Hamiltonian with a proper permutation symmetry. In its simplest case -referred to as the weak symmetry forcing -the forcing procedure takes the form of a symmetry projection in the energy expressions of the perturbation theory. In contrast, strong symmetry forcing is used to force the correct symmetry of the wavefunction corrections to the perturbation series. In the case of the many-electron theories, the symmetry forcing operator is the antisymmetrizer of all electrons, which can be written in terms of a product of antisymmetrizers of monomer A and B and the operator P , which gathers all possible permutations interchanging electrons between two interacting subsystems