© Copyright 1996 by the American Chemical Society
VOLUME 100, NUMBER 24, JUNE 13, 1996
ARTICLES Femtosecond Optical Kerr Effect Studies of Liquid Methyl Iodide Edward L. Quitevis* and Manickam Neelakandan Department of Chemistry and Biochemistry, Texas Tech UniVersity, Lubbock, Texas 79409 ReceiVed: December 11, 1995; In Final Form: March 25, 1996X
The collective polarizability anisotropy dynamics of liquid methyl iodide at room temperature and ambient pressure was studied by using optical heterodyne-detected Raman-induced Kerr effect spectroscopy (OHDRIKES) with 45 fs laser pulses. The OHD-RIKES data are analyzed by using both the model-dependent approach, which assumes four distinct temporal responses, and the model-independent Fourier transform approach, which generates a spectral density. Near zero time, the OHD-RIKES transient is dominated by the instantaneous electronic response. The short-time nuclear response is characterized by two components. The first component is interpreted as arising from an inhomogeneously broadened (fwhm ≈ 62 cm-1) underdamped intermolecular vibrational mode with a mean frequency of ∼60 cm-1. The second component is an intermediate quasi-exponential response with a 1/e time constant of ∼200 fs. At longer times, the OHD-RIKES transient decays exponentially with a 1/e time constant of 1.76 ( 0.05 ps, which corresponds to the collective reorientation time of CH3I. The spectral density peaks at ∼24 cm-1 and has a fwhm of ∼80 cm-1. The spectral density can be well fitted by an ohmic distribution function with ωc ≈ 30 cm-1. The spectral density obtained from the OHD-RIKES data is consistent with previously measured depolarized Rayleigh scattering and low-frequency far infrared absorption spectra for liquid CH3I.
I. Introduction Far infrared (FIR) absorption and depolarized Rayleigh light scattering (DRS) spectroscopy have been extensively used by experimentalists to obtain information about molecular motions in liquids.1,2 The line shape in either an FIR absorption or DRS spectrum is some functional of the Fourier transform of a time correlation function (TCF). Specifically, the line shape is related to the TCF of the total dipole moment density in FIR absorption and to the TCF of an off-diagonal component of the total polarizability tensor in DRS. For liquids composed of anisotropic molecules, the TCF can be resolved into a molecular autocorrelation, an interaction-induced autocorrelation, and a molecular-induced cross-correlation. The molecular correlation relaxes primarily through single-molecule rotation, whereas the * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(95)03700-2 CCC: $12.00
induced terms relax through intermolecular motions. The fundamental problem in this field is the separation of spectra into molecular and interaction-induced components.3 If there is a difference in the time scales of molecular reorientation and intermolecular motions, the experimental spectra can be separated, at least partially, into various contributions. This separation involves projecting out the induced part of the moment or polarizability that follows molecular reorientation.4 The component that is left over after projection gives rise to “collision”induced (CI) terms. The TCF can then be written as
C(t) ) COR(t) + CCI(t) + CCR(t)
(1)
where COR(t) is a reorientational term that corresponds to “localfield”-modified molecular rotation, CCI(t) is the collision-induced autocorrelation, and CCR(t) is the reorientational-induced crosscorrelation. Because the collision-induced terms depend on © 1996 American Chemical Society
10006 J. Phys. Chem., Vol. 100, No. 24, 1996
Quitevis and Neelakandan
Figure 1. Schematic of optical heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES) apparatus: B/S, pellicle beam splitter; L, focusing lens; LIA, lock-in amplifier; λ/2, half-wave plate; λ/4, quarter wave plate; P1, P2, P3, Glan Taylor polarizers, PD, photodiode. The self-mode-locked Ti:sapphire laser and external pulse-compensating prism-pair are not shown. See text for further details.
fluctuations of the intermolecular variables, they should relax faster than the induced moments or induced polarizabilities themselves. A spectral decomposition based on the projection representation was tested in molecular dynamics (MD) simulations of CS2 and was found to reproduce the experimentally measured DRS spectrum.5,6 Thus, for liquids of relatively slowly reorienting molecules, such as CS2, it is possible to separate the DRS spectrum into a low-frequency local-fieldmodified reorientational component and a high-frequency collision-induced component. The projection representation was also found to be successful in simulations of the FIR spectrum of CH3CN.7 However, time scale separation is not universally valid. Experiments and MD simulations show that it doesn’t work for molecules such as CO2, N2, and C2H6.8 Although some information about the reorientational and intermolecular dynamics can be obtained from spectra, the decomposition of spectra based on the projection representation may mask short-time features of the former and long-time features of latter. One of the other challenges in this field has been to try to elucidate the short-time behavior of the molecular motion in liquids. Information about the short-time dynamics, in principle, should be found in the wings of DRS spectra. However, obtaining this information is difficult because of the low intensity in the wings of the experimentally measured