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A theoretical method for investigating the inter-relation between the molecular structure and electronic structure has been established on the basis of the 252 x 252 complete energy matrices for a 3d(5) configuration ion in a tetragonal ligand field. By means of this method, which is independent of the X-ray diffraction, the local structure of the paramagnetic Mn2+ ion in perovskite fluorides A(2)MF(4) (A = K, Rb; M = Zn, Me. Cd) are determined directly by analyzing the EPR spectrum of octahedral Mn2+ center in A(2)MF(4) crystals and the optical absorption spectrum of the (MnF6)(4-) cluster. It is shown that, comparing with the octahedral cubic structure, the local microstructure in the vicinity of Mn2+ displays an elongated distortion when b(2)(0) > 0 and a compressed distortion when b(2)(0) < 0, and Delta R vs. 10(4)b(2)(0) as well as Delta R vs. 10(4)b(4)(0) in the distortion region is, respectively, approximately linear. Simultaneously, the theoretical zero-field-splitting parameters b(2)(0), b(4)(0) and b(4)(4) are in good agreement with the experimental values. (c) 2006 Elsevier Ltd. All rights reserved.