Preconditioning of self-consistent-field cycles in density-functional theory: The extrapolar method
Preconditioning of self-consistent-field cycles in density-functional theory: The extrapolar method
复制标题
密度泛函理论中自洽场循环的预处理：极外法
DOI：
10.1103/physrevb.78.045126
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发表时间：
2008
影响因子：
3.7
通讯作者：
X. Gonze
中科院分区：
文献类型：
--
作者：
P. Anglade;X. Gonze
金属系统的密度泛函理论处理所需的自洽场迭代次数随着晶胞的大小而增加，不仅对于简单混合等基本算法，而且对于更高级的方案，其中混合了过去几个步骤的结果。预处理技术有可能抑制这种增长，尽管可用的方法有很大的局限性：要么它们在具有金属和非金属区域的混合系统的情况下几乎没有什么改进，要么预处理器的计算随着系统的大小而严重缩放，具有很大的预因子。我们提出了一种近似预处理器，其预因子大大减少，使得自洽循环的数量几乎独立于系统的大小，并且在一百个原子范围内几乎不承担任何开销。磁敏度矩阵是我们方案中的一个关键要素，它是通过闭合关系来近似的。我们不使用介电矩阵的精确公式，而是依靠随机相位近似，由于波矢量截止非常低，即使对于同时具有真空和金属区域的系统，也可以进一步降低预因子。我们在规模不断增加的系统中测试了该算法，并证明了其实际用途。
The number of self-consistent-field iterations needed for the density-functional theory treatment of metallic systems grows with the size of the unit cell, not only for basic algorithms like simple mixing, but also for more advanced schemes, in which results from several past steps are mixed. Preconditioning techniques have the potential to suppress this growth, although the available methods have strong limitations: either they deliver little improvement in case of mixed systems with metallic and nonmetallic regions, or the computation of the preconditioner scales badly with the size of the system, with a large prefactor. We propose an approximate preconditioner, with tremendously reduced prefactor, that makes the number of self-consistent cycle nearly independent of the size of the system, and bears little overhead up to the one hundred atom range. The susceptibility matrix, a key ingredient in our scheme, is approximated thanks to the closure relation. Instead of using the exact formulation of the dielectric matrix, we rely on the random-phase approximation, that allows to further decrease the prefactor thanks to a very low wave vector cutoff, even for systems with both vacuum and a metallic region. We test this algorithm for systems of increasing size and demonstrate its practical usefulness.