ABSTRACT
The analytical survey of the main workable kinetic, exchange, and correlation density functionals within local and gradient density approximations is undertaken (Putz, 2008a).
3.2DENSITY FUNCTIONALS OF KINETIC ENERGY
When the electronic density is seen as the diagonal element 1 1 1(r ) (r , r )r r= the kinetic energy may be generally expressed from the Hartree-Fock model, through employing the single determinant 1 1(r , r ' )r , as the quantity (Lee and Parr, 1987):
T d[ ] ( , ' )' 'r r=− ∇
=∫
it may eventually be further written by means of the thermodynamic (or statistical) density functional (Zhao and Parr, 1992):
T k T d dBβ ρ ρ β = =∫ ∫
3 2
3 2
1( ) ( ) ( ) ( )
r r r r r
r (3.2)
that supports various specializations depending on the statistical factor particularization b.
