The density functional calculation of nuclear shielding constants using London atomic orbitals

Abstract

The theory for the calculation of nuclear shielding constants with London atomic orbitals using density functional theory is presented. The theory includes the use of a local exchange–correlation functional which depends on both the electron density ρ(r) and the paramagnetic current density jp(r). The resulting coupled-perturbed Kohn–Sham equations are presented, together with the working expression for the nuclear shielding tensor. The entire theory has been programmed and exhaustively checked, using standard Gaussian basis sets. A variety of ρ(r) dependent exchange–correlation functionals have been used, together with a current dependence suggested by Vignale, Rasolt, and Geldart. Certain numerical difficulties arose with this form which necessitated a cutoff in its evaluation for low densities. Calculations have been performed on HF, N2, CO, F2, H2O, and CH4. Including the current dependence is seen here to have a slightly deshielding effect. The major deficiency in the reported calculations appears to arise from the use of local functionals which give poor values for the Kohn–Sham eigenvalues.