DRS spectra. Understanding the short-time dynamics of liquids is the motivation for the current interest in the study of liquids through the use of nonlinear optical (NLO) time-domain techniques, such as transient grating optical Kerr effect (TG-OKE) spectroscopy,9 optical-heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD-RIKES),10-14 and impulsive stimulated Raman scattering (ISRS),15-18 with ultrafast lasers that generate sub50 fs pulses. It is well established that frequency-domain data and time-domain data are connected to each other by the Fourier transform relation. Keyes and Ladanyi19 first showed that the time dependence of the OKE response is the same as that of the Fourier transform of the DRS spectrum. This complementarity between the time domain and the frequency domain has been verified experimentally for DRS and OHD-RIKES,11,14 as well as for other techniques, including ISRS,15c,16 TG-OKE, and
stimulated gain spectroscopy (SGS).20 Because of this complementarity, time-domain data should contain the same information about the molecular dynamics of a liquid as contained in frequency-domain data. However, the short-time dynamics that show up in the low-intensity wings of the DRS spectrum are greatly enhanced in NLO time-domain data and can therefore be more accurately characterized. The transients obtained in these NLO time-domain techniques result from the interaction of the femtosecond laser pulse with molecules of the liquid through the third-order nonlinear polarizability χ(3). In OHD-RIKES, this interaction produces a transient birefringence in the liquid. The birefringence response of the liquid has an instantaneous electronic component and a noninstantaneous nuclear component. The noninstantaneous nuclear component is associated with reorientational and collision-induced dynamics. The reorientational dynamics can be divided into nondiffusive and diffusive motions. The nondiffusive reorientational dynamics are all dynamics that are not strongly overdamped. These include inertially limited rotations and librations. All of these motions contribute to the shorttime response ( 1 ps, and with β1 set equal to 88 fs. This diffusive component was then tail-matched to the short-scan OHD-RIKES signal. The short-dashed curve in Figure 1 is the tail-matched diffusive component. A reduced data set was then generated by subtracting the tail-matched long component from the short-scan OHD-RIKES signal.10c,j,l,12b,c Two noninstantaneous relaxation processes can be clearly seen when the contribution due to the long-time dynamics is subtracted from the signal, as depicted in a semilogarithmic plot (Figure 3A). From this semilogarithmic plot, one sees that the intermediate relaxation decays exponentially with a 1/e time constant of ∼200 fs. The dashed curve in Figure 3A is the convolution of the pulse autocorrelation and response function r2(t) (eq 7) with τint and β2 set equal 200 and 88 fs, respectively. This intermediate component was tail-matched to the difference signal in Figure 3A. Tail-matching the diffusive and intermediate components greatly reduces the number of parameters needed to fit the data. The best fit of the convolution of the pulse autocorrelation and the total nonlinear response function
) F{R(t)} ≡ D(∆ω)
(12)
where ∆ω is the frequency relative to the laser center frequency. D(∆ω) represents the intrinsic frequency response to a spectrally flat, δ-function excitation pulse. If one assumes that the impulse response can be written as the sum of an electronic response and a nuclear response (eq 3), D(∆ω) can be expressed as a constant A0 and the Fourier transform of the nuclear response function,
D(∆ω) ) A0 + F{r(t)}
(13)
Since A0 is real, the electronic hyperpolarizability will not contribute to Im[D(∆ω)]. Information about all possible nuclear motions is contained in the spectral density Im[D(∆ω)]. The spectral density can then be inverted to obtain the modelindependent nuclear response through the use of the equation
r(t) ) 2F
-1
{Im[D(∆ω)]}H(t-t0)
(14)
where F -1 is the inverse Fourier transform, and H(t) is a Heaviside step function, which is required to preserve causality. Figure 4 illustrates the low-frequency part of Im[D(∆ω)] between 0 and 250 cm-1 obtained from the FFT of the OHDRIKES data. The spectral band rises rapidly from 0 cm-1, peaking at ∼24 cm-1. The band then tails off at high frequencies, dropping to zero at ∼200 cm-1. The fwhm of the band is ∼80 cm-1. From this data, we calculate the value of the first spectral moment 〈∆ω〉 to be ∼60 cm-1. This value of 〈∆ω〉 is used to estimate the rise times βi in eqs 6 and 7 and the mean librational frequency in eq 8. Unfortunately, the signalto-noise ratio of the data is not good enough to be able to perform an inverse Fourier transform (eq 14) to obtain a modelindependent impulse nuclear response. The low-frequency spectral density can be fitted by the following function:
I(∆ω) ) I0(∆ω)a exp(-∆ω/ωc)
(15)
This model function has no physical significance. Its value lies in the fact that reasonable fits to the OHD-RIKES spectral
10010 J. Phys. Chem., Vol. 100, No. 24, 1996
Figure 4. Spectral density (points) obtained from OHD-RIKES data for liquid CH3I by using the Fourier transform technique. See text for details. The dashed curves are fits to the Bucaro-Litovitz (BL) equation (eq 15) with I0 ) 0.115, a ) 0.922, and ωc ) 31.5 cm-1. Also shown is the fit to the Ohmic distribution function (a ) 1) with I0 ) 0.0944 and ωc ) 29.9 cm-1.
