Towards grid-based O(N) density-functional theory methods:: Optimized nonorthogonal orbitals and multigrid acceleration
Towards grid-based O(N) density-functional theory methods:: Optimized nonorthogonal orbitals and multigrid acceleration
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DOI：
10.1103/physrevb.62.1713
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发表时间：
2000-07-15
影响因子：
3.7
通讯作者：
Bernholc, J
中科院分区：
文献类型：
--
作者：
Fattebert, JL;Bernholc, J
我们已经制定和实施了一个实空间从头计算方法的电子结构的非正交轨道定义在一个网格上。一个多重网格预条件是用来改善最速下降方向的能量泛函的迭代最小化。在非正交轨道的子空间中使用密度矩阵的形式主义，包括不饱和或部分占据的状态。由轨道的非正交实空间描述引入的自由度允许局部化约束，该局部化约束使计算的最昂贵部分的成本线性化，同时保持多重网格加速的迭代最小化的快速收敛速率。对碳纳米管的数值试验表明，对于半径为8玻尔的局域化区域，可以得到非常精确的结果。这种方法大大降低了非常大的系统的计算成本，已经在大规模并行格雷T3E计算机上实现，并在含有1000多个原子的碳纳米管上进行了测试。
We have formulated and implemented a real-space ab initio method for electronic structure calculations in terms of nonorthogonal orbitals defined on a grid. A multigrid preconditioner is used to improve the steepest descent directions used in the iterative minimization of the energy functional. Unoccupied or partially occupied states are included using a density matrix formalism in the subspace spanned by the nonorthogonal orbitals. The freedom introduced by the nonorthogonal real-space description of the orbitals allows for localization constraints that linearize the cost of the most expensive parts of the calculations, while keeping a fast convergence rate for the iterative minimization with multigrid acceleration. Numerical tests for carbon nanotubes show that very accurate results can be obtained for localization regions with radii of 8 bohr. This approach, which substantially reduces the computational cost for very large systems, has been implemented on the massively parallel Gray T3E computer and tested on carbon nanotubes containing more than 1000 atoms.