Anharmonic vibrational state calculations in the electronic excited states studied by time-dependent density functional theory

Time-dependent density functional theory (TDDFT) is combined with the correlation-corrected vibrational self-consistent field method to calculate the fundamental vibrational frequencies of the electronic excited states of diatomic, triatomic, and tetraatomic molecules. Equation of motion coupled-cluster calculations are also carried out for comparison. TDDFT is shown to provide the harmonic and anharmonic frequencies for various excited states with reasonable accuracy by using hybrid functionals, except that several vibrational modes such as hydrogen atom stretching exhibit sizable discrepancies due to the lack of orbital relaxation process in TDDFT.