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 model of the ground state and the magnetic moment of spin crossover of Fe(III) in a cu- bic ligand field has been established by diagonalizing the complete matrices for electron-electron-repulsion, ligand-field, spin-orbit-coupling, and Zeeman interactions. It is shown that the temperature dependence or unusual magnetic moment of Fe(III) in molecules is due to a large zero-field splitting and an asymmetrically high-order Zeeman effect of the electronic states between the high-spin 6A1 and the low-spin 2T2 states.

A quantum admixture model for the d5 configuration of the high-spin T low-spin (HS T LS) transition (6A1T 2T2) Fe(III) complex molecules has been established by using the UCFC scheme. The analysis shows thatthere exists an indirect spin-orbital coupling interaction between the high-spin and low-spin states via theintermediate-spin states. This interaction may be described approximately by two small matrices (the orderis 25 and 14, respectively) of the Hamiltonian, which involves the electron-electron repulsion, the ligandfield,the spin-orbit coupling, and the Zeeman interactions. By diagonalizing these matrices, the electronicand magnetic structures of the Fe(III) molecules in the spin-transition region can be derived. The resultsshow a sensitive dependence on the ratio

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.

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.