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It is customary to conceive the interactions of all the constituents of amolecular system, i.e. electrons and nuclei, as Coulombic. However, in a moredetailed analysis one may always find small but non-negligible non-Coulombicinteractions in molecular systems originating from the finite size of nuclei,magnetic interactions, etc. While such small modifications of the Coulombicinteractions do not seem to alter the nature of a molecular system in realworld seriously, they are a serious obstacle for quantum chemical theories andmethodologies which their formalism is strictly confined to the Coulombicinteractions. Although the quantum theory of atoms in molecules (QTAIM) hasbeen formulated originally for the Coulombic systems, some recent studies havedemonstrated that apart from basin energy of an atom in a molecule, itstheoretical ingredients are not sensitive to the explicit form of the potentialenergy operator. In this study, it is demonstrated that the basin energy may bedefined not only for coulombic systems but for all real-space subsystems ofthose systems that are described by any member of the set of the homogeneouspotential energy functions. On the other hand, this extension opens the doorfor seeking novel real-space subsystems, apart from atoms in molecules, innon-Coulombic systems. These novel real-space subsystems call for an extendedformalism that goes beyond the orthodox QTAIM, which is not confined to theCoulombic systems nor to the atoms in molecules as the sole real-spacesubsystems. It is termed the quantum theory of real-space open subsystems(QTROS) and its potential applications are detailed. The harmonic trap model,containing non-interacting fermions or bosons, is considered as an example forthe QTROS analysis. The QTROS analysis of bosonic systems is particularly quiteunprecedented, not attempted before.

Extending the topological analysis and seeking the real-space subsystems in non-Coulombic systems with homogeneous potential energy functions