10395
J . Phys. Chem. 1991,95, 10395-10406 emission over a broad spectral range suggests an essentially equilibrated vibrational system of the keto species produced by proton transfer. The vibrationally hot molecules cool down by collisional interaction with the surrounding solvent on a time scale of 10-50 In the femtosecond measurements, a broad interval of vibronic SI'states in the range of the keto minimum contributes to stimulated emission at a specific probe wavelength. Even for high transient temperatures of the molecules of 500-1000 K, the population density of those states is very large compared to that of levels on the high-energy tail of the distribution. As a result, the gain is not very sensitive to changes of the vibrational temperature. The cooling kinetics makes no significant contribution to the measured signal; Le., the measured time constants are identified as proton- and deuterium-transfer times. (24) Mokhtari. A,; Chebira, A,; Chesnoy, J. J. Opt. SOC.Am. B 1990, 7, 1551.
Conclusions We have studied proton and deuterium transfer in the first excited singlet state of benzothiazole compounds by femtosecond pump-probe spectroscopy. In nonpolar solvents, proton- and deuterium-transfer times of 160 and 150 fs have been found. Intramolecular proton transfer in polar solution occurs on a similar femtosecond time scale. These results suggest a barrierless potential energy surface of the excited-state reaction with a rate determined by the period of low-frequency vibrations of large amplitude. Our recent studies of benzotriazoles6 reveal similar femtosecond kinetics of proton transfer. Thus, the reaction scheme reported here may be valid for a larger class of aromatic molecules. Acknowledgment. Valuable discussions with W. Kaiser are gratefully acknowledged. Registry No. DBT (keto tautomer), 136067-11-3; DBT (enol tautomer), 30612-16-9; HBT (keto tautomer), 67294-91-1; HBT (enol tautomer), 341 1-95-8; Dl, 7782-39-0.
Intermolecular Dynamics in Acetonitrile Probed with Femtosecond Fourier Transform Raman Spectroscopy Dale McMorrow* Naval Research Laboratory, Code 461 3, Washington, D.C. 20375
and William T. Lotshaw* G.E. Research and Development, P.O. Box 8, Rm. KWD-270, Schenectady, New York 12301 (Received: March 27, 1991)
We present femtosecond optical heterodyne detected optical Kerr effect measurements of the transient birefringence of neat acetonitrile liquid. Using a recently developed Fourier transform analysis, the transient data are presented in both the timeand frequency-domain representations. The nuclear contributions to the transients, free from any distortions introduced by the electronic response, are generated from the frequency-domain data. The focus of this work is on the high-frequency dynamics associated with intermolecular vibrational degrees of freedom. We observe markedly nonexponential dynamics at short times, with the longtime relaxation characterized by an 1 . 4 9 exponential time constant. The femtosecond dynamics exhibit characteristics of rapid inhomogeneous dephasing, which accounts for -80% of the signal decay, as well as evidence for contributions from lower frequency, overdamped oscillators. The NLO intermolecular vibrational spectrum of acetonitrile exhibits a broad resonance with a band maximum of -55 cm-I and a bandwidth of 100 cm-I. The femtosecond transients emphasize the role of the (microscopic) intermolecular potential energy surfaces in shaping the short-time vibrational aspects of the intermolecular dynamics in this liquid. The possible role of similar considerations in the short-time aspects of dynamic solvation phenomena is discussed. The manifestations of intermolecular vibrational motion in solvation transients have not yet been observed experimentally but are revealed clearly in recent molecular dynamics simulations. The correspondence between certain aspects of the two experiments is noted, and experimental questions associated with the observation of intermolecular vibrational modulation of solvation transients are discussed.
