A density functional theory structures,stabilities, and study on size-dependent electronic properties of bimetallic MnAgm （M=Na,Li; n ＋ m ≤ 7） clusters

The equilibrium geometries, relative stabilities, and electronic properties of MnAgm（M=Na, Li; n ＋ m ≤ 7） as well as pure Agn, Nan, Lin （n ≤ 7） clusters are systematically investigated by means of the density functional theory. The optimized geometries reveal that for 2 ≤ n ≤ 7, there are significant similarities in geometry among pure Agn, Nan, and Lin clusters, and the transitions from planar to three-dimensional configurations occur at n = 7, 7, and 6, respectively. In contrast, the first three-dimensional （3D） structures are observed at n ＋ m = 5 for both NanAgm and LinAgm clusters. When n ＋ m ≥5, a striking feature is that the trigonal bipyramid becomes the main subunit of LinAgm. Furthermore, dramatic odd-even alternative behaviours are obtained in the fragmentation energies, secondorder difference energies, highest occupied and lowest unoccupied molecular orbital energy gaps, and chemical hardness for both pure and doped clusters. The analytic results exhibit that clusters with an even electronic configuration （2, 4, 6） possess the weakest chemical reactivity and more enhanced stability.     

Theoretical Studies of g Factors and Defect Structures for Cubic, Tetragonal, and Orthorhombic Fe+ Centers in Alkali Halides MX (M=Li,Na;X=F,Cl)

The EPR g factors for cubic, tetragonal and orthorhombic Fe centers in alkali halides MX (M = Li, Na;X = F, Cl) are calculated from second-order perturbation formulas of g factors based on cluster approach for 3d7 ions in three symmetries. From calculations, the g factors of these Fe centers in MX crystals are reasonably explained and the defect structural data for the tetragonal and orthorhombic Fe centers are estimated. The results are discussed.     

Theoretical Calculations of g Factors and Hyperfine Structure Constants for Co2+ inCd2+(I) and Cd2+(II) Sites of CsCdCl3 Crystal

The g factors g‖,g⊥ and hyperfine structure constants A‖,A⊥ for two trigonal Co2+ centers (i.e.,Co2+ in Cd2+ (I) and Cd2+ (II) sites) in CsCdCl3:Co2+ crystals are calculated from the high-order perturbation formulas based on the cluster approach.In the calculation,the contributionsfrom covalency effect and configuration interaction effect are considered and the parameters related to both effects are obtained from the optical spectrum and the structure data of the studied system.The results are in good agreement with the observed values.     

Theoretical Calculations of g Factors and Hyperfine Structure Constants for Co^2＋ in Cd^2＋（I） and Cd^2＋（Ⅱ） Sites of CsCdCl3 Crystal

The g factors g||,g⊥ and hyperfine structure constants A||,A⊥ for two trigonal Co^2 centers (i.e.,Co^2 in Cd^2 (I) and Cd^2 (Ⅱ) sites) in CsCdCl3:Co^2 crystals are calculated from the high-order perturbation formulas based on the cluster approach.In the calculation,the contributions from covalency effect and configuration interaction effect are considered and the parameters related to both effects are obtained from the optical spectrum and the structure data of the studied system.The results are in good agreement with the observed values.     

Theoretical Studies of Electron Paramagnetic Resonance Parameters for Cr4+ Ions in Ca2GeO4 Crystals

The electron paramagnetic resonance (EPR) parameters (zero-field splitting D and g factors g_||, g_⊥) of Cr⁴⁺ ions in Ca₂GeO₄ crystals have been calculated from the complete high-order perturbation formulas of EPR parameters for a 3d² ion in trigonal MX₄ clusters. In these formulas, in addition to the contributions to EPR parameters from the widely used crystal-field (CF) mechanism, the contributions from the charge-transfer (CT) mechanism (which are often neglected) are included. From the calculations, it is found that for the high valence state 3dⁿ ions in crystals, the reasonable explanation of EPR parameters (in particular, the g factors) should take both the CF and CT mechanisms into account.     

