SCDM-k：通过密度矩阵的选定列的固体定域轨道
SCDM-k: Localized orbitals for solids via selected columns of the density matrix
摘要：
最近开发的密度矩阵（SCDM）方法[J. Chem. Theory Comput. 11，1463，2015]是一种简单、鲁棒、高效且高度可并行的方法，用于利用布里渊区的$Γ$点采样从绝缘体和半导体的一组离域Kohn-Sham轨道构建定域轨道。在这项工作中，我们推广的SCDM方法的Kohn-Sham密度泛函理论计算与k点采样的布里渊区，这是需要更一般的固体电子结构计算。我们证明了我们的新方法，称为SCDM-k，是由建设规范独立，是一种自然的方式来描述本地化轨道。SCDM-k计算定域轨道而不使用优化过程，因此不会陷入局部最小值。此外，使用SCDM-k来构造正交和定域轨道的计算复杂度为O（N log N），其中N是布里渊区中的k点的总数。因此，即使当大量k点用于布里渊区采样时，SCDM-k也是有效的。我们证明了SCDM-k的数值性能，使用系统的模型潜力在二维和三维。
英文摘要：
The recently developed selected columns of the density matrix (SCDM) method [J. Chem. Theory Comput. 11, 1463, 2015] is a simple, robust, efficient and highly parallelizable method for constructing localized orbitals from a set of delocalized Kohn-Sham orbitals for insulators and semiconductors with $Γ$ point sampling of the Brillouin zone. In this work we generalize the SCDM method to Kohn-Sham density functional theory calculations with k-point sampling of the Brillouin zone, which is needed for more general electronic structure calculations for solids. We demonstrate that our new method, called SCDM-k, is by construction gauge independent and is a natural way to describe localized orbitals. SCDM-k computes localized orbitals without the use of an optimization procedure, and thus does not suffer from the possibility of being trapped in a local minimum. Furthermore, the computational complexity of using SCDM-k to construct orthogonal and localized orbitals scales as O(N log N ) where N is the total number of k-points in the Brillouin zone. SCDM-k is therefore efficient even when a large number of k-points are used for Brillouin zone sampling. We demonstrate the numerical performance of SCDM-k using systems with model potentials in two and three dimensions.
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