* withshifts in temperature, density, or viscosity.8–10 For specificmolecular systems the values ofD and oftc have been de-termined and compared with theoretical predictions. Oprediction of this model that has not been as thorougtested deals with the relative pure dephasing rates of vitional harmonics. The modulation mechanism must be inpendent of the observed harmonic and thereforetc is identi-cal for coherence at all harmonics ofvn . The spread offrequencies, however, is a different story, and does depon n, the order of the measured coherence:

D~nth harmonic![Dn;n•D. ~5!

Thus, in the fast modulation limit,T2* (n)51/Dn2 tc

51/D2n2 tc , and depends quadratically onn. In the staticlimit, T2* (n);1/Dn51/nD, leading to a linear dependence

The exposition above predicts a quadratic dependencthe rate of dephasing on the harmonic order of the coherein the fast modulation limit. Subquadratic behavior can abe expected, but only when the phase decay is clearly nexponential. In that case, when neither of the limiting cadominates the dynamics, no clear definition of a ‘‘dephastime’’ exists. Strangely enough, in the majority of castested, a subquadratic dependence ofT2* on n has beenobtained,11–13 even when the conditions for fast modulatiowere demonstrated to hold, and exponential phase decaymeasured at all harmonics.14 In a recent paper, Gayathet al. have tried to provide a mechanistic explanation withthe Kubo lineshape model to subquadraticn dependence omolecular nitrogen in various thermodynamic states, sgesting that coupling of vibration and rotation providesadditional inhomogeneous contribution to the broadeninot taken into consideration in the usual application oftheory.15 A multiphased decay of ^v(0)v(t)&, thefrequency—frequency time autocorrelation function, ovseparable and very disparate phases in time, was alsocussed as a mechanism for the nonideal relative depharates.

An alternative interpretation of the observations dscribed above is presented in a theoretical studyYamaguchi.16 A model is formulated where collisions in thliquid can induce sudden phase jumps in the vibrations,rather than being the results of many slight modulations,tifying the Gaussian approximation, the phase relaxationthe result of uncorrelated and large changes of vibratiophase. Mathematically this leads to Poisson dephasingnamics. This model is also characterized by two paramean average rate of phase changing interactions (g51/t i),and the typical size of the jump in phase (df0). Two addi-tional assumptions are applied, as presented in Eq.~6!:

H P~df!5e2df/df0/df0 , for df>0 ~6a!

and P~df!50, for df,0 ~6b!

Pi~m,t !51

m! S t

t iDe2t/t i

.

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The exponential distribution of phase jumps reflects ththermally activated nature, and Eq.~6b! describes the probability of our solute experiencingm collisions within timespant.

The resulting dephasing dynamics differ markedly frothe Kubo model. First, phase relaxation is always expontial. Second, the dephasing rates of harmonics range fquadraticn dependence when the jumps are small~back tothe Gaussian regime!, to zeron dependence when the jumpare large. At this limit, the collisions are so potent that eacan totally eliminate the solute molecule from contributingany of the harmonics. Thus, the dephasing takes place aharmonics at a rate that is identical to the rate of these cstrophic collisions. In terms of the parameters above,pure dephasing time resulting from the Poisson model is

T2* ~n!5t i b11n2~df0!2c

n2~df0!2 ~7!

leading to a gradual transition between the limiting dephing behaviors as the average phase jump increases.

The molecular system under study here is the lineariodide ion I 3

2 , which has been the subject of combined eperimental and theoretical study in our groups for sotime.17–19 Using impulsive photolysis,I 3

2 dissociation andrecombination dynamics were recorded in various polar mlecular solvents. The solvent was found to influence reacity not only by dephasing nuclear motion and dissipatiexcess photon energy, but also by determining the initialometry and degree of symmetry of the reactant.20–22 Theultrafast photoexcitation that served to vertically promomolecules onto the reactive surface, simultaneously geated vibrational coherences in the ground state through rnant impulsive stimulated Raman scattering~RISRS!,23–25

giving rise to spectral modulations observed in the UV asorption spectrum. Their decay provided a direct measurthe ensuing vibrational dephasing between low vibratiolevels of the ion.

In view of the central role played by the solvent in thphotochemistry of this ion, a specific effort was made to gdetailed insight into static and dynamic aspects of triiodsolvation in polar liquids—based upon the RISRS obseable. Starting with the study of the RISRS process itself, alater applying this knowledge to unraveling triiodide vibrtional dynamics, the following discoveries were made.

~1! RISRS proved to be a facile method for characterizground state vibrational dephasing at the bottom ofvibrational ladder.

~2! Fortuitous tuning of pump and probe frequencies, orplying properly timed multiple excitation pulses alloweselective measurement of fundamental and overtdephasing times with high precision. Comparing resuwith those reported from resonance Raman furtproved RISRS to be the only method capable of reliaT2 measurements for this system!26

~3! Independent measures ofT1 demonstrate that puredephasing dominates dephasing inI 3

2 in all solventsstudies.27

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3662 J. Chem. Phys., Vol. 118, No. 8, 22 February 2003 Gershgoren et al.

