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.