Evolution of orbital spaces along potential curves for diatomic molecules. A comparative study of Hartree–Fock, Kohn–Sham, Brueckner and multi-configurational orbital spaces

Abstract

For three isoelectronic systems: CO molecule, CN - and NO + ions we have carried out comparative studies of Kohn–Sham orbitals (KSO) generated by the most typical local, gradient-corrected and hybrid exchange–correlation (xc) potentials, Brueckner orbitals (BO) and Hartree–Fock orbitals (HFO). The relations of orbital subspaces of well defined symmetry properties have been analyzed in terms of numerical proximity indices, treated as some kind of orbital space distances. Geometric interpretation and graphical representation of these proximity relations have been proposed. The orbital space similarity relations have been studied at different interatomic distances, i.e. as a function of orbital quasidegeneracy, or a multi-configurational (MC) state character. For this reason also the orbitals spanning the CASSCF reference determinant (MC-orbitals, MCO) have been included in the analysis. Our investigations indicate, that at equilibrium bond distances KSOs are more close to BOs and MCOs than to HFOs, with the orbital similarity increasing in the sequence: local, gradient-corrected, to hybrid xc-potentials. However in many cases the distance of KSO spaces to BO or MCO ones are larger than, or comparable to the corresponding distance of HFO spaces to BO or MCO ones. Together with increasing internuclear distances the KSOs become relatively more close to BOs than to HFOs; only for the hybrid xc-potential with a large contribution of the Hartree–Fock exchange this relation is inversed. The evolution of KSO–BO proximity relations does not depend qualitatively on the total charge of the system. Our results indicate that the Kohn–Sham calculations are able to describe the MC state character in a limited region around the equilibrium bond distance.