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

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.