© Copyright 1996 by the American Chemical Society
VOLUME 100, NUMBER 21, MAY 23, 1996
LETTERS Complete Determination of Intermolecular Spectral Densities of Liquids Using Position-Sensitive Kerr Lens Spectroscopy Peijun Cong Department of Chemistry, Hong Kong UniVersity of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Yong Joon Chang and John D. Simon* Department of Chemistry and Biochemistry, UniVersity of California, San Diego, 9500 Gilman Dr., La Jolla, California 92093-0341 ReceiVed: January 23, 1996; In Final Form: March 15, 1996X
Femtosecond position-sensitive Kerr lens spectroscopy is demonstrated to facilitate the direct and complete measurement of the third-order material response function, R(3)(t). The real parts of tensor element response, (3) R(3) 1111(t) and R1122(t), for liquid CS2 have been measured and are quantitatively compared to the optical Kerr (3) effect response, R(3) 1221(t) + R1212(t). The intermolecular Raman spectral densities are also obtained for each tensor element through Fourier transform. The relationship among these spectral densities is discussed with regard to the nature of the underlying intermolecular motions in liquid CS2. Specifically, we find that the intermolecular depolarization ratio is frequency independent with a value of 0.7 ( 0.1 in the 0-150 cm-1 region.
Introduction Intermolecular interactions are important factors in determining chemical reaction mechanisms and pathways in solution. As a result there is a substantial effort to measure and calculate the intermolecular interaction potential in liquids. A current focus is on the measurement and interpretation of intermolecular spectral densities. Intermolecular spectral densities can be measured by frequency-domain, spontaneous techniques such as depolarized Raman/Rayleigh scattering, far-infrared, and microwave absorption spectroscopy.1-4 More recently, stimulated spectroscopic techniques in both the time-domain (such as femtosecond optical-heterodyne-detected Raman-induced Kerr effect spectroscopy (OHD RIKES))5-10 and the frequencydomain (such as frequency-resolved stimulated Raman gain * Corresponding author. X Abstract published in AdVance ACS Abstracts, May 1, 1996.
S0022-3654(96)00243-2 CCC: $12.00
(SRG))11-14 have been utilized to characterize the low-frequency intermolecular motions in liquids. These later techniques provide useful means to directly obtain the depolarized or anisotropic component of the material response function that describes the collective intermolecular motions. Several molecular dynamics simulation studies have addressed the connection between the nature of intermolecular forces and their manifestation in spectral densities (or more directly, time-domain correlation functions).15-17 However, the measurement of the isotropic component of the intermolecular spectral density has rarely been addressed in the literature. The depolarized spectral density alone does not seem to be sufficient to describe all aspects of intermolecular interactions. This inadequacy is illustrated recently through a comparison of benzene and benzonitrile, two different liquids that have indistinguishable librational spectral densities as © 1996 American Chemical Society
8614 J. Phys. Chem., Vol. 100, No. 21, 1996 measured by OHD RIKES.18 Recently, the OHD RIKES spectral densities have been applied to connect the solventsolvent interactions (as revealed by OHD RIKES) and solventsolute interactions (as measured by photon echo and fluorescence up-conversion experiments).19-22 Since in some of these cases a polarized spectral density might seem to be more appropriate than the depolarized spectral density, it would be speculated that these two spectral densities are qualitatively similar.21,22 To answer these questions, it is crucial to measure the polarized part of the intermolecular spectral density. A critical comparison of the polarized and depolarized components of the liquid spectral density not only can help to clarify the role (if any) of the OHD RIKES spectral density in shaping solvation dynamics but also can provide insights into the nature of intermolecular motions in terms of the underlying liquid structure and symmetry and how they are projected into different spectral components. With the goal of measuring the complete spectral densities, we previously reported the optical heterodyne detection of impulsive stimulated Raman scattering (OHD ISRS).9 In this letter, we present a complete determination of the spectral density in liquids using a different and simpler approach, position-sensitive Kerr lens spectroscopy. This technique is based on the conventional pump-probe geometry with positionsensitive detection in the probe arm. This detection scheme allows the real part of the response function to be determined without any constraint on the relative pump-and-probe polarization directions. Thus R(3) 1111(t) (parallel polarization between pump and probe) and R(3) 1122(t) (perpendicular polarization between pump and probe) are readily measured. It is shown that the difference of these response functions agrees quantitatively with the response function measured by OHD RIKES, as expected based on first principles. It should be pointed out that the imaginary part of response function (i.e., intensity gain/ loss) can be and has been measured in the same setup. However, in this letter we limit our discussions to the real part of the response function. Experimental Section The experimental setup is a standard pump-probe arrangement where the pump and probe beams cross in the liquid sample at a small angle, after appropriate delays. A dualphotodiode detector is placed in the probe beam after it passes through the sample. Using the diodes A and B, the positionsensitive signal given by [IA(t) - IB(t)]/[IA(t) + IB(t)] is linearly and selectively related to the real part of the time-dependent material nonlinear index of refraction, n2(t), and to the real part of the material nonlinear susceptibility response, R(t).27 The imaginary part of this same response can also be obtained by detecting the signal [IA(t) + IB(t)]. The light source employed is a continuous-wave, self-mode-locked Ti:sapphire laser operating at 780 nm with a pulse width of ∼30 fs (full width at halfmaximum, transform limited) at 80 MHz. The pump power delivered at the sample is ∼40 mW (∼0.5 nJ/pulse). The liquids were purchased from Aldrich and further purified through multiple filtrations to reduce light-scattering from dissolved particulate matter. The transients reported here are the results of averaging multiple individual scans and sometimes requiring a total data acquisition time on the order of 10 h. Results and Discussion Figure 1 shows the off-resonant response functions of CS2 measured by the position-sensitive detector. The upper trace is taken with parallel pump-and-probe polarizations, while the
Letters
Figure 1. Pump-probe signal of CS2 measured with a position-sensitive detector. The upper curve is obtained with parallel pump and probe polarizations, and the lower one with perpendicular polarizations.