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I. Introduction Acetonitrile can be regarded as the prototypical polar aprotic molecule, with acetonitrile liquid representing the best approximation available to an ideal dipolar fluid. Because of its large (3.92 D)I permanent dipole moment, and lack of specific (e.g., hydrogen-bonding) interactions, the dynamics of acetonitrile liquid are of tremendous theoretical, experimental, and practical importance. In this paper we utilize femtosecond nonlinear-optical (NLO) methods to observe directly the dynamics of intermolecular motion in acetonitrile liquid. The molecular dynamics of acetonitrile have been studied extensively for more than two decades utilizing numerous techniques.'-I2 We focus here on the high(1) (2) (3) (4) (5)
Steiner, P. A,; Gordy, W. J. Mol. Spectrosc. 1966, 21, 291. Bartoli, F. J.; Litovitz, T. A. J . Chem. Phys. 1972, 56, 404, 413. Kakimoto, M.; Fujiyama, T. Bull. Chem. S o t . Jpn. 1972, 45, 3021. Griffiths, J. E. J. Chem. Phys. 1973, 59, 751. Breuillare-Alliot, C.; Soussen-Jacob, J . Mol. Phys. 1974, 28, 905.
0022-3654/91/2095-10395$02.50/0
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frequency dynamics that occur on a time scale of less than 500 fs, although the longer time dynamics are revealed as well. The transients detected in this study are closely related to depolarized light-scattering (LS) ~ p e c t r a , ~ - ' ~with ' ~ ~the ' ~ -ultrafast ~~ dynamics (6) Amorim da Costa, A. M.; Norman, M. A,; Clarke, J. H. R. Mol. Phys. 1975, 29, 1975. ( 7 ) Whittenburg, S. L.; Wang, C. H. J. Chem. Phys. 1976, 66, 4255. (8) Schroeder, J.; Schiemann, V . H.; Sharko, P. T.; Jonas, J . J . Chem. Phys. 1976, 66, 3215. (9) Yarwood, J.; Arndt, R.; Doge, G . Chem. Phys. 1977,25, 3 8 7 . Doge, G.; Khuen. A,; Yarwwd, J. Chem. Plrys. 1979, 42, 331. Arnold, K. E.; Yarwood, J.; Price, A. H. Mol. Phys. 1983, 48, 451. (IO) Danninger, W.; Zundel, G. Chem. Phys. Lett. 1982, 90, 69. ( 1 1) Bohm, H. J.; McDonald, I . R.; Madden, P. A. Mol. Phys. 1983,49, 347. Bohm, H. J.; Lynden-Bell, R. M.; Madden, P. A,; McDonald, I . R. Mol. Phys. 1984,51,761. Lynden-Bell, R. M.; Madden, P. A,; Stott, D. T.; Tough, R. J . Mol. Phys. 1986, 58, 193. Westlund, P. 0.; Lynden-Bell, R. M. Mol. Phys. 1987, 60, 1189. (12) Gale, G. M.; Guyot-Sionnest, P.; Zheng, W. Q. Opt. Commun. 1986, 58, 395.
0 1991 American Chemical Society
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10396 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
corresponding to the Rayleigh “wing” region of the LS spectrum. While detailed and reliable information on such high-frequency motions has proven difficult to extract from LS spectra, NLO methods recently have demonstrated a utility for probing the short-time dynamics of intermolecular motion in condensed and thus offer an alternate source of information on this difficult spectral region. Using a recently developed Fourier-transform analysis of the transient data,u the intrinsic (&function) NLO frequency response of acetonitrile is determined directly from the measured transients. The results reveal directly the intermolecular NLO Raman spectrum of this liquid and emphasize the importance of Raman-resonant intermolecular vibrational modes in shaping its short-time dynamics. The use of Fourier-transform methods in the treatment of NLO transients offers significant advantages over the more conventional, time-domain curve-fitting procedures. A frequency-domain representation of the temporal data can reveal directly features that are only deduced from the time-domain transients after rather extensive curve fitting procedures. Even then, the conclusions are only as reliable as the models that are assumed, The FT methods utilized here have additional, practical advantages. For NLO transients measured with optical