where Â = ψ (0) | Âψ (0) is an expectation value of an arbitrary operator Â in the reference state ψ (0) . Considering only permutations that exchange only one pair of electrons between interacting monomers, i.e. approximating P ≈ P2 , one can derive an expression for the so-called S 2 approximation of the first-order exchange energy. The expression for E (10) exch (S 2 ) correction in the second quantization approach has been derived and presented for the first time in Ref. 13. Now, let us consider the truncation of the permutation operator expansion at an arbitrary number n. This results in an approximated form