Theoretical explanation of spin-Hamiltonian parameters for the rhombic Mo5+ octahedral clusters in molybdenum phosphate glasses

The high-order perturbation formulas based on the two-mechanism model are used to calculate the spin-Hamiltonian parameters (g factors g_i and hyperfine structure constants A_i, where i = x, y, z) of the rhombic Mo⁵⁺ oxygen octahedral clusters in molybdenum phosphate glasses. These formulas consist of the crystal-field mechanism in the extensively applied crystal-field theory and of the charge-transfer mechanism (which is often neglected). In the calculations, only three adjustable parameters are applied and the six calculated spin-Hamiltonian parameters are reasonably coincident with the experimental values. The results are discussed.     

Theoretical analysis of spin-Hamiltonian parameters for the rhombic Cu2+ centres in CuGaSe2 crystals

The spin-Hamiltonian parameters (g factors g_i and hyperfine structure constants A_i, where i = x, y, z) of the rhombic Cu²⁺ centres in the CuGaSe₂ crystal are determined from the high-order perturbation formulae based on the cluster approach (sometimes also called two-spin-orbit parameter model). In the studies, some parameters in the analysis of g factors for the same centre within the tetragonal symmetry approximation in the previous paper are used, and the parameter due to the perturbation of rhombic crystal field caused by a charge compensator at, e.g., [110] direction are considered. As the result of a fitting process, the determined spin-Hamiltonian parameters are in reasonable agreement with the experimental values. The results are discussed.     

Unified calculations of the optical band positions and spin-Hamiltonian parameters for V2+ ions in CdCl2 crystal

The eight optical spectral band positions and three spin-Hamiltonian parameters (g factors g_//, g_⊥ and zero-field splitting D) of V²⁺ ions in trigonal CdCl₂ crystal are calculated together from the complete diagonalisation (of energy matrix) method (CDM) based on the two-spin-orbit-parameter model (also called the cluster approach). In the model, differing from the usual one-spin-orbit-parameter model in the conventional crystal-field theory (where only the contribution to spin-Hamiltonian parameters due to the spin-orbit parameter of central dⁿ ion is considered), both the contributions from the spin-orbit parameter of central dⁿ ion and that of ligand ions are taken into account. The calculated results show reasonable agreement with the experimental values. The local lattice relaxation in the vicinity of V²⁺ ion due to the introduction of V²⁺ impurity is acquired from the calculations. The calculations of spin-Hamiltonian parameters from the CDM based on the one-spin-orbit-parameter and those from the perturbation theory method based on the two-spin-orbit-parameter model are also made for comparison. The results are discussed.     

Theoretical investigations on the spin Hamiltonian parameters and local structures for the trigonal Ni2+ centers in CsMgX3 (X=Cl,Br, I)

The spin Hamiltonian parameters (zero-field splitting and the anisotropic g factors) and the local structures for the trigonal Ni²⁺ centers in CsMgX₃ (X=Cl, Br, I) are theoretically investigated from the perturbation formulas of these parameters for a 3d⁸ ion in trigonally distorted octahedra, by including the ligand s-orbital contributions. Based on the studies, the local impurity-ligand bond angles β related to the C ₃ axis in the Ni²⁺ centers are found to be about 2° larger than the corresponding angles, β_H, in the hosts, due to the size mismatching substitution of Mg²⁺ by Ni²⁺. The theoretical results based on the inclusion of the ligand s-orbital contributions show an improvement when compared with those in the absence of the above contributions, especially for the ligand I^?.     

Studies on the local structures and the spin Hamiltonian parameters for Fe3+ in CdX (X = S,Se, Te)

The improved perturbation formulas of the spin Hamiltonian parameters (zero-field splitting D and g factors) for a 3d⁵ ion in trigonally distorted tetrahedra are constructed from the cluster approach by including both the crystal-field and charge-transfer contributions. These formulas are applied to the studies of the local structures and the electron paramagnetic resonance (EPR) spectra for Fe³⁺ in CdX (X = S, Se, Te). The impurity Fe³⁺ is found not to occupy exactly the host Cd²⁺ sites but to experience the small outward shifts 0.014 and 0.006 Å away from the ligand triangles along the C₃ axis in CdS and CdSe, respectively. The charge-transfer contributions to the spin Hamiltonian parameters are important and increase significantly with increasing atomic number of the ligand (i.e., S^2? < Se^2? < Te^2?) arising from the decreases of charge-transfer energy levels and the increases of ligand spin–orbit coupling coefficients. The results are discussed.