Hamiltonian Matrices Of 3d~3 Ions Based On The Molecular-orbital Theory And Their Application In Semimagnetic Semiconductor ZnS

3d³(Cr³⁺,V²⁺) and 3d⁷(Co²⁺,Ni³⁺) ions are relatively active transitional metal ions, and play a key role in the study of the optical spectra.. When transition-metal 3d³ and 3d7 ions are mixed into different substances, abnormal characteristics often appear, and they are important role in the study of physics and chemistry of material. The physical and chemical properties of many important industrial and biological materials are due to these ions, so they have been the focus of the study in the theoretical and experimental physics all the time.With the development of experimental technique, the experimental data are more and more accurate, in order to study them, scientists have to seek help from computer technique which is developing very quickly, so more and more scientists adopt the method of complete diagonalizing Hamiltonian matrix and regard it as an exact calculation.In the cubic crystal field, the d-orbit splits into e-orbit and t2-orbit which are distinct from each other on the covalency. The difference between the 2 kinds of orbital was neglected in the classical crystal-field theory that is a good approach at dealing with transition-metal (TM) impurity in ionic crystal. Because there is strong covalence inâ…¡-VI compounds, i.e., large electronic overlap between ligands and TM impurity, the different covalence between the t2-orbital and the e-orbital must be considered.In this thesis, based on analysis of precedent works, adopting the Tanabe-Sugano strong-field scheme, the influence of the different covalency to the inner Coulomb electron-electron repulsion(Racah)and the spin-orbi(tSO)coupling of 3d³ ions, and the outer crystal-field (CF)is discussed in detail, and a full Hamiltonian matrix for 3d³ ions within different covalent reduction factors Ne and Nt is deduced including the Coulomb electron-electron repulsion, the spin-orbit coupling, and the crystal-field interaction. In classical crystal field theory dealing with transitional metal ions , there are four parameters B,C (Racah), Dq(CF)andζ_d(SO )used to fit the optical spectra data generally. In this thesis, using a molecular-orbital approach, the Racah parameters are changed into A₁,A₂,A₃,B₁,B₂,B₃,B₄,C₁,C₂, and C3,the crystal-field parameter is changed into Dq1 and Dq 2and the spin-orbit coupling parameter is changed intoζ1andζ2.Using the present full Hamiltonian matrices for 3d³ ions and the complete diagonalizing procedure (CDP), absorption specta of V²⁺ ions in ZnS crystal with Td symmetry have been calculated, and the results agree well with the experimental data. And this thesis gets following conclusions: (1) for the difference between e-orbital and t2-orbital, the contributions of the Racah parameter A to the spectra can not be neglected; (2) the influence of the covalent factors Ne and Nt are on both the spin-orbital coupling, the electron-electron repulsion, and the crystal-field, and a small change of these factors greatly influences the calculating spectra result in ZnS:V²⁺ crystal with Td symmetry.