Transformation Version Of Density Functional Theory Research Articles

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

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.

Assessment of dynamical and nondynamical correlation energy components for the beryllium-atom isoelectronic sequence

The partitioning of electron correlation energy into dynamical and nondynamical components is examined in the context of the local-scaling transformation version of density-functional theory. An assessment is made of the relative importance of these components for the beryllium atom and its isoelectronic sequence. In particular, the problem of finding a multiconfiguration reference wave function differing only in dynamical correlation from the exact wave function is considered. It is shown that to a good approximation this reference wave function is given by Ψ=C11s22s2+C21s22p2. The concepts of “long-range” and “short-range” correlation are re-examined from a perspective based on the reference wave function.

Analysis of dynamical and nondynamical components of electron correlation energy by means of local-scaling density-functional theory

The partitioning of electron correlation energy into dynamical and nondynamical components is examined in the context of the local-scaling transformation version of density-functional theory and its connection with the Hohenberg–Kohn–Sham density-functional-theory definition of electron correlation is discussed. The relative importance of these components is analyzed with reference to the helium atom and its isoelectronic series. The present results attest to the preponderantly dynamical character of the recovered correlation energy.

Formulation of N- and v-representable density-functional theory. II. Spin-dependent systems.

The local-scaling transformation version of density-functional theory is extended to the case of spin-dependent densities. It is shown that, from the spin-dependent variational principle, there ensue spin-coupled Euler-Lagrange equations for the densities. The connection between the locally scaled external potential and the spin-dependent density is discussed.