densities are obtained. Bicaro and Litovitz33 developed this function in order to explain collision-induced light scattering in atomic liquids. With a ) 1, eq 15 becomes the ohmic distribution function. If all three parameters I0, a, and ωc are allowed to vary, then a fit of the spectral density is obtained for I0 ) 0.115, a ) 0.922, and ωc ) 31.5 cm-1 (Figure 4). For a ) 1, a fit of the spectral density gives I0 ) 0.0944 and ωc ) 29.9 cm-1 (Figure 4). Clearly, the low-frequency intermolecular spectrum for CH3I obtained in this study is well described by an ohmic distribution function. V. Discussion A. Temporal Response. This work, to our knowledge, presents the first reported femtosecond OHD-RIKES study of CH3I. Other substituted methanes have been studied by this technique.10c,13a The role of molecular symmetry in transient birefringence was considered in a study of the chlorinated methane series, CCl4, CHCl3, and CH2Cl2.10c The series of substituted methanes, CHCl3, CFCl3, CCl4, and CBrCl3, was later studied in order to understand the influence of molecular structure on intermolecular and intramolecular dynamics.13a In this series, C3V symmetry is maintained. In the OHD-RIKES data for CHCl3 and CCl3F, quantum beats are superimposed on the contributions from the intermolecular motion. In the OHD-RIKES data for CCl4 and CBrCl3, the quantum beat pattern is complex and the contribution from the intermolecular motions not as prominent. In contrast, quantum beats are not observed in the OHD-RIKES transient for CH3I, and the nuclear response appears to be due entirely to intermolecular dynamics. The lowest wavenumber Raman mode, the ν3 A1 symmetric stretch at 529 cm-1, falls outside the spectral width of the laser pulse (∼230 cm-1). Because of spectral-filter effects,10h quantum beats are absent in the CH3I OHD-RIKES transient obtained in this study. Table 1 lists the parameters that characterize the OHD-RIKES impulse response for both CH3I and CH3CN. The data for CH3CN was obtained from ref 12a. In Table 2 we also provide a list of relevant molecular parameters for these two liquids. We chose CH3CN for comparison purposes because of the enormous interest in understanding the molecular dynamics of CH3CN as a prototypical aprotic polar liquid.7,36 Ideally, one would like to have a larger data set involving a homologous series of substituted methanes. However, such data are unavailable.
Quitevis and Neelakandan The temporal behavior of the components of the nuclear response are similar for both liquids. The 1/e time constant for the diffusive response for CH3I is ∼25% times longer than that of CH3CN. A longer time constant is consistent with a higher viscosity for CH3I. The 1/e time constant for the intermediate response is ∼35% times faster for CH3I than for CH3CN. Although the mean intermolecular librational frequencies and dephasing times are nearly the same for CH3I and CH3CN (∼52-60 cm-1 and ∼200-220 fs, respectively), the width of the librational distribution is noticeably narrower for CH3I than for CH3CN (62 vs 80 cm-1). The amplitude ratio A3/A2/ A1 (librational/intermediate/diffusive) is 6.1/1.03/1.0 for CH3CN and 2.6/6.6/1.0 for CH3I. For both CH3CN and CH3I, nondiffusive motions contribute more to the nuclear response than do diffusive motions. For CH3CN, the short-time dynamics appears to mainly be librational in nature, whereas for CH3I, the librational and intermediate components contribute to almost the same extent. Also striking is the disparity in the relative contribution of the electronic response. This is evident when one visually compares the OHD-RIKES signals for these two liquids. For CH3I, the OHD-RIKES signal is dominated by the electronic hyperpolarizability, whereas the electronic and nuclear responses contribute almost equally to the overall OHD-RIKES signal for CH3CN. In contrast to the situation with liquids composed of nonpolar molecules, our current understanding of the role of collisioninduced effects in liquids composed of polar molecules is not as extensive. Results from a recent MD simulation on CH3CN36 indicate that interaction-induced terms contribute to the collective polarizability TCF, 〈Πxz(t) Πxz(0)〉, on all relevant time scales. In fact, the cross molecular-induced term is negative, is of the same magnitude, and relaxes at almost the same rate as the molecular term. Because these two terms nearly cancel, 〈Πxz(t) Πxz(0)〉 is basically dominated by the interaction-induced term. In the projection representation, the local-field-modified reorientational term is the largest contributor to 〈Πxz(t) Πxz(0)〉. However, the collision-induced terms are non-negligible. At short times (500 fs), the sum of the collisioninduced terms are negative, causing 〈Πxz(t) Πxz(0)〉 to drop below the reorientational component. MD simulations show analogous trends for CH3OH, which has nearly the same polarity as CH3CN. These results conflict with the interpretation of the intermediate and diffusive responses from the model-dependent analysis for CH3CN as being respectively due to the collisioninduced part and the reorientational part of the OHD-RIKES signal. It must be noted, however, that these simulations considered only first-order dipole-induced-dipole (DID) terms in modeling the collision-induced contributions. In the case of CS2, higher order DID terms are found to enhance the contribution of reorientation to the TCF.37 It remains to be seen whether the trends found for polar liquids will hold true when higher order DID terms are incorporated into the MD simulations. In the absence of MD simulations, the validity of the assumption of separation of time scales in the case of CH3I cannot be easily checked. For nonpolar anisotropic molecules, induced contributions are found to be more pronounced as the polarizability becomes more spherical, as measured by the ratio ∆R/R, where ∆R is the polarizability anisotropy and R is the mean polarizability.38 From Table 2 we see that the value of R for CH3I is 1.7 times larger than that of CH3CN, whereas the value of ∆R for CH3I is only 1.1 times larger than that of CH3CN. This leads to the value of ∆R/R for CH3I being 2/3 times
Liquid Methyl Iodide
J. Phys. Chem., Vol. 100, No. 24, 1996 10011
TABLE 1: Comparison of OHD-RIKES Response Parameters at 294 K liquid
electronic response A0c
acetonitrilea methyl iodideb
0.891 0.994
a
diffusive response A1c τdiff (ps) β1d (fs) 1.34 × 10-2 6.15 × 10-4
1.36 1.70
102 88
intermediate response A2c τint (fs) β2d (fs) 1.38 × 10-2 4.03 × 10-3
307 200
102 88
A3c 8.21 × 10-2 1.57 × 10-3
librational response ν˜ 0e (cm-1) τlib (fs) ∆ν˜ f (cm-1) 51.8 60
217 200
80 62
Reference 12a. b This work. c A0 + A1 + A2 + A3 ) 1. d β1 ) β2 ) 1/ω0. e ν˜ 0 ) ω0/2πc. f ∆ν˜ ) ∆(2 ln 2)1/2/(πc).
