The Exact Second Order Corrections and Accurate Quasiparticle Energy Calculations in Density Functional Theory

TL;DR

This paper introduces an exact second order correction to density functional approximations that significantly improves the accuracy of quasiparticle energy calculations, enhancing predictions of ionization potentials and spectra.

Contribution

It presents a novel quadratic correction based on second derivatives, eliminating delocalization errors in density functional theory for better quasiparticle energy predictions.

Findings

Accurate approximation of quasiparticle energies for small and medium molecules.

Improved predictions of ionization potentials and electron affinities.

Enhanced computational spectroscopy applications.

Abstract

We develop a second order correction to commonly used density functional approximations (DFA) to eliminate the systematic delocalization error. The method, based on the previously developed global scaling correction (GSC), is an exact quadratic correction to the DFA for the fractional charge behavior and uses the analytical second derivatives of the total energy with respect to fractional occupation numbers of the canonical molecular orbitals. For small and medium-size molecules, this correction leads to ground-state orbital energies that are highly accurate approximation to the corresponding quasiparticle energies. It provides excellent predictions of ionization potentials, electron affinities, photoemission spectrum and photoexcitation energies beyond previous approximate second order approaches, thus showing potential for broad applications in computational spectroscopy.