A theoretical method for studying the inter-relationships between electronic and molecular structure has been proposed on the basis of the complete energy matrices of electron-electron repulsion, the ligand field, and the spin-orbit coupling for the d(5) configuration ion in a trigonal ligand field. As an application, the local distortion structure and temperature dependence of zero-field splitting for Fe3+ ions in the Al2O3: Fe3+ system have been investigated. Our results indicate that the local lattice structure of the (FeO6)(9-) octahedron in the Al2O3: 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 radius than 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 of electronic transition energies and EPR spectra for Fe3+ ions in the Al2O3: Fe3+ system are in good agreement with the experimental findings. Moreover, to understand the detailed physical and chemical properties of the Al2O3, the theoretical values of the zero-field splitting parameters and the corresponding distortion parameters in the range 50 K <= T <= 250 K are reported first.