The MC-QTAIM: A framework for extending the atoms in molecules analysis beyond purely electronic systems

The quantum theory of atoms in molecules, QTAIM, is employed to identify AIM and quantify their interactions through the partitioning of molecule into atomic basins in the real space and it is confined only to the purely electronic systems composed of electrons as quantum particles and the nuclei as clamped point charges. The extended version of the QTAIM, called the multi-component QTAIM, MC-QTAIM, bypasses this border and makes it possible to identify AIM and quantify their interactions in systems composed of multiple quantum particles that electrons may or may not be one of their components opening a new door for the analysis of the exotic AIM and bonds. In this contribution, two conjectures, called Bader conjecture, BC, and extended Bader conjecture, EBC, are proposed as the cornerstones of the real-space partitioning of a molecule into atomic basins within the context of the QTAIM and the MC-QTAIM, respectively. A literature survey on various few-body quantum systems composed of quarks, nucleons, and elementary particles like muons and positrons is also done unraveling the fact that in all these diverse systems there are unambiguous cases of clusterizations. These clustered systems, irrespective to their components, behave as if they are molecules composed of some kind of atoms, instead of being an amorphous mixture of quantum particles. In the case of the muonic and the positronic molecules computational studies reveal that the AIM structures of these systems are well-captured by the EBC. Beyond identifying atomic basins, both QTAIM and MC-QTAIM attribute properties to AIM, which is their share from the molecular expectation values of quantum observables. It is demonstrated that not only the share from the average value of an observable may be attributed to an atomic basin, but also the fluctuation of each basin property is also quantifiable.