lower trace is obtained by setting the angle between the pump and probe polarizations to be 90°. It is noted that the electronic parts of the response are both positive, the intensity of the electronic response for the perpendicular polarization is approximately one-third of that for the parallel one. This is a consequence of the symmetry properties of the electronic hyperpolarizability tensor.23 The nuclear part of the response for the perpendicular configuration is opposite to that for the parallel configuration. This property was implied in a previous ISRS work on the same liquid but was not unambiguously resolved due to the homodyne detection.24 The sign change in the nuclear response function between the parallel and perpendicular configuration provides experimental verification that the signal detected is fully heterodyned (by the probe beam). Similar behavior of CS2 was reported by Kobayashi and coworkers in a double interferometer measurement,25 although our current study offers much improved time resolution and signalto-noise ratio. Closer in spirit to our approach, Terazima recently reported a dual-beam “thermal-lens” measurement of CS2 using 200 fs pulses.26 In this measurement, the intensity variation of the central portion of the probe beam was monitored through a small pinhole. This is equivalent, in principle, to our position-sensitive detection scheme,27 but we believe our method is more accurate because the detected signal in our approach is automatically normalized against the overall intensity change of the probe beam, thus eliminating contributions from changes in the imaginary part of the refractive index. In addition to this difference, electronic and nuclear contributions were not separated directly in the time domain measurement by Terazima due to their limited time resolution. Instead, these contributions to the signal were separated by varying the angle of the pump-and-probe polarization directions, followed by an analysis based on their spatial symmetries.28,29 Here we explain the main features of our position-sensitive technique in qualitative terms and defer a complete analysis (based on a time-dependent third-order perturbation theory in Liouville space30 and spatial charateristics of Gaussian beam propagation) to a future publication.27 In a typical pump-probe setup, the pump beam induces changes in the complex refractive index of the sample. The weak probe beam is then directed into the sample to interrogate these changes. The change in the imaginary part of the refractive index is reflected in the intensity change of the probe beam and is the quantity measured
Letters in transient absorption spectroscopy. The change in the real part of the refractive index, on the other hand, influences the propagation direction and the spot size of the probe beam. This can be understood as follows. The (real part of) refractive index change induced by a fundamental Gaussian pump beam (i.e., TEM00 mode) will have the same spatial profile as the pump beam. The sample with this pump-beam-induced refractive index change will then serve as a lenslike medium in deflecting the probe beam and thereby changing its spot size. This is similar to the thermal lens effect except the underlying dynamics involve electronic and vibrational processes. This lenslike medium is commonly referred to as a transient Kerr lens.31 For most liquids, the nuclear component of the optical Kerr constant is positive along the pump laser polarization, resulting in an increase of the refractive index and a positive (convex) lens. Accompanying this increase of the refractive index parallel to the pump laser polarization, the refractive index is decreased in the direction perpendicular to the pump beam polarization, resulting in a negative lens. This is the reason why the nuclear parts of the signal have opposite signs for parallel and perpendicular pump-probe configurations. The signal measured in our position-sensitive detection is heterodyned in the same fashion as in OHD RIKES. Specifically, the signal is derived from the probe beam, therefore it maintains a constant phase relationship with the probe pulse. The coherent interaction of the signal and the much stronger probe field provides the heterodyne detection of the material response. Under impulsive excitation conditions, the off-resonant third-order nonlinear susceptibility responsible for the parallel pump-probe configuration is χ(3) xxxx(-Ω2(probe), Ω2(pump), Ω1(probe), -Ω1(pump)) according to the Maker-Terhune notation,32,33 where |Ω1 - Ω2| represents the vibrational coherence created on the ground electronic state, and the parenthesized pump and probe indicate the origin of the frequency components. Similarly, the nonlinear susceptibility for the perpendicular configuration is χ(3) xyxy(-Ω2(probe), Ω2(pump), Ω1(probe), -Ω1(pump)). The difference between these two quantities is exactly what is measured in an OKE experiment. Dictated by the directions of pump and probe polarizations and the detection polarizer,33,34 time domain OHD RIKES experiment measures