Density functional theory study of vibronic structure of the first absorption Qx band in free-base porphin

Harmonic vibrational frequencies and vibronic intensities in the first S0→S1 (ππ∗) absorption band of free-base porphin (H2 P) are investigated by hybrid density functional theory (DFT) with the standard B3LYP functional. The S0−S1 transition probability is calculated using time-dependent DFT with account of Franck–Condon (FC) and Herzberg–Teller (HT) contributions to the electric–dipole transition moments including displacements along all 108 vibrational modes. Two weak wide bands observed in the gas phase absorption spectra of the H2 P molecule at 626 and 576 nm are interpreted as the 0–0 band of the X1 Ag→1B3u transition and the 0–1 band with largest contributions from the ν10(ag)=1610ν10(ag)=1610  cm−1 and ν19(b1g)=1600ν19(b1g)=1600  cm−1 modes, respectively, in agreement with previous tentative assignments. Both bands are induced by the HT mechanism, while the FC contributions are negligible. A number of fine structure bands, including combination of two vibrational quanta, are obtained and compared with available spectra from supersonic jet and Shpolskij matrices. Both absorption and fluorescence spectra are interpreted on ground of the linear coupling model and a good fulfillment of the mirror-symmetry rule.