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.