12600
J. Phys. Chem. 1994, 98, 12600-12608
Probing Intermolecular Dynamics in Liquids by Femtosecond Optical Kerr Effect Spectroscopy: Effects of Molecular Symmetry Hans P. Deuel, Peijun Cong,* and John D. Simon* Department of Chemistry and Institute for Nonlinear Science, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0341 Received: May 19, 1994; In Final Form: August 17, 1994@
Intermolecular dynamics in a series of nitriles and substituted methanes are investigated using opticalheterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) with -30 fs laser pulses. The results obtained unequivocally establish a correlation between molecular symmetry and the ratio of intermolecular vs intramolecular contribution to the Kerr signal. Quantitative connections between molecular anisotropy and optical Kerr measurements are discussed. The utility of low-frequency spectral densities measured by OHD-RIKES in relation to studies on dynamics in liquids is addressed.
I. Introduction The dynamical behavior of molecular liquids has attracted a considerable amount of research efforts for several decades. 1,2 Not very long ago, the experimental techniques used in probing the short time dynamics in liquids and fluids were almost exclusively carried out in the frequency domain (infrared and far-infrared absorption, Raman and Rayleigh scattering).',*With the advances in ultrafast laser technology, sub-50 fs coherent pulses can now be generated r ~ u t i n e l y . ~As a result, time domain spectroscopic techniques are becoming increasingly important. Experimental techniques that have impacted the study of liquid dynamics include time-dependent Stokes transient pump-probe absorption,*-' optical Kerr effect (OKE),12-17 coherent Raman (coherent anti-Stokes Raman scattering,'* impulsive Raman ~cattering,'~ etc.), and transient grating spectroscopies.20-22 In this paper, we focus on the application of one of the techniques, optical Kerr effect, in elucidating detailed information of molecular dynamics in liquids. More specifically, we concentrate on the influence of molecular shapes and symmetries on inter- and intramolecular dynamics as revealed by OKE spectroscopy. OKE spectroscopy is based on an optically-induced anisotropic polarization in the sample. In an optically transparent medium, this anisotropic polarization is primarily composed of birefringence. Shank et al. first demonstrated a picosecond optical Kerr shutter in CS2.23 Since then, time-resolved OKE spectroscopy has been extensively used in the study of condensed phase dynamics. Its utility was greatly enhanced with the introduction of optical heterodyne detection, whereby the real and imaginary parts of the response could be easily separated and the experimental signal becomes a linear function of the material r e s p o n ~ e . ~This ~ , ~ particular ~ form of OKE spectroscopy is commonly referred to as optical-heterodynedetected Raman-induced Kerr effect spectroscopy (OHDRIKES). The chemical systems that have been studied range from simple atomic fluids such as Xe and ArZ6to complex chemical solutions.27 The dynamical phenomena probed are equally diverse, ranging from rotational tumbling2*to coherent wave packet motion.29 The application of time-resolved OKE spectroscopy to neat liquids has evolved rapidly over the last decade. This advance
* To whom correspondence @
should be addressed. Abstract published in Advance ACS Absrmcts, November 1, 1994.
0022-365419412098-12600$04.5010
has partially been spurred by dramatic improvement in time resolution of the experiment. Greene et al. first identified a subpicosecond component in the decay of the transient birefringence in CS2.30 McMorrow et al. addressed the origin of the nonlinear response in simple liquids such as halogensubstituted methanes using a -65 fs laser source.13 Cho et al. measured the Kerr signal in a series of n-alcohols with a -30 fs pulse,31 and Chang et al. performed similar experiments in strongly hydrogen-bonding liquids such as ethylene glycol and water.14J5 The interpretation of the time domain OKE data has undergone significant advances as well. In most of the early experimental studies, the time-resolved optical Kerr decay transients were analyzed in the time domain. The emphasis was placed on identifying the different components in the multiexponential decay and assigning physical meaning to them.32.33 More recently, M c M ~ r r o wand ~ ~McMorrow and LotshawI7 introduced a Fourier transform technique that enables both the separation of nuclear contributions from electronic contributions to the Kerr signal and the deconvolution of the instrument response from the molecular response function. The only assumption made in this approach is the Born-Oppenheimer approximation. Thus, this data analysis technique is modelindependent and has become the method of choice in analyzing optical Kerr transient decay^.'^.^' This method of analysis also has the advantage that frequency domain information can be obtained directly from the time-dependent signal. A recent trend involves extending the spectroscopic information obtained in OKE experiments to other realms of liquid phase dynamics. Efforts have focused on establishing a link between OKE spectroscopy (a measure of solvent-solvent interactions) and time-dependent Stokes shift (TDSS) experiments (a measure of solvation dynamics). Two examples of this work are provided by the studies of Cho et al.35and Chang et al.14 In the first case, Cho et al. presented an example of OKE and TDSS being closely connected.35 These workers demonstrated that the same underlying low-frequency spectral density could reproduce both the C(t)measurement and the OKE decay curve in acetonitrile. In the second case, Chang and Castner went one step further and constructed C(t)'s based on the nuclear response functions extracted from OKE measurements for a number of solvents using a theory developed by Maroncelli et al.36 If these approaches prove to be general and applicable to a wide variety of liquids, OKE spectroscopy will 0 1994 American Chemical Society
