Electronic Structure and Spectrum of the NiF6−4Cluster: Results of Calculations Based on Self-Consistent-Field Models

Abstract

Restricted and unrestricted Hartree-Fock molecular-orbital self-consistent-field calculations were performed on the cluster Ni$\mathrm{F}_6^{}{}_{}{}^{-4\mathrm{}}$ with a fixed internuclear distance appropriate to KNi${\mathrm{F}}_3$. A slightly extended multicenter atomic-orbital basis was used. In contrast to the approach of earlier calculations which sought to describe $10D_q$ as a single electron promotion between $t_{2g}$ and $e_g$ antibonding (LCAO) molecular orbitals, we obtained the spectra as the difference in energy between various many-electron open-shell states. The results obtained with limited configuration interaction are in good agreement with the five observed optical absorption bands. We find that the earlier orbital picture can be approximately maintained only if the covalency parameters are obtained from the open-shell orbitals of excited states, which are solutions of the Hartree-Fock-Roothaan Hamiltonians. In these orbitals we find considerable $\sigma$ bonding and a smaller $\pi$ bonding, significant fluoride $s-p$ hybridization, and a small expansion of the $3d$ orbitals which is greater in the $t_{2g}$ than in the $e_g$ orbitals. Allowing for spin-polarization correlation in the unrestricted calculations, however, adds important contributions to transferred hyperfine interactions and neutron form factors.