Linearized Pair-Density Functional Theory for Vertical Excitation Energies

Multiconfiguration pair-density functional theory (MC-PDFT) is a computationally efficient method that computes the energies of electronic states in a state specific or state average framework via an on-top functional. However, MC-PDFT does not include state-interaction among these statets, since the final energies do not come from the diagonalization of an effective model-space Hamiltonian. Recently, multi-state extensions such as linearized (L-) PDFT have been developed to accurately model the potentials near conical intersections and avoided crossings; however, there has not been any systematic study evaluating their performance for predicting vertical excitations at the equilibrium geometry of a molecule, when the excited states are generally well separated. In this letter, we report the performance of L-PDFT on the extensive QUESTDB data set of vertical excitations using a database of automatically selected active spaces. We show that L-PDFT performs well on all these excitations and successfully reproduces the performance of MC-PDFT. These results further demonstrate the potential of L-PDFT, as its scaling is constant with the number of states included in the state-average manifold, whereas MC-PDFT scales linearly in this regard.