Scemama Anthony, Renon Nicolas, Rapacioli Mathias
Laboratoire de Chimie et Physique Quantiques, Université de Toulouse-CNRS-IRSAMC , 31062 Toulouse Cedex 04, France.
CALMIP, Université de Toulouse-CNRS-INPT-INSA-UPS , F-31062 Toulouse Cedex 4, France.
J Chem Theory Comput. 2014 Jun 10;10(6):2344-54. doi: 10.1021/ct500115v.
We present an algorithm and its parallel implementation for solving a self-consistent problem as encountered in Hartree-Fock or density functional theory. The algorithm takes advantage of the sparsity of matrices through the use of local molecular orbitals. The implementation allows one to exploit efficiently modern symmetric multiprocessing (SMP) computer architectures. As a first application, the algorithm is used within the density-functional-based tight binding method, for which most of the computational time is spent in the linear algebra routines (diagonalization of the Fock/Kohn-Sham matrix). We show that with this algorithm (i) single point calculations on very large systems (millions of atoms) can be performed on large SMP machines, (ii) calculations involving intermediate size systems (1000-100 000 atoms) are also strongly accelerated and can run efficiently on standard servers, and (iii) the error on the total energy due to the use of a cutoff in the molecular orbital coefficients can be controlled such that it remains smaller than the SCF convergence criterion.
我们提出了一种算法及其并行实现，用于解决在哈特里 - 福克或密度泛函理论中遇到的自洽问题。该算法通过使用局域分子轨道利用了矩阵的稀疏性。该实现允许有效地利用现代对称多处理（SMP）计算机架构。作为第一个应用，该算法用于基于密度泛函的紧束缚方法，其中大部分计算时间花在线性代数例程（福克/科恩 - Sham矩阵的对角化）中。我们表明，使用该算法：（i）可以在大型SMP机器上对非常大的系统（数百万个原子）进行单点计算；（ii）涉及中等大小系统（1000 - 100000个原子）的计算也得到了显著加速，并且可以在标准服务器上高效运行；（iii）由于在分子轨道系数中使用截止而导致的总能量误差可以得到控制，使其保持小于自洽场收敛标准。
