Highly efficient implementation of the analytical gradients of pseudospectral time-dependent density functional theory

The accuracy and efficiency of time-dependent density functional theory (TDDFT) excited state gradient calculations using the pseudospectral method are presented. TDDFT excited state geometry optimizations of the G2 test set molecules, the organic fluorophores with large Stokes shifts, and the Pt-complexes show that the pseudospectral method gives average errors of 0.01–0.1 kcal/mol for the TDDFT excited state energy, 0.02–0.06 pm for the bond length, and 0.02–0.12° for the bond angle when compared to the results from conventional TDDFT. TDDFT gradient calculations of fullerenes (C_n, n up to 540) with the B3LYP functional and 6-31G** basis set show that the pseudospectral method provides 8- to 14-fold speedups in the total wall clock time over the conventional methods. The pseudospectral TDDFT gradient calculations with a diffuse basis set give higher speedups than the calculations for the same basis set without diffuse functions included.