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Iterative diagonalization in augmented plane wave based methods in electronic structure calculations

机译：电子结构计算中基于增强平面波的迭代对角化

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摘要

Due to the increased computer power and advanced algorithms, quantum mechanical calculations based on Density Functional Theory are more and more widely used to solve real materials science problems. In this context large nonlinear generalized eigenvalue problems must be solved repeatedly to calculate the electronic ground state of a solid or molecule. Due to the nonlinear nature of this problem, an iterative solution of the eigenvalue problem can be more efficient provided it does not disturb the convergence of the self-consistent-field problem. The blocked Davidson method is one of the widely used and efficient schemes for that purpose, but its performance depends critically on the preconditioning, i.e. the procedure to improve the search space for an accurate solution. For more diagonally dominated problems, which appear typically for plane wave based pseudopotential calculations, the inverse of the diagonal of (H-ES) is used. However, for the more efficient "augmented plane wave+local-orbitals" basis set this preconditioning is not sufficient due to large off-diagonal terms caused by the local orbitals. We propose a new preconditioner based on the inverse of (H-[lambda]S) and demonstrate its efficiency for real applications using both, a sequential and a parallel implementation of this algorithm into our WIEN2k code.
机译：由于计算机功能的增强和算法的先​​进性，基于密度泛函理论的量子力学计算越来越广泛地用于解决实际的材料科学问题。在这种情况下，必须反复解决大型非线性广义特征值问题，以计算固体或分子的电子基态。由于该问题的非线性性质，特征值问题的迭代解可以更有效，只要它不干扰自洽场问题的收敛即可。戴维森分块方法是为此目的而广泛使用和有效的方案之一，但其性能在很大程度上取决于预处理，即为精确解决方案而改善搜索空间的过程。对于更多对角线主导的问题（通常在基于平面波的伪势计算中出现），使用（H-ES）对角线的反函数。但是，对于更有效的“增强平面波+局部轨道”基础集，由于局部轨道引起的大的非对角项，这种预处理是不够的。我们提出了一种基于（H-λS）的逆的新的预处理器，并通过将该算法的顺序实现和并行实现二者结合到我们的WIEN2k代码中，展示了其对于实际应用的效率。

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