A theoretical method for studying the inter-relation between electronic and molecular structure has been proposed by diagonalizingthe complete energy matrices for a d5 configuration ion in a trigonal ligand field. As for ZnO: Fe3+system, the local lattice distortion forthe 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) 6entity in ZnO crystal. The local lattice structure distortionparameters DR =0.119 A and Dh=0.339for Fe3+ion in ZnO: Fe3+ system are determined. Furthermore, thedisplacements DZ1=0.050 A for transition-metal ion along the C3 axis, and DZ2=0.169 A for the distance variation between theO2 along the C3 axis and the lower oxygen plane are obtained.