Some applications of the thermal single-determinant approximation

Abstract

A new extension of Hartree–Fock theory to non-zero temperature, T, namely the Thermal Single-Determinant Approximation (TSDA)—based on the variational principle of statistical mechanics—has been applied to a model of a crystal of widely separated hydrogen atoms. It is found that, in this TSDA, solutions to the equations of stationarity of the free energy consist of one-electron functions which are either spatially extended (like Bloch functions), or localized. Whereas it appears that in the standard thermal Hartree–Fock approximation (THFA) only extended solutions are possible (at finite atomic separation). Furthermore, in the TSDA at T ≠ 0 the localized solutions give a lower free energy than that corresponding to the extended solutions, and the latter is less than or equal to the free energy in the THFA. As far as we know, this is the first calculation in which a strictly variational requirement has rejected extended one-electron functions in favor of localized functions for a crystal.