Theoretical investigation of optical and paramagnetic resonance spectra of [NiF6](4-) clusters with orthorhombic symmetry.

The ground state absorption spectra of [NiF6](4-) clusters with orthorhombic symmetry (Ni(2+) in NiF2 crystal and Ni(2+)-doped ZnF2 crystal, D2h point group) are theoretically calculated and assigned by diagonalization of 45×45 complete energy matrix for 3d(8) configuration and the spin-Hamiltonian (SH) parameters (zero-field splitting D and E, and g factors gx, gy, gz) are studied by use of high-order perturbation method, in the frame of semi-empirical molecular orbital (MO) scheme based on strong crystal field framework. In those energy matrix, all the configuration interactions though the cubic crystal field (CF), the orthorhombic crystal field, the Coulomb interaction are taken into account. The calculated results are in good agreement with the experimental data.

Spin-Hamiltonian parameters for the tetragonal Gd(M)3+-F(i)- centers in CaF(2) and SrF(2) crystals.

The spin-Hamiltonian parameters (g factors g(//), g(⊥) and zero-field splittings b(2)(0), b(4)(0), b(4)(4), b(6)(0), b(6)(4)) of the tetragonal Gd(M)(3+)-F(i)(-) centers in CaF(2) and SrF(2) crystals at T≈1.8K are calculated from the diagonalization (of energy matrix) method based on the one-electron crystal field mechanism. In the calculations, the crystal field parameters used are estimated from the superposition model with the reported defect structural data obtained from the analyses of superhyperfire interaction constants at the same temperature.

Theoretical investigations of optical spectra and electron paramagnetic resonance spectra of LiCl:Ni²⁺ crystals.

The complete energy matrices (45 × 45) including low symmetry ligand field (C(4v)) and Coulomb interactions for 3d(8) ions have been constructed, and the high-order perturbation formulas of spin-Hamiltonian (SH) parameters g factors g(//), g(⊥) and zero-field splitting (ZFS) parameter D for ground state (3)A(2g) of the 3d(8) ions in the tetragonal symmetry environment have been derived. In those formulas both the crystal field (CF) mechanism and the charge transfer (CT) mechanism are taken into account. The complete energy matrices and the high-order perturbation formulas are applied to calculate the energy levels and SH parameters of the Ni(2+) ion in LiCl crystal respectively.

Research on the optical spectra, g factors and defect structures for two tetragonal Y²+ centers in the irradiated CaF₂: Y crystal.

Based on the defect models that the tetragonal Y(2+) (1) center in the irradiated CaF(2): Y crystal is due to Y(2+) at Ca(2+) site associated with a nearest interstitial F(-) ion along C(4) axis and the tetragonal Y(2+) (2) center is Y(2+) at Ca(2+) site where the tetragonal distortion is caused by the static Jahn-Teller effect, the two optical spectral bands and anisotropic g factors for both tetragonal Y(2+) centers are calculated. The calculations are made by using two methods based on the cluster approach, one is the complete diagonalization (of energy matrix) method (CDM) and another is the perturbation theory method (PTM). The calculated results for each Y(2+) center from CDM and PTM coincide and show reasonable agreement with the experimental values.

Studies of the spin-Hamiltonian parameters and defect structures for the tetragonal and cubic Yb3+ centers in AgCl crystal.

The spin-Hamiltonian parameters, g factors and hyperfine structure constants, for the tetragonal and cubic Yb(3+) centers in AgCl crystal are calculated from the complete diagonalization (of energy matrix) method. The calculations are based on the defect models that the tetragonal Yb(3+) center is formed by the substitutional Yb(3+) associated with two nearest Ag(+) vacancy (V(Ag)) along <001> and <001¯> axes (i.e.

Studies of the optical band positions and EPR g factors for Cu(H2O)6(2+) centers in Tutton salt crystals.

The optical band positions and EPR g factors g(i) (i = x, y, z) of Cu(H(2)O)(6)(2+) clusters in pure Tutton salts M(2)Cu(SO(4))(2)·6H(2)O (M = NH(4), Rb) are calculated from the complete diagonalization (of energy matrix) method based on the cluster approach. In the calculation, the superposition model with the structural data is used to obtain the crystal-field parameters. The calculated results are in reasonable agreement with the experimental values, suggesting that the complete diagonalization method and superposition model are effective in the studies of optical and EPR data.

Studies of the spin-Hamiltonian parameters and defect structures for Gd3+ ions in zircon-structure silicates MSiO4 (M=Zr, Hf, Th).

