A parallel implementation of the analytic nuclear gradient for time-dependent density functional theory within the Tamm-Dancoff approximation

We derived the analytic gradient for the excitation energies from a time-dependent density functional theory calculation within the Tamm-Dancoff approximation (TDDFT/TDA) using Gaussian atomic orbital basis sets, and introduced an efficient serial and parallel implementation. Some timing results are shown from a B3LYP/6-31G**/SG-1-grid calculation on zincporphyrin. We also performed TDDFT/TDA geometry optimizations for low-lying excited states of 20 small molecules, and compared adiabatic excitation energies and optimized geometry parameters to experimental values using the B3LYP and ωB97 functionals. There are only minor differences between TDDFT and TDA optimized excited state geometries and adiabatic excitation energies. Optimized bond lengths are in better agreement with experiment for both functionals than either CC2 or SOS-CIS(D₀), while adiabatic excitation energies are in similar or slightly poorer agreement. Optimized bond angles with both functionals are more accurate than CIS values, but less accurate than either CC2 or SOS-CIS(D₀) ones.