Exchange methods in Kohn–Sham theory

Abstract

Differences between exchange methods in exchange-only Kohn–Sham theory are highlighted by calculations of diatomic molecule total energies, uncoupled isotropic NMR shieldings, and HOMO–LUMO eigenvalue differences. Optimised effective potential (OEP) and Wu–Yang (WY) results are very similar. Localised Hartree–Fock (LHF) and Krieger–Li–Iafrate (KLI) results are close to one another, but are different to OEP and WY. Becke 1988 exchange (B88X) is different again. Shieldings reduce from OEP/WY to LHF/KLI to B88X, which is consistent with an observed reduction in HOMO–LUMO gaps. LHF, KLI, and B88X shieldings and HOMO–LUMO gaps are closer to near-exact, correlated values, than are the OEP values. These variations arise entirely due to differences in the one-electron exchange potentials, which is clearly evident in potential difference plots, relative to OEP, for the N₂ molecule. Density difference plots are also presented, which exhibit a spatial correlation with the potential differences. HOMO and LUMO probability density difference plots show a contraction of the LUMO relative to OEP, which is consistent with the NMR and HOMO–LUMO findings. Plots are also presented for near-exact, correlated Kohn–Sham calculations. The features are qualitatively similar to those observed in the LHF, KLI, and B88X plots, highlighting correlated character in these approximate exchange-only calculations.