Despite the observed uptick in error, the db-MBE(2) still offers a great improvement over the conventional, energy-based approach. With a three-body expansion, both the eb-MBE (3) and the db-MBE(3) approach chemical accuracy. For the protonated water hexamers, the db-MBE(3) further reduces the error to below 1.3 kJ/mol, while it offers little improvement for the deprotonated water hexamers. This indicates a minor discrepancy between the densitybased correction [Eq. ( )], which is calculated using approximate density functionals and HF densities, and the CCSD(T) reference to which it is compared. While the energy of the eb-MBE approaches the exact CCSD(T) value, the HF electron density used in the db-MBE scheme neither approaches an exact CC density nor the DFT density for which the approximate functionals are optimized. Despite this mismatch, the energy error formally approaches zero, as the db-MBE correction, includes only the interaction and will ultimately approach zero at sufficiently high order of the MBE.