Calculations of nonlinear spectra of liquid Xe. I. Third-order Raman response

Abstract

The one-particle Green's function method in the Dirac-Hartree-Fock framework. I. Second-order valence ionization energies of Ne through XeThe microscopic interactions and dynamics probed by third-order Raman spectroscopy in an atomic liquid ͑Xe͒ are explored within the Drude oscillator model, both numerically and analytically. Many-body polarization effects reduce the coefficient of the effective dipole-induced-dipole tensor. The isotropic part of the effective dipole-induced-dipole tensor arises primarily from the three-body interaction and is short-ranged. With an isotropic sample, the Raman response in any polarization geometry can be rigorously decomposed into an isotropic component and an anisotropic component, which primarily measure the strength and evolution of the two-body and three-body interactions, respectively. An interesting result from our analysis is the derivation of the standard mode-coupling equation for the intermediate scattering function and the mode-coupling equation for the bilinear density mode using Gaussian factorization of the memory kernel and the mean spherical approximation of the direct correlation function. The initial moment expansion along with the Gaussian factorization scheme allows us to predict the temporal profile of the Raman response function with reasonable accuracy. Furthermore, the Kirkwood superposition scheme approximates the Raman correlation function with pair distribution functions and time correlation functions and allows us to predict the ratio of the pair, three-particle, and four-particle contributions. These results, though obtained for Xe, are generally helpful in interpreting third-order spectroscopies of other liquids.

Stochastic Liouville, Langevin, Fokker–Planck, and Master Equation Approaches to Quantum Dissipative Systems

“…In practice, the fifth-order 2D Raman spectroscopy is designed to differentiate various motional modes whose origins are attributed to inhomogeneity, 24,27,28,128,129) anharmonicity, 25,[130][131][132][133] and mode coupling mechanisms, [134][135][136] and to monitor inter-and intramolecular vibrational motions. 29,30,[137][138][139][140] Third-order infrared or seventh-order Raman processes 141,142) are shown to be sensitive to the local fluctuation of the molecules surrounding the target molecules and the conformal change of molecules, 121,123,143) which are not so clear for the linear spectroscopy discussed in §4.5. Three-pulse vibrational echo techniques were applied to the molecular stretching mode 144) and hydrogen bonding interaction between the solute and the solvent.…”

“…The above expressions are used to carry out classical molecular dynamics simulations to calculate the higher-order optical response of molecular vibrational motions. [27][28][29][30][31][32] 3.3 Spontaneous emission and scattering: physical spectrum and neutron diffraction A signal emitted by an object entered in the instrument is generally expressed in the time convolution form A inst ðtÞ ¼ …”

Semiclassical mean-trajectory approximation for nonlinear spectroscopic response functions

“…͑2.1͒ by writing the coordinate operator in a harmonic approximation [40][41][42] in terms of boson creation and annihilation operators q = q + + q − , ͑3.1͒…”

“…The difficulties associated with fully quantum calculations of vibrational response functions have motivated assessments of fully classical [27][28][29][30][31][32][33][34][35][36][37][38][39] and semiclassical [40][41][42][43][44][45][46][47][48] calculations. Classical calculations permit the determination of a response function by propagating classical trajectories and stability matrices, but in general these only agree with quantum calculations at short times, [43][44][45][46][47][48][49] which may indeed suffice to describe some ultrafast experiments.…”

Thermal weights for semiclassical vibrational response functions

“…[1][2][3][4][5][6] Numerically exact quantum dynamical calculations of response functions are generally impractical for large systems, while classical calculations of nonlinear response functions can be qualitatively incorrect at long times. [7][8][9][10][11] Semiclassical approximations to quantum dynamics [12][13][14][15][16][17][18][19][20][21][22][23][24][25] have the capacity to incorporate quantum effects with a computational effort comparable to that of a purely classical calculation. One semiclassical strategy applied to the evaluation of spectroscopic response functions [26][27][28] draws on the old quantum theory 29 by propagating classical trajectories at quantized action values.…”