The unrestricted Hartree-Fock molecular-orbital self-consistent-field (MO-SCF) method is developed and applied to the problem of transition-metal ion clusters. This method removes many of the shortcomings of earlier treatments and provides, in principle, a framework for obtaining fairly accurate and meaningful results. Model calculations are reported for the KNi${\mathrm{F}}_3$ system, in which all matrix elements of the Hamiltonian are accurately computed (by the choice of a special one-center basis set) for all the electrons of the molecular cluster. Considerable variational freedom is allowed in all representations; as a consequence, significant covalent mixing is found for representations containing the metal $3s$ and $3p$ orbitals. This molecular-orbital approach thus differs greatly from the previous approach of using molecular orbitals formed as linear combination of atomic orbitals (MO-LCAO); in particular, it is emphasized that the simple (and inadequate) single-variational-parameter LCAO treatment of earlier calculations is replaced by full HF-SCF calculations in a multielectron framework including all electrons (and not just the bonding and antibonding electrons as in earlier treatments). Complete SCF calculations are carried out for both the ${\left(\mathrm{N}\mathrm{i}{\mathrm{F}}_6\right)}^{4-}$ and the ${\left({\mathrm{Ni}}_2\mathrm{F}\right)}^{3+}$ clusters (representing the metal-ion and the ligand-ion point of view, respectively) including the effects of an external crystalline field. Although these first (crude) calculations suffer from limited basis size, reasonable agreement with experiment is found for such quantities as the optical-splitting parameter $10Dq$, the transferred hyperfine interaction, and the neutron magnetic form factor.

• Received 15 December 1967

DOI:https://doi.org/10.1103/PhysRev.176.688