Probing Intermolecular Dynamics in Liquids become an even more powerful tool in studying molecular dynamics in liquids. One of the motivations for the current work is to explore the generality of such approaches. In this paper, the OKE data taken with a -30 fs pulse for two series of aprotic molecular liquids are presented. The first series that will be discussed are the nitrile solvents: acetonitrile (CH3CN), propanenitrile (CH~CHZCN), propyl nitrile ((CH3)2CHCN), and 2,2-dimethylpropanenitrile(C(CH&CN). The molecular shape becomes increasingly symmetric (approaching a sphere) with increased alkylation. The second set of molecules examined are chloroform (CHCb), trichlorofluoromethane (CC13F), tetrachloromethane (CC4), and trichlorobromomethane (CBrCl3). In this series, C3" symmetry is maintained (CC4 has a higher symmetry of Td), while the polarizability is increased. These solvent series enable systematic studies of the effects of molecular shapes and symmetry and the optical Kerr signal. The role of molecular symmetry on the origin of the nonlinear optical responses in liquids has been previously addressed by McMorrow et al.13 These authors discussed the qualitative trend of decreasing intermolecular contribution with increasing molecular symmetry in the series of molecules of CHCl3, CHZC12, and CC4. Since the trend was discussed in the context of time domain curve-fitting procedures, no quantitative information was extracted about the relative contributions of intermolecular vs intramolecular interactions to the experimental signal. In the current work, the Fourier transform technique is employed in analyzing the OKE decay transients. The relative inter- and intramolecular contributions are clearly separated in the frequency domain representation of the OKE data, thereby facilitating a quantitative comparison. In discussing the OKE signal on the two solvent sets studied, a comprehensive approach is pursued with the goal of understanding the underlying physical mechanisms and origins in the optical Ken response in simple molecular liquids. In particular, for the nitrile series, we focus on the effect of molecular shapes on the intermolecular contributions to the optical Kerr response. As molecular shapes become increasingly spherical, the anisotropy of the intermolecular interactions should decrease. Since OKE signal arises from anisotropic polarization induced by the optical field, one would expect to see a profound change in the response function arising from the intermolecular interactions. In the substituted methane series, the molecular symmetry of C3vis held essentially constant. However, the dipole moment (both direction and magnitude) and polarizability change. Thus, we can isolate the effects of polarizability and dipole-dipole interactions from molecular symmetry. These collective insights into the nature of the OKE signal provide important information about the utility of this data in interpreting other experimental studies of liquid dynamics. The remaining part of this paper is organized as follows. First, a brief description of the experimental setup is given. This is followed by discussions of the OKE experimental data and its relation to other frequency domain and time domain techniques that address liquid phase dynamics. Finally, some concluding remarks are offered based on these discussions.
11. Experimental Section Our experimental setup is similar to that reported by other group^.'^^'^^^^ Laser pulses of 30 fs duration are derived from a home-built continuous-wave self-mode-locked Tixapphire laser pumped by an Ar+ laser (Spectra-Physics Beamlok 2060). The laser repetition rate is -80 MHz, and its central wavelength is 780 nm. The laser output was stable enough to allow continuous data acquisition over many hours, which was often the time required to obtain a transient OKE decay curve with satisfactory signal-to-noise ratio.
J. Phys. Chem., Vol. 98, No. 48, 1994 12601 The laser beam was split into two portions: 96% was used as the pump and 4% served as the probe. Before the laser beam was split, it passed through a prism-pair compensation line to compensate for the positive group velocity dispersion downstream and ensure that transform-limited pulses arrived at the sample cell. (Care was taken to make sure that the same amount of optical material was passed through in both the pump and probe arms.) The pump and probe beams each passed through Glan-Taylor air-gap polarizers (Karl Lambrecht), which were oriented 45" with respect to each other. The pump and probe beams were focused into a 2 mm path length sample cell with a 5 cm focal length lens. The pump beam was blocked after it passes through the sample, and the probe beam was recollimated and directed to an analyzer polarizer oriented 90" relative to the probe polarizer. The transmission through this analyzer was detected by either a red-enhanced photomultiplier or an amplified photodiode. In order to increase the signal-to-noise ratio and avoid the complexity of dealing with a quadratic signal, a A/4 wave plate was placed between the two crossed polarizers (extinction ratio better than 5 x in the probe beam to introduce an in-quadrature local oscillator to selectively enhance the birefringence signal. The instrument response was measured by replacing the sample cell by a thin KDP crystal (200 pm) and detecting the second harmonic light that resulted from the sum frequency generation between the pump and probe beams. The time delay between pump and probe pulses was varied by translating a high-resolution mechanical stage (Klinger, resolution 0.667 fs/step) that was inserted in the optical path of the pump beam. The pump beam was modulated at -2.0 kHz to provide the reference for a lock-in amplifier. The entire experiment was controlled by a Macintosh I1 computer with a home-developed data acquisition program (LabVIEW, National Instruments) capable of automatically averaging many scans. This averaging feature was essential for obtaining a high signalto-noise OKE measurements. The liquid samples were purchased from Aldrich and further purified by multipass filtration. It was empirically found that the filtration process greatly reduced the number of small impurity particles and thus reduced the spikes caused by the scattering off these particles.
