Self-consistent-field—<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Ξ</mml:mi><mml:mi>a</mml:mi></mml:math>method: The atomic properties of several atoms using theoretical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>a</mml:mi></mml:math>parameters derived from the Fermi hole

Abstract

Theoretical parameters ${a}_{t}$ for the self-consistent-field---$\ensuremath{\Xi}a(\mathrm{S}\mathrm{C}\mathrm{F}\ensuremath{-}\ensuremath{\Xi}a)$ method are derived by considering the Fermi hole, modified from the form used to generate the theoretical $\ensuremath{\alpha}$ parameters in the $X\ensuremath{\alpha}$ 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 $Z&gt;30$ they are in error due to relativistic effects becoming important. The results from the $\mathrm{S}\mathrm{C}\mathrm{F}\ensuremath{-}\ensuremath{\Xi}a$ 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 -${\ensuremath{\epsilon}}_{i}$, the total energies $E$, the Fermi contact terms $\ensuremath{\chi}$, and the core-spin densities.