Calculation of excitation energies within time-dependent density functional theory using auxiliary basis set expansions

We demonstrate the use of an auxiliary basis set expansion for the treatment of Coulomb type matrix elements in time-dependent density functional (TDDFT) calculations. The TDDFT scheme is used for the calculation of excitation energies within the adiabatic approximation. Comparison between results obtained by approximate and exact treatments of the Coulomb matrix elements shows that the errors for the excitation energies of the valence and low-lying Rydberg states can be reduced to less than 0.02 eV without problems. Computation times are considerably reduced.