Luo Ziling, Khaliullin Rustam Z
Department of Chemistry, McGill University, 801 Sherbrooke Street West, Montreal, Quebec QC H3A 0B8, Canada.
J Chem Theory Comput. 2020 Jun 9;16(6):3558-3566. doi: 10.1021/acs.jctc.9b01286. Epub 2020 May 5.
Spatially localized one-electron orbitals, orthogonal and non-orthogonal, are widely used in electronic structure theory to describe chemical bonding and speed up calculations. In order to avoid linear dependencies of localized orbitals, the existing localization methods either constrain orbital transformations to be unitary, that is, metric preserving, or, in the case of variable-metric methods, fix the centers of non-orthogonal localized orbitals. Here, we developed a different approach to orbital localization, in which these constraints are replaced with a single restriction that specifies the maximum allowed deviation from the orthogonality for the final set of localized orbitals. This reformulation, which can be viewed as a generalization of existing localization methods, enables one to choose the desired balance between the orthogonality and locality of the orbitals. Furthermore, the approach is conceptually and practically simple as it obviates the necessity in unitary transformations and allows one to determine optimal positions of the centers of non-orthogonal orbitals in an unconstrained and straightforward minimization procedure. It is demonstrated to produce well-localized orthogonal and non-orthogonal orbitals with the Berghold and Pipek--Mezey localization functions for a variety of molecules and periodic materials including large systems with nontrivial bonding.
空间局域化的单电子轨道，包括正交和非正交的，在电子结构理论中被广泛用于描述化学键合并加速计算。为了避免局域轨道的线性相关性，现有的局域化方法要么将轨道变换约束为酉变换，即保持度量，要么在可变度量方法的情况下，固定非正交局域轨道的中心。在这里，我们开发了一种不同的轨道局域化方法，其中这些约束被一个单一的限制所取代，该限制指定了最终局域轨道集与正交性的最大允许偏差。这种重新表述，可以看作是现有局域化方法的推广，使人们能够在轨道的正交性和局域性之间选择所需的平衡。此外，该方法在概念上和实践上都很简单，因为它避免了酉变换的必要性，并允许人们在一个无约束且直接的最小化过程中确定非正交轨道中心的最佳位置。结果表明，对于各种分子和周期性材料，包括具有复杂键合的大系统，使用伯格霍尔德和皮佩克 - 梅泽伊局域化函数，该方法能产生良好局域化的正交和非正交轨道。
