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We present, within Kohn-Sham Density Functional Theory calculations, aquantitative method to identify and assess the partitioning of a large quantummechanical system into fragments. We then show how within this framework simplegeneralizations of other well-known population analyses can be used to extract,from first principles, reliable electrostatic multipoles for the identifiedfragments. Our approach reduces arbitrariness in the fragmentation procedure,and enables the possibility to assess, quantitatively, whether thecorresponding fragment multipoles can be interpreted as observable quantitiesassociated to a system's moiety. By applying our formalism within the codeBigDFT, we show that the use of a minimal set of in-situ optimized basisfunctions allows at the same time a proper fragment definition and an accuratedescription of the electronic structure.

Complexity Reduction in Large Quantum Systems: Fragment Identification and Population Analysis via a Local Optimized Minimal Basis