heterodyne detection techniques, the effects of the finite-duration/finitebandwidth optical pulses can be successfully removed (deconvoluted) from the experimental data with no pulse-shape approximations or assumed models for molecular motion.22 The resulting impulse response functions and spectra can be compared directly to the results of MD simulations or spectra measured with other techniques. In addition, for the specific case of transform-limited pulses and transparent media, the nuclear contribution to the data is automatically separated from the electronic r e ~ p o n s e . * ~The .~~ resulting nuclear response is free from any distortions associated with electronic and (symmetric) coherent coupling contributions near zero delay. This very useful result is a direct consequence of causality and the symmetry properties of the nuclear and electronic response f ~ n c t i o n s . ~ ~ . ~ ~ The organization of this paper is as follows. Following a general discussion on ultrafast molecular dynamics in liquids, and their role in chemical and photophysical events, the theoretical background necessary for understanding the experimental observables measured in a transient NLO experiment is presented. This is followed by a presentation of the essential features of the Fourier-transform treatment of the data, and a description of the experimental details. In section IV we present the femtosecond data for acetonitrile, and its corresponding frequency-domain representation, and generate the nuclear part of the NLO transient, the latter two results being a consequence of the Fourier-transform analysis noted above. In section V the subpicosecond dynamics that are associated with intermolecular vibrational degrees of freedom are discussed in greater detail, and an approximate representation of the intermolecular vibrational spectrum of acetonitrile is presented. The discussion of section VI is focused on the role of intermolecular vibrational motions in the early-time aspects of dynamic solvation phenomena. (13) Starunov, V. S. Sou. Phys. Dokl. 1968,8, 1206. Starunov, V. S. Opt. Spectrosk. (USSR) 1965, 18, 165. (14) Pinnow, D. A.; Candau, S. J.; Litovitz, T. A. J . Chem. Phys. 1967, 49,347. Bucaro, J . A.; Litovitz, T.A. J . Chem. Phys. 1971,54,3846. Dardy, H. D.;Volterra, V.; Litovitz, T. A. J . Chem. Phys. 1973, 59, 4491. ( 1 5 ) Madden, P. A. Liltrajast Phenomena IV; Auston, D. H., Eisenthal, K. B., Eds.; Springer-Verlag: New York, 1954; pp 244-251. (16) Geiger, L. C.; Ladanyi, B. M. Chem. Phys. Lett. 1989, 159, 413. (17) Kalpouzos, C.; McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A . J . Phys. Chem. 1987, 91, 2028; Chem. Phys. Lett. 1987, 136, 323. (18) McMorrow, D.; Lotshaw, W. T.;Kenney-Wallace, G . A. IEEE J . Quant. Electron. 1988, QE-24. 443. (19) Ruhman, S.; Williams, L. T.; Joly, A. G.; Kohler, B.; Nelson, K. A . J . Phys. Chem. 1987, 91, 2237. (20) Ruhman, S.; Joly, A. G.; Nelson, K. A. IEEE J . Quunt. Electron. 1988, QE-24, 460. (21) Etchepare, J.; Grillon, G.;Chambaret, J. P.; Hamoniaux, G.; Orzag, A. Opt. Commun. 1987, 63, 329. (22) McMorrow, D.;Lotshaw, W. T.Chem. Phys. Lett. 1990, 174, 85. (23) McMorrow, D. Opr. Commun. 1991,86, 236.
11. Molecular Dynamics in Liquids
The utility of NLO methods for probing the spectral region up to -150 cm-’ was first demonstrated in 1981 by Song and co-workers using a frequency-domain stimulated Raman gain technique.24 Their initial experiments on CS2liquid illustrated that NLO methods possess real advantages over spontaneous LS techniques for probing the high-frequency “wing” region of the intermolecular LS spectrum. For liquids composed of optically anisotropic species, the spontaneous LS spectrum typically consists of two distinguishable features: a sharp, approximately Lorentzian feature centered on Au = 0 that is causally related to diffusive reorientational motion of the molecules; and a broad, diffuse ‘wing” sometimes extending past 200 cm-‘ . Early investigators recognized that the Rayleigh ‘wing” contained useful information on the high-frequency motions that occur in condensed phase^.