SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems

As the second component of SPARC (Simulation Package for Ab-initio Real-space Calculations), we present an accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory (DFT) for extended systems. Specifically, employing a local formulation of the electrostatics, the Chebyshev polynomial filtered self-consistent field iteration, and a reformulation of the non-local force component, we develop a finite-difference framework wherein both the energy and atomic forces can be efficiently calculated to within desired accuracies in DFT. We demonstrate using a wide variety of materials systems that SPARC achieves high convergence rates in energy and forces with respect to spatial discretization to reference plane-wave result; exponential convergence in energies and forces with respect to vacuum size for slabs and wires; energies and forces that are consistent and display negligible ‘egg-box’ effect; accurate properties of crystals, slabs, and wires; and negligible drift in molecular dynamics simulations. We also demonstrate that the weak and strong scaling behavior of SPARC is similar to well-established and optimized plane-wave implementations for systems consisting up to thousands of electrons, but with a significantly reduced prefactor. Overall, SPARC represents an attractive alternative to plane-wave codes for performing DFT simulations of extended systems.

作为SPARC（从头算实空间计算仿真包，Simulation Package for Ab-initio Real-space Calculations）的第二组成部分，本工作提出了一套针对扩展体系的密度泛函理论（Density Functional Theory, DFT）有限差分建模方案与其并行实现方案，兼具高精度与计算效率。
具体而言，我们通过采用静电学局域化建模、切比雪夫多项式滤波自洽场迭代，以及对非局域力分量的重新表述，构建了一套完整的有限差分计算框架。在此框架下，DFT计算中的总能量与原子受力均可被高效计算至预设精度要求。
我们通过覆盖多种材料体系的测试验证表明：SPARC在空间离散化维度上，相较于基准平面波计算结果，可实现能量与受力的高收敛速率；针对薄片与纳米线结构体系，其能量与受力随超胞真空腔尺寸变化呈现指数级收敛特性；计算所得能量与受力一致性优异，且几乎不存在蛋盒效应（egg-box effect）；可精准预测晶体、薄片与纳米线的物性参数；同时在分子动力学模拟中，体系能量漂移可忽略不计。
此外我们还证实，在包含数千个电子的大规模体系中，SPARC的弱可扩展性与强可扩展性表现与成熟优化的平面波代码相近，但前置计算开销显著更低。
总体而言，针对扩展体系的DFT模拟任务，SPARC是一类极具竞争力的平面波代码替代方案。