~4! When studied in glass forming liquids, from 300–100homogeneous fundamental dephasing was obsethroughout. The dephasing times increased graduallya factor of;2 over the range, despite the drastic chanto viscosity.28

~5! T2 (n51)* /T2 (n52)* '2.5 for both ethanol and acetonitrilat 300 K.26

In the present study we investigate the mechanismsthe deviation of fundamental and harmonic pure dephastimes from the predictions of Kubo lineshape theory. In pticular, T2 (n51)* /T2 (n52)* was measured as a function of temperature, throughout the range from room temperature toof glass formation. The next section is dedicated to presing the two theories outlined above on an equal footingorder to expose the molecular consequences of the mematical assumptions and to explain the motivation ofexperiments. Following the experimental section, our reswill be presented and analyzed in terms of both models.apparent inadequacy of both in explaining our results willpresented and discussion.

II. THEORY

While the general approach represented by Yamagucstochastic model is adopted, it will first be reformulated, aconsistent quantum dynamical theory. The advantagessuch an approach are~a! that from it all the physical observables of the system can be evaluated, and~b! the simulationof inherently quantum mechanical variables, such as chanin time of molecular absorption and emission are possiThis requires abandoning a weak coupling approach, sinnecessarily leads to Gaussian dynamics. One such apprinspired by the exponential vibrational dephasing, is toscribe the open system by the Quantum Master equationthis case the state of the system is characterized by thesity operatorr of the primary system subject to the equatiof motion:

]r

]t52

i

\@H,r#1LD~r!, ~8!

whereH represents the Hamiltonian of the systems andLD

the dissipative bath contribution, which in Lindblads semgroup form becomes29

LD~r!5(i

FirFi121/2$FiFi

1 ,r%, ~9!

whereFi are a operators from the Hilbert space of the pmary system representing the dissipative force due tobath. The distinction between the Hamiltonian dynamics athe dissipative part is not unique, which reflects the fact tthe boundary between the system and the bath is arbitThe Hilbert space of the system has to include all the optors representing observables. It is customary to includeof the bath explicitly. This allows one to describe effecsuch as inhomogeneous broadening and spectral diffusThe approach is in analogy with the Brownian oscillatwhere a collective over a damped bath coordinate is incluexplicitly.30

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In light of the experimental observations, the paved road operturbation expansion assuming a weak coupling betwthe system and the bath is abandoned to a strong coupdescription. This requirement eliminates the approach baon a classical calculation of bath correlation functions. Fthe quantum case only two strong coupling limiting cashave been worked out. The analysis focuses on elastictem bath encounters for whichLD* (H)5019 ~whereLD* is thedissipative superoperator in the Heisenberg representat!.At this point we should try to classify the origin of thessystem bath elastic encounters. One possibility is thatdephasing is the result of the accumulation of rare uncolated events, i.e., a Poisson model. Each of these eventsbe described by a scattering operatorS such that after asingle event the state of the system is changed toSrS1. Thetotal dissipative rate of change under a flow of uncorrelascattering events with a rateg51/t i is then

rD5g~SrS12r!. ~10!

The Poisson model fits Lindblads form if we identify thoperator F in Eq. ~9! with AgS.29,31 The simplest puredephasing scattering operator that does not alter the enof the system is the phase shift operatorS5e2 i /hHf, wheref is the elastic phase shift characterizing the scattering evThe accumulation of these phase shifts generates the deping process leading to the equation of motion:

]r

]t52

i

\@H,r#1g~e2 i /hf@H,* #2I !r, ~11!

~where@H,* #A5@H,A#), which in the energy representatioof the density operator becomes

]rnm

]t52 ivnmrnm1g~e2 ivnmf21!rnm , ~12!

wherevnm5(En2Em)/\ is the Bohr frequency. In the harmonic casevnm5(n2m)n. It is obvious in Eq.~12! thatonly the off-diagonal terms of the density operator decThe simple Poisson model can be augmented by assumidistribution of scattering events weighted byP(f), the prob-ability density of a phase shiftf. The linearity of the Semi-group equations of motion allow averaging, leading to

]r

]t52

i

\@H,r#1gS E P~f!df~e2 i /\f@H,* #2I ! D r.

~13!

We employ a symmetrized version of phase jump probabidistribution of the exponential distribution of YamaguchEq. ~6!, i.e.,

P~f!5df0e2ufu/df0. ~14!

The exponential distribution of phase jump fits the assumtion that the process is activated, i.e., the phase jump istermined by the energyEc of the collision eventdf0

Ec /kBT. The symmetric version eliminates the frequenshift associated with the process. A different viewpoint isassume that the rate of eventsg is activated and that thephase jump distribution is normal:

IP license or copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

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3663J. Chem. Phys., Vol. 118, No. 8, 22 February 2003 Vibrational dephasing of I32 in solution

P~f!5A 1

2pse2f2/2s2

. ~15!

For the normal distribution, the averaging in Eq.~13! can becarried out explicitly, leading to

]r

]t52

i

\@H,r#1g~e~2s2/2\2!†H,@H,* #‡2I !r, ~16!

which in the energy representation becomes

]rnm

]t52 ivnmrnm1g~e~2s2/2!vnm

221!rnm . ~17!

