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E. Solvent-Assisted IVR in Ethanol

E. Solvent-Assisted IVR in Ethanol

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The first experiment to show that this system is unusual is the Raman

FID as a function of temperature (Fig. 21). Ethanol supercools easily

and forms a glass at 97 K. But unlike the experiments in supercooled

toluene (Fig. 15), the decay in ethanol at 80 K remains exponential, and

the dephasing rate is changed only slightly at low temperature. This result

eliminates shear fluctuations, density fluctuations, and other mechanisms

with an explicit viscosity dependence.

Theories based on the Enskog collision time (84) or other solid-like

approaches do not have a strongly temperature-dependent frequency correlation time. But they do have a temperature-dependent factor resulting from

the need to create the solvent fluctuations in the first place. Thus, all fastmodulation theories predict that the dephasing rate will go to zero at 0 K.



Figure 21 Raman FID (points) of the sym-methyl stretch in CH3 CD2 OH in the

liquid (295 K), in the high-temperature glass (80 K), and in the low-temperature

glass (12 K). Fits (solid curves) are based on exponential decays. The increase in

dephasing rate at low temperatures is unexpected. (Adapted from Ref. 5.)



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Vibrational Dephasing in Liquids



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The Raman FID at 12 K shows that this prediction fails (Fig. 21). The rate

is no slower at 12 K than at 80 K. In fact, it is slightly faster.

The fact that the dephasing rate is almost constant with temperature

within the glass (80–12 K) suggests that the linewidth is due to a static

distribution of structures frozen into the glass. This idea can be tested with

the Raman echo. A line dominated by static broadening will show strong

rephasing effects when 1 is increased. As Fig. 22 shows, this rephasing

does not occur in ethanol, either in the liquid, high-temperature glass, or

low-temperature glass.

The combination of FID and echo experiments has eliminated all

possibilities for pure dephasing mechanisms. Slow-modulation mechanisms

are inconsistent with the echo results; fast-modulation mechanisms are

inconsistent with a broad line persisting at low temperature. Resonant



Figure 22 Raman-echo data (points) from the sym-methyl stretch in CH3 CD2 OH

in the liquid (295 K), in the high-temperature glass (80 K), and in the

low-temperature glass (12 K). In all cases, there is no change in the decays between

1 D 0 and at 1 D 1 ps, showing that there is no slow dephasing mechanism.

(Adapted from Ref. 5.)



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energy transfer can be considered, but isotope dilution experiments have

eliminated this possibility as well (Table 1) (5). Population relaxation can

cause line broadening [Equation (20)] but the measured time of 22 ps is

much to long to contribute to the linewidth in ethanol (Table 1) (94–97).

At this point it is clear that none of the recognized dephasing

mechanisms can account for the coherence decay in ethanol. We have

proposed that solvent-induced intramolecular vibrational redistribution

(IVR) is responsible. A number of other vibrational levels of the methyl

group lie near the energy of the sym-methyl stretch, primarily the

asymmetric stretch and the overtones and combinations of the bending

modes (Fig. 23). These levels are separated by more than their respective

linewidths, so they do not undergo conventional IVR. However, they

do lie within kT of each other. It is possible that coupling to solvent

motions causes rapid transfers between these state, i.e., solvent-induced

IVR. Because the number of states involved is small, significant population

will remain in the sym-stretch, even after the IVR process is over. The



Figure 23 A proposal for dephasing in ethanol by solvent-assisted intramolecular

vibrational redistribution (IVR). The sym-methyl stretch is initially excited, but

rapidly equilibrates with one or more modes within kT (the asym-methyl stretch

and/or CH bend overtones). Dephasing occurs with this rapid equilibration time

TIVR . However, significant population remains in the sym-methyl stretch after

equilibration. Relaxation from this group of state to lower states causes the final

relaxation of the population to zero, which is measured as T1 in energy relaxation

experiments. (Adapted from Ref. 7.)



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Vibrational Dephasing in Liquids



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measured Tl reflects loss out of these nearly isoenergetic states to lower

levels and can be much slower than the IVR time TIVR .

Although TIVR may not be reflected in a Tl measurement, it will cause

dephasing in the same way that Tl would. The idea that solvent-induced

IVR may be active in methyl groups has been suggested before (92,96,97),

but there has not been a good estimate of its rate. If our proposal that the

dephasing time is primarily due to IVR is true, the time is very fast, TIVR D

225 and 365 fs at 12 K and 295 K, respectively. Within this scenario, the

fast TIVR and broad linewidth can be attributed to the hydrogen-bonding

network of ethanol, which provides an efficient bath to promote IVR.



V. SUMMARY



Before the introduction of the Raman echo, many dephasing mechanisms

had been discussed, but most experimental work had been interpreted in

terms of IBC or related theories. With the increased information available

from the Raman echo and from measurements across a wider range of

temperature, a much richer picture of vibrational dephasing is emerging.

Two features of the system are important: the intermolecular coupling

and the solvent dynamics. Each of these factors has two major components. The coupling has a long-range attractive part and a short-range

repulsive part. The dynamics has a viscosity-independent inertial part and

a viscosity-dependent diffusive part. The possible combinations between

these components are summarized in Table 2.

Because the amplitude of inertial motion is small, it causes only small

modulations of long-range interactions. There is no evidence that these

weak interactions are important in dephasing.

