**2. Theoretical Framework**

The QTAIM provides a division of space based on the topology of the electronic density. This method of wave function analysis enables the recovery of important chemical concepts, such as atoms, functional groups, atomic charges, and bond orders from either electronic structure calculations or X-ray experiments [44]. Consequently, QTAIM has been applied in the study of a wide variety of chemical and physical problems, such as the examination of different bonds [45,46], adsorption [47–49], electrical conductivity [50–52], and catalysis [53–55].

The traditional implementation of the IQA energy partition uses the atoms of QTAIM as a starting point to divide the total energy of an electronic system into the sum of self energies for each atom and interaction energies between the atoms in the system [29,30],

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

*<sup>E</sup>A*self in Equation (1) is the energy corresponding to atom *A*, which includes its kinetic energy, the electron–nucleus attraction and the interelectronic repulsion within atom *A*.

*EAB* int is the total interaction energy between atoms *A* and *B* and comprises all the possible combinations of the interaction terms between the nucleus and electrons of *A* on one hand, with the nucleus and electrons of *B* on the other.

We can also reorganise the terms included in *EAB* int in order to obtain an expression that gives us additional information about the nature of the interaction between *A* and *B*,

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

where *VAB* cl corresponds to the ionic part of the interaction energy while *VAB* xc is a term related with the covalency of the bond [56].

#### *2.1. Models to Estimate the Energies of Intramolecular Hydrogen Bonds*

The work dedicated to the estimation of the strength of intramolecular HBs has been very extensive, as reflected in the excellent review on the subject by Jabło ´nski [24]. Specifically, we will mainly focus on two indirect measurements. The first approach is based on the differences between the open and the closed conformations, referred to hereafter as the Open-Closed Method (OCM):

$$E\_{\rm IIB}^{\rm intra} \approx E\_{\rm form} = E\_{\rm closed} - E\_{\rm open}.\tag{3}$$

This methodology, albeit popular, presents two important drawbacks. First, it is not clear what geometry should be used as "open" [24]. For instance, Schuster has argued that the optimal open conformation for comparison purposes would be the one wherein minimal changes occur with respect to the closed conformation, even if its geometry is not a local minimum of the potential energy hypersurface [57]. We chose to use a different approach from that put forward by Schuster, and we considered optimised structures for both closed and open conformations of the systems under study. The other important drawback of the OCM method is that it combines changes taking place in other parts of the molecule with the energy corresponding to the HB itself [38]. Thus, stabilising and destabilising contributions, which result from other effects apart from the HB can be misattributed to this interaction. For example, steric destabilisation elsewhere in the molecule could be discounted from an examined intramolecular HB energy because it might occur that the HB is strong enough to compensate such unfavourable steric effects.

The second approximation, proposed by Espinosa et al. and denoted hereafter as Espinosa's Method (EM), is based on the topology of the electronic density, specifically, on the correlation of the potential electron energy density at the bond critical point, *<sup>V</sup>*(**<sup>r</sup>**bcp), associated with a given HB and its corresponding energy according to the empirical expression [42,43],

$$E\_{\rm HB}^{\rm intra} \approx E\_{\rm HB} = \frac{1}{2} V(\mathbf{r}\_{\rm bcp}).\tag{4}$$

This equation was put forward for the study of intermolecular HBs and has proven to be a suitable estimator for the formation energies as computed by the IQA approach in small and medium-sized water clusters, accounting for the relative order for the different types of HB contacts in these systems [58,59]. Nevertheless, some authors have questioned the uncritical use of EM for intramolecular HBs [60–62].
