Hybrid Diagonal Approximation in Time‐Dependent Auxiliary Density Functional Theory

A hybrid diagonal approximation (HDA) for time‐dependent auxiliary density functional theory (TD‐ADFT) is presented. This newly implemented method allows the use of global and range‐separated hybrid functionals in TD‐ADFT for the calculation of vertical excitation energies and corresponding oscillator strengths. To preserve the exceptional computational efficiency and low‐order scaling of TD‐ADFT, only the diagonal elements of exact exchange are included in the TD‐ADFT matrices. For singlet excitations, this approximation reaches accuracies comparable to four‐center electron repulsion integral (ERI) implementations, albeit with a fraction of the computational cost. For triplet excitations, larger deviations are found with the HDA. Despite additional integral calculations, the low‐order scaling of TD‐ADFT is preserved with the HDA. We explain this by the intact index alignment between the ERIs and the excitation vectors, which remains unaltered in TD‐ADFT with the HDA.