For the harmonic dephasing case with a frequencyn, Eq.~17! leads to

T2~n!5t i

~e~2s2/2!n2n221!

. ~18!

The exponential distribution, Eq.~15!, leads to a differentdecay pattern:

]rnm

]t52 ivnmrnm2gS vnm

2

df021vnm

2 D rnm , ~19!

which leads to theT2(n) relation of Yamaguchi, Eq.~7!.An alternative strong coupling dephasing model is ba

on the concept of the Hamiltonian of the primary systecontinuously modulated by the bath:

H5H f ~ t !, ~20!

where f (t) is the bath modulation function. A Guassiamodel is defined when the modulation function can bescribed by a Guassian stochastic process. For the harmcase f (t) is interpreted as the temporary frequency of toscillator. The dephasing is therefore a result of frequemodulation. In the fast modulation limit,

^ f ~ t !&B5v0

and

^ f ~ t ! f ~ t8!&B5Gd~ t2t8!; ~21!

Eq. ~21! leads to the following Lindblads semigroup form:32

LD~r!52G2†H,@H,r#‡, ~22!

which in the energy representation becomes

]rnm

]t52 ivnmrnm12G2vnm

2 rnm . ~23!

Equation~23! recovers the result that the dephasing ratethe nth harmonic is quadratic inn, i.e., T2(n)51/n2n2G2.This result will also be obtained in the weak coupling limComparing the Gaussian dephasing model~Eq. 23! to thePoisson dephasing model@Eqs. ~7! and ~18!#, we find thatwhen the phase jumps are small, i.e.,s or df0

21, the dephas-ing becomes the result of the accumulation of many smphase jumps naturally, leading to a Gaussian dephamodel, i.e., G25g(s2/2) for the normal distribution andG25g/df0

2 for the exponential distribution. For a largvalue of s or df0

21 each event leads to complete randoization of phase, leading to

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i.e., T2(n)51/g is independent ofn, and is proportional tothe rate of collision eventsg.

Equations~20! and ~24! represent the two limits of thePoisson model. For small jumps the dephasing rate will scquadratically with the energy gapvnm and for large phasejumps the scaling becomes independent of the energy dience. In addition, if the phase jump is activated we expthat the process will become more Gaussian at lower tperatures. If only the rate of eventsg is activated we expeca slowdown of the dephasing at lower temperature whmaintaining the Poisson character.

III. EXPERIMENT

The light pulses were generated in a 1 kHz homemademultipass amplified Ti sapphire laser system that is descriin detail elsewhere.26 The output of the 15 fs oscillator isstretched to 20 ps, and injected into a eight pass amplcavity, which is pumped with;10 mJ pulses from an intracavity doubled Q-switched Nd:YLF laser. The ultimate ouput after compression consists of a train of 28 fs pulscentered at 790 nm, containing;0.6 mJ of energy per pulsePump, push, and probe pulses were all derived by doubportions of the amplified pulses in BBO crystals that weremost, 100m thick, and were demonstrated to introduce neligible pulse broadening.

The samples were prepared as previously described,26 inethanol and in 1-methyl THF. Ethanol samples were stpered in 1 mm quartz cuvettes, which were pressed agathe cold finger of a closed cycle helium cryostat~RMC!.Methyl-THF samples were glove-box loaded into a cell cosisting of two 2 mm thick sapphire windows~crystran!, and a0.5 mm teflon spacer. The internal volume was accesthrough holes drilled in one sapphire flat, and both vacutightness around the holes, and thermal contact, werevided by indium wire pressed between the aluminum cholder and the windows. The sample temperature was reathe base of the cell, and actual solution temperatures westimated to be within 2° of these readings. The temperawas regulated by a Lake Shore 330 controller coupled tDT-400 series diode sensor. During the irradiation the samwas translated alternately inY andZ directions~X being thedirection of irradiation! via a stepper motor actuated linetranslation stage on a precision lab jack~microcontrol!. Ratesof translation were demonstrated to eliminate any local heing or sample bleaching effects. Methods of data collectand automation were as described previously.

The integrity of the cooled samples was monitoredabsorption spectroscopy. A fiber bundle halogen lailluminator–open electrode deuterium lamp combinatiproduced a stable and continuous irradiation source overrange of the triiodide UV absorption. Some scattering tbuilt up at the lower edge of the temperature range interfewith a quantitative determination of sample concentratioThe positions and widths of the two intense near-UV ban

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3664 J. Chem. Phys., Vol. 118, No. 8, 22 February 2003 Gershgoren et al.

were obtained by fitting the measured spectra to a supesition of three Gaussians bands plotted against photonergy.

