The conceptual and mathematical foundations of the MC-QTAIM

The concept of atoms in molecules (AIM) is one of the cornerstones of the structural theory of chemistry however, in contrast to the free atoms a comprehensive quantum mechanical theory of AIM has never been proposed. Currently the most satisfactory deduction of this concept is based on the partitioning methodologies that are trying to recover AIM from the ab initio wavefunctions (WF). One of these methodologies is the quantum theory of AIM (QTAIM), which retrieves AIM by an exhaustive partitioning of the one-electron density into atomic basins in real space. The molecular properties are then partitioned into the basin and inter-basin contributions as the incarnation of the AIM properties and their interaction modes. The inputs of the QTAIM partitioning scheme are the electronic WF computed from the electronic Schrodinger equation (SE), which is basically a single-component equation treating electrons as quantum particles and the nuclei as clamped point charges (CPC). A recently extended form of the QTAIM, called the multi-component QTAIM (MC-QTAIM), removes this restriction and enables AIM partitioning to be applied to the MC quantum systems. This is done using MC-WF as inputs that are derived from the MC-SE in which there are two or more types of quantum particles. This opens the possibility for the AIM partitioning of molecular systems where certain nuclei, e.g. because of their non-adiabatic coupling to electrons, must be treated as quantum particles instead of CPC. The same formalism allows the partitioning of exotic molecular systems in which there are other elementary particles like muons or positrons, in addition to electrons and nuclei. The application of the MC-QTAIM partitioning to such systems reveals that the positively charged muon may shape its own atomic basin, i.e. an example of exotic AIM, while positron may act as an agent of bonding, i.e. an example of exotic bonds.