χ(3) xyyx(-Ω2(probe), Ω2(pump), Ω1(probe), -Ω1(pump)) + χ(3) xxyy(-Ω2(probe), Ω2(pump), Ω1(probe), (3) (3) -Ω1(pump)). However, because χ(3) xxxx ) χxxyy + χxyyx + (3) χxyxy, the difference between the parallel and perpendicular (3) pump-probe configurations, χ(3) xxxx - χxyxy, is equivalent to what is measured in an OHD RIKES experiment. In Figure 2, the upper curve is the subtraction of the perpendicular response from the parallel response. The lower curve is the OHD RIKES transient taken with the same laser system.34 The agreement between these two curves are quantitative within the experimental errors, supporting that the position sensitive detection employed in the present study selectively detects the heterodyned real part of the response function. The small discrepancy around zero time delay when these two curves are overlaid arises from a slight difference in the instrument response of these two separate experiments. The signal-to-noise ratio in the position-sensitive detection is somewhat poorer. This is because the detection scheme is not background free as in the OKE detection. The spectral densities for the parallel and perpendicular geometries are obtained through the standard Fourier transformdeconvolution procedure6 and the results are displayed in Figure 3. The difference between these two spectral densities is plotted along with the OHD RIKES spectral density in the same graph.
J. Phys. Chem., Vol. 100, No. 21, 1996 8615
Figure 2. Difference between the parallel and perpendicular signals (upper curve) and the OHD RIKES transient (lower curve) of CS2. The inset shows the direct comparison of these two curves. The small discrepancy around time zero is caused by slightly different instrument response functions (45 fs FWHM for OHD RIKES and 30 fs for position-sensitive detection).
Figure 3. Spectral densities of CS2 obtained by the Fourier transformdeconvolution procedure. Triangle marker: perpendicular pump-probe configuration. Squared marker: parallel pump-probe configuration. Solid round marker: the difference between the parallel and perpendicular configurations. Solid line: OHD RIKES.
There are some small discrepancies in the low-frequency portion between the OHD RIKES and the difference spectral densities. This arises from the fact that the difference spectral density is obtained from 6.5 ps long time-domain transients, while the OKE spectral density is derived from a 5 ps scan. Other factors being equal, a longer delay time range produces more contributions to the near-zero frequency part of the spectral density through Fourier transform.34 (3) (3) When the isotropic (χ(3) xyxy) and anisotropic (χxyyx + χxxyy) spectral densities are normalized and are compared to one other, we find that they are identical in shape. This observation indicates that the intermolecular depolarization ratio,
8616 J. Phys. Chem., Vol. 100, No. 21, 1996 (3) -1 region. Our F ) (χ(3) xyyx/χxxxx), is a constant in the 0-150 cm computed F is indeed frequency independent and is 0.7 ( 0.1 throughout this spectral region. A purely depolarized mode is one where F ) 0.75. The uncertainty in the calculated value of F only allows us to make a qualitative conclusion that the underlying intermolecular modes of CS2 are essentially depolarized.
Summary We have demonstrated a powerful technique, positionsensitive Kerr lens spectroscopy, that can measure an arbitrary component of the intermolecular spectral density in liquids by incorporating position-sensitive detection into a two beam pump-probe setup. This technique maintains some of the advantages of OHD RIKES such as the simplicity of the experimental setup and the intrinsic heterodyning of the signal. More importantly, it does not have the limitations on the relative polarization directions of the pump and probe beams as in OHD RIKES, thus it can detect any component of the material response and provides information that cannot be accessed via OHD RIKES. It should find applications in a wide range of systems, especially those related to dynamics in liquids and solution. The results for CS2 using this technique are discussed in detail in this letter and compared with that measured by OHD RIKES. Results have also been obtained for benzene and other liquids and will appear in a future publication along with a detailed theoretical analysis of this relatively new detection scheme. We are also exploring ways to extend this off-resonant technique to near-resonant and resonant cases, which will enable us to directly probe solute-solvent interactions and their associated spectral densities. Acknowledgment. This work is supported by the National Science Foundation and the MFEL Program administered by the Office of Naval Research. References and Notes (1) Nielsen, O. F. Annu. Rep. Prog. Chem. Sec. C Phys. Chem. 1993, 90, 3-44. (2) Yarwood, J. Annu. Rep. Prog. Chem., Sect C, Phys. Chem. 1987, 84, 155-199. (3) Yarwood, J. Annu. Rep. Prog. Chem., Sect C, Phys. Chem. 1982, 79, 157. (4) Yarwood, J. Annu. Rep. Prog. Chem., Sect C, Phys. Chem. 1990, 87, 75-119.
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