IV. RESULTS

The center of the I32 absorption peaks red shifted, an

the bands narrowed systematically upon cooling. In ordeuncover the mechanism for the spectral narrowing obserin both solvents, a theoretical simulation of the spectra wconducted using model potentials that were described prously and used to simulate I3

2 photochemistry.18,19 Figure 1presents the widths predicted by the theory together wthose obtained from the fitting. An example of a measuspectrum along with a nonlinear least squares fit is presein the insert. The theoretical predictions lie slightly outsithe error limits of the measured widths at room temperatubut the trends of change with temperature agree well withexperimental changes. Another noteworthy result is thatwidths obtained in ethanol and in MTHF are identical witherror. This is remarkable in view of the charged nature ofchromophore, and the marked difference in polarity acharge distribution for the two solvents. While ethanol isvery polar solvent, especially adept at stabilizing localiznegative molecular charge, THF is a sparingly polar solvewhich is better at stabilizing cations. In both solvents twidth of the upper and lower energy transitions are esstially the same at the various measured temperatures.

Another unusual aspect of the temperature-depenspectra involves the spectral shifting of these peaks wtemperature. Figure 2 depicts the peak positions as a funcof the temperature in both solvents, using the designatiothe transitions used in the insert to Fig. 1. The transitenergies shift to the red as temperature is reduced, andlower of the two main absorption bands~;27 000 cm21!shifts almost two times more (Dn;450 cm21) over the

FIG. 1. A comparison of experimental and simulated peak widths at vartemperatures. An experimental spectrum is presented in the inset to destrate the quality of the fit provided by the sum of Gaussians, and to denate the peaks.

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same temperature range~300–100 K! than that above it~;34 000 cm21!. Furthermore, the effect of cooling is agaequal for both solvents, indicating perhaps that the esseeffects of cooling on the interaction of the solvent with tion is not influenced by the differences between thesesolvents.

Dephasing dynamics were recovered from RISRS sptral modulations, as previously described.26 Degenerate twoand three pulse experiments employing 390 nm pulses wused to record the decay of spectral modulations refleccoherent ground state vibrations induced by the pumpquence. The results were first fit to a sum of complex exnentials using the ‘‘filter diagonalization method.’’33 Thisproduced a perfect fit to the data, but generated a largejority of terms that were devoid of direct significance to tvibrational dynamics. Knowing the vibrational frequenciof the ions, a minimal subset of diagonalization terms twere deemed relevant were used as a first guess for fithe data using a Marquardt–Levenberg least squares arithm. Two pulse data in MTHF at three temperatures is psented in Fig. 3, along with the products of the describanalysis. The first panel shows the raw data. The secshows the modulations once subtracted from the dc baground, along with the fit provided by the filter diagonaliztion method shown as a solid black line. Finally, in the lapanel, all of the terms oscillating near the doubled frequeare isolated from all others in the diagonalization series,fit to an exponentially decaying sinusoid using least squaroutines. The motivation of this step in the analysis was fito estimate the range of confidence to assign the final pareters of the fitting, such as frequencies, phases, and deping times. Another goal was to determine whether deviatiofrom exponential decay could be discerned in the specmodulations. Within the Kubo lineshape picture, once oside the fast modulation limit, the pure dephasing no lonmakes a Lorentzian contribution to the lineshape, but ratone following a Voight function as in Eq.~4!. To test thedephasing dynamics of individual harmonics, all the termsthe filter diagonalization result aside from those exhibiting

son-g-

FIG. 2. Absorption peak positions as a function of temperature for triiodin ethanol and MTHF solutions. See the text for details.

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3665J. Chem. Phys., Vol. 118, No. 8, 22 February 2003 Vibrational dephasing of I32 in solution

frequency very near that of the harmonic of interest wsubtracted from the data. The remainder was fit to an exnentially decaying sinusoid, to a Gaussian decaying one,also to Eq.~4! multiplied by a sinusoid.

In both solvents, despite the extreme variationssample viscosity, no significant deviations from exponendecay of the dephasing in either the fundamental or first hmonic were detected. This is in accord with an earlier repof the fundamental dephasing dynamics in ethanol alone.28 Itraises the question of whether our method of measuremcaptures the dynamics from an early enough stage to athe observation of an initial fleeting Gaussian stage of reation in an intermediate dephasing regime. The answethis question is probably negative, due to the presencerapid spectral changes that accompany bond fission in3

2 ,allowing us to characterize the decay of the coherent vibtions only after a delay of;300 fs. However, the examination of Voight line functions shows that even in the caseintermediate modulation, the decay constants fit to the exnential tails that characterize later stages of phase relaxawill maintain the quadratic dependence onn.34 Accordingly,all dephasing times reported in this paper were retrievedfitting the data to exponential decays.

Results of the dephasing measurements are presegraphically in Figs. 4 and 5. The exponential phase relation times of the fundamental and the first harmonicdepicted in picoseconds along with the pure dephasing tratios as a function of the sample temperatures. The errodeterminingT2* usually reflects the scatter of values obtainfrom the analysis of multiple transient transmission measuments. In cases where the three pulse method provided mreproducible numbers for the harmonic dephasing times,error reflects the deviation of values obtained from tscheme alone. The first obvious trend is the mild increasT2 (n51)* and in T2 (n52)* , roughly by a factor of 2 as thetemperature is reduced from 300 to 100 K in both liquidBut no less important is the overall similar trend observed

FIG. 3. Transient absorption scans taken in an MTHF solution of I32 at 400

nm, following excitation at the same frequency. A three-panel chronolrepresenting the phases of signal analysis, extracting the dephasingfrom the raw spectral modulations. See the text for details.

