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Nonresonant Intermolecular Spectroscopy of Liquids


Figure 13 Room-temperature reduced spectral densities for (a) acetonitrile,

(b) benzene, (c) benzene-d6 , (d) carbon disulfide, (e) chloroform, (f) hexafluorobenzene, (g) mesitylene, and (h) 1,3,5-trifluorobenzene.

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assignments are truly meaningful. First, DID scattering from molecules with

anisotropic polarizabilities is far more complex than DID scattering from

atoms with isotropic polarizabilities, and therefore the spectral shape of

the DID scattering in a molecular liquid is unlikely to resemble that in an

atomic fluid. Second, as discussed above there is a strong, negative cross

term between DID and single-molecule scattering (23) that is not generally

taken into account in bandshape analysis of reduced spectral densities. On

the other hand, insofar as this cross term arises from motions that are

common to both single-molecule and DID scattering, it may have the same

shape as the pure single-molecule contribution to the spectrum (23). If this

is the case, and if pure DID scattering is weak [as a recent simulation

study of CS2 has suggested (86)], then the shape of the reduced spectral

density should be highly similar to the shape of the pure single-molecule


If the reduced spectral densities do indeed mirror the pure singlemolecule contribution, then at least for symmetric-top liquids, which should

have only one basic type of librational mode, it does not seem that the two

observed bands can represent two distinct types of molecular motions. Similarly, the reduced spectral densities of liquids composed of less symmetric

molecules also can often be fit to the same two types of bands, despite the

existence of multiple possible librational modes.

One possible explanation for the observation of multiple features in

reduced spectral densities is that there is considerable microscopic structure in liquids, which leads to multiple librational modes even for highly

symmetric molecules. An extreme example of such a viewpoint is the

recent suggestion that the reduced spectral density of liquid benzene can

be described completely in terms of the collective Raman-active modes of

crystalline benzene (87). While this speculation is an intriguing one, we

believe it would require an unlikely degree of local order in the liquid.

Furthermore, although hexafluorobenzene has a quadrupole moment that

is of similar magnitude to that of benzene and also has a similar crystal

structure (64), there does not appear to be a strong resemblance between

the Raman spectrum of the crystalline and liquid forms of this substance.

Thus, it seems likely that similarity between these spectra in benzene is

largely coincidental.

To develop a deeper understanding of the contributions to the intermolecular spectrum of symmetric-top liquids, it is useful to study the

spectrum as a function of some readily varied parameter. For instance,

OHD-RIKES dilution studies of CS2 in alkanes have proven quite interesting (73,83). The general trend in such studies is that the high-frequency

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Nonresonant Intermolecular Spectroscopy of Liquids


feature moves to lower frequency with increasing dilution, while the lowfrequency feature remains virtually unchanged. Furthermore, the spectrum

stops changing after a certain degree of dilution has been achieved. These

results have been interpreted both in terms of a “softening” of the intermolecular potential (73) and in terms of changes in the dominant scattering

mechanism upon dilution (83).

Studies in which OKE data for pure liquids are obtained as a function

of either temperature (26,36,41) or pressure (42) have also proven enlightening. Figure 14 shows reduced spectral densities for benzene obtained

over a broad range of temperatures. These spectra show two features that

are typical for all of the liquids that we have studied: as the temperature is lowered, the low-frequency feature moves to lower frequency and

the high-frequency feature moves to higher frequency and broadens. The

behavior of the high-frequency feature can be understood readily in terms

Figure 14 Reduced spectral density for benzene as a function of temperature.

The temperatures from top to bottom on the high-frequency side of the spectra are

267, 272, 281, 294, 299, 308, 327, 336, and 341 K. The spectra have been scaled

arbitrarily to match in intensity at 30 cm 1 .

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of the increase in density that accompanies a reduction in temperature. The

behavior of the low-frequency feature is rather less intuitive, however.

We have previously suggested that the temperature-dependent

behavior of the low-frequency feature in the reduced spectral density is

related to damping of the intermolecular modes (26). Assuming that the

damping rate is relatively independent of the frequency of a mode, below

some critical frequency the spectrum is guaranteed to be overdamped,

regardless of the nature of the damping mechanism. Since the damping rate

should decrease with decreasing temperature, so will the critical frequency.

The end result of this scenario will be increase in intensity at low frequency

as the temperature is lowered.

The low-frequency feature in the reduced spectral density corresponds

to the long-time tail of the intermolecular response function, which is

often denoted the “intermediate” response in the OKE literature (15,51).

In most liquids, this portion of the response appears to be exponential over

a significant time scale. Why this portion of the response is exponential

and what information the time scale of this exponential holds is still poorly

understood. For this reason, we have performed detailed temperaturedependent studies of the intermediate relaxation in six symmetric-top

liquids: acetonitrile, acetonitrile-d3 , benzene, carbon disulfide, chloroform,

and methyl iodide (56).

