Theoretical studies with molecular dynamics simulation and instantaneous normal modes theory: Fifth-order Raman spectroscopy and vibrational relaxation

The 5th order Raman spectroscopy was developed recently to provide detailed information on liquid dynamics. We performed the first molecular dynamics (MD) simulation of this spectrum on a liquid—liquid Xe and compared it with the prediction of instantaneous-normal-mode (INM) calculation considering only the nonlinearity (NL) of the system polarizability. In the MD simulation, we reformulated the response function so that only one Poisson bracket needed to be propagated and developed a new algorithm for propagating it, adopted a very small but physically well justified system size and improved the statistical sampling significantly through an orientational average process. Since our MD result showed remarkable difference from our NL-INM prediction, we further improved the original INM theory by including leading-order single-mode anharmonicity (ANH)—which leads to a pretty good agreement between MD and INM results. So we learned that the 5th order spectrum for an atomic liquid mainly detects the single-mode anaharmonicity. To learn more on the 5th order spectrum of a specifically molecular system, we performed MD and INM calculations on a simple mixed system—a CS₂ molecule dissolved in Xe solvents. We found that a seemingly uniquely molecular feature—the nodal line, is not necessarily molecular in nature, and that both NL and ANH mechanisms could make substantial contribution for a molecular system—their relative importance depends significantly on polarization conditions. Furthermore, strong mode-mode coupling, which is absent in atomic systems, was found in our simple molecular system. We also did an interesting study on the vibrational energy relaxation in liquids. To explain the significant difference between the vibrational friction predicted by velocity-Verlet and another much more accurate algorithm, we employed a simple model so that the difference between exact and simulated results for the friction could be assessed accurately and analytically by expanding it in a multi-phonon series. We found that the errors of velocity-Verlet result mainly arise from the strong nonlinearity of the pair interaction. A similar analysis on the mechanism tells us that the relaxation process is controlled by a single overtone that makes the largest contribution among all the overtones.