Benda Robert, Cancès Eric, Ehrlacher Virginie, Stamm Benjamin
CERMICS, Ecole des Ponts and Inria Paris, 6 & 8 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France and LPICM, CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91128 Palaiseau, France.
CERMICS, Ecole des Ponts and Inria Paris, 6 & 8 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France.
J Chem Phys. 2022 Apr 28;156(16):164107. doi: 10.1063/5.0076630.
The aim of this article is to analyze from a mathematical perspective some existing schemes to partition a molecular density into several atomic contributions with a specific focus on Iterative Stockholder Atom (ISA) methods. We provide a unified mathematical framework to describe the latter family of methods and propose a new scheme, named L-ISA (for linear approximation of ISA), which generalizes the so-called additive variational Hirshfeld method. We prove several important mathematical properties of the ISA and L-ISA minimization problems and show that the so-called ISA algorithms can be viewed as alternating minimization schemes, which, in turn, enables us to obtain new convergence results for these numerical methods. Specific mathematical properties of the ISA decomposition for diatomic systems are also presented. Numerical results on diatomic systems illustrate the proven mathematical properties.
本文旨在从数学角度分析一些现有的将分子密度划分为若干原子贡献的方案，特别关注迭代股东原子（ISA）方法。我们提供了一个统一的数学框架来描述后一类方法，并提出了一种名为L - ISA（ISA的线性近似）的新方案，它推广了所谓的加性变分赫希菲尔德方法。我们证明了ISA和L - ISA最小化问题的几个重要数学性质，并表明所谓的ISA算法可以被视为交替最小化方案，这反过来又使我们能够为这些数值方法获得新的收敛结果。还给出了双原子系统ISA分解的具体数学性质。双原子系统的数值结果说明了已证明的数学性质。