For each liquid, this portion of the response indeed appears to be

exponential over a broad range of temperatures. Given these temperaturedependent data, we can begin to delve into the nature of the intermediate

response. Figure 15 shows Arrhenius plots of the intermediate response

time, i , for all six liquids. Note that for each liquid the Arrhenius plot yields

a straight line, suggesting that the intermediate relaxation arises from some

sort of activated process. This result is an important one, because it allows

us to eliminate pure dephasing as the cause of the intermediate response.

In the diffusive limit, the angular momentum correlation time J and the

single-molecule orientational correlation time of a liquid should satisfy the




J sm D

6kB T

where I is the moment of inertia of the molecules (88). Since pure dephasing

arises from collisions, the pure dephasing time should be roughly proportional to J . However, since both i and sm exhibit Arrhenius behavior,

their product clearly cannot be inversely proportional to temperature.

Figure 16 shows that for each liquid, a plot of i versus Á/T yields

a straight line. This result, which is reminiscent of the DSE equation

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Nonresonant Intermolecular Spectroscopy of Liquids


Figure 15 Arrhenius plots of i for acetonitrile (filled circles), acetonitrile-d3

(open circles), benzene (filled triangles), carbon disulfide (open triangles), chloroform (filled squares), and methyl iodide (open squares). (From Ref. 56.)

Figure 16 Debye-Stokes-Einstein plots of i for acetonitrile (filled circles),

acetonitrile-d3 (open circles), benzene (filled triangles), carbon disulfide (open

triangles), chloroform (filled squares), and methyl iodide (open squares). (From

Ref. 56.)

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[Equation. (24)], suggests that the intermediate relaxation may be hydrodynamic in origin. If I is indeed related to hydrodynamic effects, it seems

unlikely that this decay time is related to population relaxation of the intermolecular modes. Thus we must search for another cause.

Since both coll and sm for these six liquids follow DSE behavior,

for any given liquid a plot of I versus coll or sm must be linear. However,

by comparing such plots for all six liquids, we can determine whether I is

more closely related to coll or sm . The plots of I versus coll are shown

in Fig. 17 and those versus sm in Fig. 18. Strikingly, all of the plots in

Fig. 17 fall on the same straight line, which implies that for these liquids

the value of i can be predicted at any temperature given knowledge of the

value of coll .

We have suggested recently that the above data are consistent with

motional narrowing being the source of the intermediate OKE relaxation

(56). While on short enough time scales the structure of a liquid is relatively

Figure 17 Plots of i versus coll for acetonitrile (filled circles), acetonitrile-d3

(open circles), benzene (filled triangles), carbon disulfide (open triangles), chloroform (filled squares), and methyl iodide (open squares). (From Ref. 56.)

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Nonresonant Intermolecular Spectroscopy of Liquids


Figure 18 Plots of i versus sm for acetonitrile (filled circles), acetonitrile-d3

(open circles), benzene (filled triangles), carbon disulfide (open triangles), chloroform (filled squares), and methyl iodide (open squares). (From Ref. 56.)

stable, on time scales greater than several hundreds of femtoseconds the

structure evolves. Structural evolution in turn leads to “spectral diffusion,”

i.e., fluctuations in the frequencies of the modes. At low enough frequencies,

these fluctuations occur on a time scale that is faster than the characteristic

frequencies of the modes. The frequencies of such modes are effectively

time-averaged, thus narrowing the spectrum (89).

Since the collective orientational correlation time depends on the

structure of a liquid, it is plausible that the rate of structural evolution of

the liquid is proportional to this quantity. Thus, at lower temperatures coll

is longer and therefore the structural fluctuations are slower. As a result,

motional narrowing is less effective as the temperature is lowered. While

less motional narrowing would normally lead to a slower decay in the time

domain, in this case the spectral density goes down to zero frequency. Thus,

motional narrowing can reduce the spectral density at low frequencies and

thereby decrease the intermediate relaxation time.

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Low-frequency Raman spectroscopies are useful techniques for delving into

the microscopic structure and dynamics of liquids. Low-frequency Raman

spectroscopy has become all the more powerful a tool with the advent of

both reliable femtosecond laser systems and coherent spectroscopic techniques such as OHD-RIKES. However, the relatively broad and featureless

nature of low-frequency Raman spectra continues to present challenges for

both theorists and experimentalists, although significant progress is being

made in developing means of interpreting such spectra. In the meantime,

reduced spectral densities from OHD-RIKES data have seen some success

in the prediction of solvation dynamics (81,82,90), although such successes

have not been universal. The successful implementation of higher-order

spectroscopic techniques akin to the photon echo (91,92) should also assist

greatly in the resolution of many of the outstanding issues in the lowfrequency Raman spectroscopy of liquids.


I wish to acknowledge the members of my group who obtained the data

discussed here: Brian Loughnane, Richard Farrer, Alessandra Scodinu,

Natalia Balabai, and Tomaso Baldacchini. This work was supported by the

National Science Foundation, Grant CHE-9501598. I am also a Research

Corporation Cottrell Scholar, an Alfred P. Sloan Research Fellow, and a

Dreyfus New Faculty Fellow.


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