Multi-center decomposition of molecular densities: A mathematical perspective

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.