111. Results and Data Analysis A. Data Analysis Procedure. Our data analysis procedure is depicted in Figure 1, and it follows closely the main results previously reported by McMorrow et al.17 In the top panel, the OHD-RIKES decay transient of pure acetontrile is plotted along with the background-free intensity autocorrelation function between the pump and probe pulses. This OHD-RIKES curve is composed of 1024 points and covers a total time period of 2.73 ps. The corresponding spectral resolution via the Fourier transform technique is thus 1/2.73 ps or 12.2 cm-*. The useful spectral range is limited by the frequency spread of the excitation laser source. The middle panel shows both the real and imaginary parts of the spectrum obtained by Fourier transforming the corresponding time-dependent curve. Due to the nature of the Fourier transform technique, a small uncertainty in time zero will result in small oscillations in the frequency domain spectrum. The time zero setting in the Fourier transform procedure is adjusted around the maximum of the electronic response to minimize such oscillations. The Fourier transformed autocorrelation function is shown in this panel as the dashed line (265 cm-' full width at half-maximum, 388 cm-' full width at 25% of maximum). As pointed out by M c M ~ r r o wand ~ ~McMorrow and Lotshaw,17the time-dependent response, T(t),measured in OHD-
12602 J. Phys. Chem., Vol. 98, No. 48, 1994
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Time (femtosecond)
Deuel et al.
2000
0
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lo00
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2000
Time (fs) 0
100
200 300 400 Wavenumber
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Figure 1. Procedure for Fourier transform analysis of the experimental OHD-RIKES data. (top) Time-dependent OKE signal for acetonitrile (solid line) and intensity autocorrelation between the pump and probe
Figure 2. OHD-RIKES signals for a series of nitrile solvents. With increased alkylation, the relevant importance of intra- to intermolecular contributions to the total signal increases. See text for more details.
then we have the following relations:
laser pulses (dotted line). (middle) Fourier transformed spectra: real part of the OKE signal (solid line); imaginary part of the OKE signal (dotted line); real part of the autocorrelation measurement (dashed line). (bottom) Real (solid line) and imaginary (dotted line) parts of the Fourier-transformed spectrum normalized to the autocorrelation spectrum. All the spectra shown in subsequent figures are normalized in this fashion. RIKES experiments is a convolution of the molecular nonlinear optical response function, R(t), with the background-free intensity autocorrelation function, G(*)(t)(transform limited).
T(z)
0~
J:
m
dt R(t - Z)G'2'(t)
The response function R(t) can be expressed as a sum of the electronic response function Re(?)and nuclear response function Rn(t):
R(t) = R,(t)
+ R,(O
(2)
For an off-resonant OKE-RIKES experiment, the electronic response is proportional to a &function (Born-Oppenheimer approximation): R,(t) = bd(t)
(3)
Therefore, the electronic response in the time domain is a 8-function convolved with the intensity autocomelation function of the laser pulse. It is symmetric relative to time zero and thus only contributes to the real part of a Fourier transform. If both the real and imaginary parts of the spectrum are divided by the Fourier transformed autocorrelation function, the imaginary part of the spectrum will reflect only the contributions from motions in the nuclear coordinates. The real part, after this division, contains both electronic and nuclear components. However, the electronic part will show up as a constant background in the spectrum, since it is a &function in the time domain. If we define ~ ( oas) the Fourier transform of R(t),
(4) (5)
Re ~ ( w=) b
+ Re %R,(t)}
(6)
wh re Fdesignates Fourier transform. This Fourier transform deconvolution procedure not only decouples the instrument response from the Kerr data but also isolates the nuclear contributions from those contributions that are caused by the instantaneous electronic hyperpolarizability. The lower panel of Figure 1 shows both the real and imaginary parts of the spectrum after division by the autoconelation spectrum. A constant background is clearly present in the real part of the spectrum up to 600 cm-'. This background is absent in the imaginary part, as expected. In the following sections of this paper the experimental data are treated by the same procedure; however, as we are only interested in the nuclear dynamics, only the imaginary parts of the spectra will be presented. B. Separationof Inter- and Intramolecular Contributions to the Optical Kerr Process. (a) The Nitrile Series. Figure 2 displays the OKE data of four nitriles. As a visual aid, spacefilling molecular models of the molecules studied are presented in Figure 3. As the series progresses from acetonitrile to 2,2dimethylpropanenitrile, the molecular shape evolves from being approximately cylindrical to nearly spherical. There are two prominent trends in the OKE data for these four molecules. First, the subpicosecond decay component that is pronounced in acetonitrile (the shoulder feature at 100 fs delay time) becomes less dominant with increased molecular size. For the case of 2,2-dimethylpropanenitrile,the shoulder feature is apparently absent. Second, the oscillatory quantum beat feature that is
-
J. Phys. Chem., Vol. 98, No. 48, 1994 12603
Probing Intermolecular Dynamics in Liquids
TABLE 1
nitriles CH3CN CH3CHzC.N (CH&CHCN (CH3)KCN
average polarizprincipal dipole (lImkIntra(o)) do)/ ability ' polarizabilities moment (JImkinter(o)>d o ) ti (A3) az,ap,a, (A3) (D) 0.019 0.094 0.23 0.64
4.48" 5.74,3.85, 3 M b 6.24" 8.99,5.48,4.27' 8.05" 9.83,9.07, 5.75d 9.59" 10.71.9.03, 9.03b
3.92' 4.02" 4.07' 4.29'
a Experimental value, taken from ref 38. Experimental value, z is parallel to CCN axis (ref 38). Calculated value, x is perpendicular to the CCC plane (ref 28). Calculated value, y is perpendicular to the HCCN plane (ref 38). Experimental value, taken from ref 39.
