Beck Thomas L
Departments of Chemistry and Physics, University of Cincinnati, Cincinnati, OH, USA.
Phys Chem Chem Phys. 2015 Dec 21;17(47):31472-9. doi: 10.1039/c5cp01222h.
The recent development of real-space grid methods has led to more efficient, accurate, and adaptable approaches for large-scale electrostatics and density functional electronic structure modeling. With the incorporation of multiscale techniques, linear-scaling real-space solvers are possible for density functional problems if localized orbitals are used to represent the Kohn-Sham energy functional. These methods still suffer from high computational and storage overheads, however, due to extensive matrix operations related to the underlying wave function grid representation. In this paper, an alternative stochastic method is outlined that aims to solve directly for the one-electron density matrix in real space. In order to illustrate aspects of the method, model calculations are performed for simple one-dimensional problems that display some features of the more general problem, such as spatial nodes in the density matrix. This orbital-free approach may prove helpful considering a future involving increasingly parallel computing architectures. Its primary advantage is the near-locality of the random walks, allowing for simultaneous updates of the density matrix in different regions of space partitioned across the processors. In addition, it allows for testing and enforcement of the particle number and idempotency constraints through stabilization of a Feynman-Kac functional integral as opposed to the extensive matrix operations in traditional approaches.
实空间网格方法的最新发展为大规模静电学和密度泛函电子结构建模带来了更高效、准确且适应性更强的方法。通过纳入多尺度技术，如果使用局域轨道来表示科恩-沙姆能量泛函，那么对于密度泛函问题就有可能实现线性标度实空间求解器。然而，由于与基础波函数网格表示相关的大量矩阵运算，这些方法仍然存在高计算量和高存储开销的问题。本文概述了一种替代的随机方法，该方法旨在直接在实空间中求解单电子密度矩阵。为了说明该方法的各个方面，针对简单的一维问题进行了模型计算，这些一维问题展现了更一般问题的一些特征，比如密度矩阵中的空间节点。考虑到未来计算架构越来越向并行化发展，这种无轨道方法可能会被证明是有用的。其主要优势在于随机游走的近局域性，这使得能够在跨处理器划分的不同空间区域中同时更新密度矩阵。此外，与传统方法中大量的矩阵运算不同，它允许通过稳定费曼 - 卡茨泛函积分来测试和执行粒子数和幂等性约束。
