Empirical chemical pseudopotential theory of molecular and metallic bonding

Abstract

A unified analysis of molecular and metallic bonding is presented, with chemical pseudopotential theory providing a fundamental context. Unperturbed atomic orbitals are used as the local orbital basis in the determination of the secular equation matrix elements. The two-center approximation gives an expression for the binding energy in terms of bond densities and pair interactions, the latter of which, for a given atomic species, depend only on the pair separation and not on the overall chemical environment. The repulsive and attractive pair interactions are parametrized as simple exponentials and all but nearest-neighbor interactions are ignored. More distant interactionsare shown to play a relatively insignificant role insofar as binding energy is concerned. Under a certain scaling, an expression for binding energy is obtained and shown to be nearly universal, in agreement with recent observations. The scaled binding energy depends on a single parameter S, which is essentially the ratio of the steepness of the repulsive pair interaction to that of the attractive pair interaction. Whereas the scaled binding energy shows a very weak dependence on the parameter S in the relevant domain, the preference for molecular versus metallic bonding is shown to be exponentially dependent upon it. The criterion for bonding preference is just the optimization of binding energy with respect to nearest-neighbor coordination Z, which is the dominant topological variable in the determination of binding energy. The molecular regime is characterized by S\ensuremath{\simeq}2, and the binding energy is shown to be nearly independent of the nearest-neighbor coordination Z in this case. The energetics of bondingin the molecular regime is thus dominated by nonlocal features of the topology, such as the nature and size of interaction loops. A correspondence is established between the contribution of nonlocal topological features to the binding energy, and chemical stability and reaction paths of molecular systems. As a quantitative test of the empirical-chemical-pseudopo- tential-binding energy expression, known potential-energy curves for ${\mathrm{H}}_{2}$ and symmetric linear ${\mathrm{H}}_{3}$ were used as inputs to determine the repulsive and attractive pair interactions for hydrogen pairs. These were then used to successfully predict binding energies for various other hydrogen species, including ${\mathrm{H}}_{3}$, ${\mathrm{H}}_{4}$, and ${\mathrm{H}}_{14}$, for which accurate first-principles calculations exist. A similar procedure was used for Lithium species.