The spin-Hamiltonian parameters (g factors g∥, g⊥ and zero-field splittings b2(0), b4(0), b4(4), b6(0), b6(4)) for 4f7 ion Gd3+ at the tetragonal M4+ site of zircon-structure silicates MSiO4 (M=Zr, Hf, Th) are calculated from a diagonalization (of energy matrix) method. The Hamiltonian concerning this energy matrix contains the free-ion, crystal-field interaction and Zeeman interaction terms and the 56×56 energy matrix is constructed by considering the ground multiplet 8S7/2 and the excited multiplets 6L7/2 (L=P, D, F, G, H, I). The defect structures of Gd3+ centers in the three MSiO4 crystals are yielded from the calculation.

A theoretical study on the temperature dependence of zero-field splitting for the tetragonal Cr3+ center in MgO crystal.

This paper reports a detailed theoretical calculation of the temperature dependence of zero-field splitting D (characterized by ΔD(T)=D(T)-D(0)) for the tetragonal Cr3+ center in MgO crystal by considering both the static contribution due to the thermal expansion of Cr3+ center and the vibrational contribution caused by electron-phonon (including the acoustic and optical phonons) interaction. The vibrational contribution due to the acoustic phonon is calculated using the long-wave approximation similar to the study on the specific heat of crystals and that due to optical phonon is estimated using the single-phonon model. The calculated results are in reasonable agreement with the experimental values.

Spin-Hamiltonian parameters and defect structure for the rhombic Dy3+ center in AgCl crystal.

Based on the defect model that the rhombic Dy(3+) center in AgCl crystal is formed by substitutional Dy3+ ion associated with two nearest Ag+ vacancies (VAg) along the <110> and <110> axes owing to charge compensation, the spin-Hamiltonian parameters (g factors gi and hyperfine structure constants 161Ai and 163Ai, where i=x, y, z) of this rhombic Dy3+ center are calculated from a diagonalization (of energy matrix) method. In the method, the Zeeman (or magnetic) and hyperfine interaction terms are attached to the classical Hamiltonian used in the calculation of crystal-field energy levels and a 66×66 energy matrix concerning this Hamiltonian is constructed by taking all the ground-term multiplets 6HJ (J=15/2, 13/2, 11/2, 9/2, 7/2, 5/2) into account. The calculated results (g factors gi and average |A(161Dy3+)| and |A(163Dy3+)|) are in reasonable agreement with the experimental values.

A study of the spin-Hamiltonian parameters for the trigonal Sm3+ center in La2Mg3(NO3)(12)·24H2O crystal.

This paper reports a theoretical calculation of spin-Hamiltonian parameters (g factors g//, g⊥ and hyperfine structure constants 147A//, 147A⊥, 149A//, 149A⊥) for 147Sm3+ and 149Sm3+ isotopes in the trigonal La3+ site of La2Mg3(NO3)(12)·24H2O crystal from a diagonalization (of energy matrix) method. In the method, the Hamiltonian concerning the energy matrix includes the Zeeman and hyperfine interaction terms and so there is no perturbation calculation in it. The crystal-field parameters in the energy matrix are calculated using the superposition model, in which the structural data of 12-fold coordinated site rather than those of the incorrect 6-fold coordinated site given in the previous paper are applied.

Studies on the spin-Hamiltonian parameters of CuN(6) clusters and their tetragonal distortions due to Jahn-Teller effect for Cu2+ in trigonal M(1-propyltetrazole)6(BF4)2 (M=Zn, Fe) crystals.

This paper reports the theoretical calculations for the anisotropic and isotropic spin-Hamiltonian parameters (g factors and the hyperfine structure constants) of tetragonal CuN6 octahedral clusters due, respectively, to the static and dynamic Jahn-Teller effects for Cu2+ ion in the trigonal M(=Zn, Fe) sites of M(1-propyltetrazole)6(BF4)2 crystals. The calculations are carried out using the high-order perturbation formulas based on a two-mechanism model, in which besides the contributions to spin-Hamiltonian parameters due to the crystal-field mechanism concerning the crystal-field excited states in the extensively used crystal-field theory, the contributions due to charge-transfer mechanism concerning the charge-transfer excited states (which are neglected in the crystal-field theory) are included. The calculated results are in reasonable agreement with the experimental values.

Studies of the EPR parameters and defect models for three Er3+ impurity centers in ThO2 crystals.