TABLE 2: Comparison of Molecular Properties at 294 K liquid
η (cP)
µ (D)
R (Å )
∆R (Å )
∆R/R
acetonitrile methyl iodide
0.369 0.469
36.64 6.97
3.924 1.62
4.48 7.59
1.89 2.15
0.422 0.283
a
a
a
b
3
b
3
a Reference 34. b Reference 35. c Symbols: η, viscosity; , dielectric constant; µ, dipole moment; R, mean polarizability; ∆R, polarizability anisotropy.
smaller than that of CH3CN. All things being equal, the collision-induced contribution should be more pronounced in CH3I than in CH3CN. However, MD simulations of CH3CN and CH3OH show that polarity also plays a very important role in reducing the effective polarizability anisotropy.36,39 With a dielectric constant that is an order of magnitude smaller than that of CH3CN, and a dipole moment which is 0.41 times smaller than that of CH3CN, CH3I is a considerably less polar liquid than CH3CN (Table 2). Therefore, it is not clear that collisioninduced dynamics will be as prominent in the collective polarizability anisotropy relaxation for CH3I as it is for the two highly polar liquids, CH3CN and CH3OH. A consistent interpretation of the OHD-RIKES data at long times can be obtained if we assume that separation of time scales is valid for CH3I. Prior to our work, the most extensive information about the reorientational and intermolecular dynamics in liquid CH3I was obtained from DRS data.21 Of all the DRS studies to date, those of Dill, Litovitz, and Bucaro22 appear to be the most accurate and detailed. By neglecting reorientational-induced cross terms, they separated the DRS spectrum into a reorientational component and a collision-induced component. A functional form was used for the collisioninduced component, which is based on DRS spectra of atomic liquids where reorientational contributions are absent. The collision-induced component was separated prior to Fourier transformation of the spectrum. This allowed them to determine the reorientational part of the polarizability anisotropy TCF. Dill, Litovitz, and Bucaro further neglected pair correlations in liquid CH3I and assumed that the DRS data could be described by the single-molecule polarizability TCF. For a symmetric top molecule, the single-molecule response is given by the product of the response function of the anisotropic polarizability of the molecule, which depends on the intramolecular dynamics, and the single-molecule reorientational TCF. If the molecules are assumed to be rigid, COR(t) will then be simply given by the single-molecule reorientational TCF:40,41
C2,i(t) ∝ (∆R)2〈P2[u(t)‚u(0)]〉
(16)
where u is a unit vector lying along the symmetry axis of the molecule, P2(x) is the second Legendre polynomial, and the angle brackets represent an ensemble average. If one assumes a diffusional model for molecular reorientation, C2,i(t) at long times will decay exponentially with a relaxation time given by
τ2,i ) 1/6D⊥
(17)
where D⊥ is the rotational diffusion constant perpendicular to the symmetry axis. Note that the diffusional model may not be correct at long times if memory effects are considered.41
Recent theoretical studies have shown that if molecular rotation is characterized by a memory function that decays rapidly but is not a δ-function, orientational correlation functions are predicted to decay exponentially at long times without introducing explicit models. Deviation in decay times from the diffusional limit will occur if the memory effects last long enough. From their DRS data, Dill, Litovitz, and Bucaro obtained a value of τ2,i ) 1.41 ps for CH3I at 1 bar and room temperature. This value of τ2,i is 20% smaller than our measured value of τdiff ) 1.76 ps. Our value appears to be more consistent with the assumption that the OHD-RIKES signal at long times is due primarily to reorientational dynamics, with the 1/e time constant being equal to the collective reorientation time. This can be seen as follows. By assuming that orientational variables fluctuate on a much slower time scale than angular velocities, molecular torques, etc., Keyes and Kivelson42 showed that the collective reorientational TCF decays exponentially with a reorientation time given by
τ2,c ) (g2/j2)τ2,i
(18)
where g2 is the static orientational pair correlation factor and j2 is a parameter which differs from unity only if the angular velocities of different molecules are correlated. From DRS studies of binary mixtures of CH3I and neopentane, the ratio g2/j2 was found to have a value of 1.7 at room temperature.43 Substituting our measured value of τdiff ) 1.76 ps for τ2,c into eq 18 yields a value of ∼1 ps for τ2,i instead of 1.4 ps, as determined by Dill, Litovitz, and Bucaro. Using the DebyeStokes-Einstein (DSE) model,44-46 an expression for D⊥ can be obtained which leads to the hydrodynamic form
τ2,i )
ηVF kBTS
(19)
where η is the solvent shear viscosity, F is a friction factor, kB is the Boltzmann constant, T is the absolute temperature, and S is a factor which accounts for deviations of the molecule from a sphere. For “stick” boundary conditions F ) 1 and for “slip” boundary conditions F < 1. The factor S depends on the ratio of the lengths of the molecule's major and minor axis a/b. The diffusive reorientation time for small molecules in liquids is well described by a modified form of the DSE equation:47
τ2,i ) Cη + τ0
(20)
where τ0 is the zero viscosity intercept and C is a constant, which in the DSE model would be equal to VF/(kBTS). There is currently no clear consensus on the physical significance of the zero viscosity intercept. As pointed out by Evans and Kivelson,48 the intercept does not describe the dynamics at low viscosities, but is associated with behavior at high viscosities, extrapolated to zero viscosity. DRS studies have shown the value of the intercept to be zero for CH3I in solution.43 If τ0 is set equal to zero, a value of C ≈ 2.1 ps/cP for CH3I is calculated by using a single-particle reorientation time of 1 ps and a
10012 J. Phys. Chem., Vol. 100, No. 24, 1996
Quitevis and Neelakandan TABLE 3: Comparison of Spectral Data for Methyl Iodidea spectral type
ν˜ max (cm-1)
fwhm (cm-1)
depolarized Rayleigh scatteringb far infraredc
27/24 (1.13) 56/61 (0.92)
68/80 (0.85) 100/110 (0.91)
a The first number in each entry is the value corresponding to the experimental spectra. The second number is the value for the equivalent spectra derived from the OHD-RIKES data (see Figure 5a,b). The number in parentheses is the ratio of the two values. b Bose-corrected version of the DRS spectrum obtained from ref 23 compared to Im[D(∆ω)]. c FIR spectrum obtained from ref 27 compared to R(∆ω).
