*2.1. Real Space Wavefunction Analyses*

The QTAIM theory, as originally formulated by Bader [33], is a method of wave function analysis based on the topology of the electron density *ρ*(*r*), in which the real space is fragmented in a collection of attraction basins (Ω) induced by the topology of *ρ*(*r*). In QTAIM, traditional chemical ideas, such as the concept of chemical groups or fragments, atomic charges or bond orders, emerge naturally without the need of any reference. Moreover, the QTAIM partition can be performed starting either from theoretical (electronic structure calculations) or experimental (high-resolution X-ray diffraction data [35]) determinations of the electron density of the system. This combination of robustness and practicality has made QTAIM to be widely employed to shed light into a large variety of phenomena including catalysis [36–38], electrical conductivity [39–41] and aromaticity [42–44], to name a few.

Based on a 3D partition as that defined by QTAIM, the IQA methodology [34] divides a fully interacting non-separable quantum mechanical system into chemically meaningful interacting entities. The total electronic energies in IQA can be written as a sum of one-body (intra-atomic) and two-body (inter-atomic) terms [34,45], as:

$$E = \sum\_{A} E\_{\text{self}}^{A} + \sum\_{A>B} E\_{\text{int}}^{AB} \tag{1}$$

where *E<sup>A</sup>* self is the energy of atom *A*, which includes the electron–nucleus attraction, the inter-electronic repulsion, and the kinetic energy within atom *A*. Additionally, *EAB* int is the total interaction energy between atoms *A* and *B*. This term encompasses all the available interaction terms between the nucleus and electrons within atoms *A* and *B*. The constituting terms of the total inter-atomic interaction between two atoms, *EAB* int , can be regrouped to express the latter as a sum of purely covalent (i.e., exchange-correlation, *VAB* xc ) and ionic (i.e., classical, *VAB* cl ) components:

$$E\_{\rm int}^{AB} = V\_{\rm cl}^{AB} + V\_{\rm xc}^{AB}.\tag{2}$$

Indeed, the IQA energy decomposition provides a particularly convenient way to study and characterise the chemical nature of the interaction among atoms in an electronic system.
