We have investigated total energy expressions that consist of a term describing the eigenvalue sum and a pair potential term. Such expressions can be used to fit the results of first principles total energy calculations at given structures, and then obtain the total energy of another configuration of atoms avoiding the complexity of further ab initio calculations.
In this work we present a method of fitting APW total energy results to a non-orthogonal tight-binding Hamiltonian from which the sum of the eigenvalues is derived and to a pair potential represented by a 5th order polynomial. We fit total energies for the fee and bec structures and we then obtain the elastic constants Cij in good agreement with both full potential LAPW calculations and experiment. We present results of this method for Ir.