Two-ElectronF′Centers in the Alkaline-Earth Oxides and in the Alkali Halides

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 $F^{\prime }$-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 $F^{\prime }$ 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 $F^{\prime }$ center in NaCl and in KCl agree to within 20% of the experimental values. The existence of bound excited states for the $F^{\prime }$ center in these monovalent crystals has been investigated. However, definitive statements on such states are not available at present.