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the T2 (n51)* /T2 (n52)* ratio, which for both solvents remainbelow 3 at all temperatures, reducing mildly from;2.6 tonearly 2 at 100 K. In particular, we wish to draw attentionthe fact that throughout the temperature range studied,value of 4 predicted in the Kubo theory lies outside the gerous and very realistic range of error associated withexperimental dephasing time ratio.

V. DISCUSSION

The subquadratic ratio ofT2 (n51)* /T2 (n52)* observed inthe symmetric stretch vibration of I3

2 in two solvents, studiedover a wide temperature range, is in conflict with establishtheories of vibrational dephasing in liquids. Before an altnative explanation can be considered it is important to crcally evaluate the experimental procedures. The real tpump–probe RISRS method is based on impulsively inding a coherent vibrational motion on the ground electrosurface and observing the subsequent dynamics by a wprobe pulse. It has been verified that the weak probe pulsequivalent to a position measurement of the vibratiocoordinate.26 As a result, the measurement is phase sensit

yes

FIG. 4. Pure dephasing times of the fundamental and first harmonic smetric stretching vibrations of triiodide in ethanol as a function of tempeture. The ratio of these times is also shown in the graph.

FIG. 5. The same as Fig. 4 for triiodide in MTHF.

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3666 J. Chem. Phys., Vol. 118, No. 8, 22 February 2003 Gershgoren et al.

therefore the decay of modulations with the correspondfrequency is a direct measurement of dephasing. For therent measurements of I3

2 in solution, the duration of thepump and probe pulses were an order of magnitude shothan the fundamental vibrational period. With these toolshand the evidence favoring exponential decay of the molations vs other functional forms such as Gaussian is vstrong.

The rate of dephasing also has a contribution frombrational relaxation. Moreover, for this contribution the raT2 (n51)* /T2 (n52)* is two, meaning that if the contribution ovibrational relaxation to dephasing is significant, the oserved exponential decay and subquadratic ratio can beplained. Independent measurements based on the rate orecovery of the bleach originating from the recombinationI221I, have shown vibrational relaxation times of 3–4 ps

ethanol in the same temperature range of the curexperiments.27 In THF this process is even slower andcharacterized by a decay time nearly twice that determineethanol. In addition, the experimentally determinedT1 ofdiiodide that has the same frequency, reduced mass,charge as the symmetric stretch of I3

2 is also in the range oa few picoseconds. Thus, the contribution of vibrationallaxation to dephasingT252T1 is an order of magnitudeslower than the observed phase decay rates, leading toconclusion that the dominant contribution to the decaymodulations is pure dephasing.

The established view of vibrational pure dephasingliquids assumes that the vibrational mode is weakly coupto the solvent bath. The dephasing is then the result oaccumulation of many solvent fluctuations that modulatefrequency. Such a picture is consistent with a Gaussdephasing model and the quadratic decay ratio for amonic sequence of frequencies. Anharmonicities cochange the decay ratios. For most vibrational modes theplitude of motion increases more than linearly with thebrational quantum number. This would lead to ahigher thanquadradicdecay ratio thus overruling anharmonicity as tsource of the effect.

In the gas phase, dephasing is caused by an accumtion of uncorrelated binary collisions. If the collisions asoft the total result is again caused by an accumulationmany individual events, leading to a Gaussian model. If hcollisions prevail each elastic collision leads to large reshfling of phase leading to the Poisson dephasing model.such a Poisson description be used as a model for obsedephasing of I3

2 in polar solvents? The first step is to fit thlarge body of experimental observations to this model. Tcan be done using either Eq.~18! for the normal distributionof phase jumps or Eq.~7! for the exponential distribution ophase jumps. The two parameters to be fitted are the raeventsg and the average phase jump, eithers or df0 .

As can be seen in Figs. 6 and 7, the Poisson modelthe data. Typical fitted average phase jumps are of the oof 50°–60°. From these figures it is clear that only a wetemperature dependence is observed. Also, the average pjump increases when the temperature decreases. This ovation rules out the possibility that the phase jump is avated, which favors the normal Poisson phase jump mo

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over the exponential one. In order to be able to distinguexperimentally between the two models, the dephasingof the third harmonic and higher should have been measuAlthough in some traces the third harmonic can be identifithe error bars are too large to be able to have any defiexperimental discrimination between the models. Figureshows the rate of eventsg in the Poisson model as a functioof temperature. At room temperature the average timetween events is 300 fs. At 100 K the rate of events decreato one every 600 fs.

The success of the Poisson phase jump model to fitdata motivates the search for a microscopic mechanismcould justify it. In the gas phase where collisions are rare,Poisson model is a natural consequence. In condensed mthe origins of these events are not clear. It is usually argthat the high density of the liquid phase excludes hard bin

FIG. 6. Average phase jumps as a function of temperature to fit the expmental data of I3

2 in both solvents. Solid lines refer to a normal distributiomodel, and the dashed lines to an exponential distribution of jump amtudes.

