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Computing the atomic geometry of lattice defects--point defects,dislocations, crack tips, surfaces, or boundaries--requires an accuratecoupling of the local strain field to the long-range elastic field. Periodicboundary conditions used by classical potentials or density-functional theorymay not accurately reproduce the correct bulk response to an isolated defect;this is especially true for dislocations. Recently, flexible boundaryconditions have been developed to produce the correct long-range strain fieldfrom a defect--effectively "embedding" a defect in a finite cell with infinitebulk response, isolating it from either periodic images or free surfaces.Flexible boundary conditions require the calculation of the bulk response withthe lattice Green function (LGF). While the LGF can be computed from thedynamical matrix, for supercell methods (periodic boundary conditions) it canonly be calculated up to a maximum range. We illustrate how to accuratelycalculate the lattice Green function and estimate the error using a cutoffdynamical matrix combined with knowledge of the long-range behavior of thelattice Green function. The effective range of deviation of the lattice Greenfunction from the long-range elastic behavior provides an important lengthscale in multiscale quasi-continuum and flexible boundary-conditioncalculations, and measures the error introduced with periodic boundaryconditions.Comment: 35 pages, 6 figure

Lattice Green function for extended defect calculations: Computation and error estimation with long-range forces