^^.'^ However, spectroscopists have experienced tremendous difficulty extracting detailed line shapes for these contributions to the spontaneous scattering spectra. This difficulty arises to a large extent because the Rayleigh wing is typically 1.5-2 orders of magnitude lower in intensity than the central feature.13J4 This observation explains the fact that the high-frequency wing intensity was missed or ignored in many early investigations, and why that portion of the LS spectrum apparently has been described successfully using widely divergent, and often contradictory models for molecular motion in liquids. The temporal resolution necessary to successfully resolve in the time domain the high-frequency molecular motions that contribute to the Rayleigh wing has only been achieved in the past few years, with the first such investigations into the dynamics of molecular liquids having been reported very r e ~ e n t l y . ’ ~ .For ’ ~ molecular ~~~~~~ liquids, optical pulses of duration less than 100 fs are generally necessary to obtain a reliable representation of the intermolecular dynamics,22since the duration of the optical pulse used must be less than or equal to the inverse bandwidth of the intermolecular spectrum. Many common liquids exhibit intermolecular spectra that extend to -200 cm-’, with laser pulse widths on the order of -70 fs being necessary. For more complex liquids having higher frequency intermolecular motions, pulses significantly shorter than 100 fs will be necessary to obtain data that is not significantly distorted by the spectral-filter effects of the finitebandwidth optical pulses22(for example, to resolve the intermolecular spectrum of water which extends past 1000 cm-1,26laser pulses of -20-fs duration will be required). In recent years there has been increased recognition that microscopic aspects of solvent/solute interactions can play a significant role in the dynamics and ultimate outcome of chemical and photophysical events. Excited-state intramolecular protontransfer (ESIPT)reactions provide a good example of such effects. In 3-hydroxyflavone, for example, specific intermolecular hydrogen-bonding interactions can perturb the intramolecular hydrogen bond that is necessary for tautomerization to occur, interfering with and even preventing the proton-transfer pro~ess.~’ In the presence of such perturbations, the rate of the excited-state reaction is determined by the time scale for the intermolecular process of hydrogen bond breaking (with the accompanying solvent/solute reorganization), rather than by the intrinsic intramolecular potential energy surface.27 Because the rate of hydrogen bond breaking can become very small in low-temperature viscous solutions, the ESIPT reaction in 3-hydroxyflavone can be very effectively quenched. The tautomerization of 7-azaindole in alcohol solutions provides another example. In the case of 7-azaindole, a well-defined cyclically hydrogen-bonded solvent/solute complex is necessary to catalyze the excited-state r e a ~ t i o n . ~ ~ -In ~ Othe absence of this cyclical complex, solvent/ (24) Scarparo, M. A. F.; Lee, J. H.; Song, J. J. Opt. Lett. 1981, 34, 193. (25) Green, B. I.; Farrow, R. C. Chem. Phys. Lett. 1983.98.273. Green, B. I.; Fleury, P. A.; Carter, H. L.; Farrow, R. C. Phys. Rev. A 1984,29,271. (26) Walrafen, G.E. J . Phys. Chem. 1989, 94, 2237. (27) McMorrow, D.; Kasha, M. J . Am. Chem. SOC.1983, 105, 5133; J . Phys. Chem. 1984, 88, 2235. (28) Taylor, C. A,; El-Bayoumi, M. A,; Kasha, M. Proc. Nurl. Acad. Sci. U.S.A. 1969, 63, 253.
