  QM/MM hybrid methods employ accurate quantum (QM) models only in regions of
interest (defects) and switch to computationally cheaper interatomic potential
(MM) models to describe the crystalline bulk.
  We develop two QM/MM hybrid methods for crystalline defect simulations, an
energy-based and a force-based formulation, employing a tight binding QM model.
Both methods build 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 establish explicit convergence rates in
terms of the size of QM region.
