The molecular origins of the two-dimensional Raman spectrum of an atomic liquid. I. Molecular dynamics simulation

Abstract

As complex as it may seem, a two-dimensional (fifth-order) nonresonant Raman spectrum may provide one of the simplest ways to get at the character of intermolecular dynamics in liquids. Its status as an echo spectroscopy means that it should not only permit us to survey the intermolecular vibrations, it should allow us to ascertain the extent of their coherence. Arriving at a microscopic interpretation of those spectra, however, poses some genuine theoretical challenges. We describe here the first complete molecular dynamics simulation of such a spectrum. By using classical dynamics and focusing on liquid Xe, we find that we are able to produce a spectrum strikingly similar to the experimentally reported (nonmagic-angle) spectra of liquid CS2. We observe, in particular, that there is no discernable echo, suggesting that the dynamics is strongly homogeneously broadened. We turn, in a companion paper, to the implications of these results for instantaneousnormal-mode models of liquids.

Vibrational Echoes: Dephasing, Rephasing, and the Stability of Classical Trajectories

“…The challenges posed by computing nonlinear response functions for large anharmonic systems with time-dependent quantum mechanics has motivated the analysis of these quantities within classical mechanics. [8][9][10][11][12][13][14][15][16][17] Nonlinear response functions of a classical mechanical system may not be calculated directly from a conventional, equilibrium molecular dynamics simulation, because their computation requires knowledge of stability matrices, 8 which quantify the effects of small deviations in initial conditions on classical trajectories. An alternative to simulating nonlinear response functions, which obviates the need to compute stability matrices, is to perform a nonequilibrium molecular dynamics simulation of the material system in the presence of an electromagnetic field and to evaluate numerically the appropriate low-field limit.…”

What Do We Learn from Two-Dimensional Raman Spectra by Varying the Polarization Conditions?

“…15 It was with these considerations in mind that we and a number of other groups decided to begin our analysis of 5-th order Raman spectra by thinking about the spectrum expected from an atomic liquid, liquid Xe. [16][17][18][19][20] The ability to concentrate on purely translational motion and on a single term in the dipole-induced-dipole series 17 meant that we could focus on the more basic question of what the 5-th order signal actually tells us about liquid dynamics. It could have been the case, for example, that the signal arose primarily from nonlinear coupling to the many-body polarizability, 16,17,21 a natural consequence in a nonlinear Raman experiment, but not an especially revealing piece of information about liquid motion.…”

“…[16][17][18][19][20] The ability to concentrate on purely translational motion and on a single term in the dipole-induced-dipole series 17 meant that we could focus on the more basic question of what the 5-th order signal actually tells us about liquid dynamics. It could have been the case, for example, that the signal arose primarily from nonlinear coupling to the many-body polarizability, 16,17,21 a natural consequence in a nonlinear Raman experiment, but not an especially revealing piece of information about liquid motion. What we found instead 18 was that it was largely the intrinsic anharmonicity of the molecular dynamics that generated the signal in this example.…”

“…In its most basic form, the experiment involves subjecting the sample to two pairs of visible light pulses separated by a time interval t1, followed by a measurement of the light scattering from a fifth visible pulse a time t2 later. [1][2][3] In the limit of purely classical motion, the response function for this scattering can be written as an ensemble average 16,17,21,27 ,…”

“…A consistent prediction from both Xe and CS2 molecular dynamics simulations is a ridge along the t2 axis (t1 = 0). 17,31,32 Although an unambiguous experimental observation is awkward because of hyperpolarizability and finite-pulse-duration effects, 6,7,33 it has been pointed out that this region is conceptually intriguing. If we think of the liquid's ultrafast dynamics as a superposition of various intermolecular vibrations, the suggestion is that we should regard measurements along this axis as a direct measurement of vibrational population relaxation.…”