The S(1A g)–S1(1B2u) vibronic transition in benzene: An ab initio study

Abstract

The four e2g false origin bands and the a1g progression of the S0(1Ag)–S1(1B2u) transition in benzene are simulated ab initio with the recently introduced configuration interaction singles (CIS) with 6-31G orbitals. The ground and excited state CC and CH bond lengths are optimized and compared with the experiment; the CC bond elongation upon excitation is found to be slightly underestimated. The vibrational force fields are calculated at the stationary points of S0 and S1. The 1Ag force field is calculated at the Hartree–Fock level while the 1B2u force field is calculated at the CIS level of theory. The two force fields are scaled to fit the experimental frequencies and the normal mode rotation upon excitation, i.e., the Duschinsky matrix, is obtained. In agreement with previous empirical fitting of the S1(1B2u) vibrational frequencies, the Duschinsky matrix is found to be nearly diagonal with the exception of the b2u modes submatrix which shows a large amount of mixing. The mixing of the b2u modes is larger before scaling but is subsequently reduced after scaling. The normal modes and the optimized geometries are used to calculate the amount of displacement, upon excitation, of the equilibrium position of the totally symmetric modes. This displacement causes the Franck–Condon progression and is slightly underestimated by the calculation. The intensity of the four e2g false origins in the absorption spectrum of S1 is calculated and the Herzberg–Teller intensities of the four bands are found to be very close to the experiment. In particular, the relative intensity of the CCC bend (ν6) and CC stretch (ν8) bands is nicely reproduced. This result is discussed in light of similar calculations at the semiempirical level of theory. We conclude that CIS can be of great value for the unravelling of vibronic spectra of conjugated systems.