The influence of self-consistency on nonlocal density functional calculations

A self-consistent nonlocal density functional method (NL-SCF) based on the gradient corrected exchange term by Becke Phys. Rev. A 33, 2786(1988) and a gradient corrected correlation term by Perdew Phys. Rev. B 33, 8822(1986) has been implemented into the hfs-lcao-program by Baerends et al. Chem. Phys. 2, 41(1973). An expression for the variational potential corresponding to Becke’s gradient correction has been derived. A detailed analysis is given of the change in density δρ induced by the gradient corrections. It is shown that δρ is 2 orders of magnitude smaller than the deformation density Δρ=ρmolecule−ρatom. The dipole moments calculated by NL-SCF differ as a consequence only modestly from dipole moments obtained by the local density approximation (LDA), in which the gradient corrections are absent. The importance of self-consistency for calculations on bond distances, bond energies, and vibrational frequencies are assessed by comparing results from NL-SCF calculations with data obtained by a perturbative approach (NL-P), in which densities obtained from LDA calculation were used in the evaluation of the gradient corrections. It is found that self-consistency effects are negligible for bond energies and vibrational frequencies. SCF effects were not found to be important for bond distances neither, with the possible exception of metal–ligand bonds.