A numerical study of the functional derivative of the kinetic part of the density functional correlation energy

Accurate functional derivatives of the kinetic part of the density functional correlation energy for two-electron systems are calculated numerically from the adiabatic coupling constant relation δTcγ[ρ]/δρ(r)=vcγ([ρ];r)−γ∂∂γvcγ([ρ];r). The kinetic energy potential δTcγ[ρ]/δρ(r) resembles a scaled mirror image of the correlation potential vcγ([ρ];r). Numerical results show that the correlation energy functional and the kinetic part of the correlation functional are not homogeneous of any degree in density scaling. It may still be possible to express the correlation energy as a combination of homogeneous functionals of different degrees as suggested by Lui and Parr.