College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.
J Chem Phys. 2018 Nov 21;149(19):194104. doi: 10.1063/1.5057355.
We present an accurate and efficient formulation of the stress tensor for real-space Kohn-Sham density functional theory calculations. Specifically, while employing a local formulation of the electrostatics, we derive a linear-scaling expression for the stress tensor that is applicable to simulations with unit cells of arbitrary symmetry, semilocal exchange-correlation functionals, and Brillouin zone integration. In particular, we rewrite the contributions arising from the self-energy and the nonlocal pseudopotential energy to make them amenable to the real-space finite-difference discretization, achieving up to three orders of magnitude improvement in the accuracy of the computed stresses. Using examples representative of static and dynamic calculations, we verify the accuracy and efficiency of the proposed formulation. In particular, we demonstrate high rates of convergence with spatial discretization, consistency between the computed energy and the stress tensor, and very good agreement with reference planewave results.
我们提出了一种用于实空间 Kohn-Sham 密度泛函理论计算的精确而高效的应力张量公式。具体来说，虽然采用了静电的局部公式，但我们推导出了一种适用于具有任意对称性的单元、半局部交换相关泛函和布里渊区积分的线性标度的应力张量表达式。特别地，我们重写了自能和非局域赝势能能量的贡献，以使它们适用于实空间有限差分离散化，从而使计算出的应力的精度提高了三个数量级。通过具有代表性的静态和动态计算示例，我们验证了所提出公式的准确性和效率。特别地，我们展示了随着空间离散化的高收敛速度、计算出的能量和应力张量之间的一致性以及与参考平面波结果的非常好的一致性。
