Efficient use of the resolution of the identity approximation in time-dependent density functional calculations with hybrid density functionals

An implementation of time-dependent density functional theory in various variants is reported. Use is made of the resolution of the identity (RI) approximation for both `pureʹ and hybrid density functionals. The transformation of the three-index repulsion integrals to the MO basis leads to significant computational savings (factor 2–4) in the case of hybrid functionals but is not competitive with AO direct algorithms in the case of pure functionals. The error introduced by the RI approximation on the computed transition energies is negligible (<15 cm−1). Systematic benchmark calculations are reported.