Highly optimized tight-binding model of silicon

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Abstract
We have fit an orthogonal tight-binding model of silicon with a minimal (s,p) basis and a repulsive pair potential. The pair potential and the tight-binding matrix elements are represented as cubic splines with a 5.24-Å fixed radial cutoff in order to allow maximum flexibility. Using a numerical procedure, the spline parameters were fit to simultaneously optimize agreement with ab initio force and energy data on clusters, liquid, and amorphous systems as well as experimental elastic constants, phonon frequencies, and Grüneisen parameter values. Many such fits were performed to obtain a potential that we judged to be optimal, within the implicit limitations of our potential form. The resulting optimized potential describes many properties very accurately and should be a useful model given its relative simplicity and speed. Our fitting method is not difficult to apply and should be applicable to many other systems.