Department of Physics , University of Konstanz , Universitätsstraße 10 , D-78464 Konstanz , Germany.
Department of Chemistry , Ludwig-Maximilians-Universität (LMU) Munich , Butenandtstraße 7 , D-81377 Munich , Germany.
J Chem Theory Comput. 2018 Sep 11;14(9):4567-4580. doi: 10.1021/acs.jctc.8b00122. Epub 2018 Aug 24.
In this work, we present a robust implementation of the periodic Fock exchange for atom-centered Gaussian-type orbitals (GTOs). We discuss the divergence, appearing in the formulation of the periodic Fock exchange in the case of a finite number of k-points, and compare two schemes that remove it. These are the minimum image convention (MIC) and the truncated Coulomb interaction (TCI) that we use here in combination with k-meshes. We observe artifacts in four-center integrals of GTOs, when evaluated in the TCI scheme. They carry over to the exchange and density matrices of Hartree-Fock calculations for TCI but are absent in MIC. At semiconducting and insulating systems, we show that both MIC and TCI yield the same energies for a sufficiently large supercell or k-mesh, but the self-consistent field algorithm is more stable for MIC. We therefore conclude that the MIC is superior to TCI and validate our implementation by comparing not only to other GTO-based calculations but also by demonstrating excellent agreement with results of plane-wave codes for sufficiently large Gaussian basis sets.
在这项工作中，我们提出了一种针对原子中心高斯型轨道（GTO）的稳健周期性福克交换实现。我们讨论了在有限个 k 点情况下周期性福克交换公式中出现的发散，并比较了两种消除它的方案。这是最小镜像公约（MIC）和截断库仑相互作用（TCI），我们在这里将其与 k 网格结合使用。我们观察到在 TCI 方案中评估 GTO 的四中心积分时出现了伪像。它们会传递到 TCI 的 Hartree-Fock 计算的交换和密度矩阵中，但在 MIC 中不存在。对于半导体和绝缘体系，我们表明对于足够大的超胞或 k 网格，MIC 和 TCI 都会产生相同的能量，但对于 MIC，自洽场算法更稳定。因此，我们得出结论，MIC 优于 TCI，并通过不仅与其他基于 GTO 的计算进行比较，而且通过展示对于足够大的高斯基集与平面波代码结果的出色一致性来验证我们的实现。
