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C. Intramolecular Vibrations in Carbon Tetrachloride and Chloroform

C. Intramolecular Vibrations in Carbon Tetrachloride and Chloroform

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464



Fleming et al.



Figure 10 2D fifth-order Raman spectra of (a) CCl4 , (b) CHCl3 , and (c) a 1:1

mole ratio CCl4 :CHCl3 mixture.



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are a number of cross (off-diagonal) peaks in the spectra that could

originate from the nonlinearities between the intramolecular vibrational

modes in these samples. For example, there is a strong cross peak

in the CCl4 spectrum between the 2 and 1 vibrational modes ω2 D

460 cm 1 , ω4 D 219 cm 1 . One might expect a relatively strong coupling

between these two modes as a result of the Fermi resonance between 2 2

and 1 . There are also examples of cross peaks in quadrant II such as

the peak at [ω2 D 460 cm 1 , ω4 D 219 cm 1 ] and the difference peak

at [ω2 D 219 cm 1 , ω4 D 460–219 cm 1 ]. Off-diagonal peaks are also

evident in the CHCl3 spectrum and the CCl4 :CHCl3 mixture spectrum. In

addition to the cross peaks found in the spectra for neat CCl4 and CHCl3 ,

the CCl4 :CHCl3 mixture spectrum also contains cross peaks between

modes from each of the constituents. An example is the peak at [ω2 D

368 cm 1 , ω4 D 219 cm 1 ] between the 3 mode of CHCl3 and the 2

mode of CCl4 .

While the off-diagonal peaks in the CCl4 and CHCl3 spectra could

represent intramolecular coupling between vibrations, they may also contain

contributions from intermolecular coupling. Within the direct fifth-order

response, intermolecular coupling would be required to generate cross peaks

between CCl4 and CHCl3 in the mixture spectrum (Fig. 10c). The cross

peaks between vibrational modes of CCl4 and CHCl3 in the CCl4 :CHCl3

mixture spectrum could be the result of anharmonic coupling of the involved

coordinates on the collective liquid potential or intermolecular interactioninduced effects that couple the fluctuations in the electronic states between

molecules in the polarizability. However, assigning the off-diagonal features

in any of the two-dimensional spectra to coupling between the vibrational

modes requires that the observed signal in question originate from direct

fifth-order scattering. As shown in Equation (34), and clearly demonstrated

for the intermolecular motions in CS2 , we must consider both the direct and

cascaded contributions to the measured response. Figure 11 shows simulated sequential (a) and parallel (b) cascaded two-dimensional spectra for

CCl4 . To simulate the heterodyne detected data, the spectra represent the

5

calculated jR 3 2 C 4 Ð Rcascade

2 , 4 j cross-term and were simulated

directly from the measured third-order spectrum in Fig. 4. In Fig. 11 it is

clear that cascaded responses will produce off-diagonal peaks between all of

the detected vibrational modes. Note that these off-diagonal peaks carry no

information concerning microscopic coupling between the different vibrational modes. The challenge becomes determining the relative contributions

in the measured two-dimensional spectra from the direct and cascaded

responses.



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Figure 11 Cascaded 2D fifth-order Raman spectra for CCl4 simulated directly

from the 1D spectrum shown in Fig. 4. (a) The sequential cascade spectrum. (b) The

parallel cascade spectrum. (c) A best fit to the 2D spectrum in Fig. 10a using a

linear combination of the sequential and parallel cascaded spectra. The ratio is

0.8:1 sequential:parallel.



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We can simulate the total cascaded response by a linear combination

of the sequential and parallel cascaded spectra in Fig. 11, weighting each

by the wavevector matching factors for the cascade intermediates shown in

Table 1. However, unlike the homodyne detection employed for CS2 , in this

case we must also account for the phase sensitivity inherent in a heterodyne

detected signal, [Equation (34)]. To demonstrate the consequences of phasesensitive detection, we first consider an ideal case where the direct response

and all four cascade intermediates are perfectly phase matched. In this

case, keeping in mind that R 3 and R 5 are purely real, the local oscillator

field kLO D k1 C k2 C k5 and the direct fifth-order signal field will be

purely imaginary [Equation (15)]. In other words, the local oscillator will

be perfectly in phase with the direct fifth-order signal. On the other hand,

as shown in Equation (29), the cascaded signal field will be purely real,

thus /2 phase shifted from the local oscillator and perfectly out of phase.

