Simple LCAO model

N. A. W. Holzwarth^{†}

Department of Physics, Wake Forest University, Winston-Salem, NC 27109

Abstract

†natalie@wfu.eduYour e-mail address; http: www.wfu.eduñatalieYour web page

I BASIC EQUATIONS

The purpose of this formalism is to provide a simple and reasonable interpolation scheme to model ionic materials.

The model has the following components:

1. Each ion has a position index R and a positive charge Q_{R}. The charge Q_{R} ≡ Z_{R}−z_{R}^{core} includes the nuclear charge Z_{R} and the core electron z_{R}^{core} contributions. In the model, it is represented by a spherical charge density shape function S_{R}(r) (assumed to be normalized to unity such as a Gaussian form S_{R}(r) = e^{−(r/σ_{R})^{2}}/(π^{3/2}σ^{3})) so the total density associated with the ions of the material is represented by

ρ^{ion}(r) = ∑_{R} Q_{R}S_{R}(|r − R|).  (1)

2. In addition to its charge distribution, each ion has an associated spherically symmetric local potential which is used to adjust the model electron affinities and negativities described by an amplitude V_{R} and shape function Φ_{R}(r) so that the total local potential of the material is given by

V^{loc}(r) = ∑_{R} V_{R}Φ_{R}(|r − R|).  (2)