AI 中文总结
该研究在实空间密度泛函理论中提出统一开边界静电学公式，实现对孤立及部分周期系统开边界静电学的系统处理，在SPARC代码中实现该框架，经实例验证其准确高效，可用于计算静态极化率与压电系数。
AI 中文摘要
我们提出了实空间密度泛函理论中的一种静电学公式，该公式能对孤立和部分周期系统的开边界静电学进行系统且统一的处理，包括存在沿开（有限）方向施加的均匀电场的情况。具体而言，我们构建了一个局域静电能泛函，其驻定条件可得到静电势的泊松方程，该方程分别受周期方向上的周期边界条件和开方向上的狄利克雷边界条件约束。我们采用格林函数方法，推导了由系统总电荷密度产生的狄利克雷值的解析表达式，还推导了能量、原子力和应力张量的表达式。我们在大规模并行实空间SPARC电子结构代码中实现了这些推导得到的表达式。通过代表性实例，我们验证了该框架的准确性和效率，证明了计算量随真空尺寸呈指数收敛，且与已有的平面波代码结果吻合度极高，同时在相当精度下所需的真空尺寸显著更小。由于现有实现未提供此类系统的应力，我们转而通过能量的数值导数对其进行验证，发现二者吻合度很高。最后，我们将该框架应用于计算静态极化率和压电系数，所得结果与文献报道的值吻合度极好。
英文摘要
We present an electrostatic formulation in real-space density functional theory that provides a systematic and unified treatment of the open-boundary electrostatics of isolated and partially periodic systems, including in the presence of an applied uniform electric field along the open (finite) directions. Specifically, we formulate a local electrostatic energy functional whose stationarity yields the Poisson equation for the electrostatic potential, subject to periodic and Dirichlet boundary conditions along the periodic and open directions, respectively. Using a Green's function approach, we derive analytical expressions for the Dirichlet values arising from the total charge density of the system. We also derive the expressions for the energy, atomic forces, and stress tensor. We implement the resulting expressions within the large-scale parallel real-space SPARC electronic structure code. Using representative examples, we verify the accuracy and efficiency of the framework, demonstrating exponential convergence of the computed quantities with vacuum size and excellent agreement with established plane-wave codes while requiring significantly less vacuum at comparable accuracy. Since no existing implementation provides the stresses for such systems, we instead verify them against numerical derivatives of the energy, finding close agreement. Finally, we apply the framework to compute static polarizabilities and piezoelectric coefficients, obtaining very good agreement with values reported in the literature.
