Ensuring proper short‐range and asymptotic behavior of the exchange‐correlation Kohn–Sham potential by modeling with a statistical average of different orbital model potentials

The long‐range asymptotic behavior of the exchange‐correlation Kohn–Sham (KS) potential v xc and its relation to the exchange‐correlation energy E xc are considered using various approaches. The line integral of v xc ([ρ];  r ) yielding the exchange‐correlation part Δ E xc of a relative energy Δ E of a finite system, shows that a uniform constant shift of v xc never shows up in any physically meaningful energy difference Δ E . v xc may thus be freely chosen to tend asymptotically to zero or to some nonzero constant. Possible choices of the asymptotics of the potential are discussed with reference to the theory of open systems with a fractional number of electrons. We adhere to the conventional choice v xc (∞)=0 for the asymptotics of the potential leading to ε N =− I p for the energy ε N of the highest occupied orbital. A statistical average of orbital dependent model potentials is proposed as a way to model v xc . An approximate potential v   xco SAOPwith exact −1/ r asymptotics is developed using the statistical average of, on the one hand, a model potential v   xcσ Eifor the highest occupied KS orbital ψ N σ and, on the other hand, a model potential v   xc GLBfor other occupied orbitals. It is demonstrated for the well‐studied case of the Ne atom, that calculations with the new model potential can, in principle, reproduce perfectly all energy characteristics (orbital energies and the virial integral I v =∑ σ ∫[3ρ σ ( r )+ r ⋅∇ρ σ ( r )] v xcσ ( r )  d r ) of the essentially accurate v xcσ for a particular system, as well as the slopes of v xcσ in both outer and inner regions. Atomic calculations with v   xcσ SAOPshow that this model combines good quality of the calculated energy ε N σ of ψ N σ with good quality of the calculated virial integral. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 407–419, 2000