Approximation of the exchange-correlation Kohn–Sham potential with a statistical average of different orbital model potentials

A statistical average of different model orbital potentials is proposed as a way to model the exchange-correlation Kohn–Sham potential νxcσ. An approximate potential νxcσSAOP is developed using the statistical average of a model potential νxcσEi with exact asymptotics for the highest occupied KS orbital ψNσ with a model potential νxcGLB for other occupied orbitals, which has a proper atomic shell structure. To get exact asymptotics, an exponential integral function E1(1/xσ) of the dimensionless gradient argument xσ is employed within νxcσEi. For the Ne atom calculations with the new model potential can, in principle, reproduce perfectly all energy characteristics (orbital energies and the virial integral Iν=∑σ ∫[3ρσ(r)+r·∇ρσ(r)]νxcσ(r) dr) of the essentially accurate νxcσ for a particular system, as well as the slopes of νxcσ in both outer and inner regions. Atomic calculations with νxcσSAOP show that this model gives a good quality of both the calculated energy εNσ of ψNσ and of the calculated virial integral.