On the theoretical investigation of vibronic spectra of ethylene by ab initio calculations of the Franck–Condon factors

The vibronic spectra of ethylene have been studied using ab initio molecular orbital methods. Geometries of the singlet π–π*, π–3s, and π–3p excited electronic states have been optimized at the CIS and CASSCF levels of theory with the 6-311(2+)G* basis set. Vertical and adiabatic excitation energies, calculated by the multireference configuration interaction (MRCI) and equation-of-motion coupled cluster (EOM-CCSD) methods are in quantitative agreement with experiment. Vibrational frequencies and normal coordinates for the ground and excited states are used for the calculations of vibrational overlap integrals and Franck–Condon factors, taking into account distortion, displacement, and normal mode mixing (up to four modes). Major features of the observed absorption spectrum of ethylene have been interpreted on the basis of the computed Franck–Condon factors. The role of each electronic state in the spectra has been clarified; the π–3s transition corresponds to the distinct intensive peaks in the 57 000–61 000 cm−1 energy region, the less intensive distinct bands in the interval of 62 000–65 000 cm−1 are due to the π–3pσ states and the π–π* peaks constitute the continuum underlying the spectrum. The theoretical vibronic spectrum is in qualitative agreement with the experimental one, except of some details. Possible reasons for the discrepancies between theory and experiment are also discussed.