In this ideal example, the heterodyne signal contains only the desired direct

fifth-order signal.

Unfortunately, real experiments seldom, if ever, present the ideal case.

In these experiments the phase matching is not perfect. Equation (12) shows

how a deviation from perfect phase matching will result in a complex value

of the phase matching factor, F, and a phase shift in the emitted signal field.

The magnitudes of the phase matching factors in Table 1 shows that both

of the sequential intermediates deviate from perfect phase matching under

the assumption of delta-function beam diameters. In addition, due to the

finite dimensions of the incoming laser pulses, there will be a range of

phase matching conditions for all of the considered processes associated

with the range of incoming beam angles. To see how the phase matching

condition can effect the phase of the emitted signal field, consider the

sequential intermediate kseq D k1 k2 k3 . The magnitude of the phase

matching factor is shown in Table 1 as 0.77. This value is the magnitude of

the complex value for the phase matching factor, F D 0.27 C iŁ 0.72. The

large imaginary component in F will result in a large imaginary component in the emitted field, Equation (29), which would be in-phase with the

ideal local oscillator discussed in the previous paragraph. With our experiments containing a range of phases for the potential signals and the local

oscillator, it becomes quite complicated to directly simulate the cascaded

response.

Although the complexity of the experiment makes it very difficult

to generate an exact simulation of the expected cascaded response, it is

possible to demonstrate that the measured spectra cannot be the result of

cascaded processes alone. A linear least-squares fit to the measured CCl4



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Fleming et al.



spectrum using a linear combination of the sequential and parallel cascade

simulations, Figs. 11a and 11b, is shown in Fig. 11(c). A comparison of

Fig. 11c and Fig. 10a shows that the measured CCl4 spectrum cannot be

quantitatively simulated considering only the cascaded processes. Ab initio

calculation on CHCl3 have found that for the lower-frequency intramolecular modes in CHCl3 , such as those shown in Fig. 10b, the direct fifthorder signal is within the same order of magnitude as the cascaded signal

(30,34). The direct response becomes the dominant response for the highest

frequency intramolecular modes ω > 1000 cm 1 reflecting the increase in

magnitude of the cubic anharmonicity with increasing frequency. With the

magnitude of the direct fifth-order signal within an order of magnitude of

the cascaded signal, and considering the potential discrimination against the

cascades provided by the heterodyne detection, it is reasonable to conclude

that Spectra in Fig. 10 contain significant contributions from the direct fifthorder Raman response. This result provides clear evidence of the ability to

measure the direct fifth-order signal. Unfortunately, our current inability

to satisfactorily deconvolve the direct and cascaded contributions to the

measured spectra significantly compromises our ability to obtain conclusions concerning the microscopic coupling between the observed vibrational

modes.

D. Future Experimental Directions



Based on the current experimental evidence, it is clear that the key to the

successful application of two-dimensional nonresonant Raman spectroscopy

lies in finding experimental solutions to the problem of contamination from

cascading third-order signals. From Equation 30, there are a few obvious

experimental adjustments that can be made to improve the ratio of direct to

cascaded fifth-order signals, such as using a shorter optical path length and

a longer wavelength radiation source. One can also consider lowering the

number density, N, to improve the ratio. This idea can readily be applied

to the case of well-defined intramolecular vibrations, where the polarizability can be considered molecularly additive, by simply lowering the

concentration of the chromophores of interest. Note that the number density

dependence also provides an indication of whether the signal originates

from the direct or cascaded processes since the signal will have an N2 or N

dependence (N4 or N2 for homodyne detection), respectively (Equation (15)

and (29)]. However, variation of the number density cannot easily be

applied to the case of intermolecular motions. The main problem lies in how

to experimentally vary the concentration of intermolecular chromophores.



