Fifth-order raman spectrum of an atomic liquid: simulation and instantaneous-normal-mode calculation

Higher-order optical correlation spectroscopy in liquids

Linear optical spectroscopies have long been used to study the behavior of liquids. Laser technology has progressed to the point that it has become possible to perform nonlinear optical experiments that probe higher-order correlation functions in liquids, opening a new window into our understanding of the microscopic details of solution-phase processes. Here we review advances that have been made in recent years in employing higher-order electronic and vibrational spectroscopies to study liquid-state dynamics and structure.

Generalized Langevin equation approach to higher-order classical response: second-order-response time-resolved Raman experiment in CS2

A simple, systematic generalized Langevin equation approach for calculating classical nonlinear response functions is formulated and discussed. The two-time Poisson brackets appearing at second and higher order are rendered tractable by a physically motivated approximation. The method is used to calculate the fifth order (second order response) Raman response of liquid CS2. Agreement with simulation is good, but the simplicity of the theoretical expression suggests that the path to obtaining qualitatively new information about liquids with the fifth order experiment is uncertain. Further applications of the basic approach are suggested.

Heterodyne-detected fifth-order nonresonant Raman scattering from room temperature CS2

Actively phase-locked heterodyne-detected fifth-order nonresonant Raman scattering from room temperature CS2 has been measured. The experimental signals have similar magnitudes, shapes, and sign changes as calculated responses obtained via molecular dynamics simulations [S. Saito and I. Ohmine, Phys. Rev. Lett. 88, 207401 (2002)]. The measured signals contain sign changes that appear to be associated with the coupling of rotational motions both to each other and to translational motions.

Off-resonant fifth-order response function for two-dimensional Raman spectroscopy of liquids CS2 and H2O

The off-resonant fifth-order response functions for two-dimensional (2D) Raman spectroscopy of molecular liquids CS2 and H2O are investigated by using molecular dynamics calculation. This spectroscopy, able to deal with a phase space dynamics, shows the existence of nodal lines in several polarization tensor elements [see L. Kaufman et al., Phys. Rev. Lett. 88, 207402 (2002) for experimental results]. The nodal property is found to arise from the dynamical couplings among rotational modes, not accounted for in a normal mode picture. The effects of anharmonicities and "mode coupling through polarizability" are also investigated by comparing the 2D Raman signal with a constant temperature velocity reassignment echo method.

Mode-coupling theory for multiple-point and multiple-time correlation functions

We present a theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system. Such higher-order correlation functions have attracted much interest recently in the context of various forms of multidimensional spectroscopy, and have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques that are used to isolate the slow time evolution of dynamical variables by expanding the slowly evolving component of arbitrary variables in an infinite, "multilinear" basis composed of the products of slow variables of the system. Using the formalism, a formally exact mode coupling theory is derived for multiple-point and multiple-time correlation functions. The resulting expressions for higher-order correlation functions are made tractable by applying a rigorous perturbation scheme, called the N-ordering method, which is exact for systems with finite correlation lengths in the thermodynamic limit. The theory is contrasted with standard mode coupling theories in which the noise or fluctuating force appearing in the generalized Langevin equation is assumed to be Gaussian, and it is demonstrated that the non-Gaussian nature of the fluctuating forces leads to important contributions to higher-order correlation functions. Finally, the higher-order correlation functions are evaluated analytically for an ideal gas system for which it is shown that the mode coupling theory is exact.

Dynamics of supercooled water in configuration space

We study the potential energy surface (PES) sampled by a liquid modeled via the widely studied extended simple point charge (SPC/E) model for water. We characterize the curvature of the PES by calculating the instantaneous normal mode (INM) spectrum for a wide range of densities and temperatures. We discuss the information contained in the INM density of states, which requires additional processing to be unambiguously associated with the long-time dynamics. For the SPC/E model, we find that the slowing down of the dynamics in the supercooled region-where the ideal mode coupling theory has been used to describe the dynamics-is controlled by the reduction in the number of directions in configuration space that allow a structural change. We find that the fraction f(dw) of the double-well directions in configuration space determines the value of the diffusion constant D, thereby relating a property of the PES to a macroscopic dynamic quantity; specifically, it appears that square root D is approximately linear in f(dw). Our findings are consistent with the hypothesis that, at the mode coupling crossover temperature, dynamical processes based on the free exploration of configuration space vanish, and processes requiring activation dominate. Hence, the reduction of the number of directions allowing free exploration of configuration space is the mechanism of diffusion implicitly implemented in the ideal mode coupling theory. Additionally, we find a direct relationship between the number of basins sampled by the system and the number of free directions. In this picture, diffusion appears to be related to geometrical properties of the PES, and to be entropic in origin.

Mode-coupling theory of the fifth-order Raman spectrum of an atomic liquid

A fully microscopic molecular hydrodynamic theory for the two-dimensional (fifth-order) Raman spectrum of an atomic liquid (Xe) is presented. The spectrum is obtained from a simple mode-coupling theory by projecting the dynamics onto bilinear pairs of fluctuating density variables. Good agreement is obtained in comparison with recently reported molecular dynamics simulation results. The microscopic theory provides an understanding of the timescales and molecular motions that govern the two-dimensional signal. Predictions are made for the behavior of the spectrum as a function of temperature and density. The theory shows that novel signatures in the two-dimensional Raman spectrum of supercritical and supercooled liquids are expected.