The Duschinsky effect has been shown to be significant in spectroscopy and dynamics of molecules that
involve the π−π* transitions. In this paper, we present a derivation of exact expressions for optical absorption
and radiationless transitions in polyatomic molecules with displaced−distorted−rotated harmonic potential
surfaces. In the formulation, we take into account the temperature effect exactly. The application of this new
formulation is demonstrated for ethylene and allene, where the Duschinsky effect in the first singlet excited
electronic state is very strong.