随机密度泛函理论
Stochastic density functional theory
摘要：
密度泛函理论（DFT）的线性缩放实现仅当应用于具有大于其Kohn-Sham密度矩阵（DM）的范围的物理尺寸的系统时才达到其预期的效率范围。这引起了一个问题，因为许多类型的感兴趣的大系统具有相当宽的DM范围，因此不适合使用DFT方法进行分析。出于这个原因，最近提出的随机DFT（sDFT），避免详尽的DM评估，正在成为一个有吸引力的替代线性尺度方法。这篇评论开发了一个通用的制定sDFT的（非）正交基表示，并提供了一个分析的统计误差（SE）的计算。使用一个新的高斯型基集实现sDFT，适用于水团簇和硅纳米晶体，它演示并解释了标准偏差和偏差如何依赖于各种类型的计算中的采样率和系统大小。我们还发展了基组嵌入碎片理论，证明了它的实用性，减少能源，态密度和核力计算的SE。最后，我们讨论了sDFT的算法复杂度，表明它具有CPU壁时间线性缩放。该方法在分布式处理器上并行化良好，具有良好的可扩展性，因此可以在即将到来的exascale计算架构中找到使用。
英文摘要：
Linear-scaling implementations of density functional theory (DFT) reach their intended efficiency regime only when applied to systems having a physical size larger than the range of their Kohn-Sham density matrix (DM). This causes a problem since many types of large systems of interest have a rather broad DM range and are therefore not amenable to analysis using DFT methods. For this reason, the recently proposed stochastic DFT (sDFT), avoiding exhaustive DM evaluations, is emerging as an attractive alternative linear-scaling approach. This review develops a general formulation of sDFT in terms of a (non)orthogonal basis representation and offers an analysis of the statistical errors (SEs) involved in the calculation. Using a new Gaussian-type basis-set implementation of sDFT, applied to water clusters and silicon nanocrystals, it demonstrates and explains how the standard deviation and the bias depend on the sampling rate and the system size in various types of calculations. We also develop basis-set embedded-fragments theory, demonstrating its utility for reducing the SEs for energy, density of states and nuclear force calculations. Finally, we discuss the algorithmic complexity of sDFT, showing it has CPU wall-time linear-scaling. The method parallelizes well over distributed processors with good scalability and therefore may find use in the upcoming exascale computing architectures.
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