Collision-induced intramolecular nonradiative transitions through vibronic coupling are calculated by the resolvent method for medium-size molecules (intermediate case). The time-dependent perturbation theory is treated by an inverse Laplace transformation of the resolvent (i ‖ [E−H]−1 ‖ i). The poles and residues of the resolvent are obtained by the Baker–Sasakawa (BS), Brillouin–Wigner (BW), and Rayleigh–Schrödinger (RS) perturbation expansion methods, with the BS method giving the best values. A collision-induced stochastic perturbation method is introduced for obtaining the imaginary part of the eigenvalues, i.e., the line breadth of vibronic levels which indicates the occurrence of vibrational or rotational relaxations in the final electronic state. The calculated value of the 1A″→3A″ intersystem crossing rate of propynal shows good agreement with the experimental value. The calculated damping pattern of the excited state shows oscillatory behavior. The present theory affords an explanation for intramolecular multifrequency quantum beats.