Ab initio study of the excited singlet states of all-trans $α,ω$-diphenylpolyenes with one to seven polyene double bonds: Simulation of the spectral data within Franck–Condon approximation

Computational simulations of the electronic spectra with ab initio electronic structure calculations are presented for all-trans $α,ω$-diphenylpolyenes with the polyene double bond number $(N)$ from 1 to 7. A direct comparison of the fluorescence spectra of diphenylpolyenes was made between the results of highly accurate calculations and the experimental data for the systems with various chain lengths. For the realistic simulation of the emission, the total vibrational wave function was described approximately as a direct product of one-dimensional (1D) vibrational wave functions along the normal coordinates that are determined from the vibrational analysis of the ground state. The observed spectra can be reproduced in a computationally efficient way by selecting effective C–C and $C=C$ stretching modes for the constructions of the 1D vibrational Hamiltonians. The electronic structure calculations were performed using the multireference Møller–Plesset perturbation theory with complete active space configuration interaction reference functions. Based on the vertical excitation energies computed, the lowest singlet excited state of diphenylbutadiene is shown to be the optically forbidden $2A1g$ state. The simulations of fluorescence spectra involving vibronic coupling effects reveal that the observed strong single $C=C$ band consists of two major degenerate vibrational $C=C$ modes for the shorter diphenylpolyenes with $N=3$ and 5. Further, the relative intensities of the C–C stretching modes in the fluorescence spectra tend to be larger than those of the $C=C$ stretching modes for the systems with $N$ over 5. This indicates that the geometric differences of the energy minima between the ground $(1A1g)$ and $2A1g$ states grow larger towards the direction of the C–C stretching mode with increasing $N$⁠.