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

Abstract

A relationship between the auxiliary density, ρ̃(r),defined within the framework of the weighted density approximation and thekinetic energy modulating factor, AN([ρ(r)]; r),which appears in the local-scaling transformation version of density functionaltheory is presented. This relationship imposes the condition of positiveness on thekinetic energy modulating factor and this, in turn, leads to an importantmathematical condition on any approximate kinetic energy density functional. Itis shown that two well-known approximate kinetic energy density functionals donot satisfy the above relationship at distances very close to the nucleus. Byforcing a given approximate kinetic energy density functional to obey theabove condition, both the kinetic and exchange energies can be obtainedwithin a framework similar to that of the weighted density approximation.Results on some closed-shell atomic systems provide support for those ideas.