Application of time-dependent density functional theory to electron-vibration coupling in benzene

Optical properties of symmetry-forbidden π-π transitions in benzene are calculated with the time-dependent density functional theory (TDDFT), using an adiabatic LDA functional. Quantities calculated are the envelopes of the Franck-Condon factors of the vibrationally promoted transitions and the associated oscillator strengths. The strengths, which span three orders of magnitude, are reproduced to better than a factor of two by the theory. Comparable agreement is found for the Franck-Condon widths. We conclude that rather detailed information can be obtained with the TDDFT and it may be worthwhile to explore other density functionals. The time-dependent density functional theory (TDDFT) has proven to be a surprisingly successful theory of excitations and particularly the optical absorption strength function. The theory is now being widely applied in both chemistry and in condensed matter physics. The literature in quantum chemistry is cited in a recent study on the electronic excitations in benzene [1]. Benzene is an interesting molecule for testing approximations because its spectra have been very well characterized, both electronic and vibrational. In this note we will apply the TDDFT to coupling between vibrational and electronic excitations. In our previous studies, we have investigated many different electronic structure questions using a rather simple version of the density functional theory, the local density approximation (LDA). Our emphasis has been to study the overall predictive power of a fixed functional rather than to try to find the best functional for each properties. The approximation scheme we consider is straightforward and uses the same computer programs as for calculating purely electronic excitations. We treat the electronic dynamics in the adiabatic approximation, taking the same energy function for the dynamic equation as is used in the static structure calculation. In our view, this is the only consistent scheme available that guarantees conservation of the oscillator sum rule. The electron-vibration coupling is treated in a vertical approximation, so only information at frozen nuclear coordinates is required. ∗E-mail: [email protected]