Calculation of the defect kinetic energy in Kohn-Sham theory by means of local-scaling transformations

The kinetic-energy difference ΔT=T-${\mathit{T}}_{\mathit{s}}$[${\mathrm{\rho }}_0$] is calculated for the helium isoelectronic series and for the beryllium atom. ${\mathit{T}}_{\mathit{s}}$[${\mathrm{\rho }}_0$] is in this case the kinetic energy corresponding to a noninteracting N-particle system which, however, has the same density ${\mathrm{\rho }}_0$ as the exact interacting system. These densities ${\mathrm{\rho }}_0$ were assumed in the present case to be well represented by those coming from the optimal Hylleraas-type expansions for the He isoelectronic series and by the Bunge-Esquivel 650-term configuration-interaction wave function for Be. The calculations are carried out by means of a constrained variational method based on local-scaling transformations. The connection between this approach and the one based on the Kohn-Sham equations is discussed.