Excitation energies from density functional perturbation theory

TL;DR

This paper explores two perturbative methods based on density functional theory to accurately compute atomic excitation energies, comparing their performance and improvements over existing approaches using various exchange-correlation potentials.

Contribution

It introduces and evaluates two perturbative schemes for excitation energies using the Kohn-Sham Hamiltonian with accurate exchange-correlation potentials, comparing their effectiveness and improvements over prior methods.

Findings

First-order corrections improve excitation energies, especially in one scheme.

Zeroth-order Kohn-Sham eigenvalue differences nearly bracket experimental energies.

Perturbation theory results are compared with $ riangle$SCF and TDDFT methods.

Abstract

We consider two perturbative schemes to calculate excitation energies, each employing the Kohn-Sham Hamiltonian as the unperturbed system. Using accurate exchange-correlation potentials generated from essentially exact densities and their exchange components determined by a recently proposed method, we evaluate energy differences between the ground state and excited states in first-order perturbation theory for the Helium, ionized Lithium and Beryllium atoms. It was recently observed that the zeroth-order excitations energies, simply given by the difference of the Kohn-Sham eigenvalues, almost always lie between the singlet and triplet experimental excitations energies, corrected for relativistic and finite nuclear mass effects. The first-order corrections provide about a factor of two improvement in one of the perturbative schemes but not in the other. The excitation energies within perturbation theory are compared to the excitations obtained within $\Delta$SCF and time-dependent density functional theory. We also calculate the excitation energies in perturbation theory using approximate functionals such as the local density approximation and the optimized effective potential method with and without the Colle-Salvetti correlation contribution.