Intermolecular Dynamics in Acetonitrile solute configurational relaxation into the reactive configuration must occur prior to the proton-transfer ~tep.~’*~O The effective rate of the net reaction is determined by this rearrangement step?’ which depends on the chemical anisotropy of both reacting species, as well as the time scale for fluctuations in the local solvent/solute configuration.30 The examples just described involve specific interactions between solvent and solute molecules. As is evident, such interactions can have a dramatic effect on the evolution of a potentially reactive chemical event. Equally important, however, are solvent effects of a less specific character, the most noteworthy of these being evident in the stabilization of ground and electronically excited states. The current interest in the dynamic solvation of molecular species dates back to a large body of steady-state spectroscopic work on solvent-dependent spectral shifts in absorption and emission spectra.31 Nonspecific solvent effects that are important in the stabilization of molecular species include dipole-dipole interactions, dipole-induced-dipole interactions, and the general polarization effect.31b The role of specific solvent/solute interactions on the energetics of electronic transitions was first made explicit in the now classic work of Brealy and Kasha on the effect of hydrogen-bonding on 1) ?r* transition^.^^ A discussion of the relevance of the current measurements to problems in solvation dynamics will be presented in a later section of this paper. At this time we would like to underscore some of the more significant points of that discussion. For phenomena that occur on a time scale of less than a few hundred femtoseconds, the dynamics are determined more by the characteristics of the potential energy surfaces involved, and less by the macroscopic properties of the solvent, such as viscosity and dielectric constant. This is true whether we are referring to motion in a neat solvent, as is probed in the N L O experiments of this paper, or whether we are concerned with the inner-shell solvation dynamics of an electronically excited species. In the simplest approximation we may consider the case of an anisotropic probe molecule in a locally harmonic intermolecular potential. When the probe molecule experiences an externally applied torque, its dynamics at the earliest times are determined solely by its molecular moment of inertia and the curvature of the intermolecular potential energy surface. This description remains valid until some perturbation disrupts the relevant potential; such disruptions occur in liquids on a time scale of typically 200-500 fs. In the limiting case of a spherical cavity (e.g., a flat potential), the probe molecule will experience free, or inertial, rotation. As the curvature of the intermolecular potential is increased, the motion becomes oscillatory. These oscillations can be of translational or orientational (librational) origin, or both, with the latter case (both) being expected in real solutions of anisotropic molecules. Because the intermolecular potential is a microscopic property of the liquid, the high-frequency motions discussed here are not predicted by the various continuum theories of solvation phenomena. Femtosecond N L O experiments on numerous liquids, however, reveal that the dominant contribution to the short-time dynamics is associated with intermolecular vibrational moti o n ~ . ~ ~ - Therefore, ~ ~ , ~ ~it.is~expected ~ - ~ ~that analogous vibrational motions will have a significant influence on the short-time dynamics of solvation phenomena [this correspondence between the high-frequency aspects of intermolecular motion in neat solvents and the short-time aspects of dynamic solvation phenomena has been suggested previously35 but has not, as yet, been elaborated on]. Unfortunately, experimental methods have not yet achieved -+
(29) McMorrow, D.; Aartsma, T. J. Chem. Phys. Lett. 1986, 125, 581. (30) McMorrow, D. Bull. Am. Phys. SOC.1988, 33, 1635. (31) See, for example: (a) Bayliss, N. S.; McRae, E. G. J . Phys. Chem. 1954, 58, 1006. (b) McRae, E. G. J . Phys. Chem. 1956, 61, 562. (32) Brealey, G. J.; Kasha, M. J . Am. Chem. SOC.1955, 77, 4462. (33) Kalpouzos, C.; McMorrow, D.; Lotshaw, W. T.; Kenney-Wallace, G. A. Chem. Phys. Lett. 1988, 150, 138; 1989, 155, 240. (34) Lotshaw, W. T.; McMorrow, D.; Kenney-Wallace, G. A. Proc. SPIE 1988, 981, 20. (35) Lotshaw, W. T.; Kalpouzos, C.; McMorrow, D.; Kenney-Wallace, G.
A. In Ultrafast Phenomena VI: Yajima, T., Yoshihara, K., Harris, C. B., Shionoya, S., Eds.; Springer: New York, 1984; pp 537-541.
