On optimal values of alpha for the analytic Hartree-Fock-Slater method
  We have examined the performance of the analytic Hartree-Fock-Slater (HFS) method for various alpha (Slater's exchange parameter) values and empiricaly determined the optimal alpha value by minimizing the mean absolute error (MAE) in atomization energies of the G2 set of molecules. At the optimal alpha the HFS method's performance is far superior with the   MAE of 14 kcal/mol than that of the local density approximation (MAE ~ 36 kcal/mol) or the Hartree-Fock theory (MAE ~ 78 kcal/mol). The HFS exchange functional with alpha = 0.7091 is found to perform significantly better than the Kohn-Sham exchange functional for equally weighted atoms H-Kr. We speculate that use of this alpha value may be useful in parametrization of empirical exchange-correlation functionals. 
Rajendra R. Zope and Brett I. Dunlap (US Naval Research Laboratory,   Washington DC)