alkali metals using several atomic potentials. The core-Hartree and Kohn-Sham potentials were those favored in Ref. [@sapcheng] from the five atomic potentials, based on local density theory, considered in that work.

In the Hartree-Fock approximation, Eq. (\[eq:rel\]) is first solved self-consistently for all orbitals of the core, and $V_{\rm el}$ represents the direct and exchange Hartree-Fock potentials of the core electrons. The core is then frozen, and the energies and wave functions for the valence electron are found in this potential. (Explicit expressions for the relativistic Hartree-Fock potentials may be found in, e.g., Ref. [@johnson_book].)

In the core-Hartree approximation, the procedure is similar to that for Hartree-Fock, though the exchange potential is altogether excluded. In the Kohn-Sham approximation, a local form for the exchange potential is used, $V_{\rm exch}^{\rm KS}(r)=\frac{2}{3}( \frac{81}{32\pi^2}
\rho_{\rm el}(r))^{1/3}$, where $\rho_{\rm el}(r)$ is the total (core and valence) electronic density, with each electron contributing $\rho_i(r)=(f_i(r)^2+\alpha^2 g_i(r)^2)/r^2$. (The upper and lower radial components of each orbital, $f_i$ and $g_i$, respectively, are normalized according to $(f_i^2+\alpha^2g_i^2)dr=1$.) The Latter correction [@latter] is enforced to give the orbitals the correct asymptotic behaviour: the total potential $V_{\rm tot}=V_{\rm nuc}+V_{\rm
el}$ is set to $1/r$ when $V_{\rm tot}$ falls below $1/r$. In 