Figure 3. Space-fillingmodels for the series of nitrile solvents studied. Starting from upper left comer (clockwise): CH3CN, CH3CH2CN. (CH&CCN, and (CH3)zCHCN. With increased alkylation, the shape of the molecule transforms from rodlike to nearly spherical. I
I I\\
,
I
\
II h
HCCl,
I
\
I
1,
I
\
'\,
CH,CN
\
,'\-
f
I
i' '\,
I
'\ ; !
CH,CH,CN
/\
Time (fs) '~,
'\,
Figure 5. OHD-MKES signals for a series of substituted methanes.
/\
(CH,),CHCN ,'
,\,
/\ 1 :
\. 0
100
/
'\ 200
I
1
300
400
f
Wavenumber Figure 4. Normalized imaginary parts of the Fourier transformed data shown in Figure 2.
present in acetonitrile increases its prominence and becomes the dominant component in 2,2-dimethylpropanenitrile. The subpicosecond decay feature is due to intermolecular motions such as libration. The quantum beat feature is caused by intramolecular low-frequency coherent vibrational motions. Thus, without any further data analysis, this set of time-domain data clearly establishes the qualitative correlation between the shape of the molecule and the relative weight of intra- and intermolecular contributions to the OKE signal. To obtain more quantitative information about the inter- and intramolecular contributions, this time domain set of data is converted to frequency domain spectra by the procedure outlined in the last section. The results are shown in Figure 4. In this figure, the inter- and intramolecular contributions are clearly separated: The intermolecular contributions are reflected by a broad spectral feature in the 0-150 cm-' region, and the intramolecular components are converted from persisting oscillations in the time domain to isolated peaks in the frequency domain. The quantum beat feature in the acetonitrile spectrum is located at 370 cm-' and has been observed before.35 It is due to the C-CN bending mode.37 The quantum beat feature
grows in importance and becomes the most dominant feature in 2,2-dimethylpropanenitrile.The intermolecular contribution, on the other hand, decreases in relative weight down the series. A readily observable trend is that the width of spectral distribution becomes narrower as the molecule becomes more symmetric. The relative weights of inter- and intramolecular contributions are listed in Table 1. These weights are obtained by taking the ratio between the area covered by the intramolecular modes and the area covered by the 0-150 cm-' region. Also listed are the average polarizability volume, principle p~larizabilities,~~ and dipole moments,39 since these are the most pertinent quantities in addressing intermolecular interactions in aprotic liquids. In this series of molecules, acetonitrile and 2,2-dimethylpropanenitrile are symmetric tops (ignoring barriers to internal rotation for the CH3 groups in 2,2-dimethylpropanenitrile, treating them as one "atomic" group). On the other hand, propanenitrile and 2-methylpropanenitrile are asymmetric tops. Thus, molecular size, shape, and symmetry vary simultaneously across this series. However, the dipole moments, which derive much of their contribution from the CN group, remain a constant value of approximately 4 D.39 (b) The Substituted Methane Series. To further isolate the relative importance of these effects on the OKE signal, a group of substituted methanes were studied. In this series, the symmetry is maintained to be C3" (with the exception of CC4), and effects of permanent anisotropic polarizability are studied. Figure 5 shows the OKE data for CC13H, CC13F, CC4, and CBrCl3. Figure 6 shows the corresponding spacing-filling models for these molecules. As the series evolves, the molecules start off as oblate symmetric tops (CC13H and CC13F)
Deuel et al.
12604 J. Phys. Chem., Vol. 98, No. 48, 1994
TABLE 2 (Jrm&intra(o))
methanes HCCl3 FCCl3
cc4
BCC13
(J&inter(o))
0.30 0.52 4.45 1.32
average principal dipole do)/ polarizabilities polarizabilities moment dw) C i (A3) Qi, a1 (A3>. (D) 8Sb 5.9, 9.4b l.Old 5.8, 10.4‘ 0.4Y’ 9.5‘ 10.5, 10Sb 0.00 10Sb nae 11.7‘ 12.2, 11.4“
a q l is the polarizability along the C3 axis. Experimental value, taken from ref 38. ‘Calculated value based on an atomic dipole interaction model (ref 38) and geometric parameters from ref 39. Experimental value, taken from ref 39. e na = not available.
Figure 6. Space-filling models for the series of substituted methanes studied. Starting from upper left comer (clockwise): CCl3H, CCLF, CC13Br, and CC4.
I’
HCCl,
i I
,
CICCl,
0
100
200
300
400
500
0
100
200
300
400
500
Wavenumber Wavenumber Figure 7. Normalized imaginary parts of the Fourier transformed data shown in Figure 5.
