2.4. Quantum Chemistry Calculations. The primary electronic structure method used in this work is HF-3c, which starts from a minimal-basis Hartree-Fock (HF) calculation then add three empirical corrections. The latter are parameterized for use with a specific basis set ("MINIX"), so in what follows we will not indicate the basis set for HF-3c calculations, as it is always MINIX. Some conventional DFT calculations are performed as well, using the ωB97X-V functional 54 as a representative example that performs well for smallmolecule van der Waals complexes. (For molecules with 100 atoms, DFT performs less well; 56 fragmentation may be a useful approach to exploit its better performance in small non-covalent complexes.) Basis sets used for the ωB97X-V calculations are minimally augmented ("ma") versions of the standard Karlsruhe basis sets, which are known as def2-ma-SVP, def2-ma-TZVP, and def2-ma-QZVP. (These are proper subsets of the basis sets def2-SVPD, def2-TZVPD, and def2-QZVPD. ) Diffuse basis functions are important for non-covalent DFT calculations, even when triple-ζ basis sets are employed, but minimal augmentation appears to be sufficient. Our preference for the simple MBE(n) fragmentation scheme that is described in Sec-tion 2 .1, without any kind of charge embedding, is based on a desire to use diffuse basis functions and large basis sets. Fragment-based charge embedding tends to be unstable in the presence of diffuse basis functions. For all calculations, the self-consistent field convergence threshold was set to 10 -8 E h and the integral and shellpair drop tolerances were both set to 10 -12 a.u.. The latter setting is appropriate for calculations in mediumsize molecules where diffuse functions are used, as looser thresholds may engender convergence problems. Previous work applying MBE(n) to thermochemical calculations in large enzyme models has demonstrated that low-dielectric boundary conditions are necessary to make MBE(n) converge in the presence of ionic fragments, as will inevitably arise when native protonation states are considered. Therefore, all quantum chemistry calculations reported here use a conductor-like polarizable continuum model (C-PCM), with a dielectric constant ε = 4. This is implemented using the switching/ Gaussian discretization procedure. C-PCM calculations use a van der Waals molecular cavity, constructed from modified Bondi atomic radii, with R vdW = 1.2R Bondi . The van der Waals surface is discretized using atom-centered Lebedev grids. For the n-body DFT calculations, this discretization employs 110 Lebedev points for hydrogen and 194 points for other nuclei, whereas the HF-3c subsystem calculations and the HF-3c full-protein calculations use 50 points for hydrogen and 110 for other nuclei. A conjugate gradient PCM solver was used for the full-protein calculations.