Franck—Condon Factors for Polyatomic Molecules

General expressions are derived for calculating Franck—Condon factors for most transitions of polyatomic molecules (excluding transitions between linear and bent configurations) in the harmonic oscillator approximation. The derivation employs the method of generating functions and also linear transformation of normal mode coordinates between initial and final states. Input data required in the general case are geometries, frequencies, and vibrational force fields for the initial and final states. Explicit algebraic expressions are presented for the transition between linear, symmetric, triatomic initial and final states. The results are used to show that fragmentation cannot result from direct vertical ionization to the ground electronic states of CS2+ and CO2+ or to the excited 2IIu state of CO2+. An attempt was made to fit the experimental photoionization data for C2H2 and C2D2. This resulted in an estimated increase of 0.05 Å in the equilibrium C–C bond distance and no change in the C–H bond distance in C2H2+ as compared to C2H2.