g. gallot et al- non-monotonic decay of transient infrared absorption in dilute hdo/d2o solutions

8/3/2019 G. Gallot et al- Non-monotonic decay of transient infrared absorption in dilute HDO/D2O solutions

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Non-monotonic decay of transient infrared absorption in

dilute HDO=D2O solutions

G. Gallot a, N. Lascoux a, G.M. Gale a, J-Cl. Leicknam b,*,S. Bratos b, S. Pommeret c

a Laboratoire d'Optique Quantique, Ecole Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, Franceb Laboratoire de Physique Theorique des Liquides, Unite de Recherche Associee au CNRS, Physique Theoretique des Liquides,

Universite Pierre et Marie Curie, Case courrier 121, 4 Place Jussieu, Tour 16, 75252 Paris Cedex 05, Francec CEA/Saclay, DSM/DRECAM/SCM/URA 331 CNRS, 91191 Gif-sur-Yvette Cedex, France

Received 7 December 2000; in nal form 15 February 2001

Abstract

Transient infrared absorption of diluted HDO=D2O solutions is measured with 150 fs laser pulses. The signal in-tensity decays in a heavily non-exponential way, and its variation is often non-monotonic; no quantum beats are

observed. These eects are ascribed to the simultaneous presence of solvent and population dynamics in low lying

vibrational states, and to a partial cancellation of the bleach and absorption intensities. 2001 Elsevier Science B.V.

All rights reserved.

1. Introduction

The short time relaxation of photoexcited

molecules in dense phases, immediately after ex-

citation, has been a subject of considerable inter-

est. Most often the excitation is in the visible

spectral range. If the laser pulse duration is com-

parable to the vibrational oscillation period, mol-

ecules are excited coherently and they oscillate in

phase. Damped quantum beats may then be ob-

served by the help of various non-linear spectros-

copies such as spontaneous uorescence,

transmission correlation, transient absorption,

transient birefringence and dichroism. Informa-

tion concerning vibrational motions in the ground

and excited electronic states of the system is ob-

tainable in this way.

The laser excitation may also be infrared.

However, a number of technical diculties had to

be overcome to proceed further. The published

work mainly refers to the diluted solution

HDO=D2O, an isotopic variety of liquid water.The OH O motions were `photographed' in realtime, but no oscillations were observed: they are

too strongly damped to be `seen' [1,2]. The loss of

the initial phase coherence is due to three mecha-

nisms: the population relaxation, spectral diusion

and orientational relaxation. (i) The vibrational

population relaxation time sp, was measured by a

number of authors [14]; values between 1 and 2 ps

were reported. It exhibits a pronounced tempera-

ture [5] and frequency [6] dependence. (ii) Spectral

diusion evolves over time scales of the order of

sX, the mOH frequency shift correlation time; it was

29 June 2001

Chemical Physics Letters 341 (2001) 535539

www.elsevier.nl/locate/cplett

* Corresponding author. Fax: +33-1-44275100.

E-mail address: [email protected] (J.-C. Leicknam).

0009-2614/01/$ - see front matter

2001 Elsevier Science B.V. All rights reserved.PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 5 2 4 - 3


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found equal to 0.70.8 ps, both by theory [7] and

experiment [1,2]. (iii) The orientational relaxation

time so was provided by the NMR and molecular

dynamics studies; values of the order of 2.5 ps were

proposed in the literature [811]. Although there

are still controversies, there is an overall agreement

on this picture.

The purpose of this Letter is to reexamine the

decay of the transient infrared absorption of di-

luted HDO=D2O solutions with 150 fs resolution.A large number of pump and probe frequencies

were employed. The absorption was shown to

decay in a heavily non-exponential way and often

is non-monotonic. The `reading' of the spectra is

dicult, and their interpretation requires a con-

siderable theoretical eort. The observed eectsare ascribed to the simultaneous presence of sol-

vent and population dynamics, and to a partial

cancellation of the bleach and absorption intensi-

ties. For earlier work on this problem, see [12].

2. Experiment

The experimental set-up employed was de-

scribed elsewhere [1,2]; it is only sketchily

redescribed here. Its central element is a titaniumsapphire amplier which drives an optical para-

metric amplier system producing a 10 lJ pump

pulse and a 1 lJ probe pulse. They are both

tunable from 2800 to 3800 cm1, have a duration

of 150 fs and a spectral width of 65 cm1. The

angle between the pump and the probe beams,

polarized in the same direction, is 15. The pump is

chopped at 500 Hz to obtain dierential spectra,

with and without excitation.

