Hartree-Fock level in the context of local-scaling transformations

Calculation of the energy and wavefunction for the beryllium atom at the Hartree-Fock level by in the context of local-scaling transformations 

The Hartree-Fock method involves the optimization - via energy minimization -of a single Slater determinant wavefunction. This process is usually carried out by solving the single-particle Hartree-Fock equations. From the Hartree-Fock orbitals one can construct the Hartree-Fock density pur- 

In the spirit of the local-scaling version of density functional theory, we deal below with the calculation of the Hartree-Fock wavefunction and energy by means of a constrained variation at fixed density p(r) = phf( ) as well as by intra-orbit and inter-orbit optimizations. 

Density-constrained determination of the Hartree-Fock wavefunc-tion 

Consider an orbit-generating wavefunction, g [ x, ] such as the one given by Eq. (73), constructed from the atomic orbitals (.x,) which are products of radial functions times spherical harmonics. We assume that the radial functions are expanded as in Eq. (106) in terms of Slater type orbitals (Eq. (107)). The energy as a functional of the density and of the orbit-generating wavefunction is given by 

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