VandeVondele Joost, Borštnik Urban, Hutter Jürg
Department of Materials, ETH Zurich , Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland.
Physical Chemistry Institute, University of Zurich , Winterthurerstrasse 190, CH-8057 Zurich, Switzerland.
J Chem Theory Comput. 2012 Oct 9;8(10):3565-73. doi: 10.1021/ct200897x. Epub 2012 Mar 14.
In this work, the applicability and performance of a linear scaling algorithm is investigated for three-dimensional condensed phase systems. A simple but robust approach based on the matrix sign function is employed together with a thresholding matrix multiplication that does not require a prescribed sparsity pattern. Semiempirical methods and density functional theory have been tested. We demonstrate that self-consistent calculations with 1 million atoms are feasible for simple systems. With this approach, the computational cost of the calculation depends strongly on basis set quality. In the current implementation, high quality calculations for dense systems are limited to a few hundred thousand atoms. We report on the sparsities of the involved matrices as obtained at convergence and for intermediate iterations. We investigate how determining the chemical potential impacts the computational cost for very large systems.
在这项工作中，研究了线性缩放算法在三维凝聚相系统中的适用性和性能。采用了一种基于矩阵符号函数的简单而稳健的方法，并结合了一种不需要规定稀疏模式的阈值矩阵乘法。已经对半经验方法和密度泛函理论进行了测试。我们证明，对于简单系统，含100万个原子的自洽计算是可行的。通过这种方法，计算的成本在很大程度上取决于基组质量。在当前的实现中，对密集系统的高质量计算仅限于几十万原子。我们报告了收敛时以及中间迭代时所涉及矩阵的稀疏性。我们研究了确定化学势如何影响非常大系统的计算成本。