Temporal evolution of the system was followed

over several ps. Three pump frequencies X1 were

employed at 3510, 3420 and 3300 cm1; and in

each of these three cases, spectral transients were

recorded for a large set of probe frequencies X2.

Typical results are illustrated in Fig. 1a; the

following observations merit attention. (i) Initial

decay of the signals is always heavily non-

exponential. A narrow component with a width of

the order of 1 ps coexists with a broad component

extending over 2 ps or more. (ii) The decay is notnecessarily monotonic; an overshoot from the

initial absorption to the nal bleach is often

observed. (iii) The maxima of the bleach and

absorption transients do not coincide. The

absorption component peaks at earlier times than

its bleach counterpart; however, the positions of

their maxima depend distinctly on X2. (iv) The

spectra do not vary very much with the excitation

frequency X1.

3. Theory

The theory is based on an expression for the

pumpprobe signal recently proposed by Bratos

Fig. 1. Time-resolved pumpprobe infrared spectra of a diluted HDO=D2O solution. The wave number of the pump is 3510 cm1, and

those of the probe are 3510, 3380, 3360, 3340, 3320 and 3300 cm 1. Experiment is illustrated in Fig. 1a, and theory in Fig. 1b.

536 G. Gallot et al. / Chemical Physics Letters 341 (2001) 535539


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and Leicknam [13]. If SX1;X2; s is dened astemporally integrated probe absorption in pres-

ence of the pump minus the probe absorption in its

absence, then

SX1;X2; s

2

h3

Im

II

I0

I0

I0

dtds1 ds2 ds3

&

h _E2r; tEr; t s3Er; t s3 s2

Er; t s3 s2 s1iE

hM0Ms1Ms1 s2Ms1 s2 s3iS

':

1

Eq. (1) contains two 4-time correlation functions:the correlation function of the total and probe

electric elds E and E2, and that of the electric

dipole moment Mof the system. The average h iS isover the states of the non-perturbed liquid sample,

and the average h iE

is over all possible realizations

of the incident electric elds. The symbol [ , ] de-

notes a commutator, the dot a time derivative and

s the time delay of the probe with respect to the

pump. For a description of higher-order correla-

tion functions, see [14].

The present problem was modeled as follows. (i)

The spectrally active OH vibration of a HDO

molecule is assimilated to a three-level quantum

system perturbed by stochastic solventsolute in-

teractions; the energy level diagram is illustrated in

Fig. 2. (ii) The dipole moment of the molecule is

governed by the equation

dM

dt

i

hH;M CM; 2

where H is an adiabatic Hamiltonian of the liquid

mixture, and C the Pauli relaxation matrix. (iii)

The correlation between vibrational and rotational

motions is neglected. (iv) The pump and probe

electric elds E1X; t and E2X; t are given aGaussian form and random phases, /1t and/2t, independent of each other.

The detailed calculations are described in [13];

they are only sketchily reproduced here. The di-

pole moment correlation function hM0Ms1;Ms1 s2;Ms1 s2 s3i is calculated by: (i)determining the time evolution ofMs by the helpof Eq. (2), (ii) employing the cumulant expansion

theorem and (iii) considering time scales inherent

to this problem. The resulting correlation function

then appears as a sum of terms proportional to

as2 exp

12s21

s23b s1s3bs2 s3

; 3

where as hu20u2si is the rotational corre-lation function of the unit vector ~u along the OHbond of HDO; bs hx0xsic is the frequencyshift correlation function, where the index c indi-

cates a cumulant, and b b0. In conformitywith computer simulation results of [7,911], the

decay of as and bs is supposed to be mono-exponential with time constants so and sX.

The electric eld correlation function h _E2r; tEr; t s3 Er; t s3 s2 Er; t s3 s2 s1iEmay be evaluated by (i) decomposing E1 and E2into individual exponentials, (ii) neglecting non-

secular contributions to it and (iii) treating the

random phases /1t and /2t by the help of thecumulant expansion theorem. The nal result then

appears as a sum of terms proportional to

expct21 t22 t

H23 t

H24

exp12t1 t2

2/ 1

2t3 t4

2/; 4

where t1; t2; t3 and t4 are the various combinationsof times t; t s3; t s3 s2; t s3 s2 s1.Moreover, tH t s, / h _/21i h

_/22i whereas c

determines the temporal width of the pump and

probe electric elds.

The last step of the calculation consists in

performing multidimensional integrations over

t; s1; s2 and s3 in Eq. (1). They were realizednumerically by the help of a specially written

algorithm. No approximations were required to

Fig. 2. Low lying OH stretching energy levels of an HDO

molecule. The frequency of the v 0 3 v 1 transition isequal to X01, and that of the v 1 3 v 2 transition is equalto X12.

