In the context of exchange interactions, the antisymmetrizer serves as the pivotal operator. Its definition for a case of Symmetry-Adapted Perturbation Theory is given in the equation (2). The antisymmetrization operator for the dimer system can be expressed through the antisymmetrizers of the monomers and the permutation operator P that interchanges the electronic coordinates between the interacting subsystems. Due to the representation of the dimer wavefunction through products of Slater determinants of individual monomers, the action of the antisymmetrizer, in this case, can be reduced to that of the 1 + P operator, with one representing the identity operator, or in other words, the trivial permutation. As stated in equation ( ), the permutation operator P can be represented as a series of P2n operators, each permuting exactly n pairs of electrons. In this section, we demonstrate that in the second quantization formalism, the general P2n operator is defined as