and become a spherical top (CCl4) and a prolate symmetric top (CC13Br). In both chloroform and fluorotrichloromethanethere are quantum beats superimposed on contributions from intermolecular motions. The quantum beats are much less damped in chloroform than in fluorotrichloromethane. By simple visual inspection, there is no clear distinction between chloroform and trichlorofluoromethane as to which molecule has more contributions from intermolecular dynamics. In C c 4 and CC13Br, the OKE decay transients exhibit rich intramolecular dynamic behavior as seen by the intricate patterns of quantum beats. However, intermolecular contributions are not clearly present at all. These ambiguities are readily resolved by the Fourier transformed spectra, displayed in Figure 7. In the spectrum for chloroform, two quantum beat peaks are present at 262 and 366 cm-’. These are the Raman-active modes v3 (polarized, but has a significant depolarization ratio) and 2)6 (depolarized):0 The intermolecularpart of the spectrum carries much less weight than in the nitrile series. For the case of carbon tetrachlororide, the relative intermolecular contribution is down by a factor of 5 from chloroform, as compared with the peak amplitude of the quantum beats. Two intense quantum beat peaks are located at 220 and 3 11 cm-l. These can be assigned to the v2 and 214 modes in the corresponding depolarized Raman ~pectrum.~’For CC13Br, there are three quantum beat peaks that are clearly resolved in the frequency domain spectrum: 189, 224, and 293 cm-’. These are the 0 6 , v3, and v5 modes, re~pectively.~’The existence of the 293 cm-’ peak was speculated in a previous OKE work but not clearly observed
experimentally due to the bandwidth limit of the laser employed:’ The relative weight of the intermolecular contribution is slightly more than in carbon tetrachloride. For CC13F, its Fourier transformed spectrum qualitatively resembles that of chloroform. The quantum beat frequencies are 244, 317, and 397 cm-’. However, the intermolecular part of the spectrum is slightly narrower than that of chloroform and there are three, instead of two, quantum beat frequencies present in the intramolecular part. Table 2 lists the relative weights of the intra- vs intermolecular contributions to the OKE signal, obtained in the same fashion as for Table 1. The intermolecular contributions are cut off at 120 cm-’, due to the narrower spectral distribution exhibited by this series of molecules. Also listed in this table are the average polarizability volume, principal polari~abilities,~~.~~ and dipole moments.39
IV. Discussion Intermolecular contributions decrease in importance with increasing molecular symmetry and polarizability in the nitrile series, while for the intramolecular components the trend is reversed. For the methane series, the molecular symmetry is not varied. However, the polarization volume does increase from H to Br across this series. The molecular shape starts off near a “pancake” for CC13H, approaches a nearly perfect sphere in CCl4, and becomes a slightly elongated sphere in CCl3Br. The intermolecular fraction of the OKE signal declines with increasing “sphericalness”, and once again, the intramolecular part exhibits the opposite trend. These are the overall trends observed in the OKE measurements of these two solvent series. In the following subsections we discuss our current understanding of these observations and their possible utility in other related research areas in liquid phase dynamics. (a) Origin of the Intermolecular Components in OKE Spectroscopy. The intramolecular vibrational spectrum obtained from the Fourier transform of time domain OKE transients is equivalent to the frequency domain depolarized Raman spectrum. This connection can be rigorously proven theoretically and has been demonstrated experimentally for a number of m o l e ~ u l e s , 4 ~present - ~ ~ work included. The lowfrequency intermolecular spectrum obtained in this manner should also be proportional to the same depolarized Raman cross section. Even though a direct comparison is not available at the present time due to the difficulty associated with measuring Raman spectra in this 0-200 cm-’ region, there is no reason to doubt the validity of this connection, since it is based on first principles. Given this connection, the trend (see Tables 1 and 2) exhibited in both the nitrile and methane series is not surprising. The increase of intramolecular contributions with increasing molecular size and polarizability results in part from an increased number and/or cross section of depolarized Raman-active vibrational normal modes that fall within the detection window
J. Phys. Chem., Vol. 98, No. 48, 1994 12605
Probing Intermolecular Dynamics in Liquids of 0-500 cm-’ that is accessed by the 30 fs pulse used in our OKE experiment. Even for a symmetric molecule like CC4, there are asymmetric vibrational normal modes that can contribute to the depolarized Raman spectrum. However, the simple few-body normal-mode picture does not apply to intermolecular motions. Intermolecular vibrational modes in liquids are caused by collective, small-amplitude motions (thermal fluctuations) that involve many molecules. Thus, when we consider the intermolecular vibrational spectrum in liquids, we have to consider the collective nature of these intermolecular motions. Since OKE spectroscopy is equivalent to the depolarized Raman process, we consider the intermolecular OKE spectrum in terms of anisotropic vibrational Raman cross sections. The intermolecular vibrational spectrum is in principle determined mainly by pairwise intermolecular potentials, modified somewhat by many-body effects in liquids. With increasing dispersive forces across the nitrile and the methane series, the intermolecular vibrational absorption spectrum should become broader and shift to higher energy, thereby reflecting the presence of a deeper intermolecular potential well. However, the anisotropy in intermolecular interactions may not increase as the potential well deepens. In fact, it is likely the intermolecular potential becomes more isotropic. Consider, for example, a pair of acetonitrile molecules. The antiparallel arrangement of these two molecules is energetically more favored than the perpendicular configuration. This difference accounts for the relatively