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

## TL;DR

This paper extends the quantum theory of atoms in molecules to non-Coulombic systems with homogeneous potential energy functions, enabling the identification of new real-space subsystems beyond atoms, exemplified by a harmonic trap model.

## Contribution

It introduces QTROS, an extended formalism for analyzing real-space subsystems in non-Coulombic systems, including bosonic systems, beyond traditional QTAIM.

## Key findings

- Basin energy can be defined for all systems with homogeneous potential energy functions.
- QTROS allows identification of novel real-space subsystems in non-Coulombic systems.
- Analysis of bosonic systems with QTROS is demonstrated for the first time.

## Abstract

It is customary to conceive the interactions of all the constituents of a molecular system, i.e. electrons and nuclei, as Coulombic. However, in a more detailed analysis one may always find small but non-negligible non-Coulombic interactions in molecular systems originating from the finite size of nuclei, magnetic interactions, etc. While such small modifications of the Coulombic interactions do not seem to alter the nature of a molecular system in real world seriously, they are a serious obstacle for quantum chemical theories and methodologies which their formalism is strictly confined to the Coulombic interactions. Although the quantum theory of atoms in molecules (QTAIM) has been formulated originally for the Coulombic systems, some recent studies have demonstrated that apart from basin energy of an atom in a molecule, its theoretical ingredients are not sensitive to the explicit form of the potential energy operator. In this study, it is demonstrated that the basin energy may be defined not only for coulombic systems but for all real-space subsystems of those systems that are described by any member of the set of the homogeneous potential energy functions. On the other hand, this extension opens the door for seeking novel real-space subsystems, apart from atoms in molecules, in non-Coulombic systems. These novel real-space subsystems call for an extended formalism that goes beyond the orthodox QTAIM, which is not confined to the Coulombic systems nor to the atoms in molecules as the sole real-space subsystems. 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 for the QTROS analysis. The QTROS analysis of bosonic systems is particularly quite unprecedented, not attempted before.

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Source: https://tomesphere.com/paper/1706.02767