The two-component quantum theory of atoms in molecules (TC-QTAIM): foundations

The foundations of the two-component quantum theory of atoms in molecules (TC-QTAIM) are addressed in this contribution. In this regard, the theory is presented in an axiomatic manner and the main theorems describing regional properties of atoms in molecules are considered in detail. This is an extension of the orthodox quantum theory of atoms in molecules (QTAIM) for dealing with non-adiabatic wavefunctions of usual molecules as well as extracting the regional quantum structure of exotic species from the corresponding wavefunctions. The best examples of the latter are positronic and muonic species. The computational study of a model system consisting of a clamped lithium nucleus, four electrons, and a positively charged quantum particle carrying a unit of positive charge with a variable mass, m = 200–1013 me, supplements the theoretical argument demonstrating unambiguously that the TC-QTAIM analysis yields reasonable results. It reveals that the contribution of the positively charged particle in the topological analysis and basin properties is non-negligible. Most importantly, it is demonstrated that by increasing the mass of the positive particle, the TC-QTAIM analysis tends toward the QTAIM analysis of the lithium hydride system considered within the clamped nucleus paradigm. This result seems to indicate that the orthodox QTAIM is just the asymptote of the TC-QTAIM, the latter encompasses the former. Thus, one may claim that the TC-QTAIM is a unified framework for the AIM analysis of vast variety of quantum systems.