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In this contribution, pursuing our research program extending the atoms inmolecules analysis into unorthodox domains, another key ingredient of thetwo-component quantum theory of atoms in molecules (TC-QTAIM) namely, thetheory of localization/delocalization of quantum particles, is disclosed. Theunified proposed scheme is able not only to deal with thelocalization/delocalization of electrons in/between atomic basins, but also totreat nuclei as well as exotic particles like positrons and muons equally.Based on the general reduced second order density matrices forindistinguishable quantum particles, the quantum fluctuations of atomic basinsare introduced and then used as a gauge to quantify thelocalization/delocalization introducing proper indexes. The explicitmass-dependence of the proposed indexes is demonstrated and it is shown that asingle localization/delocalization index is capable of being used for all kindof quantum particles regardless of their masses or charge content. For variousnon-Born-Oppenhiemer (non-BO) wavefunctions, including Hartree-product as wellas singlet and triplet determinants, the indices are calculated and thenemployed to rationalize the localization/delocalization of particles in aseries of four-body model systems consist of two electrons and two positivelycharged particles with variable mass. The ab initio FV-MC_MO derived non-BOwavefunctions for the four-body series are used for a comprehensivecomputational TC-QTAIM analysis, including topological analysis as well asbasin integrations, in a wide mass region, m=10me-10^13me (me stands forelectron mass), disclosing various traits in these series of species that areunique to the TC-QTAIM. Finally, it is concluded that the proposedlocalization/delocalization scheme is capable of quantifying quantum tunnelingof nuclei for systems containing delocalized protons.

theoretical chemistry accounts

The Two-Component Quantum Theory of Atoms in Molecules (TC-QTAIM): The  unified theory of localization/delocalization of electrons, nuclei and exotic  elementary particles