Otero-de-la-Roza Alberto
Departamento de Química Física y Analítica and MALTA Consolider Team, Facultad de Química, Universidad de Oviedo, 33006 Oviedo, Spain.
J Chem Phys. 2022 Jun 14;156(22):224116. doi: 10.1063/5.0090232.
The quantum theory of atoms in molecules (QTAIM), developed by Bader and co-workers, is one of the most popular ways of extracting chemical insight from the results of quantum mechanical calculations. One of the basic tasks in QTAIM is to locate the critical points of the electron density and calculate various quantities (density, Laplacian, etc.) on them since these have been found to correlate with molecular properties of interest. If the electron density is given analytically, this process is relatively straightforward. However, locating the critical points is more challenging if the density is known only on a three-dimensional uniform grid. A density grid is common in periodic solids because it is the natural expression for the electron density in plane-wave calculations. In this article, we explore the reconstruction of the electron density from a grid and its use in critical point localization. The proposed reconstruction method employs polyharmonic spline interpolation combined with a smoothing function based on the promolecular density. The critical point search based on this reconstruction is accurate, trivially parallelizable, works for periodic and non-periodic systems, does not present directional lattice bias when the grid is non-orthogonal, and locates all critical points of the underlying electron density in all tests studied. The proposed method also provides an accurate reconstruction of the electron density over the space spanned by the grid, which may be useful in other contexts besides critical point localization.
由巴德及其同事提出的分子中原子的量子理论（QTAIM），是从量子力学计算结果中获取化学见解的最常用方法之一。QTAIM的基本任务之一是确定电子密度的临界点，并计算其上的各种量（密度、拉普拉斯算子等），因为已发现这些量与感兴趣的分子性质相关。如果电子密度以解析形式给出，这个过程相对简单。然而，如果密度仅在三维均匀网格上已知，确定临界点则更具挑战性。密度网格在周期性固体中很常见，因为它是平面波计算中电子密度的自然表示形式。在本文中，我们探讨了从网格重建电子密度及其在临界点定位中的应用。所提出的重建方法采用多调和样条插值，并结合基于前分子密度的平滑函数。基于这种重建的临界点搜索准确、易于并行化，适用于周期性和非周期性系统，当网格非正交时不会出现方向晶格偏差，并且在所研究的所有测试中都能定位底层电子密度的所有临界点。所提出的方法还能在网格跨越的空间上准确重建电子密度，这在临界点定位之外的其他情况下可能也有用。
