论文标题
使用数值原子轨道的大型周期系统的有效混合密度计算
Efficient Hybrid Density Functional Calculations for Large Periodic Systems Using Numerical Atomic Orbitals
论文作者
论文摘要
我们为在数值原子轨道（NAO）基础函数框架内构建（筛选）Hartree-fock Exchange（HFX）矩阵的（筛选）Hartree-fock Exchange（HFX）矩阵的有效，线性规模的实现。我们的实现是基于身份近似的局部分辨率，通过仅计算两个中心数量，可以获得两电子库仑排斥积分，这一功能对NAOS非常有益。通过利用基本功能的局部性和中间三指张量的有效预筛选，可以实现相对于系统大小构建HFX矩阵的计算成本的线性缩放。由于MPI/OpenMP混合并行化策略，我们的实现非常平行，用于分发计算负载和内存存储。所有这些因素加在一起，以实现大型周期系统的高效混合功能计算。在这项工作中，我们描述了Abacus代码软件包中实现的HFX构建的关键算法和实现详细信息。我们在系统大小和CPU核心的数量方面的实现性能和可伸缩性对于最高4096个原子的选定基准系统得到了证明。
We present an efficient, linear-scaling implementation for building the (screened) Hartree-Fock exchange (HFX) matrix for periodic systems within the framework of numerical atomic orbital (NAO) basis functions. Our implementation is based on the localized resolution of the identity approximation by which two-electron Coulomb repulsion integrals can be obtained by only computing two-center quantities -- a feature that is highly beneficial to NAOs. By exploiting the locality of basis functions and efficient prescreening of the intermediate three- and two-index tensors, one can achieve a linear scaling of the computational cost for building the HFX matrix with respect to the system size. Our implementation is massively parallel, thanks to a MPI/OpenMP hybrid parallelization strategy for distributing the computational load and memory storage. All these factors add together to enable highly efficient hybrid functional calculations for large-scale periodic systems. In this work we describe the key algorithms and implementation details for the HFX build as implemented in the ABACUS code package. The performance and scalability of our implementation with respect to the system size and the number of CPU cores are demonstrated for selected benchmark systems up to 4096 atoms.
