Ligand field theory for the orbit–lattice coupling coefficients to E strains of d5 ions in tetrahedral symmetry

Abstract

A molecular orbital model has been elaborated to determine the orbit–lattice coupling coefficients to strains of symmetry E of the orbital triplet states of d5 ions in tetrahedral symmetry. The wave functions and energies of the monoelectronic molecular orbitals have been determined for a tetrahedral molecule MnX4 in a crystal and for a slightly distorted molecule of symmetry D2d corresponding to a strain Eθ. It is shown that in D2d symmetry, the splitting of the monoelectronic molecular orbitals e and t2 is due to the variations of the group overlap integrals and the variation of the crystal electrostatic field with respect to their values in cubic symmetry. The orbit–lattice coupling coefficients which are independent of the spin–orbit interactions, are obtained by diagonalizing the Tanabe–Sugano matrices for the orbital triplet states and then using the molecular orbitals in D2d symmetry as zero-order wave functions in a first-order perturbation scheme. The proposed model for the orbit–lattice coupling coefficients of the orbital triplet states 4T1 and 4T2 at lower energy for Mn2+ in ZnS and ZnSe gives theoretical values which differ at most by 30% from the experimental values. It is shown that three fifths of the theoretical values for the orbit–lattice coupling coefficients are due to the variations of the group-overlap integrals, the remaining part of the theoretical values being due to the variations of the crystal electrostatic field describing the Coulomb’s interaction in the molecular model.