The electron paramagnetic resonance (EPR) parameters (g factors and hyperfine structure constants of the ground state, and g factors of the first excited state) of three (one cubic and two trigonal) Er(3+) centers in fluoride-type ThO(2) crystal are studied from a diagonalization (of energy matrix) method. In the method, the Zeeman and hyperfine interaction terms are added to the classical Hamiltonian, and a 52 x 52 energy matrix concerning the ground multiplet (4)I(15/2) and the first to third excited multiplets (4)I(13/2), (4)I(11/2) and (4)I(9/2) is established for a 4f(11) ion in trigonal crystal field and under an external magnetic field. From the studies, the EPR parameters for three Er(3+) centers in ThO(2) are reasonably explained, the defect models for the two trigonal Er(3+) centers suggested in the previous paper are confirmed and the defect structures of the two trigonal centers are obtained.

Spin-Hamiltonian parameters and angular distortion for the trigonal Nd(3+) center in congruent LiNbO(3).

The 52x52 energy matrix related to the ground multiplet (4)I(9/2) and the first to third excited multiplets (4)I(11/2), (4)I(13/2) and (4)I(15/2) for 4f(3) ions in trigonal crystal field under an external magnetic field is established. By diagonalizing the energy matrix, the spin-Hamiltonian parameters (g factor g(parallel), g(perpendicular) and hyperfine structure constants (143)A(parallel), (143)A( perpendicular), (145)A(parallel), (145)A( perpendicular)) of the trigonal Nd(3+) center in congruent LiNbO(3) crystal are calculated. The calculated results are in reasonable agreement with the experimental values.

Studies of the spin-Hamiltonian parameters and the Jahn-Teller distortions for tetragonal Cu(H(2)O)(6)(2+) clusters in trigonal A(2)Mg(3)(NO(3))(12).24H(2)O (A=La, Bi) crystals.

The anisotropic and isotropic spin-Hamiltonian parameters (g factors and hyperfine structure constants) of tetragonal Cu(H(2)O)(6)(2+) clusters due, respectively, to the static and dynamic Jahn-Teller effects for Cu(2+) in trigonal A(2)Mg(3)(NO(3))(12).24H(2)O (A=La, Bi) crystals are calculated from the high-order perturbation formulas based on the cluster approach. In the approach, the admixture between the d orbitals of 3d(n) ion and the p orbitals of ligand ion via covalence effect is considered.

Investigations of the optical spectra and EPR g factors for the tetragonal Cu2+ centers in trigonal ZnCO3 crystal.

Two distinctive theoretical methods, the complete diagonalization (of energy matrix) method (CDM) and the perturbation theory method (PTM), are employed to calculate the optical band positions and EPR g factors g(||), g(perpendicular) for the tetragonal Cu(2+) centers in trigonal ZnCO(3) crystal. The results from the two methods coincide and are also in good agreement with the experimental values. So both the CDM and PTM are adequate for the investigations of optical and EPR data for d(9) ions in crystals.

Defect structure and spin-Hamiltonian parameters for the CuCl(6)(4-) cluster in the tetragonal RbCdCl(3):Cu(2+) crystal.

The tetragonal distortion (characterized by R( parallel)-R( perpendicular) where R( parallel) and R( perpendicular) denote the metal-ligand distances parallel with and perpendicular to the tetragonal axis, respectively) for CuCl(6)(4-) cluster in the tetragonal RbCdCl(3):Cu(2+) crystal is studied by calculating its spin-Hamiltonian (SH) parameters (g factors g( parallel), g( perpendicular) and hyperfine structure constants A( parallel), A( perpendicular)). The calculations are performed by using the complete high-order perturbation formulas for 3d(9) ions in tetragonal symmetry based on a two-mechanism model, in which both the widely-used crystal-field (CF) mechanism and the charge-transfer (CT) mechanism (which is omitted in CF theory) are considered. From the calculations, the SH parameters are reasonably explained and the tetragonal distortion R( parallel)-R( perpendicular) approximately 0.

[Studies of the g factor and optical spectra for CaZrO3:Mn4+ crystal].

The complete high-order perturbation formula of g factor for 3d(3) ions in cubic octahedral site was derived. In the formula, both the contribution delta g(CF) to g-shift delta g (= g-g(s), where g(s) = 2.0023) due to crystal-field (CF) mechanism (related to the interactions of CF excited states with the ground state) and that (delta g(CT)) due to charge-transfer (CT) mechanism (related to the interactions of CT excited states with the ground state, which is omitted in crystal-field theory) are included.

