Pair-Pair Approximation to the Generalized Many-Body Expansion: An Alternative to the Four-Body Expansion for ab Initio Prediction of Protein Energetics via Molecular Fragmentation.

We introduce a "pair-pair" approximation to the generalized many-body expansion (pp-GMBE) as an approximation to a traditional four-body expansion, the latter of which is accurate but quickly becomes numerically unstable and ultimately intractable as the number of "bodies" (fragments) increases. The pp-GMBE method achieves a good balance between accuracy and efficiency by defining significant fragment pairs and then fragment quartets. An efficient fragmentation scheme is introduced for proteins such that the largest subsystems contain about 60 atoms. Application of the pp-GMBE method to proteins with as many as 70 amino acids (1142 atoms) reveals that pp-GMBE energies are quite faithful to those obtained when the same level of density functional theory is applied to the entire macromolecule. When combined with embedding charges obtained from natural population analysis, the pp-GMBE approach affords absolute energies that differ by 1-3 kcal/mol from full supersystem results, but it yields conformational energy profiles that are practically indistinguishable from the supersystem calculation at the same level of theory.