Pauli-Force Model Potential for Solids

Abstract

A model potential previously applied to molecules is adapted to the study of structural trends in solids. The potential, which has simple analytic one-electron eigenfunctions and eigenvalues, is based upon a Pauli-force concept and retains the salient features of ab initio pseudopotentials. The eigenvalues are of the quantum-defect form, so that treatment of the energy dependence of the potential parameter is particularly straightforward. A form factor is calculated in a local-screening approximation, and algebraic expressions for a core radius $r_c$ and the form-factor node $q_0$ are obtained. These expressions have transparent physical interpretations, and form the basis for a discussion of chemical trends in $r_c$ and $q_0$ in terms of a few simple parameters. The connection with well-known local model potentials is briefly explored.