Figure 5. (A) Comparison of Bose-corrected depolarized Rayleigh scattering (DRS) spectrum (solid curve) and OHD-RIKES spectral density Im[D(∆ω)] (dashed curve). (B) Comparison of far infrared (FIR) spectrum (solid curve) with R(∆ω) ) ∆ω Im[D(∆ω)] (dashed curve). DRS and FIR spectra were taken from refs 23 and 27, respectively. See Table 3 for comparison of spectral parameters.
viscosity η ) 0.469 cP. This value of C agrees quite well with the theoretically predicted value of 2.2 ps/cP for slip boundary conditions. B. Spectral Response. The spectral density of CH3I obtained from the OHD-RIKES data by using the Fourier transform technique is similar in shape to those of other substituted methanes.13a The spectral densities have the characteristic shape of a Poley-Hill band49,50 which is observed in the low-frequency FIR absorption spectra of liquids and which is associated with the reorientational and intermolecular dynamics of the liquid. The spectral densities for these molecules are well described by the ohmic distribution function. For the methane series, CHCl3, CFCl3, CCl4, and CBrCl3, fits of the spectral densities to ohmic distribution functions are obtained for ωc values corresponding to 20.3, 13.9, 16.8, and 15.3 cm-1, respectively.13a For CH3CN, a fit of the spectral density to an ohmic distribution function was obtained for an ωc value of 32.5 cm-1.13a Compared to the methane series, CH3I (ωc ) 29.9 cm-1) has a broader spectral density. Given that the temporal behavior of the nuclear responses are similar for CH3I and CH3CN, it is not surprising that the widths of the spectral densities for these liquids are approximately equal. The DRS intensity SDRS(∆ω) and Im[D(∆ω)] are related to each other by the equation10n,11,12b,c
SDRS(∆ω)[1 - exp(-p∆ω/kBT)] ∝ Im[D(∆ω)] (21) where [1 - exp(-p∆ω/kBT)] is the Bose factor. Figure 5A
compares Im[D(∆ω)] to the Bose-corrected DRS spectrum for CH3I obtained by Lund et al.23 With the exception of the region of very small wavenumbers, there is good overlap between the OHD-RIKES spectral density and the Bose-corrected DRS spectrum over the indicated range. The agreement is probably not perfect because of the quality of either the Rayleigh wing spectrum and/or OHD-RIKES signal. Low-noise OHD-RIKES signals are needed in order to obtain an accurate Fourier transform.10m,n Nonetheless, the peak maxima and widths for the Bose-corrected DRS spectrum and the OHD-RIKES spectral density agree within 10-15% (Table 3). The spectrum near the origin should reflect the Lorentzianshaped pure diffusive reorientational response. Indeed, the sharp feature in the DRS spectrum near the origin is probably the pure rotational response. However, it appears to be too sharply peaked. The sharpness is an artifact resulting from fact that the Bose-corrected DRS spectrum in Figure 5A was obtained from data taken with a double monochromator. DRS data taken with a high-resolution interferometer do not yield spectral densities which peak as sharply near the origin.14 Unfortunately, we are unable to resolve this diffusive reorientational feature in the spectral density obtained in this study. For τdiff ) 1.76 ps, the corresponding Lorentzian-shaped pure rotational response will have a half-width at half-maximum of ∼3.0 cm-1, which is less than the 12 cm-1 FFT spectral resolution. Deuel et al.13a have argued that Im[D(∆ω)] is not a general spectral distribution and is sensitive to only the anisotropic part of the intermolecular potential. In contrast, the low-frequency FIR spectrum measures the averaged intermolecular interactions and therefore should be broader and peak at a higher frequency than Im[D(∆ω)]. Indeed, Deuel et al. have shown that the lowfrequency FIR spectrum is broader than Im[D(∆ω)] for CCl4 and CH3CN. This is also true for CH3I: The fwhm of Im[D(∆ω)] and the low-frequency FIR spectrum are, respectively, 80 and 100 cm-1, with the corresponding peak maximum at 24 and 56 cm-1 (Table 3). However, to make meaningful comparisons between the OHD-RIKES spectral response and the low-frequency FIR absorption spectrum, Im[D(∆ω)] must be converted into a quantity which is analogous to an FIR absorption coefficient. When comparing DRS to low-frequency FIR absorption, a quantity R(∆ω) is constructed which is proportional to the energy absorbed in a scattering experiment:
RDRS(∆ω) ) ∆ωSDRS(∆ω)[1 - exp(-p∆ω/kBT)]
(22)
Lund et al.23 have confirmed this relationship for CH3I, to the extent that the frequency maximum of RDRS(∆ω) matches that of the low-frequency FIR absorption (∼60 cm-1). It follows then from eqs 21 and 22 that the low-frequency FIR absorption spectrum should be compared to ∆ω Im[D(∆ω)] and not to Im[D(∆ω)].10n,12c Such a comparison is made in Figure 5B with the FIR spectrum taken from ref 27. Multiplying Im[D(∆ω)] for CH3I by ∆ω increases the width of the spectrum by 20 cm-1
