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A new methodology of binding energy calculation with respect to different spin arrangements for a multiatomic electron system is developed from the first principle in the frame of the exchange perturbation theory (EPT). We developed EPT formalism in the general form of the Rayleigh-Srchödinger expansion with a symmetric Hamiltonian, taking into account an exchange and nonadditive contributions of a superexchange interaction. The expressions of all corrections to the energy and wave function were reduced to the nonsymmetric Hamiltonian form. The EPT method is extended for the case of degeneracy in the total spin of a system. As an example of the application of the developed EPT formalism for the degeneracy case, spin arrangements were considered for the key Mn -O-Mn ( Mn : Mn 3+ or Mn 4+ ) fragments in manganites. In Mn -O-Mn for La 1/3 Ca 2/3 MnO 3 are in good agreement the obtained estimations of Heisenberg parameter and binding energy with the available experimental data.

We unify the method of exchange perturbation theory for multicenter systems. For the case of exchange degeneracy in the total spin of the system we give a secular equation that is more compact and convenient for calculations than those obtained earlier. On the basis of this formalism we develop an algorithm for calculating the Heisenberg parameter for magnetic materials. Finally, we calculate the characteristics of antiferromagnetic transitions for the high-Tc materials La 2-x MeCuO 4 and YBa 2 Cu 3 O 6 .

In this paper. weak lonlivtion of a new kind is studied. Within the hamework of the new developing theory, electron exchange is shown to alter the angular distribution of scattered elecbons. The nnge of energies of incident el@" for which exchange effects are important is estimated.

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