Ionic character of polar crystals: An extended Mulliken scheme for electronegativities

The total energy of an atom can be expressed in terms of the charge q on the atom as E(q)=E(0)+αq+βq²+γq³. It is shown that the expected charge transfer q, which brings the intra-atomic energy of the atoms to a minimum, between otherwise isolated noninteracting atoms, is proportional to the difference in the α's of the constituent elements, i.e., q=c Δα. Thus α provides a well-defined electronegativity scale, and if the third-order term γq³ may be neglected, then α=Φₘ, which is the original Mulliken scale. The quadratic term βq² acts to oppose charge transfer, and therefore the coefficient c, relating q to Δα, depends on what elements are involved and on their relative concentration in a well-defined manner. This implies an asymmetry in charge transfer with concentration. Spectroscopic data indicate that γ, though small, is not negligible and, in such a case Φₘ is not a proper electronegativity. The extended Mulliken scheme, involving α and β, is relevant to the energetics of charge transfer and hence to the ionic character of insulating and semiconducting compounds. It allows simple baseline estimates to be made of such character. Other factors contribute to charge transfer and some of the complications associated with transition-metal compound formation are explored.