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An approximation is presented which can efficiently decrease the computational expenses of configuration interaction singles (CIS) and time-dependent density functional theory (TDDFT) methods employing hybrid functionals. The approach is the adaptation of the local density fitting scheme developed for Hartree-Fock (HF) calculations for excited states and reduces the quartic scaling of the methods to cubic. It can also be applied to related methods, such as the time-dependent HF and Tamm-Dancoff approximation TDDFT approaches. Our benchmark calculations show that, for molecules of 50-100 atoms, average speedups of 2-4 can be achieved for CIS and TDDFT calculations at the expense of negligible errors in the calculated excitation energies and oscillator strengths, but for bigger systems or molecules of localized electronic structure significantly larger speedups can be gained. We also demonstrate that the approximation enables excited-state calculations on a single processor even for molecules of 1000 atoms using basis sets augmented with diffuse functions including more than 17 000 atomic orbitals.

Reduced-Scaling Approach for Configuration Interaction Singles and Time-Dependent Density Functional Theory Calculations Using Hybrid Functionals