Covalency in Crystal Field Theory: KNiF3

The theory of covalency in crystal field phenomena is examined, using, as example, the Ni-${\mathrm{F}}_6$ complex in KNi${\mathrm{F}}_3$. The Hund-Mulliken-Van Vleck molecular orbital-linear combination of atomic orbitals treatment is followed. The role of the antibonding and bonding electrons in the complex is discussed from a multielectron point of view. The exact self-consistent one-electron Hamiltonian is discussed in some detail. Emphasis is placed on elucidating the source and nature of the covalent effects appropriate to the various physical phenomena. We find that it is the covalent mixing of those bonding electrons having no antibonding partners which contribute to all experimental observables (including the crystal field splitting 10 $\mathrm{Dq}$, transferred hyperfine interactions, neutron magnetic form factors, and superexchange interactions). This view of covalency differs markedly from the one followed by Sugano and Shulman, in that the covalency of the antibonding electrons, which are assigned the sole role in their approach, is totally irrelevant. Quantitative numerical estimates (using approximations to the exact Hamiltonian) are given for the two models of the covalent effects in KNi${\mathrm{F}}_3$, i.e., "unpaired" bonding and antibonding; they are shown to differ strongly. The relative roles of overlap and covalency are discussed; covalency is found to play an important but by no means dominant role. Numerical agreement between the present inexact cluster theory and experiment is found to be poor. The various sources of this disagreement are reviewed.