The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 10397 sufficient time resolution to observe these ultrafast solvation phen~mena’~ (effective instrument functions of -100 fs will be necessary22). The situation is different in molecular dynamics (MD) computer simulations. MD simulations provide a powerful tool for investigating the short-time aspects of solvation phenomena, with several such simulations having been performed recently.3w3 An important point here is that an understanding of the intermolecular potential energy surfaces involved is a necessary starting point for any computer simulation. Many of the simulations reported to date36*38,42,43 reveal short-time dynamical characteristics that are strikingly similar to those observed in the transient NLO experiments on bulk solvents. 111. Theory It is well recognized that an intense, linearly polarized optical pulse will induce in a transparent material a transient birefringence, An(& which can be represented in the general form
where Ipmp(t) represents the intensity envelope of the laser pulse, @;&(f) is the real part of N L O polarization impulse response function, and 6n,,(t)and 6n,(t) are the refractive index changes parallel and perpendicular to the plane of polarization of the pump pulse, respectively. Equation 1 is a special case of the more general expression for the material excitation, Q ( t ) ,
where the Ei(t) represent the electric field envelopes of the optical pulse(s) and
+
aUkl(t)= @;i,(t) i@$/(t)
(2b)
where @Fil(t)and @$!(t) are associated with refractive index and matter/keld energy exchange (gain/lms) transients, respecti~ely.7~ The impulse response function Oijk/(t) consists of electronic and nuclear contributions which, if all of the optical frequencies involved lie well below any electronic absorption (e.g., a transparent material), can be expressed in the form
where gijdt) = bs(t)
(3b)
is the purely electronic hyperpolarizability which is instantaneous on the time scale of the applied laser pulse. In these expressions, b is a scalar constant associated with the amplitude of the electronic contribution, is the NLO impulse response function for the nuclear prt of the material excitation, and @&) is related to x ( ~through ) a Fourier-transform relationship. The nuclear response @“,,Jt) contains contributions from inter- and intramolecular motions of the nucleii, including molecular vibrations (interand intramolecular), translations, and rotations, all of which contribute to the subpicosecond NLO transients observed for molecular liquids. It is important to note that, while the ‘interacti~n-induced”’~J~ contributions to LS spectra and NLO transients are associated with distortions of the electronic po(36) Maroncelli, M.; Fleming, G. R. J . Chem. Phys. 1988, 89, 5044. (37) Karim, 0. A,; Haymet, A. D. J.; Banet, M. J.; Simon, J. D. J . Phys. Chem. 1988, 92, 3391. (38) Bader, J. S.; Chandler,-D. Chem. Phys. Lett. 1989, 157, 501. (39) Barnett, R. B.; Landman, U.;Nitzan, A. J . Chem. Phys. 1989, 90, 4413. (40) Zhu, S. B.; Lee, J.; Zhu, J. B.; Robinson, G. W. J . Chem. Phys. 1990, 92, 5491. (41) Levy, R. M.; Kitchen, D. B.; Blair, J. T.; Drogh-Jespersen, K. J . Phys. Chem. 1990, 94, 4470. (42) Maroncelli, M. J . Chem. Phys. 1991, 94, 2084. (43) Fonseca, T.; Ladanyi, B. M. J . Phys. Chem. 1991, 95, 21 16; also
presented at “Photoinduced Proton Transfer Dynamics in Chemistry, Biology, and Physics”, Conference in Honor of Michael Kasha, Tallahassee, FL, Jan 8, 1990.
McMorrow and Lotshaw
10398 The Journal of Physical Chemistry, Vol. 95, No. 25, 1991
larizabilities, these distortions are causally related to motions of the nucleii, and thus constitute part of anuC(f). Equation 3a is a consequence of 3b, and is a statement of the Born-oppenheimer (BO) a p p r ~ x i m a t i o n . The ~ ~ validity of the BO approximation leads to the important result44 (4) @nuc(t) a ( [ x i j ( t ) t ~ k / ( O ) l) H ( t ) where H ( t ) is the unit step function. Expression 4 reveals that the nuclear impulse response function is determined by the ensemble-averaged correlation function of the linear susceptibilities, xlj. Thus, within the Bom-oppenheimer approximation, the NLO nuclear impulse response can be related directly to the spontaneous scattering cross ~ e c t i o n . ~ ~ , ~ ~ The functional form of the signal detected in a third-order NLO experiment depends on numerous parameters. In general, however, the transients fall into one of two classes: those that are quadratic, and those that are linear in x ( ~ )The . most common situation is the quadratic case, in which the detected signal (neglecting any "coherent-coupling" contributions) is of the general form S(7) = X I d t Iprobe(t - 7)lQ(t)12
(5)
This expression is applicable to experiments performed in the crossed polarizer (homodyne) OKE config~ration~~ as well as the various transient-grating (three-beam) geometries commonly ~ t i l i z e d . l ~ -Note ~ ' that, in this case, the signal is proportional to
I@ i j d t ) 12.
