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.

中文翻译：

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CALANIE：对总能量的各向异性弹性校正，以减轻周期性边界条件的影响

摘要 CALANIE（各向异性弹性能计算）计算机程序评估对局部物体总能量的弹性相互作用校正，例如使用从头算或分子静力学方法模拟的材料中的缺陷，由于使用周期性边界条件. 使用完全弹性各向异性格林函数形式计算的校正来自缺陷与其自身周期性平移图像之间的弹性相互作用。由缺陷产生的长程弹性位移场在弹性偶极子近似中描述。该方法的应用通过两个案例研究来说明，一个涉及 FCC 金中点缺陷和空位迁移的从头研究，另一个涉及位错环的分子静力学模拟。我们探索了该方法作为模拟单元大小的函数的收敛性，并注意到在缺陷的大小与模拟单元的大小相当的极限中考虑弹性校正的重要性。程序摘要 程序名称： CALANIE，版本 2.0 程序文件 doi：http://dx.doi.org/10.17632/3h6xffk9h6.1 许可条款：Apache 许可证，版本 2.0 编程语言：C/C++ 问题性质：周期性边界条件（ PBCs）通常用于从头算和分子静力学原子尺度模拟的背景下。晶体材料中的局部缺陷，使用 PBC 模拟，与其自身周期性平移的图像弹性相互作用，这会导致计算出的缺陷形成和迁移能量出现系统误差。评估由缺陷与其周期性图像之间的弹性相互作用产生的总能量的校正，以减轻对 PBC 产生的总能量的贡献，是使用 PBC 执行的任何准确总能量计算的重要方面。求解方法：局部缺陷与其周期性平移图像之间的相互作用能量在线性弹性近似中计算。弹性相互作用的能量用缺陷的弹性偶极张量和弹性格林函数解析表示。计算偶极张量的元素作为评估缺陷形成能量的模拟的一部分。弹性格林函数及其一阶和二阶导数是根据材料的弹性常数进行数值计算的。该方法和相应的数值程序在 CALANIE 计算机程序中实现。该程序评估局部缺陷的弹性偶极张量的矩阵元素以及对使用周期性边界条件产生的总能量的弹性校正。限制： 该方法假定线性弹性近似的有效性。这限制了弹性校正评估的准确性，如果缺陷的大小与模拟单元的大小相当，则弹性校正的评估精度会降低。不寻常的功能：一个开源代码，包含相关理论概念、算法和数值实现的全部细节。该程序评估局部缺陷的弹性偶极张量的矩阵元素以及对使用周期性边界条件产生的总能量的弹性校正。限制： 该方法假定线性弹性近似的有效性。这限制了弹性校正评估的准确性，如果缺陷的大小与模拟单元的大小相当，则弹性校正的评估精度会降低。不寻常的功能：一个开源代码，包含相关理论概念、算法和数值实现的全部细节。该程序评估局部缺陷的弹性偶极张量的矩阵元素以及对使用周期性边界条件产生的总能量的弹性校正。限制： 该方法假定线性弹性近似的有效性。这限制了弹性校正评估的准确性，如果缺陷的大小与模拟单元的大小相当，则弹性校正的评估精度会降低。不寻常的功能：一个开源代码，包含相关理论概念、算法和数值实现的全部细节。如果缺陷的大小与模拟单元的大小相当，则精度会降低。不寻常的功能：一个开源代码，包含相关理论概念、算法和数值实现的全部细节。如果缺陷的大小与模拟单元的大小相当，则精度会降低。不寻常的功能：一个开源代码，包含相关理论概念、算法和数值实现的全部细节。