Clearly, this energy must diverge if any ∆ ab i j becomes zero, i.e. for metallic systems. In principle a small constant δ could be added to the denominator to avoid this. Such a level-shift prevents the division by zero, thus regularizing the MP2 correlation energy expression. This raises the question of how large the regularizer δ should be, however. Unfortunately, it has been found that there is no simple answer to this question: no single value of δ can both restore Coulson-Fisher points for single bond breaking and retain good thermochemical performance for weakly correlated systems. In other words, the δ -regularization approach is not flexible enough to fix the divergence of MP2 while retaining its merits.