Abstract
We develop and analyze QM/MM (quantum/classic) hybrid methods for crystalline defects within the context of the tight-binding model. QM/MM methods employ accurate quantum mechanics (QM) models only in regions of interest (defects) and switch to computationally cheaper interatomic potential molecular mechanics (MM) models to describe the crystalline bulk. We propose new energy-based and force-based QM/MM methods, building on two principles: (i) locality of the QM model; and (ii) constructing the MM model as an explicit and controllable approximation of the QM model. This approach enables us to rigorously establish convergence rates in terms of the size of the QM region.
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