Bridging the Gap between Variational and Perturbational DFT-Based Methods for Calculating Excited States.

A thorough investigation of the delta self-consistent field (ΔSCF) method within the restricted-open Kohn-Sham (ROKS) formalism has been carried out. The ROKS-based ΔSCF targets unmixed singlet excited electronic states, avoiding the need for a spin purification procedure. A modification of the maximum overlap method to improve the convergence of the ΔSCF method is presented, in addition to a molecular orbital tracking and order-preserving algorithm. For benchmarking purposes a large-scale comparison with time-dependent density functional theory (TDDFT) was conducted: both single- and multi-reference singlet and triplet excited electronic states of various molecules were reproduced using ΔSCF and compared to the states provided by TDDFT. Besides the excitation energies, we also compared the electron densities and the transition dipole moments of the molecules between the two methods.