Structure and Stability ofHCenters

The distortion around and the relaxation energy for a substitutional ${\mathrm{Cl}}_2^{-}$ molecular ion ($H$ center) in NaCl and KCl have been obtained for both the $〈110〉$ and $〈111〉$ orientations by a method involving the calculation of electrostatic, polarization, dipole-dipole, and repulsive energies according to the usual pointlattice model. The binding energy of the free ${\mathrm{Cl}}_2^{-}$ molecule was taken, however, from the quantum-mechanical calculations of Wahl and Gilbert. The relaxation of about 20 neighboring ions has been taken into account using five independent parameters in minimizing the energy relative to a perfect lattice. It was not found possible, with this model, to account for the preferred $〈110〉$ orientation of the $H$ center, the $〈111〉$ direction being preferred by about 0.2 eV. It appears necessary to take into account the known fact that the hole associated with the halogen molecule is not localized on the molecule but spreads a little onto two collinear halogen ions. This effect, treated in an approximate manner, leads to an $H$ center which is stable in the $〈110〉$ direction. It also explains qualitatively the orientation of $H$ centers in mixed crystals.