UNTANGLING THE PHYSICAL CONTRIBUTIONS TO INSTANTANEOUS NORMAL-MODE APPROXIMATIONS - INHOMOGENEOUS BROADENING, MOTIONAL NARROWING, AND ENERGY RELAXATION

An instantaneous normal mode (INM) approach to vibrational lineshapes, including motional narrowing, is presented. Simulations and calculati ons are carried out for a diatomic in Lennard-Jones solvent as a funct ion of vibrational frequency, with an emphasis on determining the cont ributions of different physical relaxation mechanisms. The velocity co rrelation of a bond is easily related to a bond-weighted INM density o f states, containing both resonant energy relaxation (ER) and unnarrow ed inhomogeneous broadening. An effective weighted density of states o r static spectrum, the distribution of an effective time-dependent fre quency Omega(t), is introduced and proposed as a measure of the inhomo geneous linewidth only. It is found that the vibrational INM: are in t he motionally narrowed or fast modulation limit; motional narrowing of INM cannot be ignored. A dynamic spectrum containing only :he motiona lly narrowed inhomogeneous spectrum and corresponding pure dephasing r elaxation is isolated. Reintroducing energy relaxation results in exce llent agreement with simulation. The validity of INM approximations an d the relative importance of different relaxation mechanisms as a func tion of vibrational frequency is analyzed. It is suggested that, throu gh INM, a role may be found for motional narrowing in intermolecular d ynamics. (C) 1998 American Institute of Physics.