The Hartree-Fock-Slater equations for the two-electron orbitals localized about an anion vacancy in MgO, CaO, NaCl, and KCl have been solved numerically in the point-ion-lattice potential. The ionic polarization of the nearest-neighbor ions is treated in a self-consistent manner. It is found that the low-lying ${F}^{\ensuremath{'}}$-center states for MgO and CaO have the following order for increasing values of the energy: $^{1}S(1s, 1s)$, $^{3}P(1s, 2p)$, $^{1}P(1s, 2p)$, and either $^{3}S(1s, 2s)$ or $^{1}S(1s, 2s)$. The states $^{3}S(1s, 2s)$ and $^{1}S(1s, 2s)$ both lie above the other three states, but whether the $^{3}S(1s, 2s)$ state lies above or below the $^{1}S(1s, 2s)$ state depends upon the ionic polarization of the crystal potential. The above ordering, the optical absorption and emission energies between the states $^{1}S(1s, 1s)$ and $^{1}P(1s, 2p)$, and the spin-forbidden emission energy from the state $^{3}P(1s, 2p)$ to the state $^{1}S(1s, 1s)$ agree reasonably with the experimental ordering of the states and with the experimental transition energy values for CaO, respectively. The same physical model gives very different results for the ${F}^{\ensuremath{'}}$ center in NaCl and in KCl. It is found that only the ground state $^{1}S(1s, 1s)$ contains spatially compact (bound) electronic orbitals. The ground-state energies of the ${F}^{\ensuremath{'}}$ center in NaCl and in KCl agree to within 20% of the experimental values. The existence of bound excited states for the ${F}^{\ensuremath{'}}$ center in these monovalent crystals has been investigated. However, definitive statements on such states are not available at present.