Tractable theory of nonlinear response and multidimensional nonlinear spectroscopy

Abstract

Nonlinear spectroscopy provides insights into dynamics, but the response functions required for its interpretation pose a challenge to theorists. We proposed an approach in which the fifth-order response function [R5( t1, t2)] was expressed as a two-time classical time correlation function (TCF). Here, we present TCF theory results for R5( t1, t2) in liquid xenon. Using a first-order dipole-induced dipole polarizability model, the result is compared to an exact numerical calculation showing remarkable agreement. In addition, R5( t1, t2) is calculated using the exactly solved polarizability model, yielding different results and predicting an echo signal.

Time correlation function and finite field approaches to the calculation of the fifth order Raman response in liquid xenon

“…1 for the reduced temperature, T * = 1.0. The TCF calculation constitutes a prediction of the experimental or simulation result, and is quite different from an earlier calculation employing a first order dipole induced dipole approximation 10,19,27 for the polarizability. Both methods predict a single peak along t 2 with the maximum occurring at t 2 Ϸ 125 fs with similar decay times along both axes.…”

“…[2][3][4][5][6][7][8][9] Furthermore, the signals attained are very difficult to interpret; thus numerically demanding theoretical approaches have been pursued by many researchers. 1, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] One such theoretical approach is a computationally tractable two-time classical time correlation function ͑TCF͒ theory for the quantum response function. 10,22,26,27 The relative simplicity of the theory, writing the response function in terms of a single classical multitime TCF, also offers the possibility of gaining insight into what physical phenomena are usefully probed by 2D Raman experiments.…”

“…29 Although multidimensional nonlinear spectra cannot be expressed exactly in terms of classical TCF, 21 the TCF approach was first shown to be effective by comparison with the only exact classical calculation available at the time. However, those calculations were done using approximations for the polarizability that made them physically less relevant, and only the fully polarized spectrum 10,19 was considered. In the classical limit, appropriate for low frequency intermolecular spectra, the TCF method essentially provides an approximation to the Poisson bracket calculation that otherwise requires the extremely demanding calculation of the stability matrix.…”

How a solute-pump/solvent-probe spectroscopy can reveal structural dynamics: Polarizability response spectra as a two-dimensional solvation spectroscopy

“…[48][49][50][51][52] Their development retreats to the quantum mechanical analogue of Eq. (A1) (with timedependent quantum mechanical operators and commutators in the place of classical dynamical variables and Poisson brackets) expressed in terms of real and imaginary parts of quantum time correlation functions, builds in a relationship between those parts valid for harmonic systems, and then identifies the real part of the quantum time correlation function with its classical analogue.…”

“…Some of these have made use of generalized-Langevin-equation 40,41 and modecoupling 42-47 frameworks, but there has also been a novel formulation in which the classical results have been predicted based on approximations to the quantum mechanical analogue. [48][49][50][51][52] We propose yet another approach here. What turned out to be key for our purposes was the realization that for the kinds of problems of interest in solvation spectroscopy, the time scales T and t are usually going to be widely separated.…”