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A. Concentration Fluctuations in CH3I:CDCl3

A. Concentration Fluctuations in CH3I:CDCl3

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Vibrational Dephasing in Liquids


Figure 9 Shift in the peak frequency of the isotropic Raman line of the sym-methyl

stretch in CH3 I as a function of concentration in CDCl3 . The shift is relatively and

linear with concentration. The peak frequency in pure CH3 I is 2951 cm 1 . (From

Ref. 4.)

There is a Lorentzian component of about 5.5 cm 1 FWHM, which is

concentration independent. All of the concentration variation is due to a

Gaussian component, which is nearly absent at the ends of the concentration

range but reaches a maximum size of 4.25 cm 1 in the 50:50 mixture. The

Lorentzian shape of the concentration independent component is suggestive

of a fast modulation dephasing. The Gaussian shape of the concentration

dependent component is suggestive of a slow modulation process.

Results of the Raman echo experiment on this system are shown in

Fig. 12. The interpretation of these data proceeds by comparison with a

series of models, which are constrained to be consistent with the linewidth

and FID data. The simplest model assumes that the entire linewidth/FID

is due to fast modulation processes, including the concentration-dependent

process. The predictions are shown as solid curves in Fig. 12. At long

1 and 3 , the predicted signal is substantially smaller than the observed

signal. The enhanced signal results from a rephasing induced by the echo

sequence and indicates that a slow modulation process must be present. On

the other hand, the rephasing is not complete, so there must be a significant

fast-modulation process as well.

The next obvious model is a combination of one fast process

corresponding to the concentration-independent Lorentzian component of

Copyright © 2001 by Taylor & Francis Group, LLC



Figure 10 Width (FWHM) of the isotropic Raman line of the sym-methyl stretch

. Voight fits give Lorentzian

in CH3 I as a function of concentration in CDCl3

and Gaussian

contributions to the line shape. The Lorentzian component is

consistent with a concentration independent fast-modulation process. The Gaussian

component suggests an additional contribution from slow concentration fluctuations.

(From Ref. 4.)


Figure 11 Raman FID of the sym-methyl stretch in 50:50 CH3 I:CDCl3 showing

a nonexponential decay (points). The fit (solid curve) is a combination of fast

(T2 D 2.0 ps) and slow ω D 4.25 cm 1 dephasing processes. (From Ref. 4.)

Copyright © 2001 by Taylor & Francis Group, LLC

Vibrational Dephasing in Liquids


Figure 12 Raman-echo data from the sym-methyl stretch in 50:50 CH3 I:CDCl3

(points). Three models for the dephasing are shown: solid, fast modulation only;

dashed, fast and static modulation; dotted, fast and intermediate (5 ps) modulation. The best fit (dotted) is consistent with interaction of the vibration with

local-concentration fluctuations. The fits are constrained to be consistent with FID

and line shape data. (From Ref. 6.)

Copyright © 2001 by Taylor & Francis Group, LLC



the line shape and one static process corresponding to the concentrationdependent Gaussian component. This model predicts the dashed curves

in Fig. 12. The predicted intensity at large delays is larger than in the

fast-modulation model in qualitative agreement with the data. But at a

quantitative level this model overestimates the magnitude of the rephasing,

and the predicted signal is too large at long times.

The third model assumes that the concentration fluctuations are long

lived but not static. The dotted line in Fig. 12 shows good agreement with

the data assuming a lifetime of 5 ps for the concentration fluctuations. A

range of lifetimes from 4 to 7 ps is compatible with the data. This model

not only agrees with the Raman echo data, it is also matches the FID and

Raman line shape and peak position data as well. The lifetime found in

the Raman echo implies that the Gaussian component of the line shape

4.25 cm 1 is actually motionally narrowed from the full distribution of

frequencies 5.15 cm 1 .

This type of lifetime data is almost impossible to extract accurately

and unambiguously from line shape or FID data alone. Figure 11 shows

that the second, infinite-lifetime model fits the FID very well. The Raman

echo gives the lifetime information that is key to testing Schweizer and

Chandler’s analysis.

By extending Schweizer and Chandler’s theory (88) to concentration

fluctuations (see next section), we can relate the experimental dephasing

parameters to molecular properties. From the size of the frequency shift

upon dilution and the distribution of frequencies, the average number of

solvent molecules perturbing the vibration is found to be 5.4. This result is

close to the number of solvent molecules in the first solvation shell of the

vibrating molecule. Thus, the relevant solute-solvent interaction has a range

of approximately one molecular diameter. From the long range, we infer that

the coupling is due to the attractive portion of the intermolecular potential.

From the diffusion constant, the time for exchange of molecules in and out

of the first solvation shell is estimated to be 6–10 ps, a range that overlaps

with the experimental range of perturbation lifetimes. This system is a good

example of a long-range attractive interaction producing a slow modulation

of the vibration, as anticipated by the Schweizer-Chandler model.

B. Density Fluctuations in Acetonitrile

The experiments in CH3 I:CDCl3 mixtures show that a long-range attractive

interaction can make a vibration sensitive to fluctuations in the local composition. Do similar fluctuations in local density also perturb vibrations, even

Copyright © 2001 by Taylor & Francis Group, LLC

Vibrational Dephasing in Liquids


in a pure liquid? This question is the main topic of Schwiezer and Chandler’s original theory (88). In their original paper, they not only point out

the possibility of dephasing from density fluctuations, they also propose a

method of estimating its magnitude from gas-to-liquid frequency shifts. This

method predicts that in many common liquids, the magnitude of dephasing

from density fluctuations will be similar to the magnitude from collisional


Because density fluctuations produce a long-lived perturbation,

whereas collisional dynamics are fast, the Raman echo is a definitive

experiment for testing this prediction. An excellent system for this test

is the sym-methyl stretch of acetonitrile (3). There have been many

Raman line shape studies of this mode, which concluded that the IBC

theory of collisional dynamics alone can account for the linewidth

(84,90,91,133,134). On the other hand, calculations by George and Harris

using Schweizer and Chandler’s theory predicted that a substantial fraction

of the linewidth is due to density fluctuations (135).

The Raman FID for this mode (Fig. 13) is a single exponential with

T2 D 0.82 ps, as expected from previous line shape measurements. Corresponding Raman echo results are shown in Fig. 14. The fit curves are

derived from the FID by assuming that all the frequency modulations are

fast. Simulations show that a slow component with a width of ω ½ 1 cm 1

Figure 13 Raman FID of the sym-methyl stretch in CH3 CN (points). The exponential fit (solid curve) is consistent with the isotropic Raman line shape. (Adapted

from Ref. 3.)

Copyright © 2001 by Taylor & Francis Group, LLC

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A. Concentration Fluctuations in CH3I:CDCl3

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