Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

Quantum-chemical calculations of enzymatic thermochemistry require hundreds of atoms to obtain converged results, severely limiting the levels of theory that can be used. Fragment-based approaches offer a means to circumvent this problem, and we present calculations on enzyme models containing 500–600 atoms using the many-body expansion with three- and four-body terms. Results are compared to benchmarks in which the supramolecular enzyme–substrate complex is described at the same level of theory. When the amino acid fragments contain ionic side chains, the many-body expansion oscillates under vacuum boundary conditions, exaggerating the role of many-body effects. Rapid convergence is restored using low-dielectric boundary conditions. This implies that full-system calculations in the gas phase are inappropriate benchmarks for assessing errors introduced by fragment-based approximations. For calculations with dielectric boundary conditions, a three-body protocol with distance cutoffs retains sub-kcal/mol fidelity with respect to a supersystem calculation at the same level of theory, as does a two-body protocol when combined with a full-system correction at a low-cost level of theory. Both calculations dramatically reduce the cost of large-scale enzymatic thermochemistry, paving the way for application of high-level ab initio methods to very large systems.