Liquid Methyl Iodide and shifts the spectrum to higher frequencies by 32 cm-1. This results in the R(∆ω) representation of the OHD-RIKES spectral response being in good agreement with the low-frequency FIR absorption spectrum. The values of the peak maximum and spectral width of the OHD-RIKES spectrum are within ∼10% of the corresponding values for the low-frequency FIR absorption spectrum (Table 3). MD simulations show that in the projection representation the reorientational part dominates the dipole moment density TCF for CH3CN, with the collision-induced part being negligible.36 As stated earlier, it is also the largest contributor to the collective polarizability anisotropy, but it is by no means the dominant: collision-induced terms contribute substantially at all times. Clearly, differences in the relative contributions of local-field-modified reorientational vs collision-induced dynamics should be reflected in differences between R(∆ω) and the low-frequency FIR absorption spectrum. In the case of CH3I, R(∆ω) roughly matches the low-frequency FIR absorption spectrum. Thus, for CH3I, the molecular motions that determine the DRS spectrum must be essentially the same as those that determine the low-frequency FIR absorption spectrum. This would imply that the reorientational term and the collisioninduced terms are present to the same extent in both the dipole moment density and the collective polarizability anisotropy TCFs or that one is more dominant than the other in both TCFs. However, our analysis of the diffusive response part of the OHD-RIKES data for CH3I leads to the conclusion that collective diffusive reorientation dominates collision-induced dynamics at long times. It is difficult to reconcile this conclusion and the overlap of R(∆ω) with the low-frequency FIR absorption spectrum, unless one assumes that reorientational dynamics dominates collision-induced dynamics over much of the relevant time scale for both types of experiments. This would be very surprising because the reorientational motion probed in an FIR experiment is that of the dipole moment of the molecule, which is first rank, whereas, the reorientational motion probed in DRS and OHD-RIKES experiments is that of the off-diagonal element of the polarizability tensor of the molecule, which is second rank. It is not clear that the two should relax at the same rate. C. Intermolecular Vibrational Mode Description. Thus far, we have attempted to interpret the OHD-RIKES data using the framework of reorientational vs collision-induced dynamics in the tradition of DRS spectroscopy. Although a great deal of information can be gleaned from experimental data by using this standard approach, its weakness lies in that assumptions must be made in order to separate spectral or temporal data into reorientational and collision-induced components. As we showed above, in this framework the interpretation of the OHDRIKES, low-frequency FIR absorption, and DRS data for CH3I is not clear-cut. An alternative approach, which is gaining wide acceptance, is the treatment of the molecular dynamics of liquid in terms of collective harmonic normal modes of the liquid. This approach is not new and dates back to Maxwell, who recognized that for short enough times a liquid behaves in many respects like a solid. Indeed there have been many phonon-like formulations of liquids. Obviously, for longer times this picture breaks down. The observation of collective oscillations of the liquid in femtosecond OHD-RIKES10-13 and ISRS15-17 experiments lends credence to this normal mode picture. It has now been rigorously established that, for short enough (10 cm-1) part of Im[D(∆ω)] will largely reflect the collective intermolecular vibrational motions of the liquid. From the collective normal mode perspective, the subpicosecond response of the OHD-RIKES signal has a natural interpretation. McMorrow and Lotshaw10k have proposed that this response arises from underdamped, critically damped, and overdamped motions of a single inhomogeneously broadened intermolecular vibrational mode. In this single oscillator model, the constructive interference of critically damped and overdamped oscillations gives rise to the intermediate quasiexponential response. The presence or absence of oscillations in the OHD-RIKES signal is determined by the relative values of the frequency of the oscillator ω0, the inhomogeneous width ∆ωi, and the homogeneous dephasing rate γ ) 1/τlib. The dephasing rate γ is associated with processes that destroy the coherence of the oscillators. These processes involve both phase and energy relaxation. If ω0 > γ, the oscillators are underdamped. On the basis of the librational parameters obtained from the fit of the OHD-RIKES data, CH3I is in the underdamped limit (ω0 ) 1.13 × 1013 s-1 > γ ) 5.0 × 1012 s-1). However, because the inhomogeneous width is nearly equal to the mean oscillator frequency for CH3I (∆ωi ) 1.17 × 1013 s-1 ≈ ω0 ) 1.13 × 1013 s-1), the different-frequency oscillators destructively interfere and no distinct oscillations occur in the OHD-RIKES signal. VI. Conclusions In principle, the information content of the OHD-RIKES spectral density is identical to that of the DRS spectrum. However, femtosecond techniques allow one to observe directly in the time domain short-time dynamics which are difficult to characterize in the frequency domain. The OHD-RIKES transient for liquid CH3I at room temperature and ambient pressure is dominated at early times by the electronic hyperpolarizability. The noninstantaneous nuclear