A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizing the complete energy matrices for a d(5) configuration ion in a trigonal ligand field. As for ZnO:Fe3+ system, the local lattice distortion for the 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)(6-) entity in ZnO crystal. The local lattice structure distortion parameters Delta R = -0.119 A and Delta theta = 0.339 degrees for Fe3+ ion in ZnO:Fe3+ system are determined. Furthermore, the displacements Delta Z(1) = -0.050 A for transition-metal ion along the C-3 axis, and Delta Z(2) = -0.169 A for the distance variation between the O-2(-) along the C-3 axis and the lower oxygen plane are obtained. (c) 2006 Elsevier B.V. All rights reserved.