FIG. 7. Rate of phase jumps to fit the experimental data in both solveThe solid and dashed curves refer to the normal and exponential distribuof phase jump amplitudes, respectively.

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3667J. Chem. Phys., Vol. 118, No. 8, 22 February 2003 Vibrational dephasing of I32 in solution

collisions. Triiodides ionic character suggests long-rangeteractions with the surrounding polar solvent molecules. Tpicture would favor a Gaussian dephasing model acculated from many small contributions. In metals scatteringpolarization waves have been identified as a source of Pson dephasing.35 A possibly more appropriate model for I3

2

could be a rare solvent rearrangement process aroundsolute. In any case, the mechanism responsible for phdecay in then1 of I3

2 must also explain the negligible temperature dependence of bothT2* and the ratio T2* (n51)/T2* (n52). We note in passing that in earlier studievibrational dephasing in glass-forming liquids is rapidoverwhelmed by inhomogeneous contributions, as soonthe solvent viscosity increases significantly.36 The lack of asimilar effect here may be due to the brevity of the stagedephasing here at all temperatures.

But, the search for a molecular mechanism for explaing our findings is further complicated by realizing just howidespread deviation from quadratic harmonic pure dephing times actually is. A wide variety of molecular vibrationin solution have shown similar behavior, suggesting thatobserved phenomenon of deviations from Kubo lineshpredictions is quite general.14,15This fact alone suggests thathe underlying mechanism might be common to all the cimolecular systems. However, they vary so drastically boththe nature of the solvent–solute interaction potentials, instructure of the vibrators, and in the frequencies of the stem and the bath, that at present a general mechanism eus. We can, however, rule out mechanisms proposed inliterature, which are based on the gradual transition fromto slow modulation while climbing the harmonic ladder. Thcan be based on the perfect exponential character ofdephasing dynamics observed throughout.

The consequence of the discussion above is thatcommonly used picture of vibrational dephasing basedthe weak coupling between system and bath is expected tdeficient. This means that established computational produres based on a combination of molecular dynamicsobtaining the bath correlation functions, and perturbattreatments for calculating spectroscopic observables, camisleading.37,38A consistent theoretical model should therfore explain the minor frequency shift of the symmetstretch of I3

2 as well as the strong collision characteristicsthe dephasing. More work both experimental and theorethas to be performed before such a theory can be establis

VI. CONCLUSIONS

The pure dephasing times of I32 in two glass-forming

liquids have been measured in the time domain from 3down to 100 K, both at the fundamental frequency andfirst harmonic. The exponential phase decay was foundincrease gradually from;1 to ;2 ps over this range for bothsolvents. The ratio of fundamental to harmonic pure dephing times remained in the range 2–2.7 at all temperatuand showed only a slight dependence on temperature.widely used Kubo lineshape model which predicts a ratio4 for these dephasing times is incapable of explaining th

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results. Furthermore, similar deviations have been encotered in a growing number of small molecular systemssolution, indicating the generality of this finding. A schemassuming Poisson collision statistics consistently matchesdata.

ACKNOWLEDGMENTS

Enlightening discussions with E. Geva, R. Lynden-BeJ. Skinner, and B. Bagchi are gladly acknowledged. Resewas supported by the Israel Science Foundation. The Faand Fritz Haber research centers are supported by the Merva Gesellschaft, GmbH, Munich, Germany.

1J. T. Hynes, inThe Theory of Chemical Reactions, edited by M. Baer~CRC, Boca Raton, FL, 1985!, Vol. 4.

2~a! D. W. Oxtoby, Adv. Chem. Phys.40, 1 ~1979!; ~b! D. W. Oxtoby,Annu. Rev. Phys. Chem.32, 77 ~1981!.

3W. D. Rothchild, Dynamics of Molecular Liquids~Wiley, New York,1984!.

4G. R. Fleming,Chemical Applications of Ultrafast Spectroscopy~OxfordUniversity Press, New York, 1986!.

5A. Laubereau and W. Kaiser, Rev. Mod. Phys.50, 607 ~1978!.6R. Kubo, p. 23, inFluctuation, Relaxation and Resonance in MagneSystems, D. Ter Haar~Oliver and Boyd, Edinburgh, 1962!.

7F. Lindenberger, C. Rauscher, H.-G. Purucker, and A. LaubereauRaman Spectrosc.26, 833 ~1995!.

8S. F. Fischer and A. Laubereau, Chem. Phys. Lett.35, 6 ~1975!.9R. Lyndenn-Bell, Mol. Phys.33, 907 ~1977!.

10D. W. Oxtoby, J. Chem. Phys.70, 2605~1979!.11C. Brodbek, I. Rossi, Nguyen-Van-Tanh, and A. Ruoff, Mol. Phys.32, 71

~1976!.12R. Arndt and J. Yarwood, Chem. Phys. Lett.45, 155 ~1977!.13A. B. Myers and F. Markel, Chem. Phys.149, 21 ~1990!.14K. Tominaga and K. Yoshihara, J. Phys. Chem. A102, 4222~1998!.15N. Gayathri and B. Bagchi, J. Phys. Chem. A103, 9579~1999!.16T. Yamaguchi, J. Chem. Phys.112, 8530 ~2000!; T. Yamaguchi and Y.

