Dpto. de Química, Facultad de Ciencias y Tecnología, Universidad de Carabobo, Ciudad Universitaria, Bárbula, Valencia, Venezuela.
J Comput Chem. 2012 Dec 5;33(31):2526-31. doi: 10.1002/jcc.23083. Epub 2012 Aug 2.
The topological study of the electronic charge density is useful to obtain information about the kinds of bonds (ionic or covalent) and the atom charges on a molecule or crystal. For this study, it is necessary to calculate, at every space point, the electronic density and its electronic density derivatives values up to second order. In this work, a grid-based method for these calculations is described. The library, implemented for three dimensions, is based on a multidimensional Lagrange interpolation in a regular grid; by differentiating the resulting polynomial, the gradient vector, the Hessian matrix and the Laplacian formulas were obtained for every space point. More complex functions such as the Newton-Raphson method (to find the critical points, where the gradient is null) and the Cash-Karp Runge-Kutta method (used to make the gradient paths) were programmed. As in some crystals, the unit cell has angles different from 90°, the described library includes linear transformations to correct the gradient and Hessian when the grid is distorted (inclined). Functions were also developed to handle grid containing files (grd from DMol® program, CUBE from Gaussian® program and CHGCAR from VASP® program). Each one of these files contains the data for a molecular or crystal electronic property (such as charge density, spin density, electrostatic potential, and others) in a three-dimensional (3D) grid. The library can be adapted to make the topological study in any regular 3D grid by modifying the code of these functions.
电子电荷密度的拓扑研究有助于获取关于分子或晶体中键的种类（离子键或共价键）和原子电荷的信息。为此研究，有必要在每个空间点上计算电子密度及其电子密度导数，最高可达二阶。在这项工作中，描述了一种基于网格的此类计算方法。该库在三维上实现，基于规则网格中的多维拉格朗日插值；通过对所得多项式进行微分，得到了每个空间点的梯度向量、Hessian 矩阵和拉普拉斯公式。更复杂的函数，如牛顿-拉普森方法（用于找到梯度为零的临界点）和 Cash-Karp Runge-Kutta 方法（用于绘制梯度路径），也被编程实现。由于在某些晶体中，晶胞的角度不为 90°，因此所描述的库包括线性变换，用于在网格扭曲（倾斜）时校正梯度和 Hessian。还开发了一些函数来处理包含网格的文件（来自 DMol®程序的 grd、来自 Gaussian®程序的 CUBE 和来自 VASP®程序的 CHGCAR）。这些文件中的每一个都包含分子或晶体电子特性（如电荷密度、自旋密度、静电势等）在三维（3D）网格中的数据。通过修改这些函数的代码，库可以适应在任何规则的 3D 网格中进行拓扑研究。
