Interplay of inhomogeneity and anharmonicity in 2D Raman spectroscopy of liquids

Molecular vibrational modes of liquids are studied using the multi-mode Brownian motion model. We examine the effects of inhomogeneity on anharmonic contribution to the 2D Raman spectroscopy. We consider three types of inhomogeneous distribution of local oscillators and present analytical expressions for the 2D signal where the lowest-order anharmonicity is taken into account. Numerical estimations of them in the case of a simple single-mode system clarify the effects of the inhomogeneity. A multi-mode system with anharmonicity and nonlinear polarizability is also studied and numerically compared with a recent experiment on CS2, which suggests a minor role of the inhomogeneity in this substance.