Self-consistent-field—Ξamethod: The atomic properties of several atoms using theoreticalaparameters derived from the Fermi hole

Theoretical parameters $a_t$ for the self-consistent-field—$\Xi a(\mathrm{S}\mathrm{C}\mathrm{F}-\Xi a)$ method are derived by considering the Fermi hole, modified from the form used to generate the theoretical $\alpha$ parameters in the $X\alpha$ method, because of including explicit self-interaction in the Hamiltonian, which scales the exchange potential. The $a_t$ for all elements in the Periodic Table are given, to compare with previous compilations. For $Z>\mathrm{}30\mathrm{}$ they are in error due to relativistic effects becoming important. The results from the $\mathrm{S}\mathrm{C}\mathrm{F}-\Xi a$ method with $a_t$ have been compared with those previously calculated for ${\mathrm{Cu}}^{+}$, ${\mathrm{Mn}}^{2+}$, Ne, and Ar for the one-electron energies -${\epsilon }_i$, the total energies $E$, the Fermi contact terms $\chi$, and the core-spin densities.