A relationship between the weighted density approximation and the local-scaling transformation version of density functional theory

Abstract

A relationship between the auxiliary density, ρ̃(r), defined within the framework of the weighted density approximation and the kinetic energy modulating factor, AN([ρ(r)];r), which appears in the local-scaling transformation version of density functional theory is presented. This relationship imposes the condition of positiveness on the kinetic energy modulating factor and this, in turn, leads to an important mathematical condition on any approximation kinetic energy density functional. It is shown that two well-known approximate kinetic energy functionals do not satisfy the above relationship at distances very close to the nucleus. By forcing a given approximate kinetic energy density functional to obey the above condition, both the kinetic and exchange energies can be obtained within a framework similar to that of the weighted density approximation. Results on some closed-shell atomic systems provide support for those ideas.