Untangling the physical contributions to instantaneous normal mode approximations: Inhomogeneous broadening, motional narrowing, and energy relaxation

Abstract

An instantaneous normal mode (INM) approach to vibrational lineshapes, including motional narrowing, is presented. Simulations and calculations are carried out for a diatomic in Lennard-Jones solvent as a function of vibrational frequency, with an emphasis on determining the contributions of different physical relaxation mechanisms. The velocity correlation of a bond is easily related to a bond-weighted INM density of states, containing both resonant energy relaxation (ER) and unnarrowed inhomogeneous broadening. An effective weighted density of states or static spectrum, the distribution of an effective time-dependent frequency Ω(t), is introduced and proposed as a measure of the inhomogeneous linewidth only. It is found that the vibrational INM are in the motionally narrowed or fast modulation limit; motional narrowing of INM cannot be ignored. A dynamic spectrum containing only the motionally narrowed inhomogeneous spectrum and corresponding pure dephasing relaxation is isolated. Reintroducing energy relaxation results in excellent agreement with simulation. The validity of INM approximations and the relative importance of different relaxation mechanisms as a function of vibrational frequency is analyzed. It is suggested that, through INM, a role may be found for motional narrowing in intermolecular dynamics.