In this method, pair correlation energies are used for regularization instead of the correlation energy per atom. Consequently, each electron-pair i j has a different regularizer. In this sense, BGE2 is related to the coupled electron pair approximation (CEPA) and xBW2 can be considered an 'averaged' BGE2. This averaging has the advantage that (unlike BGE2) xBW2 is invariant to unitary orbital transformations, although the BGE2 regularization is arguably more flexible. More generally, the interative nature of the xBW2 equation resembles coupled cluster theory, where the coupling between individual amplitudes is replaced by an average coupling term that is the same for all amplitudes.