Molecular orbital theory for Cu²⁺ in tetrahedral co-ordination

Theoretical calculations for the model of Birman, in which the infra-red emission from copper-doped zinc sulphide is attributed to an internal transition of the Cu²⁺ ion, indicate that configurational d-p mixing produced by the odd harmonics of the tetrahedral crystal field cannot account for the observed absorption (or emission) intensities for transitions internal to the Cu²⁺ centre, in either copper-doped zinc sulphide or copper-doped zinc oxide. Calculations show that the intensity must depend on a strong interaction between the Cu²⁺ ion and the zinc sulphide (or zinc oxide) lattice. Such a strong interaction with the lattice would mean g factors significantly reduced from the free-electron value, and probably a short spin-lattice relaxation time. These two effects, taken in conjunction with one another, are probably the reason why the electron spin resonance signal of Cu²⁺ in zinc sulphide is difficult to detect. Finally certain shortcomings of the Birman model are discussed.