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.

中文翻译：

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局部混合密度泛函的高效线性定标半数值方法

局部混合泛函，即局部依赖于精确交换能量密度的泛函，泛化了全局混合泛函的流行类别，并将密度泛函的适用性扩展到需要精确描述静态相关性的电子结构。但是，与传统的Kohn-Sham密度泛函理论相比，较高的计算成本限制了它们的广泛应用。在这里，我们提出一种低因子线性缩放方法，通过采用半数值积分方案来评估局部混合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是通过解析进行的，而另一积分是使用积分网格进行数值的。通过结合preLinK方法可以实现较高的计算效率[J. Kussmann和C. Ochsenfeld，J.化学。物理 2013 138，134114]与网格点批次积分的明确的筛选，以尽量减少筛选开销。与现有的基于S结和P结的方法相比，这种称为preLinX的新方法对包含四个碱基对的DNA片段的性能提高了8倍。这样，我们的方法允许以与全局混合功能相似的成本评估本地混合功能。对于包含1000个以上原子的大型系统，演示了所提出方法的线性缩放行为，效率，准确性和多节点并行化。