Theory of bonding of transition metals to nontransition metals

We present a theory of the chemical bond in compounds consisting of both transition metals and nontransition metals. Chemical trends in the bonding properties are established by directly comparing the total energies of a large number of such compounds with the total energies of their constituents. These chemical trends are analyzed in terms of the $s$-, $p$-, and $d$-like state densities of the compounds and the constituents. Rather different types of bonding are shown to result when the atomic $s$ and $p$ levels of the nontransition metal lie above, below, and near the energy of the transition-metal $d$ level. The heat of compound formation is shown to result from a competition between two simple physical effects: (1) the weakening of the transition-metal bonds by the lattice dilatation required for the accommodation of the nontransition metal, and (2) the increased bonding which results from the occupation of the bonding members of the hybrid states formed from the interaction between the transition-metal $d$ states and the $s\ensuremath{-}p$ states on the nontransition metal. Our theoretical values for the heats of formation of these compounds are generally similar to those given by Miedema's empirical formula. Distinctive aspects of the variation of the heat of formation with the number of valence electrons reveal, however, that the microscopic picture on which the empirical formula is based is quite different from that given by our self-consistent energy-band theory.