The optimum scale factor for the Slater free-electron exchange approximation for atoms has been obtained by minimizing the total electronic energy. In general, the scale factor lies between the Slater and the Gaspar-Kohn-Sham limit of 1 and $\frac{2}{3}$, respectively. The variation that occurs as the different shells are populated is qualitatively understandable in terms of the inhomogeneity of the over-all charge distribution.

• Received 13 June 1969

DOI:https://doi.org/10.1103/PhysRevA.1.37