  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.
