Local geometry and resonant vibrations of Cu+:NaF. Results of ab initio perturbed ion, cluster-in-the-lattice calculations involving clusters of 179 ions

Abstract

The ground state electronic structure and energy of a CuF92Na5−86 cluster (Cu+ plus 12 shells of neighbors) embedded into a quantum lattice representing the NaF crystal are determined by using the ab initio perturbed ion (aiPI) method, with unrelaxed Coulomb–Hartree–Fock (uCHF) correlation energy corrections. Parallel calculations are performed on the NaF92Na5−86 cluster of the pure crystal in order to identify the changes induced by the impurity and to estimate the systematic errors in our calculations. The geometry of the first four shells (32 ions) is allowed to relax by following symmetric breathing modes. An inwards relaxation of −0.12 Å is predicted for the nearest neighbors (nn) shell, but negligible relaxations are found for the outer shells. The substitution of the Na+ ion by the Cu+ impurity is favored by −1.03 eV. The Cu+ ion is found to occupy an on-center octahedral position. The 138 independent Oh force constants corresponding to the vibration of the Cu+ and its first four shells of neighbors are then numerically computed from the aiPI energy using a Richardson iterated, finite-difference limit formula. These force constants give the vibrational modes of the impurity center. Strong couplings are found among vibrational modes of adjacent shells. Vibration frequencies characteristic of the doped system are obtained at 206 cm−1 (1a1g), 108 cm−1 (1t1u), and 173 cm−1 (1eg) determined mainly by the motions of the CuF6 octahedron.