Department of Chemistry and Center for Integrated Protein Science (CIPSM) , University of Munich (LMU) , D-81377 München , Germany.
J Chem Theory Comput. 2018 Jul 10;14(7):3451-3458. doi: 10.1021/acs.jctc.8b00062. Epub 2018 Jun 15.
Local hybrid functionals, that is, functionals with local dependence on the exact exchange energy density, generalize the popular class of global hybrid functionals and extend the applicability of density functional theory to electronic structures that require an accurate description of static correlation. However, the higher computational cost compared to conventional Kohn-Sham density functional theory restrained their widespread application. Here, we present a low-prefactor, linear-scaling method to evaluate the local hybrid exchange-correlation potential as well as the corresponding nuclear forces by employing a seminumerical integration scheme. In the seminumerical scheme, one integration in the electron repulsion integrals is carried out analytically and the other one is carried out numerically, employing an integration grid. A high computational efficiency is achieved by combining the preLinK method [ J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 2013 138, 134114 ] with explicit screening of integrals for batches of grid points to minimize the screening overhead. This new method, denoted as preLinX, provides an 8-fold performance increase for a DNA fragment containing four base pairs as compared to existing S- and P-junction-based methods. In this way, our method allows for the evaluation of local hybrid functionals at a cost similar to that of global hybrid functionals. The linear-scaling behavior, efficiency, accuracy, and multinode parallelization of the presented method is demonstrated for large systems containing more than 1000 atoms.
局部杂化泛函，即依赖于精确交换能密度的局域泛函，推广了广受欢迎的全局杂化泛函类，并将密度泛函理论的适用性扩展到需要准确描述静态相关的电子结构。然而，与传统的 Kohn-Sham 密度泛函理论相比，其更高的计算成本限制了它们的广泛应用。在这里，我们提出了一种低预因子、线性标度方法，通过采用半数值积分方案来评估局部杂化交换相关势以及相应的核力。在半数值方案中，电子排斥积分中的一个积分进行解析计算，另一个积分进行数值计算，采用积分网格。通过将 preLinK 方法[J. Kussmann 和 C. Ochsenfeld，J. Chem. Phys. 2013 138，134114]与批处理网格点积分的显式屏蔽相结合，实现了高计算效率，以最小化屏蔽开销。这种新方法，称为 preLinX，与现有的 S-和 P-结方法相比，对于包含四个碱基对的 DNA 片段，性能提高了 8 倍。通过这种方式，我们的方法可以以类似于全局杂化泛函的成本评估局部杂化泛函。对于包含超过 1000 个原子的大型系统，展示了所提出方法的线性标度行为、效率、准确性和多节点并行化。
