基于数值原子中心轨道的准四分量相对论密度泛函理论的大规模并行实现
A Large-scale Parallel Implementation of Quasi-Four-Component Relativistic Density Functional Theory with Numeric Atom-centered Orbitals
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中文总结 AI 辅助
本研究实现了基于数值原子中心轨道的准四分量相对论DFT的大规模并行版本，通过ELPA库求解本征值问题，在含3383个原子的钙钛矿体系上验证了其高效可扩展性，拓展了相对论DFT的应用规模。
中文摘要 AI 辅助
我们提出了一种针对分子和周期性固体的完全相对论密度泛函理论（DFT）的大规模并行实现，采用准四分量（Q4C）方法和数值原子中心轨道基组。该方法在非均匀实空间积分网格上应用域分解方法，通过高效的分布式内存和计算并行实空间操作实现Q4C哈密顿矩阵元的N阶缩放积分。接着，我们构建二维块循环分布布局的哈密顿矩阵和重叠矩阵，所得广义本征值问题采用大规模并行ELPA本征值求解库求解。我们在多个MPI任务和计算节点上对内存使用、并行效率和可扩展性进行基准测试。该算法拓展了周期性固体完全相对论DFT模拟的应用范围，测试单元胞原子数达3383个（基函数数216628个），且可能仍远低于该实现的实际极限。作为演示，我们计算了单元胞含3383个原子的掺杂有机-无机杂化钙钛矿(PEA)₂(Pb₁₋ₓBiₓ)I₄（PEA=苯乙铵）的完全相对论能带结构，在336至672个物理CPU核心间展现出近乎理想的可扩展性。
英文摘要
We present a large-scale parallel implementation of fully relativistic density functional theory (DFT) for both molecules and periodic solids, using the quasi-four-component (Q4C) method and numeric atom-centered orbital basis sets. Our approach employs a domain decomposition method on nonuniform real-space integration grids, which enables order-N integration of the Q4C Hamiltonian matrix elements using efficient, distributed-memory and compute-parallel real-space operations. Next, we build the Hamiltonian and overlap matrices in a two-dimensional block-cyclic distribution layout. The resulting generalized eigenvalue problems are solved with the massively parallel ELPA eigenvalue solver library. We benchmark memory usage, parallel efficiency, and scalability across multiple MPI tasks and compute nodes. This algorithm extends the reach of fully relativistic DFT simulations for periodic solids, tested up to 3,383 atoms per unit cell (216,628 basis functions) and likely still well below the true reach of the implementation. As a demonstration, we calculate the fully relativistic band structure for a 3,383 atom-per-unit-cell doped hybrid organic-inorganic perovskite, (PEA)2(Pb1-xBix)I4 (PEA=phenethylammonium), showing nearly ideal scalability between 336 and 672 physical CPU cores.
