Following structure relaxation, most crystallographic water molecules were removed except for those that were directly coordinated to the ligand or to ionic moieties. (All of the ligands are charge neutral, but most of the proteins contain at least one charged moiety.) Structures for 181L and 1LI2 contain two Cl -ions each, and 3HUA contains a charged phosphate group. Within LIDS, the 1MMQ and 1ZP5 structures each contain four charged metal ions (Zn 2+ and Ca 2+ ), with Zn 2+ loosely coordinated to the ligand. Ionic cofactors were combined into a monomer with their nearest residues (within 2.5 Å) to improve monomer stability of the MBE(n) calculations and to reduce the number of fragments. For 1MMQ and 1ZP5, however, Zn 2+ cannot be combined with the ligand because that would be incompatible with computing the interaction energy for removing the ligand. This has implications for the magnitude of the many-body effects in these systems, as discussed in Section 3 .2.