**3. Results**

We present the main results of this investigation in three parts. First, the effect of the monosubstitution in malondialdehyde by the EWG and EDG considered in this work. Second, we will shed some light on the origin of the strong positional dependency of the substitution. Furthermore, third, we will compare the IQA results with the estimations put forward in Equations (3) and (4).

#### *3.1. Influence of Substitution on RAHB Energetics*

The IQA methodology partitions the energy of an electronic system into intra- and interatomic terms, a condition that allows the study of individual interactions within a molecule. An important characteristic of IQA is that this partition is carried out without using any reference system or empirical data. These features make IQA arguably the gold standard among the different methodologies, geometric or energetic alike, to study intramolecular interactions, including RAHBs. Figure 2 shows the excellent correlation between IQA interaction energies and the intramolecular hydrogen bond distance for the examined RAHBs.

The values for the interaction energy corresponding to the O···H contact with respect to those of malondialdehyde are reported in Table 1. The same chart reports the dissection of the IQA interaction energies into classical and exchange-correlation components. The relevance of the former over the latter contributions is conspicuous for malondialdehyde and the investigated EWGs and EDGs.

**Figure 2.** Correlation between IQA interaction energies in kcal/mol and OH···H distances in angstroms.

**Table 1.** IQA interaction energies (*E*int), as well as its classical (*V*cl) and exchange-correlation (*V*xc) parts, for the investigated O···H RAHB contacts with respect to those in malondialdehyde (Table S1). The values are reported in kcal·mol−1.


We note that the monosubstitution in different positions can either weaken or strengthen the associated RAHB. For example, the −CF3 group weakens the RAHB when it is bonded directly to the carbonyl group, but it has the opposite effect in positions 2 and 3. Concerning the halogens, they decrease the intensity of the O···H interaction when they are located in positions 1 and 2. On the other hand, they decrease the magnitude of the interaction energy when they are bonded to the enolic carbon. Mesomeric structures sugges<sup>t</sup> that the influence of EWGs via resonance would be more noticeable on the RAHB strength when the EWG is bonded to the *α* carbon (Figure 3). The effect of the EWG are therefore more likely interpreted to occur via inductive effects. Furthermore, the influence of these groups is most obvious when they are close to the HB donor. Nevertheless, Table 1 shows that the exchange-correlation contribution to bonding also increases when EWG is bonded to the *β* carbon, and thus resonance effects cannot be completely neglected.

**Figure 3.** Resonance effect of an electron withdrawing substituent at position 2 in the examined RAHBs.

With respect to the examined EDG, we note that these groups have a minimal effect (a slight reduction) when they are located at position 2. Notwithstanding when they are at position 1 and especially at position 3, they notably increase the RAHB interaction energy. This effect can be understood in terms of the mesomeric structures shown in Figure 4. Interestingly, the substitution in position 3 has the most conspicuous influence effect, leading in all cases to a strengthening of the interaction.

**Figure 4.** Resonance effect of an electron donating substituent at position 3 in the examined RAHBs.

The above-mentioned effects can be used as guidelines by synthetic chemists to modulate the strength of RAHBs, via the electron withdrawing or donating features of a given substituent, together with its position in the conjugated system.

#### *3.2. Comparison between IQA, OCM, and EM Methods*

Table 2 reports the different assessments of the RAHB energy considered in this paper, namely, IQA, OCM, and EM. Figure 5 shows the relationship between (i) the IQA interaction energy and (ii) the formation energy computed with the OCM method together with the HB energy calculated using EM. As we can appreciate from the left side of Figure 5, the IQA interaction energy is not correlated with the *E*form results yielded by the OCM approach. The fact that these results are unconnected can be associated with the main thesis of this work: the breaking of an RAHB can trigger a rearrangemen<sup>t</sup> in the electronic density, which is unrelated to the energetic features of the investigated RAHB [38]. Indeed, these unavoidable modifications take place in molecular regions unrelated to the RAHB. This fact makes the OCM (*E*form) unsuitable as a parameter for the assessment of the formation energies of the RAHBs under consideration.


**Table 2.** IQA interaction energies (*E*int), formation energies (*E*form) computed by means of the OCM (expression (3)), and H-bond interaction energies (*E*HB) estimated via Equation (4) for the investigated O···H RAHB contacts. The values are reported in kcal·mol−1.

**Figure 5.** Correlation of IQA interaction energies with (**left**) OCM values of *E*form and (**right**) EM results of *E*HB.

Contrary to this fact, the correlation between the values of *E*int and those corresponding to Equation (4) are excellent. In all cases, IQA interaction energies and Espinosa's empirical formula produce indeed the same relative strengths for the studied systems. This observation indicates that for typical RAHBs, Equation (4) is able to qualitatively recover the interplay between the *π*-skeleton and the O···H−O moiety.

The good agreemen<sup>t</sup> between *E*int and *E*HB should not be interpreted as an uncritical approval to the use of Equation (4) for the estimation of relative RAHB strengths. Certainly, different authors have pointed out a series of deficiencies for this empirical formulation. Here we mention two of these potential problems. First, the values resulting from Equation (4) are always negative, a circumstance that always points to an attractive interaction. Nevertheless, certain C−H···O contacts are repulsive in nature [62]. The use of Formula (3) to describe these contacts would produce a qualitatively incorrect result. Second, Equation (4) is not transferable to other contacts, such as H···F, where a different scaling factor from that used in Equation (4) needs to be used [73].

We finally state what we consider the limits for the reasonable application of EM on the study of intramolecular HBs in general and RAHB in particular. Given that Equation (4) is unable to distinguish between attractive and repulsive interactions, it should be only applied when no doubt can arise regarding the attractive nature of the contact. Additionally, although *E*int and *EHB* follow the same strength order, their magnitudes are not comparable. Therefore, the EM should primarily be used to study intramolecular contacts where the interaction mainly involve the same atomic species. This situation might be the case, for instance, in different substitutions in an aromatic ring adjacent to the O−H···O group [74] or changes in the protonation degree in an intramolecular HB [75].
