Local Excitation Approximations to Time-Dependent Density Functional Theory for Excitation Energies in Solution.

We derive, implement, and test three different local excitation approximations (LEAs) to time-dependent density functional theory (TDDFT) that are designed to be extremely efficient for computing excitations that are localized on a single chromophore surrounded by explicit solvent molecules. One of these approximations is equivalent to the "TDDFT for molecular interactions" [TDDFT(MI)] method that we have introduced previously, which exploits non-orthogonal, absolutely-localized molecular orbitals to approximate full TDDFT for systems consisting of multiple, weakly-coupled chromophores. Further approximations are possible when the excitation is localized on only a single subsystem and are introduced here to reduce the cost of LEA-TDDFT(MI) with respect even to TDDFT(MI). We apply these methods to compute solvatochromatic shifts for the n → π* excitations in aqueous acetone and pyridine. The LEA-TDDFT(MI) method accurately reproduces the solvent-induced blue shifts in these systems, at a significant reduction in cost as compared to conventional TDDFT.