Parametrization and performance appraisal of the analytic and variational X$\alpha$ method

The linear combination of atomic orbitals, analytic and variational implementation of Slater's X$\alpha $ method that allows arbitrary scaling of the exchange-correlation potential around each atom has been formulated. The method is numerical integration free, and thus delivers machine-precision energies that are stationary in all respects. One choice of scaling uses the $\alpha $s that give exact atomic energies. We present the results of a performance assessment of this method by calculating the atomization energies and total energies of the G2 and extended G2 sets of molecules. Similar calculations for uniform $\alpha $ are also appraised. Minimizing the mean absolute error in both the X$\alpha $ energies and the Hartree-Fock energies shows that Slater's exchange functional with $\alpha $ = 0.7091 performs significantly better than the G\'{a}sp\'{a}r-Kohn-Sham exchange functional for these molecules and for equally weighted atoms H-Kr. The Office of Naval Research, directly and through the Naval Research Laboratory, and the DoD's High Performance Computing Modernization Program, through the Common High Performance Computing Software Support Initiative, Project MBD-5, supported this work. The calculations were performed at the Army Research Laboratory Major Shared Resource Center (ARL MSRC).