Coupling constants with vibrations and the 10Dq parameter for Cr3+ in fluorides: Microscopic analysis

The strong dependence on the metal-ligand distance, R, of the cubic field-splitting parameter, 10Dq, for Cr3+ impurities in fluorides as well as the origin of the coupling constants (V-A and V-E) with the A(1g) and E-g modes of the CrF63- unit in the T-4(2g) State are explored in detail. By means of multiple-scattering X alpha and self-consistent-charge extended Huckel methods, it is shown that the value of both V, and VE constants as well as the R dependence of 10Dq, strongly depend upon the small amount of 2s(F-) admixture present in the antibonding e(g)* (similar to x(2) - y(2),3z(2) - r(2)) level. Furthermore when the 2s(F-) orbitals are removed from the basis set the calculated Huang-Rhys factors, S-i (i = A;E), and Stokes shift, E-S, decrease by, at least, one order of magnitude. A reasonable explanation on simple grounds of these relevant but unexpected facts is also reported. This analysis indicates that a similar behavior should also be found for other d cations surrounded by anions like chlorine, bromine, fluorine, or oxygen. The present study also explains the large R dependence displayed by the isotropic superhyperfine constant, A(s), for 3d impurities involving sigma electrons in the ground state.