response at early times is well described by three components: librational, intermediate, and diffusive. The assignment of the intermediate response to collision-induced effects seems in doubt when viewed in light of MD simulations of similar molecules. We showed that the 1/e time constant of the diffusive response component of the OHD-RIKES data can be interpreted as a collective reorientation time. It seems highly unlikely, therefore, that collision-induced effects contribute to the long-time behavior of the OHD-RIKES signal to any large extent. MD simulations show that the shape of the FIR absorption spectum of CH3CN is determined mainly by the reorientational component of the dipole density TCF. Given that R(∆ω) overlaps with the FIR absorption spectrum, there is reason to believe then that the OHD-RIKES signal is mainly dominated by reorientational relaxation in CH3I. This behavior would contradict MD simulations which show collision-induced terms to be non-negligible. However, detailed MD simulations to date have focused on strong polar liquids. Clearly, MD simulations must be done to determine the actual extent to which collisioninduced dynamics contribute to both the dipole moment density and collective polarizability anisotropy TCFs for liquids composed of weak polar molecules. Finally, it would be extremely useful to compare the INM spectrum of liquid CH3I obtained from MD simulations with the OHD-RIKES spectral density. Acknowledgment. This research was supported by the Texas Higher Education Coordinating Board Advanced Research Program (003644-057) and the Robert A. Welch Foundation (D-1019). We thank Professors H. Kapteyn and M. Murnane
10014 J. Phys. Chem., Vol. 100, No. 24, 1996 for their advice in building the Ti:sapphire laser system, V. Van Duzee for assistance in the analysis of the data, and Professor R. E. Wilde for many stimulating discussions about the liquid state dynamics of CH3I. References and Notes (1) Spectroscopy and Relaxation of Molecular Liquids; Steele, D., Yarwood, J., Eds.; Elsevier: New York, 1991. (2) Collision- and Interaction-Induced Spectroscopy; Tabisz, G. C., Neuman, M. N., Eds.; Kluwer: Netherlands, 1995. (3) For a review, see: Madden, P. A. In ref 1, pp 124-173. (4) Keyes, T. F.; Kivelson, D.; McTague, J. P. J. Chem. Phys. 1971, 55, 4096. (5) Cox, T. I.; Battaglia, M. R.; Madden, P. A. Mol. Phys. 1979, 38, 1539. (6) Madden, P. A.; Tildesley, D. J. Mol. Phys. 1985, 55, 969. (7) Edwards, D. M. F.; Madden, P. A. Mol. Phys. 1985, 51, 1984. (8) For a review, see: Ladanyi, B. M. In ref 1, pp 484-533. (9) (a) Deeg, F. W.; Stankus, J. J.; Greenfield, S. R.; Newell, V. J.; Fayer, M. D. J. Chem. Phys. 1989, 90, 6893. (b) Deeg, F. W.; Fayer, M. D. J. Chem. Phys. 1989, 91, 2269. (c) Greenfield, S. R.; Sengupta, A.; Stankus, J. J.; Terazima, M.; Fayer, M. D. J. Phys. Chem. 1994, 98, 313. (10) (a) Kalpouzos, C.; Lotshaw, W. T.; McMorrow, D.; KenneyWallace, G. A. J. Phys. Chem. 1987, 91, 2028. (b) Lotshaw, W. T.; McMorrow, D.; Kalpouzos, C.; Kenney-Wallace, G. A. Chem. Phys. Lett. 1987, 136, 323. (c) McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A. J. Quantum Electron. 1988, QE-24, 443. (d) McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A. In AdVances in Laser Science III, Optical Science and Engineering Series 9; Tam, A. C., Gole, J., Stwalley, W. C., Eds.; American Institute of Physics: New York, 1988; p 674. (e) Kalpouzos, C.; McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A. Chem. Phys. Lett. 1988, 150, 138. (f) Kalpouzos, C.; McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A. Chem. Phys. Lett. 1989, 155, 240. (g) Lotshaw, W. T. McMorrow, D.; Kenney-Wallace, Proc. SPIE, 1988, 981, 20. (h) McMorrow, D.; Lotshaw, W. T. Chem. Phys. Lett. 1990, 174, 85. (i) McMorrow, D. Opt. Commun. 1990, 86, 236. (j) McMorrow, D.; Lotshaw, W. T. J. Phys. Chem. 1991, 95, 10395. (k) McMorrow, D.; Lotshaw, W. T. Chem. Phys. Lett. 1991, 178, 69. (l) McMorrow, D.; Lotshaw, W. T. Chem. Phys. Lett. 1993, 201, 369. (m) Palese, S.; Schilling, L.; Miller, R. J. D.; Staver, R. P.; Lotshaw, W. T. J. Phys. Chem. 1994, 98, 6308. (n) Lotshaw, W. T.; McMorrow, D.; Thantu, N.; Melinger, J. S.; Kitchenham, R. J. Raman Spectrosc. 1995, 26, 571. (11) Cho, M.; Du, M.; Scherer, N. F.; Fleming, G. R.; Mukamel, S. J. Chem. Phys. 1993, 99, 2410, (12) (a) Chang, Y. J.; Castner, E. W., Jr. J. Chem. Phys. 1993, 99, 113. (b) Chang, Y. J.; Castner, E. W., Jr. J. Chem. Phys. 1993, 99, 7289. (c) Chang, Y. J.; Castner, E. W., Jr. J. Phys. Chem. 1994, 98, 9712. (13) (a) Deuel, H. P.; Cong, P.; Simon, J. D. J. Phys. Chem. 1994, 98, 12600. (b) Deuel, H. P.; Cong, P.; Simon, J. D. J. Raman Spectrosc. 1995, 26, 523. (14) Kinoshita, S.; Kai, Y.; Yamaguchi, M.; Yagi, T. Phys. ReV. Lett. 1995, 75, 148. (15) (a) Ruhman, S.; Williams, L. R.; Joly, A. G.; Kohler, B.; Nelson, K. A. J. Phys. Chem. 1987, 91, 2237. (b) Ruhman, S.; Joly, A. G.; Kohler, B.; Williams, L. R.; Nelson, K. A. ReV. Phys. Appl. 1987, 22, 1717. (c) Ruhman, S.; Joly, A. G.; Nelson, K. A. J. Quantum Electron. 1988, 24, 460. (d) Kohler, B.; Nelson, K. A. J. Phys. Chem. 1992, 96, 6532. (16) Waldman, A.; Banin, U.; Rabani, E.; Ruhman, S. J. Phys. Chem. 1992, 96, 10842.
