Multireference Density Functional Theory for Accurate Description of Ground and Excited States with Renormalized Singles

We applied renormalized singles (RS) in the multireference density functional theory (DFT) approach to calculate accurate electronic energies of ground states and excited states for molecular systems. The multireference DFT approach, developed recently, determines the total energy of the $N$-electron system as the sum of the (N-2)-electron energy from a density functional approximation (DFA) and the two-electron addition excitation energies from the particle-particle Tamm-Dancoff approximation (ppTDA) linear response approach. The ppTDA@RS-DFA approach first constructs the RS Hamiltonian to capture all singles contributions of the (N-2)-electron auxiliary system described by a chosen DFA. Then the RS Hamiltonian is used in ppTDA to calculate two-electron addition excitation energies. The total energy is optimized with the optimized effective potential (OEP) method. The multireference description of both the ground and excited states of the N-electron systems comes naturally through the linear response theory. We show that the ppTDA@RS-DFA approach provides considerable improvement over the ppTDA@DFA, the original approach without using RS, and describes both ground state and excited state properties accurately, with electron densities preserving the proper symmetry for systems having strong (static) correlation. For ground states, ppTDA@RS-DFA properly describes dissociation energies, equilibrium bond lengths and the dissociation curves of all tested molecules, and the double bond rotation of ethylene. For excited states, ppTDA@RS-DFA provides accurate excitation energies of molecular systems and largely eliminates the dependence on the choice of the DFA. ppTDA@RS-DFA thus provides a promising and very efficient multireference approach to systems with static correlation.