while only assuming that the products are strongly orthogonal, as in GFT. For this calculation, we need to find the expressions for the matrix elements Θ Ĥ Φ , in order to build the full-system Hamiltonian matrix in the basis of APC-embedded products. We do this simply by noticing that the two forms of the full-system Hamiltonian, given in equations ( ) and ( ), are of the same shape. This implies that the expressions for Θ Ĥ Φ have to be of the same shape as the GFT expressions ( ), ( ) and (10) for ⟨Θ|H|Φ⟩. Considering the relationships given in expression (15), one sees that only the following modifications