Some Remarks on Exchange Inhomogeneity Corrections in Many-Electron Systems

Abstract

In the preceding paper Sham pointed out that a number of people have by now calculated the first principles value of the second order exchange inhomogeneity parameter β. Ma and Ortenburger¹ find a value of 0.0011 (in the units of HVDO), Liberman² finds 0.0016, while the nomencal work of Gel dart and Taylor³ would seem to support the smaller value. In any case the theoretical value for β is considerably smaller than the values obtained empirically by Herman, Van Dyke, and Ortenburger^4,5 from self-consistent calculations for a number of representative atomic systems. In the work of HVDO the optimum value of β is found to be about 0.005; the inclusion of exchange inhomogeneity corrections with this coefficient leads to a considerable improvement in the total energy: this is lowered about half of the distance between the best energy obtained ignoring these corrections. and the exact Hartree-Fock total energy.