Electron–vibration Coupling in Time-Dependent Density-Functional Theory: Application to Benzene

As a test of the time-dependent density-functional theory (TDDFT) for electron–vibration coupling, we apply it to the optical properties of the π–π* transitions in benzene. Quantities calculated are the envelopes of the Franck–Condon factors of the electronic transitions and the oscillator strengths of symmetry-forbidden transitions. The strengths of the π–π* transitions span three orders of magnitude and are reproduced to better than 35% by the theory. Comparable agreement is found for the Franck–Condon widths. We conclude that rather detailed information about the effects of the electron–vibrational coupling can be obtained with the TDDFT.