Spin-Hamiltonian parameters and local structures for Co4+ and Ir4+ impurity centers in the tetragonal phase of SrTiO3.

The calculated results in the recent paper about the spin-Hamiltonian (SH) parameters (g factors g (//), g perpendicular and hyperfine structure constants A(//), A perpendicular) and the local structures of Co4+ and Ir4+ impurity centers in the tetragonal phase of SrTiO3 are doubtful because there are several mistakes in the calculations. So, we restudy the SH parameters and local structures by using the correct methods and parameters. From the studies, for Co4+ and Ir4+ in SrTiO3, the SH parameters are explained rationally, the signs of hyperfine structure constants A(//), A perpendicular are obtained and the suitable and more detailed local structures are given.

EPR parameters and defect structures for the Co2+ ions in LiNbO3 and LiTaO3 crystals.

The electron paramagnetic resonance (EPR) parameters (g factors g parallel, g perpendicular and hyperfine structure constants A parallel, A perpendicular) for Co2+ ions in LiNbO3 and LiTaO3 crystals are calculated from the second-order perturbation formulas based on the cluster approach for 3d7 ions in trigonal octahedral clusters. The calculated results are in reasonable agreement with the experimental values. From the calculations, the negative sign of A parallel for Co2+ in the two crystals and the more exact and rational values of A parallel for Co2+ in LiTaO3 are suggested.

Investigations of the optical and EPR spectra for VO2+ in LiKSO4 crystals.

The optical spectra and EPR spectra (characterized by the spin-Hamiltonian parameters g(//), g(perpendicular), A(//) and A(perpendicular)) for the molecular ion VO2+ in LiKSO4 crystals are calculated from two microscopic theory methods, one of which is the complete diagonalization (of energy matrix) method (CDM) and the other is the perturbation theory method (PTM). The calculated three optical absorption bands and four spin-Hamiltonian parameters from the two methods are not only close to each other, but also in reasonable agreement with the experimental values. It appears that both theoretical methods are effective in the explanation of optical and EPR spectra for 3d1 ions in crystals.

Theoretical calculations of spin-Hamiltonian parameters for CsCdX(3):Ni(2+) (X=Cl, Br) crystals from the two-mechanism model.

The high-order perturbation formulas of spin-Hamiltonian (SH) parameters (g factors g( parallel), g( perpendicular) and zero-field splitting D) for 3d(8) ions in trigonal octahedral sites of crystals are derived considering not only the crystal-field (CF) mechanism, but also the charge-transfer (CT) mechanism (which is neglected in the extensively used CF theory). From these formulas and by considering the suitable impurity-induced local lattice relaxation, the SH parameters of CsCdX(3):Ni(2+) (X=Cl, Br) crystals are calculated. The results are in reasonable agreement with the experimental values.

Zero-field splittings and local tilting angles tauMn2+ for Mn2+ in ZnGeP2 and CdGeP2 crystals.

The electron paramagnetic resonance (EPR) zero-field splittings (ZFSs) D of Mn2+ in ZnGeP2 and CdGeP2 crystals are calculated from both the microscopic spin-orbit coupling mechanism and the empirical superposition model. From the calculations, the ZFS D of ZnGeP2:Mn2+ is reasonably explained by using the local tilting angle tauMn2+ (rather than the corresponding angle tauZn2+ in the host crystal) and the local tilting angle tauMn2+ (which has not been reported) in CdGeP2:Mn2+ is estimated. The intrinsic ZFS parameter b2(R0) approximately -0.

Defect model and EPR parameters for the tetragonal Yb3+ center in KTaO3 crystal.

The defect model of the tetragonal Yb3+ (at K+ site) center in KTaO3 crystal is suggested, i.e., Yb3+ ion does not occupy the ideal K+ site, but is displaced by an amount DeltaZ along one of 100 axes because of the much smaller ionic radius of Yb3+ compared with that of the replaced K+.

[Investigation of optical and EPR spectra of ZnO : V3+ crystal].

In the present paper, the 45 X 45 energy matrix of the 3d2 ions in trigonal symmetry with the strong-field-coupling mechanism is established. The forty-five optical energy levels and five EPR parameters (including the zero-field splitting D, g factors g//, g perpendicular and hyperfine structure constants A//, A perpendicular) of ZnO : V3+ cryst are calculated from the diagonalization of this complete energy matrix. The calculated results are in agreement with the observed values.