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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⟩: Mn3+ or Mn4+) fragments in manganites. In ⟨Mn⟩–O–⟨Mn⟩  for La1/3Ca2/3MnO3 are in  good agreement the obtained estimations of Heisenberg parameter and binding energy with the available experimental data

Exchange Perturbation Theory for Multiatomic Electron System and Its Application to Spin Arrangement in Manganite Chains