Stationary nature of the density-functional free energy: Application to accelerated multiple-scattering calculations

Abstract

The number of operations required for conventional density-functional algorithms grows as the cube of the number of atoms, N. For large systems the computing requirements are unattainable. To overcome this limitation it is acceptable to approximate those variables with respect to which the free energy is stationary. We show that the stationarity of the free energy with respect to electron density, one-electron potential, chemical potential, occupation function, and temperature allows for very useful approximations leading to rapid and accurate determination of the free energy. Here we discuss approximations involved in calculating the finite temperature electron density needed to evaluate the Harris-Foulkes free energy. Of particular importance are (1) an electron density at each site that is based on exact solution of the Poisson equation combined with a solution of the multiple-scattering problem in which only scattering from a small cluster of sites surrounding the site in question is retained and (2) an approximate occupation function having a finite number of poles in the complex energy plane. The intention is to develop, within density-functional theory, an O(N) scalable first-principles scheme, based on spatially local multiple-scattering methods, for calculating free energies of large systems.