Dynamics of radiationless transitions: effects of displacement-distortion-rotation of potential energy surfaces on internal conversion decay rate constants

General expressions for calculating the internal conversion decay rate constants between two adiabatic electronic states and between two diabatic electronic states are derived. The expressions include the displacements, distortions, and rotations of potential energy surfaces as well as the temperature. For illustration, internal conversion rate constants between various singlet electronic states of ethylene and between the first excited S1 and the ground S0 singlet electronic states of azulene are calculated.