Hamiltonian theory for vibrational dephasing rates of small molecules in liquids

Abstract

A technique is developed for solving the generalized Langevin equation (GLE) describing anharmonic oscillators in the weak coupling limit. The GLE is rewritten as a Hamiltonian with a nonlinear system coupled to an infinite bath of harmonic oscillators. A normal mode transformation followed by a perturbation technique is used to obtain the fluctuating system frequency. When the method is applied to a single oscillator with cubic anharmonicity, both the classical and quantal dephasing rates are shown to be equal to the well-known result of Oxtoby. The technique is also applied to a system with more than one vibrational degree of freedom (linear triatomic molecules) to obtain the dephasing rates for the symmetric and antisymmetric normal modes. The effects of system anharmonicity on frequency shifts are investigated.