Himura, ibid. 114, 3029~2001!.17U. Banin and S. Ruhman, J. Chem. Phys.98, 4391~1993!.18U. Banin, R. Kosloff, and S. Ruhman, Isr. J. Chem.33, 141 ~1993!.19G. Ashkenazi, U. Banin, A. Bartana, R. Kosloff, and S. Ruhman, A

Chem. Phys.100, 229 ~1997!.20E. Gershgoren, E. Gordon, and S. Ruhman, J. Chem. Phys.106, 4806

~1997!.21R. M. Lynden-Bell, R. Kosloff, S. Ruhman, D. Danovich, and J. Vala,

Chem. Phys.109, 9928~1998!.22H. Sato, F. Hirata, and A. B. Meyers, J. Phys. Chem. A102, 2065~1998!.23J. Chesnoi and A. Mochtari, Phys. Rev. A38, 3566~1988!.24W. T. Pollard and R. A. Mathies, Annu. Rev. Phys. Chem.43, 497~1992!.25U. Banin, A. Bartana, S. Ruhman, and R. Kosloff, J. Chem. Phys.101,

8461 ~1994!.26E. Gershgoren, J. Vala, R. Kosloff, and S. Ruhman, J. Phys. Chem. A105,

5081 ~2001!.27Z. Wang, T. Wasserman, E. Gershgoren, J. Vala, R. Kosloff, and

Ruhman, Chem. Phys. Lett.313, 155 ~1999!.28Z. Wang, T. Wasserman, E. Gershgoren, and S. Ruhman, J. Mol. Liq86,

229 ~2000!.29G. Lindblad, Commun. Math. Phys.48, 119 ~1976!.30S. Mukamel,Nonlinear Optical Spectroscopy~Oxford University Press,

Oxford, 1995!.31D. M. Lockwood, M. Ratner, and R. Kosloff, Chem. Phys.268, 55 ~2001!.32V. Gorini and A. Kossakowski, J. Math. Phys.17, 1298~1976!.33J. W. Pang, T. Dieckmann, J. Feigon, and D. Neuhauser, J. Chem. P

108, 8360~1998!; V. A. Mandelshtam,ibid. 108, 9999~1998!.34R. Kosloff, Physica A110, 346 ~1982!.35T. Klamroth, P. Saalfrank, and U. Hofer, Phys. Rev. B64, 035420~2001!.36A. Tokmakoff and M. D. Fayer, J. Chem. Phys.103, 2810~1995!.37D. W. Oxtobi, D. Levesque, and J.-J. Weis, J. Chem. Phys.68, 5528

~1978!.38K. F. Everitt and J. L. Skinner, J. Chem. Phys.115, 8531~2001!.

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CHAPTER VI

Summary

To date, considerable work has been done on triiodide in our lab as well as in other

labs. Vohringer et. al. explored the nature of both the energy partitioning and subsequent

dynamics of the energy dissipation the diiodide ions generated in the impulsive photodis-

sociation reaction of triiodide at 400 nm [93]. To gain insight into the vibrational product

state distributions as a function of time and to get the desire information about the vibra-

tional energy relaxation of the diatomic product, they recorded the transient absorption

signal and calculated the instantaneous absorption spectra of the diiodide product ions.

These spectra allow insight into the vibrational product state distributions as a function

of time. The excess vibrational energy of the diiodide product was found to be amaz-

ingly small and the vibrational energy relaxation was found to be extremely rapid with

two distinct time scales. An ultrafast subpicosecond component, which accounts for the

dissipation of most of the energy followed by thermalization near the bottom of the diio-

dide potential on a time scale of several picoseconds. They related the first process with

recoil of the fragments in the exit channel of the potential energy surface where the second

process represents relaxation in the asymptotic limit, where the interaction between the

53

54

atom to the diatom fragments becomes negligible.

In a related study, Vohringer et. al. used the photoselection technique to studied the

optical anisotropy decay of diiodide ions [94]. The decay of the spatial diatomic fragment

distribution found to occurs on three time scales. On an ultrashort time scale, an inertial

contribution with correlation time of 450 fsec Gaussian decay was observed. This ultrafast

component reflects substantial rotational excitation of the diatomic product, which result

from the broken symmetry induced by the liquid solvent environment. An intermediate

process is characterized by exponential contribution to the anisotropy decay with time

constants of 2 ps. Finally, on a longer times scales, an exponential decay with time constant

of 12 psec was linked to the rotational diffusion of the diatomic fragment.