Table 2 Classification of Dephasing Mechanisms by Type

of Intermolecular Potential, Type of Solvent Dynamics, and

Speed of the Resulting Frequency Modulation



Potential

Dynamics



Long range

(attractive)



Short range

(repulsive)



Inertial/Collisional

Diffusive



Weak (fast)

S-C (slow)



IBC/phonon (fast)

VE (fast-slow)



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Long-range attractive interactions can be effectively modulated by

diffusive dynamics, which have a much larger amplitude. SchweizerChandler theory treats dephasing from these effects. They produce slowmodulation dephasing, even at low viscosity. However, the diffusive motion

must be along a coordinate with weak correlations. In the case of density

fluctuations, the strong correlations between molecular positions suppress

fluctuations to such an extent that dephasing by density fluctuations is not

important in most simple liquids. This case is illustrated by acetonitrile

(3) and benzonitrile (10,11) (Section IV.B). However, if a coordinate with

weak correlations is introduced, dephasing by long-range forces can become

significant. This case was illustrated by the mixture containing methyl

iodide in which the number of methyl iodide neighbors is the weakly

correlated coordinate (Section IV.A).

In pure liquids, short-range repulsive forces are responsible for most

of the dephasing. The viscoelastic theory describes the interaction of

these forces with the diffusive dynamics of the liquid (Section IV.D). The

resulting frequency modulation is in the fast limit in low-viscosity liquids

but can reach the slow-modulation limit at higher viscosities. This type of

dephasing was seen in supercooled toluene (Section IV.C).

Short-range forces interacting with inertial dynamics are at the

heart of IBC and related theories (Section II.C). These processes always

produce fast-modulation dephasing. The existing studies are still unclear

on the role of this kind of dephasing. Reasonable candidates exist,

for example, the temperature-independent component of dephasing in

toluene (Section IV.D). Additional studies are needed to make a conclusive

assignment.

The enduring conclusions from dephasing studies are that there are a

plethora of potential dephasing mechanisms, and the dominant mechanisms

can change depending on the system examined. The framework just outlined

is a useful organization of current results but probably does not exhaust the

possibilities that might be found in a wider variety of systems. The ethanol

study is a case in point, where none of the standard dephasing processes

applies, and a new IVR process had to be postulated (Section IV.E).

Several fundamental questions have been raised by these investigations and hopefully will be answered in the near future. One set of questions

concerns the role of inertial dynamics coupled by short-range forces. A

clear example of this type of process has not yet been unambiguously

identified. An important question is whether this type of dephasing is dominated by vibrational anharmonicity or by nonlinear coupling. In the case of

vibrational anharmonicity, the degree of coherence in the inertial dynamics



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Vibrational Dephasing in Liquids



431



becomes a central issue. The IBC and VE theories make opposite and

extreme assumptions about this coherence and make diametrically opposed

predictions regarding the resulting dephasing.

A long-range goal of studying vibrational dephasing is to gain insight

into solvent effects in general. An important step in attaining this goal is

to make quantitative connections between the vibrational dephasing in a

given liquid and other dynamical processes. The VE theory holds promise

in this regard. An analogous VE theory of electronic solvation already exists

(140,145), and an analogous theory of molecular rotation is easy to envision.

Future studies will tell whether the VE framework can successfully unify

these different dynamical processes.

The existing techniques of Raman FID and Raman echo in combination with studies extending across wide temperature and viscosity ranges

have the potential to answer all these questions. With the ever-increasing

sophistication of ultrafast laser technology, these experiments are becoming

easier and more accessible. Armed with these techniques and the understanding obtained in simple liquids, vibrational dephasing also promises to

be a route to deciphering the dynamics of more complex systems, such as

polymers and biological systems.



ACKNOWLEDGMENTS



I thank the coworkers who helped with the original work discussed here:

Prof. David A. Vanden Bout, Dr. Laura J. Muller, Dr. John E. Freitas,

Dr. Xiaotian Zhang, and Hugh H. Hubble. I also thank Dr. Xun Pan and

Prof. Richard MacPhail of Duke University for providing the Raman line

shape data on CH3 I:CDCl3 . This work was supported by the National

Science Foundation.

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10

Fifth-Order Two-Dimensional Raman

Spectroscopy of the Intermolecular

and Vibrational Dynamics in Liquids

Graham R. Fleming and David A. Blank∗

University of California at Berkeley, and Lawrence Berkeley National

Laboratory, Berkeley, California



Minhaeng Cho

Korea University, Seoul, South Korea



Andrei Tokmakoff

Massachusetts Institute of Technology, Cambridge, Massachusetts



I. INTRODUCTION



In recent years there has been significant interest in the extension of

nonlinear optical spectroscopy to higher orders involving multiple time

and/or frequency variables. The development of these multidimensional

techniques is motivated by the desire to probe the microscopic details

of a system that are obscured by the ensemble averaging inherent in

linear spectroscopy. Much of the recent work to extend time domain

vibrational spectroscopy to higher dimensionality has involved the use

of nonresonant Raman-based techniques. The use of Raman techniques

has followed directly from the rapid advancements in ultrafast laser

technology for the visible and near-IR portions of the spectrum. Time

domain nonresonant Raman spectroscopy provides access to an extremely

Ł



Current affiliation: University of Minnesota, Minneapolis, Minnesota



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