*2.5. QTAIM-Based Methods*

By operating with the topology of the electron density distribution, the Quantum Theory of Atoms in Molecules (QTAIM) created by Bader [94–96] makes it possible to divide the space of a molecule into closely adjoining, i.e., non-overlapping, three-dimensional subspaces. According to QTAIM, they are understood as individual atoms. These atoms are separarated from each other by surfaces through which there is no electron density gradient flow, and atomic nuclei are most often attractors of this gradient field. Importantly, the possibility of unequivocally defining the space of an atom in a molecule, introduced by QTAIM, enables the determination of many atomic quantities by integration over the volume of a given atom. Yet another useful result of QTAIM are the concepts of the so-called bond path (BP) and bond critical point (BCP) [94–96]. The latter is a saddle point in the electron density distribution that features positive curvature (thus, experiencing the minimum) in the direction of the two neighboring nuclei and negative curvatures (thus, experiencing maxima) in the two perpendicular directions, and the former is a pair of gradient vector paths originating at this BCP and terminating at both nuclei. Thus, a bond path is also a ridge of the highest electron density between a pair of the so linked atoms. For this reason, the pattern of such electron density ridges, i.e., bond paths (the so-called molecular graph) very often corresponds to the pattern of bonds that are drawn by chemists, i.e., the structural formula [97]. The fundamental issue in the theory of inter- and intramolecular hydrogen bonds or other stabilizing interactions is that, according to QTAIM [94–96], the simultaneous presence of a bond path and a bond critical point between any pair of atoms is a necessary and sufficient proof that this bond (interaction) is stabilizing [98]. This view has resulted in many people using the presence of a bond path as a sufficient criterion for the presence of a hydrogen bond (or other bonding interaction) between a pair of atoms. Unfortunately, this happens without even specifying the bonding (interaction) energy value, in a way ignoring the fact that the hydrogen bond must be stabilizing to deserve this name. However, it should be noted that the treatment of both BP and BCP as sufficient evidence for stabilizing interaction has been criticized [99–114], as it turns out that the presence of these topological features between a pair of atoms in general does not determine the stabilizing or destabilizing nature of the interaction between the pair [112,113].

However, in the context of this article, it is more important that QTAIM makes it possible to determine the interatomic interaction energy. The first of these methods was proposed by Espinosa et al. [115] and it is based on a quantity computed at the bond critial point of the interaction, the energy of which is to be determined. The another method is based on the partition of the total energy of a system into individual monoatomic and diatomic contributions and functions under the name of Interacting Quantum Atoms (IQA) [116,117]. These two methods will now be discussed in the next two subsections.
