Thomas-Fermi-Dirac-Weizsacker

The minimization of this functional, which includes second order gradient corrections leads to the relativistic analogous of the Thomas-Fermi-Dirac-Weizsacker model and constitutes the state of the art in relativistic semiclassical approaches for many-electron systems. 

Thomas-Fermi-Dirac-Weizsacker Density Functional Formalism Applied to the Study of Many-electron Atom Confinement by Open and Closed Boundaries... 

It seems that this variational method should be the method of choice for generating the Fukui function. Unfortunately, accurate determination of the hardness kernel is complicated by the lack of an accurate explicit kinetic energy functional, T[p]. Nonetheless, Eq. (40) has been applied to the Hiickel model [49] and Eq. (42) has been applied to the Thomas-Fermi-Dirac-Weizsacker approximation of F[p] [47]. 

Following the success of the von Weizsacker approach in improving the Thomas-Fermi kinetic functional. Sham showed in 1971 that an analogous correction to the Dirac exchange functional can be derived, Kleinman later demonstrated that the Sham derivation was flawed and that his correction was too small by exactly 10/7, It is now agreed that the correct second-order alpha exchange functional is... 

Analytical representations of the Thomas-Fermi (TF) or TF-Dirac (TFD) potentials were used in [25]. The TFD-Weizsacker (TFDW) variational equations are solved numerically to obtain total energies of the ground term in [26]. These energies are also calculated in an explicit parameter-free approximation [27]. 

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