Geometry equilibration of crystalline defects in quantum and atomistic descriptions

We develop a rigorous framework for modeling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problem on a discrete energy space and establish qualitatively sharp far-field decay estimates for the equilibrium configuration. This work extends [V. Ehrlacher, C. Ortner and A. Shapeev, Analysis of boundary conditions for crystal defect atomistic simulations, Arch. Ration. Mech. Anal. 222 (2016) 1217–1268] by admitting infinite-range interaction which in particular includes some quantum chemistry based interatomic interactions.