Global density of states: An nth moment potential

Abstract

Here is presented a reworking of a moments based method (global density of states, or GDOS) for computing total energies and atomic forces from an orthogonal tight binding Hamiltonian. The primary strengths of GDOS are that the atomic forces are guaranteed to be exact derivatives of the energy, and the number of integrals is independent of the number of atoms. The revised method described here uses recursion coefficients and vectors directly, avoiding the need to work explicitly with moments. This allows larger numbers of moments (recursion levels) to be used, leading to improved convergence. This is demonstrated for a hard problem for this method: the vacancy in Si. If sufficient numbers of moments are included, good convergence of both energies and forces is indeed found.