I think I've understand why the real Eigenfunctions of Hamiltonian belong to a given irreducible representation and I've read that also MOs have to transform as irreducible representation due to the commutation properties of the individual hamiltonian and the point group operators.
My question is how the fact that real solutions have this symmetry is exploited in practice (no need complex discussions, only intuitive ones). And mainly if and how the fact that we try to construct correct symmetry MOs is exploited in methods like CI.
