Notice that since energies are negative for a ground state problem, the denominator of Eq. 17 cannot diverge even if E (0) I approaches E (0) as long as E and E are non-zero. Since zero cumulative correction of the energy at second order implies that the unperturbed wavefunctions already describe the system exactly, this case can in practice be neglected. Thus, BW2 is a regular perturbation theory for all systems of interest.