The aim of this talk is to present 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 will present a unified mathematical framework to describe the latter family of methods and present a new scheme, named L-ISA (for linear approximation of ISA). Several important mathematical properties of the ISA and L-ISA minimization problems will be presented. In particular, it can be shown that the so-called ISA algorithms can be viewed as alternating minimization schemes, which was not known until recently and 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. Comparisons of different numerical schemes on several molecules will be presented, as well as advantages and drawbacks of each approach.
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