Density scaling and relaxation of the Pauli principle

The relaxation of the Pauli principle associated with density scaling is examined. Scaling the density has been investigated in the development of density functional computational methods with higher accuracy. Scaling the density by ρ(r)ζ=ρ(r)∕ζ reduces the number of electrons to M=N∕ζ when ζ>1. The minimum kinetic energy of the scaled density, Ts[ρ∕ζ], can be scaled back to the N-electron system by multiplying the M-electron Kohn-Sham-type occupation numbers by ζ to produce Tζ[ρ]. This relaxes the Pauli principle when the orbital occupation numbers are greater than 1 in the N-electron system. The effects of antisymmetry on solutions to the Kohn-Sham equations are examined for Ne and the Be isoelectronic series. The changes in Tζ[ρ] and the exchange energy Exζ[ρ] when ζ is varied show that these two quantities are inextricably linked.