Ab Initio Embedded Cluster Study of <i>F </i>and <i>M</i> Centers in LiF

Ab initio computations using an embedded cluster method have been employed to study the electronic structure and excitation energies of an M center (an electron pair associated with two neighboring vacancies) in LiF crystals. For comparison, the results for an F center (one electron and one vacancy) computed in the same way have also been studied. The ab initio approach consisted of the Hartree−Fock approximation applied to Li14F13e, Li15F20e27- and Li10F18e210- clusters of Li+ and F- ions about the crystal vacancies employing each of two differing basis sets. The contribution from the remainder of the infinite ionic lattice was computed using the Ewald transformation. No other constraints were applied to the wave function. For the M center, both 〈100〉 and 〈110〉 orientations were considered. The energy difference corresponding to the gain or loss of an electron by the F center, F + e- → F- and F → F+ + e-, and to loss of electrons from the M center, M → M+ + e- and M → M2+ + 2e-, were compared. The electron isodensity surfaces of the Σ-type states of the 〈110〉 M center and the computed energy differences confirm the “molecular” nature of the M center in the 〈110〉 orientation. The Π-type states, however, are delocalized. The computed energy of the vertical transition to the first Σ state, 2.41 and 1.47 eV for the two basis sets, respectively, are compared with the experimental absorption energy, 2.79 eV. These calculations provide a framework to interrelate the energies and electron densities of the differing species. The advantages and limitations of the present computational approach are discussed.