NLO observables that are linear in x ( ~are ) obtained through the implementation of optical heterodyne detection technique^.^^ In OHD methods a local oscillator field is allowed to mix coherently with the signal field at the detector, giving rise to a signal of the form S ( T )= X I d t ELO*(t- T) Ej(t - T) Q ( r )
(6)
where ELo(t)is the local oscillator. Details of the implementation of OHD in the transient OKE experiment are given in the Experimental Section. The signals detected with O H D methods exhibit several advantages over those of the quadratic NLO techniques, including an increased signal amplitude and improved signal-to-noise ratio.47c The primary advantages of optical heterodyne detection in the current study are (i) the signal amplitude is linear in x ( ~ resulting ), in the elimination of troublesome cross terms;47(ii) the signal is linear in both the pump and probe pulse i n t e n ~ i t i e s(iii) ; ~ ~ by controlling the phase of the local oscillator field, either the real or imaginary part of the response @ ( t ) can be independently detected;47and (iv) for transform-limited optical pulses the effective instrument function is represented by the experimentally measurable laser pulse intensity autocorrelation function,'8,22making deconvolution procedures possible without any detailed pulse-shape information.22 The significance of point (iii) is worth elaborating on briefly. When dealing with transparent materials, it is commonly assumed (although not always stated) that contributions from the imaginary part of the nonlinear-optical response function, @!tr(t), are negligible. In this case, eq 5 can be written in the t6rm = JIdt
Iprobe(l
- 7)[AnWl2
(7)
and the detected signal can be interpreted simply in terms of the temporal evolution of the induced birefringence (eq 1). It is evident from eqs 1 and 2 that eq 5 and eq 7 are equivalent only in the special case that @ $ ( t ) = 0. While this approximation is exact for a transparent medium for excitation by a single monochromatic field (because Im x ( ~=) 0 for Au = 0), and is quite good for many (44) Hellwarth, R. W. frog. Quant. Electron. 1977, 5 , I . (45) Loring, R. F.; Mukumel, S.J . Chem. Phys. 1985, 83, 2116. (46) Duguay, M. A,; Hansen, J. W. Appl. Phys. Letf. 1969, 15, 192. Sala, K.; Richardson, M. C. Phys. Reu. A 1975, 12, 1036. (47) (a) Eesley, G.L.; Levenson, M. D.; Tolles, W. M. IEEE J . Quant. Electron. 1978, QE-14, 45. (b) Levenson, M. D.; Eesley, G . L. Appl. Phys. 1979, 19, 1 . (c) Eesley, G . L. Coherent Raman Spectroscopy; Pergamon: New York, 1981.
cases of pulsed excitation using pulses longer than a few picoseconds (this, of course, depends on the material), it breaks down quite dramatically for most condensed-phase materials when the pulse durations become subpicosecond. This is because the different frequency components of spectrally broad femtosecond optical pulses can interact through coherent Raman processes with the low-lying inter- and intramolecular vibrational (or rotational) resonances of condensed-phase m a t e r i a l ~ . ' ~ - ~The ~ %fact ~ * that Raman resonances possess nonvanishing real and imaginary parts is well recognized and is immediately evident by inspection of the (frequency-domain) OHD Raman-induced Kerr effect literat~re:~ whether the resonance is intramolecular or intermolecular in origin is immaterial. Thus, we may make the general statement that if any Raman-active resonance of a material lies within the bandwidth of the exciting or probing laser pulses, the transients measured in OHD (eq 6) and quadratic (eq 5 or 7) N L O experiments are not equivalent. To quantify these statements, we have performed OHD OKE experiments on several molecular liquids using local oscillators that are either in phase or 90" out of phase with the probe field (cf., Experimental Section). Assuming perfect optics and neglecting any frequency dependence of the X/4 waveplate, these configurations will lead to detection of the imaginary and real parts of re~pectively.