Abstract Small displacement methods have been successfully used to calculate the lattice dynamical properties of crystals. It involves displacing atoms by a small amount in order to calculate the induced forces on all atoms in a supercell for the computation of force constants. Even though these methods are widely in use, to our knowledge, there is no systematic discussion of optimal displacement directions from the crystal’s symmetry point of view nor a rigorous error analysis of such methods. Based on the group theory and point group symmetry of a crystal, we propose displacement directions, with an equivalent concept of the group of k , deduced directly in the Cartesian coordinates rather than the usual fractional coordinates, that maintain the theoretical maximum for the triple product V spanned by the three displacements to avoid possible severe roundoff errors. The proposed displacement directions are generated from a minimal set of irreducible atomic displacements that keep the required independent force calculations to a minimum. We find the error in the calculated force constants explicitly depends on the inverse of V and inaccuracy of the forces. Test systems such as Si, graphene, and orthorhombic Sb 2 S 3 are used to illustrate the method. Our symmetry-adapted atomic displacement method is shown to be very robust in treating low-symmetry cells with a large ‘aspect ratio’ due to huge differences in lattice parameters, use of a large vacuum height, or a very oblique unit cell due to unconventional choice of primitive lattice vectors. It is expected that our atomic displacement strategy can be used to address higher-order interatomic interactions to achieve good accuracy and efficiency.

中文翻译：

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用于晶格动力学研究的有效的对称性适应原子位移方法

摘要 小位移法已成功用于计算晶体的晶格动力学特性。它涉及将原子少量移动，以计算超胞中所有原子的感应力，以计算力常数。尽管这些方法被广泛使用，但据我们所知，没有从晶体对称性的角度对最佳位移方向进行系统讨论，也没有对这些方法进行严格的误差分析。基于群论和晶体的点群对称性，我们提出了位移方向，具有 k 群的等效概念，直接在笛卡尔坐标而不是通常的分数坐标中推导出，保持三个位移跨越的三重乘积 V 的理论最大值，以避免可能的严重舍入误差。建议的位移方向是从一组最小的不可约原子位移中生成的，这些位移将所需的独立力计算保持在最低限度。我们发现计算的力常数的误差明显取决于 V 的倒数和力的不准确性。Si、石墨烯和斜方晶Sb 2 S 3 等测试系统用于说明该方法。由于晶格参数的巨大差异、使用大真空高度或由于非常规而导致的非常倾斜的晶胞，我们的对称适应原子位移方法在处理具有大“纵横比”的低对称晶胞时非常稳健。原始点阵向量的选择。