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The typical approach taken when attempting to vary the concentration of

intermolecular modes is the use of binary mixtures. When one considers

the many body nature of the intermolecular modes and the complexity of

binary mixtures, it is not directly evident that there is any proportionality

between the ill-defined concept of concentration for intermolecular modes

and the binary mixture fraction. An additional complication in the use of

binary mixtures comes from the significant changes in the polarizability

weighted density of states as a function of binary mixture fraction. In other

words, the intermolecular spectrum is changing with binary mixture fraction. These types of effects are clearly evident in third-order measurements

of CS2 in binary mixtures (3).

Other experimental considerations that can aid in improving the ratio

of direct to cascaded signals have already been introduced above; they are

the exploitation of phase matching and the use of phase-sensitive detection

to remove the cascaded third-order processes. For example, it should be

possible to improve the discrimination provided by phase matching geometry 8c with small alternations in the geometry and the use of smaller

diameter input fields. This would have to be accompanied by improvements in detection sensitivity to allow detection of the much smaller direct

fifth-order signal. However, phase-sensitive detection currently appears to

hold the greatest promise in the pursuit of the uncontaminated direct fifthorder signal. The intrinsic heterodyne experiments presented above give a

clear indication of the ability of phase-sensitive detection to aid in discriminating against the cascaded signals while providing the additional sensitivity

necessary to measure spectra from systems with polarizabilities that are less

than that of CS2 . Many of the problems associated with the intrinsic heterodyne experiment, such as the time dependence and spatial phase dependence

of the local oscillator, can be remedied using an external local oscillator.

One possibility would be to use one of the five input beams as the local

oscillator, spatially and temporally overlapping the signal and LO in an

interferometer after the sample. Another approach would be the use of

diffractive optics to generate, in addition to the five input fields, a local

oscillator field along the signal direction. Examples of this approach have

been demonstrated in four wave-mixing experiments (41,42).

V. CONCLUDING REMARKS



In this chapter we have demonstrated the great promise of two-dimensional

Raman spectroscopy to go beyond the ensemble average of linear

spectroscopy and reveal the microscopic details that underlie the vibrational



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spectral density. This technique can be applied to a wide frequency range;

from intermolecular motions on time scales as long as many nanoseconds

to well-defined intramolecular vibrations on femtosecond time scales. The

technique has the potential to determine both the nature of coupling between

motions on different time scales, i.e., anharmonicity in the vibrational

potential or nonlinearity in the polarizability, and to quantify these

couplings. We have also demonstrated that the experimental implementation

of this technique poses many challenges. Currently the greatest hindrance

to measuring the unadulterated direct fifth-order two-dimensional Raman

response comes from interfering cascaded third-order signals. Using an

intrinsic heterodyne detection geometry, we showed that signals from the

intramolecular vibrations in CCl4 and CHCl3 that contain contributions

from the direct fifth-order response can be measured. From this result

we can confidently conclude that experimental progress in the near future

will bring measurements of the direct fifth-order two-dimensional Raman

response that will realize the potential held by this technique.



ACKNOWLEDGMENTS



The authors would like to acknowledge the funding agencies that made

possible the work presented — NSF and CRM-KOSEF. The authors would

like to acknowledge Laura Kaufman, who made important contributions

to the experiments demonstrating third-order cascading in CS2 , and Jaeyoung Sung, who made important contributions to the theoretical background

section of this chapter.

REFERENCES

1.

2.

3.

4.

5.

6.

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Mukamel S. Principles of Nonlinear Optical Spectroscopy. New York: Oxford:

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McMorrow D, Thantu N, Melinger JS, Kim SK, Lotshaw WT. J Phys Chem

100:10389–10399, 1996.

Lotshaw WT, McMorrow D, Thantu N, Melinger JS, Kitchenham R. J Raman

Spectrosc 26:571–583, 1995.

Tanimura Y, Mukamel S. J Chem Phys. 99:9496–9511, 1993.

Ernst R, Bodenhausen G, Wokaun A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Oxford: Clarendon Press, 1987.

Slichter CP. Principles of Magnetic Resonance. 3rd ed. New York: Springer,

1978.



