A Relationship between the Weighted Density Approximation and the Local-Scaling Transformation Version of the Density Functional Theory

REINALDO PIS DIEZ; VALENTIN V KARASIEV

JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS

IOP PUBLISHING LTD

Año: 2003 vol. 36 p. 2881 - 2890

0953-4075

A relationship between the auxiliary density, ρ˜(r), defined within theframework of the weighted density approximation and the kinetic energymodulating factor, AN ([ρ(r)]; r), which appears in the local-scalingtransformation version of density functional theory is presented. Thisrelationship imposes the condition of positiveness on the kinetic energymodulating factor and this, in turn, leads to an important mathematical condition on any approximate kinetic energy density functional. It is shown that two well-known approximate kinetic energy density 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 similarto that of the weighted density approximation. Results on some closed-shell atomic systems provide support for those ideas.