Extent of Delocalization of Vibrational Modes in Liquids as a Result of Competition between Diagonal Disorder and Off-Diagonal Coupling

Abstract

The changes in the extent of delocalization of vibrational modes in liquids arising from the competition between diagonal disorder and off-diagonal coupling in the vibrational exciton picture are examined theoretically. Calculations of vibrational modes and polarized Raman spectra are carried out on a model liquid system, in which spherical particles interact with each other by the Lennard-Jones and dipole−dipole interactions, and a one-dimensional oscillator (representing a vibrational degree of freedom) with a transition dipole and a Raman tensor is buried in each particle. The diagonal disorder is assumed to be in a Gaussian form, and the transition dipole coupling is introduced as the off-diagonal coupling in the vibrational Hamiltonian. The magnitude of the Raman noncoincidence effect (NCE), which is the phenomenon that the vibrational frequency positions of the isotropic and anisotropic components of a Raman band do not coincide and is often used as an experimental measure of the delocalization of vibrational modes, is calculated. In addition, two theoretical measures of the delocalization of vibrational modes are introduced, and their changes with the thermodynamic state of the liquid, the diagonal disorder, and the strength of the off-diagonal coupling are examined. It is shown that the extent of delocalization of vibrational modes is correlated with the “NCE detectability”, defined as the ratio of the magnitude of the NCE and the isotropic or anisotropic Raman bandwidth. This result indicates that the extent of delocalization of vibrational modes in a vibrational band that shows the NCE may be estimated from the observed spectral profile of the band. The size of the space in which vibrational spectra can probe structural formation is also discussed.