large intermolecular contribution to the OKE signal observed for neat CH3CN. If we substitute this pair of acetonitrile molecules with a pair of 2,2-dimethylpropanenitrile molecules, the energy difference in the parallel vs perpendicular configuration is significantly reduced. This is because dispersive forces, over dipole-dipole interactions, constitute a much larger fraction of total intermolecular interactions in 2,2-dimethylpropanenitrile. The bulkiness of the 2,2dimethylpropanenitrilegroup also increases the average distance between the CN groups (steric hindrance) and thus reduces the stabilization due to dipole-dipole interactions. Thus, the parallel and perpendicular arrangements for a pair of 2,2dimethylpropanenitrile molecules are not very different in energy. The lack of anisotropy in intermolecular interactions in 2,2-dimethylpropanenitrile accounts for the small intermolecular contribution to the OKE spectrum. The same arguments apply to the trend observed for the methane series. Since chloroform is the least symmetric molecule in shape among the four, it thus has the largest contribution from intermolecular interactions. Carbon tetrachloride is a spherical molecule and has no permanent anisotropic polarizability. Consequently, it has the smallest amount of contribution from intermolecular interactions. The intermolecular contributions in CC4 are purely interaction (or collision) induced. Bromotrichloromethane is close to carbon tetrachloride in overall polarizability. However, it has a larger intermolecular component in the OKE spectrum than carbon tetrachloride due to the fact that it possesses a permanent dipole. CCl3F fits between CCl3H and CC13Br in the trend. Quantitative information about the degree of anisotropy in intermolecular interactions is directly reflected in the permanent anisotropic polarizabilities (we refer to anisotropy as Iq1- all/ a). The most anisotropic molecule in the nitrile series, acetonitrile, has the largest permanent anisotropic polarizability, while 2,2-dimethylpropanenitrile, the most symmetric member of the group, possesses the smallest anisotropy in the polarizability ellipsoid. In the methane series, the most symmetric solvent, CC4, has no permanent anisotropic polarizability. For
I
I
I
I
---__
(CH,),CCN
0
20
40
60
80
100
120
Wavenumber Figure 8. Fits of the low-frequency normalized imaginary parts of the Fourier-transformed data for the nitrile series to an Ohmic distribution function: @(a)= o exp(-do,). The values of the wc’s are 32.5, 28.8, 24.9, and 20.3 cm-’ for CHsCN, CH~CHZCN, (CH+ CHCN, and (CH&CCN, respectively.
the rest of the halomethanes studied here, the anisotropy decreases from H to Br. For both series of liquids, the intermolecular contribution to the Kerr signal strongly correlates with the‘ degree of differences in principal polarizabilities of the individual molecules; the more anisotropic in polarizability, the more intermolecular contribution is present in the optical Kerr response. Average polarizability or polarity alone is not the determining factor. In some sense, this is a “selection rule” for OKE spectroscopy in liquids. As a consequence, despite the versatility of OKE spectroscopy, it is best suited to study the orientational dynamics of liquids composed of molecules with strongly anisotropic polarizabilities. (b) The Intermolecular Depolarized Raman Spectral Distribution. The time-dependent data give the intermolecular depolarized Raman spectral distribution in the 0-200 cm-’ region. We stress the fact that only the depolarized Raman spectral distribution is measured, not a general, universal spectral density of the liquid. This fact places important limits on the range of dynamic problems that this particular spectral density is applicable to in liquids. This point will be discussed in detail in the final subsection of this paper. Following the procedure outlined by Cho et al.,31we fit the OKE intermolecular spectral densities by an Ohmic distribution function, e ( w ) = w exp(-w/w,), which originated from the paper by Legget et al.44 While this approach does not provide any more insight into the underlying physics than the raw spectrum, it produces analytic description of the spectrum that can be used in subsequent calculations. Figure 8 displays such fitting results for the nitrile series. The depolarized Raman spectral density decreases in width and shifts to lower frequency from acetonitrile to 2,2-dimethylpropanenitrile. The fitting parameters confirm this trend: The 0,’s are 32.5, 28.8, 24.9, and 20.3 cm-’ for CH3CN, CH3CH2CN, (CH3)2CHCN, and (CH3)3CCN, respectively. All four spectral densities can be reproduced by the simple Ohmic function, as long as the intensities for the region below 20 cm-’ region (which is due to rotational diffusion) is ignored.
12606 J. Phys. Chem., Vol. 98, No. 48, 1994
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0
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Figure 9. Fits of the low-frequency normalized imaginary parts of the Fourier transformed data for the substituted methane series to an Ohmic distribution function: e ( w ) = OJ exp(-oh,). The values of the wc's are 20.3, 13.9, 16.8, and 15.3 cm-' for CC13H, CCljF, CC4,
and CCl3Br, respectively. I
I
I
Figure 11. Comparison of the depolarized Raman spectral density to
the far-infrared absorption spectrum for CC4. The dotted line is the infrared spectrum, and the solid line with open circles is the depolarized Raman spectral density. The two curves are scaled to have the same maximum amplitude; the absolute cross sections are not known. cant. The differences of the OKE spectral density and farinfrared absorption spectrum in these two rather different liquids, CH3CN and CC4, clearly indicate that the OKE spectral density is an incomplete measure of the overall intermolecular interactions in liquids. Since OKE spectroscopy is only sensitive to the anisotropic part of the spectral density, other approaches are needed to provide more detailed information on the complete spectral density. For isotropic liquids, there are only two independent x(3)tensor elements ~ l ~ l l ( wand) x1122(0))!