Allowance for change in the solvent frequency spectrum in the theory of nonadiabatic transitions

An explicit expression for the correlation function (CF) of a vibrational subsystem with memory about the electronic subsystem is obtained. The CF is represented in terms of the retarded Green functions of the vibrational subsystem for various electronic states. The singular equations for the CF are solved by means of reducing them to the canonical system and the Riemann problem of the jump of a vector-function with subsequent nonlinear factorisation. Using this, the exact solution of the problem for an arbitrary initial CF is obtained and the influence of the change of the solvent frequency at radiationless transition on the rate constant is calculated.