Slater's exchange paramters for analytic and variational xalpha calculations

We treat the local exchange parameter, alpha, of the Slater's Xalpha method as a fitting parameter and determine its value by constraining some physical quantity obtained from the self-consistent solution of the Xalpha method to be equal to its "exact" value. Thus, the alpha values that reproduce the exact atomic energies are obtained for four different combinations of basis sets. A similar set of alpha values that is independent of basis set is obtained from numerical calculation. The alpha values are obtained for the atoms H through Cl. The performance of the analytic Slater-Roothaan (SR) method, that permits calculations to be performed accurate to machine precision, is examined using these set of alpha values for atomization energies of molecules belonging to the G2 set. The calculations indicate that the average absolute and mean errors are larger than those obtained using the Hartree-Fock alpha values in the SR method, but smaller than those for the standard Hartree-Fock theory or Kohn-Sham local density approximation. Alternative set of alpha values is determined by matching the highest occupied eigenvalue of the SR method to negative of the first ionization potential. Finally, the alpha values for the diatomic molecules of these atoms that yield the "exact" atomization energy are obtained. We find that the alpha values for the diatomic molecules show much larger deviation than what is observed for the atomic alpha values. The results obtained are useful in the development of the analytic Slater-Roothaan Xalpha method for molecular calculations.