G. Gallot et al. / Chemical Physics Letters 341 (2001) 535539 537


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do it; in particular, the overlap of the pump and

probe pulses was fully accounted for. The spectra,

calculated by using this model, are shown in

Fig. 1b; the agreement with experimental data of

Fig. 1a is extremely satisfactory.

4. Discussion

The following picture of non-monotonic pump

probe absorption in HDO=D2O is suggested bythis work. Let us rst suppose that the lowest ex-

cited vibrational level is non-degenerated and well

isolated from all other states (Fig. 3a); the decay of

transient absorption is then basically mono-expo-

nential, with a time constant equal to the popu-

lation relaxation time sp. The situation is dierent,

if this state is replaced by a continuous sequence of

excited vibrational states (Fig. 3b). The pump then

generates a wave packet propagating in the liquid

at scales of the order of the solvent relaxation time

sX. Transient absorption will exhibit two decay

times, sp and sX. Let us nally assume that the

vibrator contains two continuous, well-separated

sequences of states (Fig. 3c). The pumpprobe

signal remains comparable to that just described,

but may have a positive or a negative amplitude

(induced absorption or bleach). A partial com-

pensation of these two components of the signal

may stop its decline, or even produce its ampli-

cation! This last case is closely related to the ex-

perimental reality. As the OH vibrationalfrequency depends on the OH O bond length,the continuous sequences of excited states in Fig. 3

are those of individual OH vibrators, captured in

OH O bonds of dierent lengths.The observed material entirely conforms to this

picture; see Fig. 1a. The short time component of

the signal is generated by the solvent relaxation

and decays with a time sX; and its long time

component is due to the population relaxation and

decays with a time sp > sX. Their relative intensi-

ties are X1, X2 dependent; the solvent relaxationdominates ifX1 X2 0 or X1 X2 X01 X12,whereas the population relaxation dominates

otherwise; this point is discussed in [15]. Finally,

analyzing computer generated data conrms that

the non-monotonic time evolution of SX1;X2; smainly results from a competition between the

bleach and the induced absorption.

The calculated values of time constants are

sX 0:7 ps, sp 1=C 1:3 ps and so 2:5 ps;they are exactly the same as those given by [1,2]. It

is also noteworthy that a good agreement between

theory and experiment was reached by maintain-

ing the population relaxation time sp equal for the

v 1 6 v 0 and v 2 2 v 1 transitions;these two times are probably not too dierent in

reality. The theory is the simplest for the 3510

cm1 series; additional degrees of freedom, such as

OH bending, are involved in the 3420 cm1 and

3300 cm1 series.

Comparison with the literature data brings out

the following points. (i) Although shortly men-

Fig. 3. Decay of transient infrared absorption (schematically).

(a) The excited vibrational state is isolated; the decay of the

signal exhibits the time sp. (b) The excited state takes part in a

continuous sequence of excited vibrational states; the signal

decays on two time scales, sp and sX. (c) There exist two con-

tinuous sequences of vibrationally excited states; depending on

the choice of the pump and probe frequencies, X1 and X2, the

signal intensity may either decrease or increase with the time

delay s.

538 G. Gallot et al. / Chemical Physics Letters 341 (2001) 535539


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tioned by Woutersen and Bakker [12], it is the rst

time that non-monotonic decay of infrared ab-

sorption is fully examined for a large number of

pump and probe frequencies. However, this eect

has already been discovered and interpreted in the

visible spectral region by Kimura et al. [16], Sch-

wartz and Rossky [17] and Pommeret et al. [18].

(ii) The OH motions are quantum mechanical here

and in [12]. The remaining degrees of freedom are

treated by classical molecular simulation in this

work, and by employing the semi-empirical

Brownian oscillator model in WoutersenBakker's

paper. (iii) The presence of two time scales sX and

sp, as well as the cancellation of bleach-induced

absorption intensities, makes `reading' of the ex-

periment dicult. Nevertheless, correctly inter-preted, it provides new values for sX: measuring

solvatochromic shifts no longer is the only way of

studying solvent relaxation.

Acknowledgements

The authors would like to thank the GDR 1017

of the CNRS for its support during this work. The

Laboratoire d'Optique Quantique is a `Unite

Mixte de Recherche' no. 7645 of the CNRS andthe Laboratoire de Physique Theorique des Liqu-

ides is a `Unite Mixte de Recherche' no. 7600 of

the CNRS.

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