STATIONARY NATURE OF THE DENSITY-FUNCTIONAL FREE-ENERGY - APPLICATIONTO ACCELERATED MULTIPLE-SCATTERING CALCULATIONS

The number of operations required for conventional density-functional algorithms grows as the cube of the number of atoms, N. For large syst ems the computing requirements are unattainable. To overcome this limi tation 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 potent ial, chemical potential, occupation function, and temperature allows f or very useful approximations leading to rapid and accurate determinat ion of the free energy. Here we discuss approximations involved in cal culating the finite temperature electron density needed to evaluate th e Harris-Foulkes free energy. Of particular importance are (1) an elec tron density at each site that is based on exact solution of the Poiss on equation combined with a solution of the multiple-scattering proble m in which only scattering from a small cluster of sites surrounding t he site in question is retained and (2) an approximate occupation func tion having a finite number of poles in the complex energy plane. The intention is to develop, within density-functional theory, an O(N) sca lable first-principles scheme, based on spatially local multiple scatt ering methods, for calculating free energies of large systems.