Eigenvalues, integer discontinuities and NMR shielding constants in Kohn—Sham theory

Abstract

Kohn—Sham eigenvalues are determined from coupled cluster electron densities. The calculated HOMO—LUMO eigenvalue differences are compared with those from conventional generalized gradient approximation (GGA) exchange-correlation functionals for a range of small molecules. In all cases, GGA HOMO—LUMO differences are smaller than those calculated from the coupled cluster densities. When the GGA HOMO—LUMO differences are explicitly corrected—such that they equal those calculated from electron densities—significant improvements in NMR shielding constants are obtained. The eigenvalues calculated from electron densities are also used to approximate the magnitude of the integer discontinuity in the exact exchange-correlation potential. The value of the Kohn—Sham HOMO eigenvalue is then considered. Although HOMO eigenvalues from high quality, asymptotically vanishing, exchange-correlation potentials are close to the negative of the ionization potential, HOMO eigenvalues from the GGA functionals are shifted upwards by approximately 50% of the calculated integer discontinuity. An alternative approach for correcting NMR shielding constants is investigated.