论文标题
单电子轨道的直接无约束的可变度定位
Direct unconstrained variable-metric localization of one-electron orbitals
论文作者
论文摘要
在电子结构理论中广泛使用了空间定位的单电子轨道，正交和非正交的轨道来描述化学键合和加速计算。为了避免局部轨道的线性依赖性，现有的定位方法要么限制轨道转换为单位，即保留度量，要么在可变度量方法的情况下，请修复非正交局部化轨道的中心。在这里，我们开发了一种不同的方法来进行轨道定位，其中这些约束被单个限制代替，该限制指定了最终集合局部轨道的最大偏差与正交性的最大偏差。这种重新制定可以看作是现有本地化方法的概括，使人们能够选择轨道正交性和局部性之间的所需平衡。此外，该方法在概念上和实际上是简单的，因为它避免了单一转换的必要性，并允许在不受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。事实证明，它可以与Berghold和Pipek-Mezey定位函数一起生产良好的正交和非正交轨道，用于多种分子和周期性材料，包括具有非平凡键合的大型系统。
Spatially localized one-electron orbitals, orthogonal and nonorthogonal, 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 nonorthogonal 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 to determine optimal positions of the centers of nonorthogonal orbitals in a unconstrained and straightforward minimization procedure. It is demonstrated to produce well-localized orthogonal and nonorthogonal orbitals with the Berghold and Pipek-Mezey localization functions for a variety of molecules and periodic materials including large systems with non-trivial bonding.
