The electronic structure of trigonal fivefold-coordinated Fe(III) molecules has been studied. Theligand-field model that we use takes into account the covalency effect which modifies the ligand-field pa-rameters. The complete matrices for electron-electron repulsion, ligand-field, and spin-orbit coupling, have been diagonalized, including the Zeeman interaction in the case of magnetic-property calculations. The energy levels position can be expressed as a function of the ratio A/C, A being the energy gap 6.4 1-4E, and the spin-orbit-coupling parameter. It is shown that, by varying this ratio, the intermediate spin level 4E(aT1) can be stabilized as the ground state, instead of the 4A2(aT1) level in the case of a tetragonal distortion. Near the crossover point (6Al-aE transition), strong quantum admixtures and large zero-field splittings occur: the ground Kramers doublet contains 41% high-spin state and 59% 5 intermediate-spin state; the corresponding ground-state wave functions are associated with MJ=

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.

The EPR zero-field splitting of Fe3+in a trigonal-symmetry crystal field has been calculated on the basis of the complete matrices for ligand-field spin-orbit coupling of the d~configuration with C3 symmetry. The absorption spectrum, the EPR zero-field-splitting axial parameters D and F, and the cubic parameter a for the Fc3+ ion in sapphire have been interpreted uniformly.

The relationship between the EPR cubic-field parameter 10g(a), the covalence factor N, and the crystal-field strength Dq has been established by diagonalizing the complete matrices for ligand-field and spin-orbit coupling. A general method for calculating the local thermal-expansion coefficient of the im-purity ion has been proposed. It is shown that the experiment of Rubio and Medrano is in agreement with the infrared and Raman spectra.

Using the method of dynamical algebras, the solution of a homotriparticle linear spin cluster seach particlewith S=1/2d in a rotating magnetic field is obtained. We derive degeneracy energy levels and each level's Berry phase of this system. The Berry phase as a function of v and u has been determined by using the relationbetween the Berry phase and the angular velocityv of the rotating magnetic field as well as the angle ubetween the magnetic field and Zaxis. We obtain the changing diagram of the Berry phase of the basis state.