We present, within Kohn–Sham density functional theory calculations, a quantitative method to identify and assess the partitioning of a large quantum-mechanical system into fragments. We then show how within this framework simple generalizations of other well-known population analyses can be used to extract, from first-principles, reliable electrostatic multipoles for the identified fragments. Our approach reduces arbitrariness in the fragmentation procedure and enables the possibility to assess quantitatively whether the corresponding fragment multipoles can be interpreted as observable quantities associated with a system moiety. By applying our formalism within the code BigDFT, we show that the use of a minimal set of in situ-optimized basis functions allows at the same time a proper fragment definition and an accurate description of the electronic structure.

We would like to thank Thierry Deutsch for valuable discussions and Fátima Lucas for providing various test systems and helpful discussions. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DEAC02-06CH11357. SM acknowledges support from the European Centre of Excellence MaX (project ID 676598). LG acknowledges support from the EU ExtMOS project (project ID 646176) and the European Centre of Excellence EoCoE (project ID 676629).

Peer Reviewed