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 is developed using the statistical average of a model potential Kohn-Sham potential v(xc sigma). An approximate potential v(xc sigma)(SAOP) is developed using the statistical average of a model potential y(xc sigma)(Ei) With exact asymptotics for the highest occupied KS orbital psi(N sigma) with a model potential v(xc)(GLB) for other occupied orbitals, which has a proper atomic shell structure. To get exact asymptotics, an exponential integral function E-1(l/x(sigma)) of the dimensionless gradient argument x(sigma) is employed within v(xc sigma)(Ei). For the Ne atom calculations with the new model potential can, in principle, reproduce perfectly all energy characteristics (orbital energies and the virial integral I-v= Sigma(sigma) integral[3 rho(sigma)(r) + r . del rho(sigma)(r)]v(xc sigma)(r)dr) of the essentially accurate v(xc sigma) for a particular system, as well as the slopes of v(xc sigma) in both outer and inner regions. Atomic calculations with v(xc sigma)(SAOP) show that this model gives a good quality of both the calculated energy E-N sigma of psi(N sigma) and of the calculated virial integral. (C) 1999 Elsevier Science B.V. All rights reserved.