Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, United States.
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States.
J Chem Theory Comput. 2020 Jun 9;16(6):3757-3785. doi: 10.1021/acs.jctc.9b01167. Epub 2020 May 14.
By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal density functional theory (DFT) and thereby furnish a more accurate and reliable description of the underlying electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we describe a linear-scaling approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions (MLWFs)) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based molecular dynamics (AIMD) simulations of large-scale condensed-phase systems of interest at the hybrid DFT level. We focus our theoretical discussion on the integration of this approach into the framework of Car-Parrinello AIMD, and highlight the central role played by the MLWF-product potential (i.e., the solution of Poisson's equation for each corresponding MLWF-product density) in the evaluation of the EXX energy and wave function forces. We then provide a comprehensive description of the exx algorithm implemented in the open-source Quantum ESPRESSO program, which employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the high-performance computing (HPC) resources available on current- and next-generation supercomputer architectures. This is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when AIMD simulations of liquid water are performed in the canonical () ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT-based AIMD simulations of condensed-phase systems containing 500-1000 atoms (e.g., (HO)) with a wall time cost that is comparable to that of semilocal DFT. In doing so, exx takes us one step closer to routinely performing AIMD simulations of complex and large-scale condensed-phase systems for sufficiently long time scales at the hybrid DFT level of theory.
通过包含一小部分精确交换（EXX），杂化泛函降低了半局域密度泛函理论（DFT）中的自相互作用误差，从而为生物学、化学、物理和材料科学中整个系统的基础电子结构提供了更准确和可靠的描述。然而，与评估所有所需 EXX 量相关的高计算成本限制了杂化 DFT 在处理大分子和复杂凝聚相材料中的应用。为了克服这一限制，我们描述了一种线性标度方法，该方法利用占据轨道的局域表示（例如，最大局域化 Wannier 函数（MLWFs））来利用有限隙系统中量子力学交换相互作用的实空间评估中的稀疏性。在这项工作中，我们详细描述了在杂化 DFT 水平上执行大尺度凝聚相系统的基于 MLWF 的分子动力学（AIMD）模拟所需的理论和算法进展。我们的理论讨论重点是将这种方法集成到 Car-Parrinello AIMD 的框架中，并强调了 MLWF 乘积势（即对应于每个 MLWF 乘积密度的泊松方程的解）在评估 EXX 能量和波函数力中的核心作用。然后，我们全面描述了在开源 Quantum ESPRESSO 程序中实现的 exx 算法，该程序采用混合 MPI/OpenMP 并行化方案来有效地利用当前和下一代超级计算机体系结构上可用的高性能计算（HPC）资源。接下来，我们对在正则（canonical）系综中进行液体水的 AIMD 模拟时，该方法的准确性和并行性能（例如，强和弱缩放）进行了批判性评估。在获得 HPC 资源的情况下，我们证明了 exx 使得基于杂化 DFT 的 AIMD 模拟能够在 500-1000 个原子的凝聚相系统（例如（HO））中进行，其壁时间成本与半局域 DFT 相当。这样，exx 使我们更接近于在杂化 DFT 理论水平上对复杂和大规模凝聚相系统进行足够长时间的常规 AIMD 模拟。
