Pujal Leila, van Zyl Maximilian, Vöhringer-Martinez Esteban, Verstraelen Toon, Bultinck Patrick, Ayers Paul W, Heidar-Zadeh Farnaz
Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7N 3N6, Canada.
Departamento de Físico-Química, Facultad de Ciencias Químicas, Universidad de Concepción, Concepción, Chile.
J Chem Phys. 2022 May 21;156(19):194109. doi: 10.1063/5.0089466.
We develop a variational procedure for the iterative Hirshfeld (HI) partitioning scheme. The main practical advantage of having a variational framework is that it provides a formal and straightforward approach for imposing constraints (e.g., fixed charges on certain atoms or molecular fragments) when computing HI atoms and their properties. Unlike many other variants of the Hirshfeld partitioning scheme, HI charges do not arise naturally from the information-theoretic framework, but only as a reverse-engineered construction of the objective function. However, the procedure we use is quite general and could be applied to other problems as well. We also prove that there is always at least one solution to the HI equations, but we could not prove that its self-consistent equations would always converge for any given initial pro-atom charges. Our numerical assessment of the constrained iterative Hirshfeld method shows that it satisfies many desirable traits of atoms in molecules and has the potential to surpass existing approaches for adding constraints when computing atomic properties.
我们为迭代赫希费尔德（HI）划分方案开发了一种变分程序。拥有变分框架的主要实际优势在于，它为在计算HI原子及其性质时施加约束（例如，对某些原子或分子片段设定固定电荷）提供了一种形式化且直接的方法。与赫希费尔德划分方案的许多其他变体不同，HI电荷并非自然地源于信息论框架，而只是目标函数的一种逆向工程构造。然而，我们使用的程序相当通用，也可应用于其他问题。我们还证明了HI方程总是至少有一个解，但我们无法证明其自洽方程对于任何给定的初始原原子电荷都总是收敛的。我们对约束迭代赫希费尔德方法的数值评估表明，它满足分子中原子的许多理想特性，并且在计算原子性质时添加约束方面有潜力超越现有方法。
