If higher-order terms such as ∆E IJKL are negligible, then the formal complexity of the electronic structure problem is dramatically reduced. By decomposing a large (and potentially intractable) calculation into a collection of independent or loosely-coupled subsystem calculations, fragment-based quantum chemistry represents one of the most promising ways to extend electronic structure theory to exascale computer architectures. The MBE in eqn. (1) forms the basis of a wide variety of fragment-based approximation schemes. These have been used in hybrid quantum mechanics/molecular mechanics approaches, as a basis for developing classical force fields for water-water and ion-water * herbert@chemistry.ohio-state.edu interactions, as a means to elucidate the nature of intermolecular interactions, and as a way to overcome the dimensionality problem in machine learning. In principle, correlated wave function models can be used for the electronic structure, since only small n-body subsystem calculations are required, but density functional theory (DFT) has also been suggested for general use in force-field development. One can imagine the MBE as a means to accelerate DFT-based ab initio molecular dynamics simulations, and the low cost of DFT calculations make this an attractive choice for generating the enormous data sets that are necessary for machine learning applications. It is these DFT-based applications (and potential applications) that concern us.