Vibrational energy transfer from resummed evolution operators

This paper describes the application of our recently derived infinite order evolution operator expansion and resummation technique to the problem of vibrational energy redistribution in molecules. For a standard mass tensor coupled model of a linear hydrocarbon we show how the resummation technique allows the derivation of an approximate evolution operator that in a single time step accurately reproduces vibrational dynamics for over 25 fs in hydrocarbons. This single time evolution operator can be calculated efficiently enough so that long time dynamics with multiple time steps seem to now be within reach. In addition, the structure of the theory is such that longer chain hydrocarbons can be efficiently "built up" from shorter chain molecules. The theory starts with an adiabatic approximation which describes coupled vibrational degrees of freedom by uncoupled but guage shifted evolution operators. A modified version of this adiabatic approximation shows promise for application to molecules of a size too large to be handled exactly.