Quitevis and Neelakandan (17) Vo¨hringer, P.; Scherer, N. F. J. Phys. Chem. 1995, 99, 2684. (18) Chang, Y. J.; Cong, P.; Simon, J. D. J. Phys. Chem. 1995, 99, 7857. (19) Keyes, T.; Ladanyi, B. M. Mol. Phys. 1979, 37, 1643. (20) Miller, R. S.; MacPhail, R. A. Chem. Phys. Lett. 1995, 241, 121. (21) Yarwood, J.; Evans, M. W. AdV. Mol. Relax. Interact Processes 1981, 21, 1, and references cited therein. (22) Dill, J. F.; Litovitz, T. A.; Bucaro, J. A. J. Chem. Phys. 1975, 62, 3839. (23) Lund, P. A.; Nelson, O. F.; Praestgaard, E. Chem. Phys. 1978, 28, 167. (24) O’Neil, G. P.; Khuen, A.; Yarwood, J.; Birch, J. R.; Price, A. H. J. Mol. Struct. 1982, 80, 383. (25) Jain, S. R.; Walker, S. J. Phys. Chem. 1971, 75, 2942. (26) Sato, K.; Ohkubo, Y.; Moritsu, T.; Ikawa, S.; Kimura, M. Bull. Chem. Soc. Jpn. 1978, 51, 2493. (27) Vij, J. K.; Kalmykov, Y. P. J. Chem. Phys. 1993, 99, 2506. (28) Asaki, M.; Huang, C. P.; Garvey, D.; Zhou, J.; Kapteyn, H. C.; Murnane, M. M. Opt. Lett. 1993, 18, 977. (29) Levenson, M. D.; Eesley, G. L. Appl. Phys. 1979, 19, 1. (30) Lynden-Bell, R. M.; Steele W. A. J. Phys. Chem. 1984, 88, 6514. (31) Madden, P. A. In Ultrafast Phenomena IV; Auston, D. H., Eisenthal, K. B., Eds.; Springer-Verlag: New York, 1984; pp 244-251. (32) Greene, B. I.; Fleury, P. A.; Carter, H. L., Jr.; Farrow, R. C. Phys. ReV. A 1984, 29, 271. (33) (a) Bucaro, J. A.; Litovitz, T. A. J. Chem. Phys. 1971, 54, 3846. (b) Bucaro, J. A.; Litovitz, T. A. J. Chem. Phys. 1971, 55, 3585. (34) CRC Handbook of Chemistry and Physics, 75 Ed.; CRC Press: Cleveland, 1994. (35) Applequist, J.; Carl, J. R.; Fung, K.-K. J. Am. Chem. Soc. 1972, 94, 2952. (36) Ladanyi, B. M.; Skaf, M. S.; Liang, Y. Q. In ref 2, pp 143-157. (37) Geiger, L. C.; Ladanyi, B. M. J. Chem. Phys. 1987, 87, 191. (38) Keller, M.; Mueller, A.; Reh, M.; Ro¨der, Steele, W. A.; Versmold, H. In ref 2, pp 87-106. (39) Skaf, M. S.; Fonseca, T.; Ladanyi, B. M. J. Chem. Phys. 1993, 98, 8929. (40) Rothschild, W. G. Dynamics of Molecular Liquids; Wiley: New York, 1984; Chapter 2. (41) Steele, W. A. In ref 1, pp 63-123. (42) Keyes, T.; Kivelson, D. J. Chem. Phys. 1972, 56, 1057. (43) Cheung, C. K.; Jones, D. R.; Wang, C. H. J. Chem. Phys. 1976, 64, 3567. (44) (a) Einstein, A. InVestigations on the Theory of Brownian Motion; Dover: New York, 1956. (b) Ann. Phys. (Leipzig) 1905, 17, 549. (45) Debye, P. Polar Molecules; Dover: New York, 1929; pp 72-85. (46) Dote, J. L.; Kivelson, D.; Schwartz, R. N. J. Phys. Chem. 1981, 85, 2169. (47) (a) Alms, G. R.; Bauer, D. R.; Brauman, J. I.; Pecora, R. J. Chem. Phys. 1973, 59, 5310. (b) Bauer, D. R.; Brauman, J. I.; Pecora, R. J. Am. Chem. Soc. 1974, 96, 6840. (48) Evans, G. T.; Kivelson, D. J. Chem. Phys. 1986, 84, 385. (49) Poley, J. Ph. J. Appl. Sci. 1955, 4B, 337. (50) Hill, N. E. Proc. Phys. Soc. 1963, 82, 723. (51) (a) Buchner, M.; Ladanyi, B. M.; Stratt, R. M. J. Chem. Phys. 1992, 97, 8522. (b) Stratt, R. M.; Cho, M. J. Chem. Phys. 1994, 100, 6700. (c) Ladanyi, B. M.; Stratt, R. M. J. Phys. Chem. 1995, 99, 2502. (d) Ladanyi, B. M.; Stratt, R. M. J. Phys. Chem., 1996, 100, 1266.
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