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 states since the final energies do not come from the diagonalization
of an effective model-space Hamiltonian. Recently, multistate extensions
such as linearized PDFT (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 paper, 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.