Time-dependent density functional theory gradients in the Amsterdam density functional package: geometry optimizations of spin-flip excitations

An implementation of time-dependent density functional theory (TDDFT) energy gradients into the Amsterdam density functional theory program package (ADF) is described. The special challenges presented by Slater-type orbitals in quantum chemical calculation are outlined with particular emphasis on details that are important for TDDFT gradients. Equations for the gradients of spin-flip TDDFT excitation energies are derived. Example calculations utilizing the new implementation are presented. The results of standard calculations agree well with previous results. It is shown that starting from a triplet reference, spin-flip TDDFT can successfully optimize the geometry of the four lowest singlet states of CH₂ and three other isovalent species. Spin-flip TDDFT is used to calculate the potential energy curve of the breaking of the C?CC bond of ethane. The curve obtained is superior to that from a restricted density functional theory calculation, while at the same time the problems with spin contamination exhibited by unrestricted density functional theory calculations are avoided.