~ While OKE spectroscopy measures the anisotropic part (2~1212(w)= x1111(w) - x1122(0)), other forms of coherent four-wave-mixing spectroscopy can be employed to gain a more complete picture of the low-frequency spectral density. For example, polarizationselective transient grating spectroscopy is capable of detecting a particular x(3)component (or a particular combination of ~ ( ~ 1 components) originating from nuclear coordinates while totally eliminating the component that is due to electronic hyperpolari~ability.~~ If one combines OKE spectroscopy and polarization-selective transient grating spectroscopy, in addition to farinfrared absorption measurements, a more comprehensive understanding of the low-frequency modes in liquids will emerge. Such efforts are currently underway in this laboratory, and results from such studies will be detailed in the future. (c) Applications of Low-Frequency Intermolecular Spectral Densities Measured in OKE Spectroscopy to Solvation Dynamics. Recently, efforts to apply the spectral densities (or the nuclear response function in the time domain) as measured via OKE spectroscopy to predict solvation dynamic^^-^ have appeared. Cho et al.35 developed a unified theory of both solvation dynamics and OKE spectroscopy based on a Brownian oscillator description of the solvent intermolecular dynamics.49 These authors hypothesized that the same spectral density is responsible for both the ultrafast relaxation dynamics of solvation and optical Kerr effect. This hypothesis was tested for the case of acetonitrile. As pointed out by Maroncelli et al., this model does not depend on solvent polarity in any direct way.36 Polarity could play a role in shaping the solvation dynamics through influencing the solvent spectral density. However, the spectral densities for the methane series (which include polar (e.g., CC13H) as well as nonpolar (CC4) solvents) measured in this current work closely resemble each other. They do not show any direct correlation with polarity. Since a broader spectral distribution translates into a faster time domain decay, some unexpected and unphysical predictions would be obtained using the hypothesis proposed by Cho et al.:35 CC4 would exhibit slower solvation dynamics than CCl3H but faster than
1 . 50 100 150 200
0
Wavenumber Figure 10. Comparison of the depolarized Raman spectral density to
the far-infrared absorption spectrum for acetonitrile. The dotted line is the infrared spectrum, and the solid line with open circles is the depolarized Raman spectral density. The two curves are scaled to have the same maximum amplitude; the absolute cross sections are not known. For the methane series, there is no simple trend. CC13H, the most anisotropic member of the group, has the broadest distribution with an w , value of 20.3 cm-'. This seems to be conforming with the trend observed for the nitrile solvents. However, the second most anisotropic molecule in the methane series, CCLF, has the narrowest spectral distribution with a wc of 13.9 cm-', while the totally isotropic molecule CC4 has a broader distribution (w, = 16.8 cm-') than the anisotropic and more polarizable molecule CC13Br (w, = 15.3 cm-l). To further illustrate the nature of the spectral density measured through OKE spectroscopy, far-infrared spectra of CH3CN and CC4 are taken from the l i t e r a t ~ r eand ~ ~ .plotted ~ ~ against the deconvoluted imaginary part of the Fourier transformed OKE transients in Figures 10 and 11, respectively. For cc14, the far-infrared spectrum is much broader and maximizes at a much higher frequency than the corresponding depolarized Raman spectrum. The reason for this discrepancy lies in the fact that infrared absorption measures directly the averaged intermolecular interactions, while OKE spectroscopy is only sensitive to the anisotropic part of the intermolecular potential. For a liquid that has strong dispersive intermolecular interactions but very little anisotropy, like CC4, the difference between these two types of measurements is expected to be very pronounced. However, even for the most anisotropic liquid that is studied in this paper, C H F N , the difference between the far-infrared absorption and depolarized Raman spectra is still quite signifi-
J. Phys. Chem., Vol. 98, No. 48, 1994 12607
Probing Intermolecular Dynamics in Liquids CC13F and CCl3Br. In light of our experimental results, the validity of the theoretical connection between TDSS and OKE requires further study. In a related work, Castner and co-workers utilized the nuclear response functions measured by OKE spectroscopy for water, ethylene glycol, and triacetin to predict C(t) for these solvents. These workers assumed that the OKE data represented the single molecule dipole correlation function, C l ( t ) (=(p(O) p(t))lp2, where p is the transition dipole). Using the approach of Maroncelli et a1.,26 the solvent relaxation function C(t) could then be constructed by the following equation:
where a,is the dipole density of the In light of the data presented above, there are two problems with this approach. First, C(t)for CC4 will be a constant of 1 within this model, as CC4 is nonpolar and a,(CC4) = 0. This is clearly an unphysical result. Second and more importantly, correlation functions measured via Raman spectroscopy (either in time domain or frequency domain) are generally not equivalent to a dipole correlation function. In fact, for a symmetric vibration in a symmetric top molecule, the depolarized Raman correlation function is connected to the dipole correlation function byS0
(9) where p is the anisotropic Raman tensor, P ~ ( xis) the second Legendre polynomial, and Tr denotes trace. Based on these observations, this proposed connection between OKE and solvation dynamics also needs further examination. Finally, Scherer and co-workers have used the spectral density functions measured in OKE experiments to predict photon-echo transients. These calculations provide good agreement (comparable to Brownian oscillator models) to experimental twopulse photon-echo measurement^.^^ However, it is likely that a spectral density measured with a vertical-horizontal (VH) geometry (OKE arrangement, ~ 1 2 1 2 ) is not the appropriate response function to use to predict signals measured in the vertical-vertical (photon echo, ~ 1 1 1 1 )setup. A spectral density measured with the same polarization geometry is optimal. The differences between the spectral densities obtained by these two polarizations could be significant and should be addressed.
