Kramers-Fokker-Planck equation for polyatomic molecules

摘要

Starting from the microscopic Hamiltonian of a whole solution system, we have derived a Kramers-Fokker-Planck (KFP) equaiton for polyatomic molecules by using Zubarev's technique of nonequilibrium statstical distribution function. For the purpose, a set of normal coordinates of a solute molecule is defined at a stationary point on the free energy surface. In the normal coordinate representation, the expression of the KFP equation includes not only the deformation originating in the Coriolis coupling but also the friction tensor inducing a new type of coupling. For demonstration, two examples are examined. First, under the approximation of adiabatic elimination of fast variables, a one-dimensional KFP equation is derived from the above KFP equation, which corresponds to the euqation that Kramers first derived intuitively for one-dimensional chemical reaction model in solution. Second, assuming a mnodel system which describes simultaneously a couple of vibrational and rotational moitions, a two-dimensional KFP equation is solved numericaly to invstigate the role of the friction tensor. It is found that the off-diagonal friction coupling reduces the diagonal friction influence.