In a different paper, Vohringer et. al. measured the transient absorption signal of the

triiodide photodissociation reaction using 266 nm excitation light. They notice the sig-

nature of a tree body dissociation [95]. Information about the yield of diiodide product

formation, or equivalently, about the 3 body photodissociation yield, can be obtained from

time resolved experiments, probing at 400 nm. Ground state diiodide and triiodide ions

show approximately the same absorption cross-section at 400 nm. Hence, a unity quan-

tum yield for diiodide formation results in a zero transient signal, provided that vibrational

energy relaxation in the diiodide fragments is complete. Conversely, finite residual bleach

at 400 nm then reflects a finite quantum yield for diiodide formation or three-body disso-

ciation. The measured transient signal does display finite residual bleach, which remains

constant for delay times longer than 10 ps. Its magnitude corresponds to approximately

20% of the initial bleach, meaning that only 80% of the initially photoexcited triiodide

55

molecules have formed ground state diiodide ions and iodine radicals or recombine to

the parent ion. The residual 20% of the parent molecules undergo three body dissocia-

tion to iodide ions and two iodine radicals either in their spin-orbit ground state or evenly

distributed between the two spin-orbit states of atomic iodine.

Zanni et. al. studied the photodissociation dynamics of gas phase triiodide following

400nm excitation [96], using femtosecond photoelectron spectroscopy [97, 98](FPES). In

a FPES experiment the ion is electronically excited with a femtosecond pump pulse. The

resulting non-stationary state is photodetached by the probe pulse while the photoelectron

spectrum is measured, using the relation:

Vertical detachment energy (VDE)=~ω-electron kinetic energy

one can utilize the photoelectron spectrum and the fact that every species have a different

energy range signature, to provide the complete time dependent behavior of all the ions

involved in the reaction, using a single probe wavelength.

The main gas phase results are: Both I− and I−2 photofragments are observed, where

the efficiency of I− formation is 50%. One and two dimension wavepacket simulation at-

tributes the formation of I− to three-body dissociation. The formation of I− continues until

600 fsec, after which no additional changes are observed. The nascent I−2 is formed in a

coherent superposition of its vibrations levels, which will dephase due to the anharmonic-

ity of the potential. However, the luck of collision in the gas phase will enable a rephasing

process. While the rephasing time is determined by the topology of the potential energy

surface (frequency and anharmonicity) and the average vibration state of the photoproduct,

the spread of the superposition will define the dephasing time. The coherences of the ini-

56

tially formed I−2 oscillate at a period of 550 fsec, indicating an average quantum number of

v=67 (v=12 in solution). Taking into account the anharmonicity, the calculated rephrasing

time is 45 psec, in close agreement with the experimental result. The dephasing time of

the coherences is 4 psec, implying that a wide distribution of I−2 is populated during the

excitation. The broad spread of the superposition is consistent with the maximum popu-

lated vibration level of v=110, calculated from the direct measure of VDE. RISRS induced

by the pump pulse result in modulation of the photoelectron spectrum. The frequency as-

sociated with this oscillation is 112 cm-1 that was assigned to the I−3 symmetric stretch on

the ground electronic state. In the absence of any perturbing interactions, the modulation

seems to last to infinity.

Zhu et. al. study the gas phase photodissociation of the triiodide, using photofrag-

ment mass spectroscopy [99]. Measuring the product branching ration as a function of

the photon excitation energy, they conclude that there are at least three type of dissoci-

ation process that should be taken into account: three body dissociation and two body

dissociation leading to either I− + I2 or I−2 + I.

The work on this system that was carried out in our group, which is the basis of this

thesis, imply the following:

Our first topic of interest proves that the perturbation theory is incapable of reproducing

key aspects of impulsive excitation, even at moderate conversion levels. After Verifying

that RISRS is a robust spectral tool, we also show that a) appropriate selection of the

pump/probe frequencies enables to retrieve the relaxation dynamics of higher harmonics,

and/or weak vibrational modes, and b) delicate control of the probe chirp can determine

57

the position and momentum of the dynamical hole in the RISRS experiment. Applying

the same methodology to retrieve the dephasing time of different harmonics as a function

of temperature, we show that the dephasing dynamics of the first and second harmonics of

the symmetric stretch do not confirm the predictions of either the Kubo line-shape theory

or the Poisson model.

Following the experiments discussed above, further experiments were made to inves-

tigate the cage effect. The results suggest that the recombination process is completed

in three times scale that were assign to three independent kinetics pathways. The fastest,

on the order of 2 psec, is a direct recombination and vibrational relaxation. The second,

with a 40 psec time scale, seems to be a long-lived complex, while the longest is a sal-

low decay of 350 psec that might be due to geminate pairs that already escape the solvent

cage. Changing the solvent, effect drastically on the relative amplitudes of the different

pathways, but does not change the decay times. A related study on the temperature depen-

dence of the recombination presses [100], imply that the complex is a bound excited state,

formed directly through the photoexcitation process.

Despite all the work that has been done to date on the photodissociation of triiodide, the

properties of the system as well as its interactions with different solvents still bare much

study. In particular, the exact nature of the long-lived complex is still unclear. A possible

way to resolve its properties is to use the TRISRS [66] spectroscopy to measure the vibra-

tional frequency of the complex. Another important aspect is the formation of the reaction

product. Following the excited superposition created by the impulsive excitation [60], as a

function of temperature can be used as a window to the reaction product. Finally, resolving

58

the dephasing dynamics of the a-symmetric stretch as a function of temperature will help

in understanding the role of the solvent in the photo dissociation reaction.

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