V. Conclusions In this paper a systematic study of the effects of molecular shapes and symmetry on the optical Kerr response has been presented for two series of liquids. The relative contributions from inter- and intramolecular components to the overall OKE signal were discussed in detail. The general trend observed in both series of liquids is that the relative weight of intermolecular contribution decreases with increasing symmetry and declining anisotropy in the polarizability ellipsoid. This trend is accounted for by the anisotropy in molecular interactions. The experimental results also exhibit rich intramolecular dynamics. We defer a detailed analysis and discussion about the intramolecular vibrational dynamics in these and other liquids to a later publicati~n.~~ In addition to the analysis of the relative importance of intravs intermolecular response, the intermolecular spectral densities measured in OKE spectroscopy are determined. The results are discussed in terms of intermolecular interactions and could serve as starting points for further theoretical investigations into the nature of these liquids. Furthermore, the nature of the spectral density derived from OKE measurement is discussed. It is stressed that OKE based spectral density is only a
measurement of the depolarized Raman spectrum. The ability to use this spectral density in predicting solvation dynamics is
explored. Significant problems are encountered using existing theories. This work should serve as a word of caution in attempting to (0ver)generalize the spectral density measured in OKE to other areas of ultrafast dynamics in condensed media. To overcome the limitations imposed by OKE spectroscopy, the polarization-selective transient grating technique is proposed as a complementary tool in probing different elements of the Raman polarizability tensor. Coupled with far-infrared absorption spectroscopy, this approach will provide a more comprehensive understanding of the low-frequency intermolecular vibrational modes which are important to many facets of dynamics in condensed media. Finally, it should be pointed out that the nature of intermolecular dynamics in liquids is far from being understood. Recently, new theoretical approaches, such as instantaneous normal-mode analysis, have emerged for the simulation of shorttime dynamics in l i q ~ i d s . ~We ~ -hope ~ ~ our current work, along with other recent experimental studies, will serve to spur further theoretical interests in reaching the collective goal of understanding the liquid phase dynamics at a molecular level.
Acknowledgment. We thank Professors Norbert Scherer, Richard Stratt, and Thomas Keyes for providing preprints (refs 51 and 53-55) prior to publications. We also thank Dr. Robert M. Whitnell for his help in generating the spacing-fillingmodels used in Figures 3 and 6 . This work is supported by the National Science Foundation and the MMFEL Program administered by the Office of Naval Research. References and Notes (1) Rothschild, W. G. Dynamics of Molecular Liquids; John Wiley & Sons: New York, 1984. (2) Spectroscopy and Relaxation of Molecular Liquids; Steele, D., Yanvood, J., Eds.; Elsevier: Amsterdam, 1991. (3) See, for example: (a) Zhou, J. P.; Huang, C. P.; Shi, C. Y.; Murnane, M. M.; Kapteyn, H. C. Opt. Lett. 1994,19, 126-128. (b) Lemoff, B. E.; Barty, C. P. J. Opt. Lett. 1992, 17, 1367-1369. (4) Barbara, P. F.; Jarzeba, W. Adv. Photochem. 1990, IS, 1 . (5) Maroncelli, M.; MacInnis, J.; Fleming, G. R. Science 1989, 234, 1674-1681. (6) Maroncelli, M. J. Mol. Liq. 1993, 57, 1-37. (7) Simon, J. D. Acc. Chem. Res. 1988, 21, 128-134. (8) Rosker, M. J.; Wise, F. W.; Tang, C. L. Phys. Rev. Lett. 1986, 57, 321 -324. (9) Wise, F. W.; Rosker, M. J.; Tang, C. L. J . Chem. Phys. 1987, 86, 2827-2832. (10) Cong, P.; Yan, Y. J.; Deuel, H. P.; Simon, J. D. J . Chem. Phys. 1994, 100, 7855-7866. (1 1) Cong, P.; Deuel, H. P.; Simon, J. D. Chem. Phys. Lett. 1993, 212, 361-373. (12) Righini, R. Science 1993, 262, 1386-1390. (13) McMorrow, D.; Lotshaw, W. T.; Kenney-WallaceIEEEJ. Quantum Electron. 1988, QE-24, 443. (14) Chang, Y. J.; Castner, E. W. J. Chem. Phys. 1993,99,7289-7299. (15) Chang, Y. J.; Castner, Jr., E. W. J . Chem. Phys. 1993, 99, 113125. (16) Wynne, K.; Galli, C.; Hochstrasser,R. M. Chem. Phys. Lett. 1992, 193, 17-22. (17) McMorrow, D.; Lotshaw, W. T. J . Phys. Chem. 1991,95, 1039510406. (18) Laubereau, A,; Kaiser, W. Rev. Mod. Phys. 1978, 50, 607. (19) Ruhman, S.; Joly, A. G.; Kohler, B.; Williams, L. R.; Nelson, K. A. Rev. Phys. Appl. 1987, 22, 1717. (20) Eichler, H. J.; Gunthar, P.; Pohl, D. W. Laser Induced Dynamic Gratings; Springer: Berlin, 1986. (21) Fayer, M. D. Annu. Rev. Phys. Chem. 1982, 33, 63-87. (22) Fourkas, J. T.; Fayer, M. D. Acc. Chem. Res. 1992,25, 227-233. (23) Ippen, E. P.; Shank, C. V. Appl. Phys. Lett. 1975, 26, 92-93. (24) Eesley, G. L.; Levenson, M. D.; Tolles, W. M. IEEE J. Quantum Electron. 1978, 14, 45. (25) Levenson, M. D.; Kano, S. S. Introduction to Nonlinear Laser Specfroscopy; Academic Press: San Diego, 1988.
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