First-principles energy density and its applications to selected polar surfaces

Abstract

Density-functional theory has been successfully applied in solid-state calculations where it has been customary to extract a single number, the total energy. Within this formalism, we show that one can, in addition, define a local energy density scrE(r) which is a sum of kinetic, Maxwell, exchange-correlation, and other contributions that depend on the external potential. Despite the inherent nonuniqueness of scrE(r), we show that it can be used to calculate well-defined energies from integrals over regions, e.g., at surfaces. We present explicit calculations for the Si(111) ideal surface as a test case and we demonstrate the power and efficiency of the method by determining energies of two inequivalent GaAs(100) surfaces from a single calculation.