Electronic structure of theFcenter in a lithium-fluoride crystal by the method of linear combinations of atomic orbitals

The method of linear combinations of atomic orbitals has been applied to perform a first-principles calculation of the electronic structure of the $F$ center in a lithium-fluoride crystal. The one-electron Hamiltonian includes the Coulomb and exchange interaction due to all atoms (or ions) in the crystal and the trapped electron. Slater's approximation for exchange is used. Relaxation displacement of the surrounding lattice sites resulting from the presence of the $F$ center is neglected. The $F$-center wave functions are expanded as linear combinations of localized orbitals centered at atomic sites up to the sixth (the seventh in one case) nearest neighbors to the vacancy. The computational work is greatly facilitated by the Gaussian technique which enables us to evaluate all the multicenter integrals associated with the Hamiltonian matrix elements analytically or in terms of the error function. An initial crystal potential is constructed by assuming the charge distribution of the ${\mathrm{Li}}^{+}$ and ${\mathrm{F}}^{-}$ ions in the $F$-center crystal to be the same as those in the perfect crystal. The solution of this initial Hamiltonian is then used for an iterative calculation to take into account the effect of electronic polarization. The energies of the ground state and the ${\Gamma }_4^{-}$ excited state have been calculated and the energy difference agrees well with the experimental absorption frequency. The theoretical values of the hyperfine contact-interaction constants are also in good agreement with experiments.