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8. Abella ID, Kurnit NA, Hartmann SR. Phys Rev 141:391–141, 1966.

9. Hartmann SR. Sci Am 218:32–40, 1968.

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11. Steffen T, Fourkas JT, Duppen K. J Chem Phys 105:7364–7382, 1996.

12. Cho M. in Lin SH, Villaeys AA, Fujimura Y, eds. Advances in Multi-Photon

Processes and Spectroscopy. Vol. 12. Singapore: World Scientific, 1999,

pp 229.

13. Tanimura Y. Chem Phys 233:217–229, 1998.

14. Okumura K, Tanimura Y. J Chem Phys 106:1687–1698, 1997.

15. Okumura K, Tanimura Y. J Chem Phys 107:2267–2283, 1997.

16. Mukamel S, Piryatinski A, Chernyak V. Acc Chem Res 32:145–154, 1999.

17. Saito S, Ohmine I. J Chem Phys 108:240–251, 1998.

18. Murry RL, Fourkas JT. J Chem Phys 107:9726–9740, 1997.

19. Murry RL, Fourkas JT, Keyes T. J Chem Phys 109:7913–7922 1998.

20. Hahn S, Park K, Cho M. J Chem Phys, in press.

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24. Tokmakoff A, Lang MJ, Larsen DS, Fleming GR, Chernyak V, Mukamel S.

Phys Rev Lett 79:2702–2705, 1997.

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272:48–54, 1997.

26. Tokmakoff A, Fleming GR. J Chem Phys 106:2569–2582, 1997.

27. Tokmakoff A, Lang MJ, Jordanides XJ, Fleming GR. Chem Phys

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28. Tominaga K, Keogh GP, Naitoh Y, Yoshihara K. J Raman Spectrosc

26:495–501, 1995.

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30. Tominaga K, Yoshihara K. Phys Rev Lett 76:987–990, 1996.

31. Tominaga K, Yoshihara K. J Chem Phys 104:4419–4426, 1996.

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42. Goodno GD, Astinov V, Miller RJD. J Phys Chem B 103:603–607, 1999.



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11

Nonresonant Intermolecular

Spectroscopy of Liquids

John T. Fourkas

Eugene F. Merkert Chemistry Center, Boston College, Chestnut Hill,

Massachusetts



1. INTRODUCTION



The dynamics of a chemical process can change considerably in going from

the gas phase to the liquid phase. One fundamental reason for such differences is that liquids are able to solvate chemical species. For example,

solvation might stabilize the transition state in a chemical reaction to a

greater extent than it stabilizes the reactants, thereby accelerating the reaction rate. Of course, solvation itself is a dynamic process, which has

important implications for chemical processes in solution. If the lifetime of a

transition state is shorter than the inherent dynamic time scale of the solvent,

for instance, solvation will not be able to stabilize the transition state to

the fullest possible extent. The above example illustrates the importance of

gaining a molecular-level understanding of the dynamics of solvents.

Although the microscopic motions in a liquid occur on a continuum

of time scales, one can still partition this continuum into two relatively

distinct portions. The short-time behavior in a liquid is characterized by

frustrated inertial motions of the molecules. While an isolated molecule

in the gas phase can translate and rotate freely, in a liquid these same

motions are interrupted by collisions with other molecules. Liquids are

dense enough media that collisions occur very frequently, so that molecules

undergo pseudo-oscillatory motion in the local potentials defined by their



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nearest neighbors. Given the heterogeneity of local environments in a liquid,

these intermolecular vibrations are characterized by a broad distribution of

inherent frequencies, ranging from a few to perhaps 200 cm 1 . However,

since the structure of a liquid evolves with time, an intermolecular vibrational mode cannot retain its identity indefinitely. In practice, the local mode

picture breaks down on time scales longer than a picosecond or so. On these

longer time scales, the microscopic motions in a liquid are nonoscillatory

and irreversible, as the positions and orientations of the molecules in a

liquid evolve diffusively.