~'The results of one such example, for benzene liquid, has been published.I8 The essential fact here is that, for benzene, the amplitude of the out-of-phase OHD experiment is only a factor of 6 larger than that of the in-phase experiment. Thus, in constructing pl,kr(t)12,cross terms involving the real and imaginary parts of will be quite significant, complicating greatly the interpretation and analysis of the data. The complications noted in the previous paragraphs can be alleviated through the use of OHD techniques. In particular, for transform-limited optical pulses and a local oscillator phase-shifted by 90" with respect to the probe field, eq 6 takes on a particularly simple and useful form:I8 T(T) = X1Gh2)(7 - f ) @ F ; / ( r ) dt = Ch2)(7)m Ryk1(7)(8) where Gd2)(7) is the zero-background intensity autocorrelation function of the laser pulse and, to be consistent with earlier notation, we have made the substitution Rl,k,(t)= @;;,(t). It should be noted that R ( t ) is a real, causal function of time. We have developed a Fourier-transform deconvolution method that takes advantage of the particularly simple functional form of eq 8. This method, which we refer to as the Fourier-transform four-wave mixing (FT 4WM) methodZ2(i) generates directly the NLO frequency response of the material; (ii) separates the nuclear and electronic contributions to the NLO material response; and (iii) generates the impulse response function for nuclear motion. The FT 4WM method has been described;22in what follows we summarize the essential features. In considering the dynamical response of a transparent material to an ultrashort optical pulse it is useful to consider both the timeand frequency-domain representations. We may define the function &(Au) as the Fourier transform of Rykl(t) Dijd
Aw) = XIRijk/(t)eJAuf dt = 3 R , k / ( t ) I
(9)
where AW = Iw, f on[.D l , k c ( Ais~ )the frequency-domain representation of the birefringent response and may be regarded as the intrinsic nonlinear-optical frequency response of the material to a 6-fpnction optical pulse. While the information content of Dl,kl(Au) is identical with that of RIJkl(f),it is often more straightforward to interpret spectral features than dynamical waveforms. as will be demonstrated in the following sections. Referrini back to ea 8. because both T ( s ) and EL2)(7)are experimenGly measured-quantities, it is straightforward io extract DdAu)3with no the impu1se frequency pulse-shape approximations or assumed models:22 3{G6*)(7)13(R;,d7)I DijdAu) =
- 31T(7)) I
3[lCh2)(7)t
3FJb2)( 7)1
(10)
The Journal of Physical Chemistry, Vol. 95, No. 25, 1991 10399
Intermolecular Dynamics in Acetonitrile This result is a direct consequence of eq 8 and the use of optical heterodyne detection techniques. The analogous manipulations are not possible for the quadratic NLO observables. The function Df,kl(Ao) has several unique and desirable properties that can be utilized to reveal details of the NLO response that are not easily extracted from the measured dynamical waveform. Using eqs 3 and 9 the function D,kl(Aw) can be expressed in terms of the constant b and nuclear impulse response function Rnuc(t): ~m D ~ , ~ ~ (=A~m ~ )~ I R ~ , , ( ~ ) J Re D f , d A u ) = b
+ Re Y{Rnuc(OI
(1la) (1 lb)
Because b is a real constant, the electronic hyperpolarizability contributes only to Re Drlkl(Au).Consequently, Im Dl,kl(Aw)is determined solely by the nuclear part of R ( t ) . In addition, causality considerations require that Rnuc(t) = 23-'{Im Di,dAu)lH(t - t o )
(12)
and the impulse response function for nuclear motion is determined uniquely by Im Dykl(Au).All information on the nuclear part of the birefringent material response is contained in the imaginary part of Df,kl(Au).Given this result, the substitution of (12) into (8) gives directly the nuclear part of the measured transient,
*
Tnuc(7) = Gb2'(~) Rnuc(T)
(13)
This is a significant result that permits the nuclear part of an OHD NLO transient to be viewed and analyzed independent of any nonresonant electronic or symmetric coherent-coupling effects that can obscure the nuclear response near zero delay. These procedures should be applicable to any N L O spectroscopy that is quadratic in the applied laser i n t e n ~ i t i e s . ~The ~ deconvolution procedure is limited by the bandwidth of the exciting and probing laser pulses, and the signal-to-noise characteristics of the data. Using the 65-fs optical pulses of the current experiment we easily have spectral features up to 314 cm-' (9.95 THz; the v4 mode of CC14), but the spectral data typically becomes quite noisy for Au greater than -250 cm-I. This limitation, however, may be alleviated through the use of shorter optical pulses. If intermolecular and other low-frequency motions of condensed phases are the primary interest, then optical pulses of
