RESCU: A real space electronic structure method

详细信息    查看全文

• 作者：Vincent Michaud-Rioux ; ^{vincentm@physics.mcgill.ca" class="auth_mail" title="E-mail the corresponding author} ; Lei Zhang ^{zhanglei@physics.mcgill.ca" class="auth_mail" title="E-mail the corresponding author} ; Hong Guo ^{guo@physics.mcgill.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Density-functional theory ; Methods of electronic structure calculations ; Finite-difference methods ; Self-consistent-field methods
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：307
• 期：Complete
• 页码：593-613
• 全文大小：1450 K

文摘

In this work we present RESCU, a powerful MATLAB-based Kohn–Sham density functional theory (KS-DFT) solver. We demonstrate that RESCU can compute the electronic structure properties of systems comprising many thousands of atoms using modest computer resources, e.g. 16 to 256 cores. Its computational efficiency is achieved from exploiting four routes. First, we use numerical atomic orbital (NAO) techniques to efficiently generate a good quality initial subspace which is crucially required by Chebyshev filtering methods. Second, we exploit the fact that only a subspace spanning the occupied Kohn–Sham states is required, and solving accurately the KS equation using eigensolvers can generally be avoided. Third, by judiciously analyzing and optimizing various parts of the procedure in RESCU, we delay the 160fb527b45a" title="Click to view the MathML source">O(N³)$O(N^3)$ scaling to large N  , and our tests show that RESCU scales consistently as O(N^2.3)$O(N^{2.3})$ from a few hundred atoms to more than 5000 atoms when using a real space grid discretization. The scaling is better or comparable in a NAO basis up to the 14,000 atoms level. Fourth, we exploit various numerical algorithms and, in particular, we introduce a partial Rayleigh–Ritz algorithm to achieve efficiency gains for systems comprising more than 10,000 electrons. We demonstrate the power of RESCU in solving KS-DFT problems using many examples running on 16, 64 and/or 256 cores: a 5832 Si atoms supercell; a 8788 Al atoms supercell; a 5324 Cu atoms supercell and a small DNA molecule submerged in 1713 water molecules for a total 5399 atoms. The KS-DFT is entirely converged in a few hours in all cases. Our results suggest that the RESCU method has reached a milestone of solving thousands of atoms by KS-DFT on a modest computer cluster.