CALANIE: Anisotropic elastic correction to the total energy, to mitigate the effect of periodic boundary conditions

Abstract CALANIE (CALculation of ANIsotropic Elastic energy) computer program evaluates the elastic interaction correction to the total energy of a localized object, for example a defect in a material simulated using an ab initio or molecular statics approach, resulting from the use of periodic boundary conditions. The correction, computed using a fully elastically anisotropic Green’s function formalism, arises from the elastic interaction between a defect and its own periodically translated images. The long-range field of elastic displacements produced by the defect is described in the elastic dipole approximation. Applications of the method are illustrated by two case studies, one involving an ab initio investigation of point defects and vacancy migration in FCC gold, and another a molecular statics simulation of a dislocation loop. We explore the convergence of the method as a function of the simulation cell size, and note the significance of taking into account the elastic correction in the limit where the size of the defect is comparable with the size of the simulation cell. Program summary Program Title: CALANIE, version 2.0 Program Files doi: http://dx.doi.org/10.17632/3h6xffk9h6.1 Licensing provisions: Apache License, Version 2.0 Programming language: C/C++ Nature of problem: Periodic boundary conditions (PBCs) are often used in the context of ab initio and molecular statics atomic scale simulations. A localized defect in a crystalline material, simulated using PBCs, interacts elastically with its own periodically translated images, and this gives rise to a systematic error in the computed defect formation and migration energies. Evaluating the correction to the total energy resulting from effects of elastic interaction between a defect and its periodic images, to alleviate the contribution to the total energy arising from PBCs, is an essential aspect of any accurate total energy calculation performed using PBCs. Solution method: The energy of interaction between a localized defect and its periodically translated images is computed in the linear elasticity approximation. The energy of elastic interaction is expressed analytically in terms of the elastic dipole tensor of the defect and elastic Green’s function. Elements of the dipole tensor are computed as a part of the simulation evaluating the formation energy of the defect. Elastic Green’s function and its first and second derivatives are computed numerically from the elastic constants of the material. The method and the corresponding numerical procedures are implemented in the CALANIE computer program. The program evaluates matrix elements of the elastic dipole tensor of a localized defect and the elastic correction to the total energy arising from the use of periodic boundary conditions. Restrictions: The approach assumes the validity of the linear elasticity approximation. This limits the accuracy of evaluation of the elastic correction, which becomes less precise if the size of the defect is comparable with the size of the simulation cell. Unusual features: An open source code, containing full detail of the relevant theoretical concepts, algorithms and numerical implementation.