Ideally, one would like to be able to study the specific solvent

dynamics associated with a chemical process of interest. While a number

of techniques exist for achieving this end (1–5), they also tend to give

rather indirect information about the relevant molecular motions of the

solvent. However, the molecular dynamics of a solvent around a solute can

be described to a first approximation by the dynamics of the pure solvent.

Thus, there is considerable interest in trying to understand the inherent

microscopic dynamics of pure solvents.

Three types of techniques are widely used to probe the microscopic

dynamics of pure liquids: inelastic neutron scattering (6), far-infrared (FIR)

spectroscopies (7), and low-frequency Raman spectroscopies (8). Of these,

inelastic neutron scattering is the most general, in that it is capable of

probing all of the microscopic motions of a liquid. On the other hand, it

is also an expensive technique that can only be performed at a limited

number of sites in the world. Conversely, FIR and Raman techniques are

subject to spectroscopic selection rules, and therefore cannot probe all of the

microscopic dynamics of a liquid. As is the case for intramolecular vibrational spectroscopies, due to different selection rules intermolecular IR and

Raman techniques yield complementary information. Technical limitations

have in the past made good FIR sources and detectors expensive, which

has limited the application of FIR spectroscopies to liquids [although this

situation may be changing with the advent of pulsed THz radiation sources

based on ultrafast laser systems (9)]. On the other hand, Raman techniques,

by virtue of being nonresonant, can be implemented with relatively inexpensive visible sources and detectors. Accordingly, low-frequency Raman

spectroscopies have been an extremely popular means of studying liquid

dynamics and will be the subject of this chapter.

The earliest and simplest nonresonant technique for studying intermolecular dynamics was spontaneous low-frequency Raman spectroscopy

(also known as Rayleigh-wing spectroscopy) (8). In its most basic implementation, a reasonably powerful monochromatic laser beam travels through



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the liquid of interest. Scattered light is collected at a right angle to the

laser path and is then dispersed by a monochromator. Thermally excited

intermolecular dynamics lead to frequency shifts in the scattered light via

the Raman effect, so that the inelastic scattering spectrum yields direct

information about the intermolecular modes of the liquid.

Spontaneous scattering is a relatively weak process, and so coherent

spectral techniques such as nearly degenerate four-wave mixing (10) and

stimulated Raman gain (11) spectroscopies have been developed over the

past few decades for studying low-frequency Raman modes. Spontaneous

Raman techniques rely on vacuum fluctuations to provide one of the three

photons needed to generate the scattered signal; furthermore, because the

direction of propagation of the vacuum photon is indeterminate, the spontaneous Raman signal radiates in every direction. In coherent Raman spectroscopies, lasers provide all of the photons needed. These techniques therefore

stimulate motion in the intermolecular modes that they probe, rather than

relying on thermal fluctuations to excite them. As a result, coherent spectroscopies generate considerably more intense signals than do spontaneous

spectroscopies. In addition, the wave vectors of the three incident photons

are well defined in coherent spectroscopies, such that the signal propagates

in a unique direction. The trade-off is that a minimum of two lasers of

different frequencies, at least one of which is tunable, must be employed

to accomplish this end.

An alternate approach is to perform coherent Raman spectroscopy

in the time domain rather than in the frequency domain. In this case, a

single laser that produces short pulses with sufficient bandwidth to excite

all of the Raman modes of interest is employed. One pulse or one pair

of time-coincident pulses is used to initiate coherent motion of the intermolecular modes. The time dependence of this coherence is then monitored

by another laser pulse, whose timing can be varied to map out the Raman

free-induction decay (FID). It should be stressed at this point that the information contained in the Raman FID is identical to that in a low-frequency

Raman spectrum and that the two types of data can be interconverted by

a straightforward Fourier-transform procedure (12–14). Thus, whether a

frequency-domain or a time-domain coherent Raman technique should be

employed to study a particular system depends only on practical experimental considerations.

While a large number of coherent, time-domain, low-frequency

Raman spectroscopies have been developed (15–18), they all fall under the

general category of optical Kerr effect (OKE) spectroscopy (19,20). The

Kerr effect is a phenomenon that occurs when a polar liquid is subjected



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