The complete energy matrix including all the spin states is constructed for d4ions in tetragonal symmetry within a strong-field representation. The excitationlevels, fine-structure splitting, and EPR parameters in Rb2CrCl4 and CrF2 arestudied with the energy matrix. The contributions of the spin singlets to zerofieldsplitting (ZFS) are investigated for the first time. The results show thatthe spin-singlet contribution to D is negligible, but the contributions to a and Fcannot be neglected.

An analysis of the relationship between the EPR trigonal-field parameters and the local crystal structure of octahedral Mn2+ centre indiamagnetic garnets is presented by diagonalizing the complete energy matrices for a d5 configuration ion in a trigonal ligand-field. Boththe second-order and fourth-order EPR parameters D and (a-F) are taken simultaneously into the structural investigation. It is shownthat the local lattice structure around an octahedrally coordinated Mn2+ centre in diamagnetic garnets have expansion distortions, whichmay be attributed to the fact that the radius of Mn2+ ion is larger than that of Al3+ or Ga3+ ion, and the Mn2+ ion will push the oxygenligands outwards. The local lattice structure parameters R and h for octahedral Mn2+ ion centre in the crystals are determined, respectively.Meanwhile, it is also demonstrated that the empirical impurity-ligand distance R RH

A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizingthe complete energy matrices for a d5 configuration ion in a trigonal ligand field. As for ZnO: Fe3+system, the local lattice distortion forthe tetrahedral Fe3+ centers in zinc oxide has been investigated by considering the second-order and fourth-order EPR parameters D and (a-F) simultaneously. The results indicate that the local lattice structure around tetrahedral Fe3+ centers exhibits a compression distortion, i.e., the (FeO4) 5 entity in ZnO: Fe3+ system is smaller than the (ZnO) 6entity in ZnO crystal. The local lattice structure distortionparameters DR =0.119 A and Dh=0.339for Fe3+ion in ZnO: Fe3+ system are determined. Furthermore, thedisplacements DZ1=0.050 A for transition-metal ion along the C3 axis, and DZ2=0.169 A for the distance variation between theO2 along the C3 axis and the lower oxygen plane are obtained.

The EPR zero-field splitting parameters and structural distortion of Mn2+-doped (CH3)4NCdCl3 crystal in high-temperature phaseshave been studied by diagonalizing the complete energy matrices. The zero-field splitting parameters D and (aF) are demonstrated tobe negative and positive, respectively, and obtain a reasonable explanation together. Simultaneously, the distortion magnitude of locallattice structure around the Mn2+ ion in this crystal is determined, namely, DR=0.13A ˚ and Dh=2.975for T=124 K; DR =0.12A ˚ and Dh=2.610for T=297 K; DR=0.26A ˚ and Dh=2.870for T=573K. From the structural distortion, we deducethat a new structural phase transition should occur to the (CH3) 4NCdCl3 crystal at temperatures ranging from 297 to 573 K. This is alsoin agreement with recent differential scanning calorimetric measurements.

By diagonalizing the complete energy matrices for a d5 configuration ion in a trigonal ligand-field and considering the second-order,fourth-order EPR parameters D and (a-F) simultaneously, the substitution position of Mn2+ion in the CaCO3: Mn2+system has beenstudied by analyzing the optical absorption and EPR spectra of single crystal and the ostracum layer of operculum of fresh water snailPila globosa. The results show that in the single crystal there is an obvious compressed distortion DR=0.158A and Dh=0.70, and thedistortion in P. globosa is DR=0.107A and Dh=0.34～0.23. Meanwhile the EPR parameters 104(a-F)=7.02-7.29cm 1 and104a=6.35cm 1 are predicted in P.globosa.

The EPR spectra of octahedral Fe3+ center in lutetium aluminum garnet have been studied by means of the complete energy matricesfor a d5 configuration ion in a trigonal ligand–field. It is manifested that the local lattice structure around an octahedrally coordinatedFe3+ center has an expansion distortion from that of undistorted host Al3+ ion. The expansion distortion can be ascribed to the fact thatthe radius of Fe3+ ion is bigger than that of Al3+ion, and consequently the Fe3+ ion pushes the oxygen ligands outwards. Simultaneously,for the octahedral Fe3+ center in the crystal, the local lattice structure parameters, R=(2.007±0.022)A andh=(52.708 ± 0.032), which reflect the interactions between impurity and crystal lattice, are determined from our calculation, andEPR parameters a, D, and (a-F) also get a unified explanation.

A covalent heterodinuclear magnetic exchange interaction formula has been established and the antiferromagneticcoupling phenomena of both heterodinuclear MnIIIFeIII and homodinuclear FeIIFeII spin-clusters in complex moleculeshave been studied. It is demonstrated that the antiferromagnetic phenomenon of transition-metal ion-pairs in moleculesshould be attributed to the combined effect of the direct-exchange interaction, the kinetic exchange interaction and thecovalent effect; the strong antiferromagnetic characteristic of MnIIIFeIII cluster in [L0MnIII

A theoretical method for describing magnetic-exchange-interactions in covalent molecular systems is established byintroducing covalent effect into Girerd-Journaux-Kahn’s (GJK) magnetic formula and adopting our Double-Slater-Function (DSF) calculation method. The calculations show that the exchange coupling parameter J depends sensitivelyon the covalent factor N; the stronger the covalent effect the stronger the antiferromagnetic exchange interaction; thedirect-and kinetic-exchange interactions are both important. The calculation for MnIII-O-MnIII spin-clusters inMn2Oð5-NO2saldienÞ2 reveals that about 30% of the antiferromagnetic contribution comes from covalent effect, andthat the theoretical values J ¼111:02 to138:85 cm 1 agree well with the experimental findings ðJðexpt:Þ ¼ 120 cm 1Þ.

A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizing the complete energy matrices for a d5 configuration ion in a trigonal ligand fieldand considering the second-order and fourth-order EPR parameters D and (a - F) simultaneously. As forZnSiF6

A theoretical method for studying the inter-relationships between electronic and molecular structure has beenproposed on the basis of the complete energy matrices of electron-electron repulsion, the ligand field, andthe spin-orbit coupling for the d5 configuration ion in a trigonal ligand field. As an application, the localdistortion structure and temperature dependence of zero-field splitting for Fe3+ ions in the Al2O3:Fe3+ systemhave been investigated. Our results indicate that the local lattice structure of the (FeO6)9- octahedron in theAl2O3: Fe3+ system has an elongated distortion and the value of distortion is associated with the temperature.The elongated distortion may be attributed to the facts that the Fe3+ ion has an obviously larger ionic radiusthan the Al3+ ion and the Fe3+ ion will push the two oxygen triangles upward and downward, respectively,along the 3-fold axis. By diagonalizing the complete energy matrices, we found that the theoretical results ofelectronic transition energies and EPR spectra for Fe3+ ions in the Al2O3: Fe3+system are in good agreementwith the experimental findings. Moreover, to understand the detailed physical and chemical properties of theAl2O3, the theoretical values of the zero-field splitting parameters and the corresponding distortion parametersin the range 50 Ke Te 250 Kare reported first.