*3.2. Electronic Structure Topological Analysis on the Basis of Quantum Theory of Atoms in Molecules (QTAIM)*

Quantum theory of atoms in molecules (QTAIM) served as a method of choice to investigate the electronic properties of the studied molecules. The visualization and the results concerning the covalent and non-covalent interactions of the experimental and optimized structures of the studied dimers are presented in Table 2 and in Figure 7.

**Figure 6.** Potential of mean force (PMF) for the proton motion in the hydrogen bond of examined dimers with respect to the distance between the proton and its acceptor. (**D**) 2,6-difluorobenzamide and (**E**) 4-hydroxybenzoic acid.

**Table 2.** QTAIM-derived properties at BCPs for examined dimers from the structure deposited in the CCDC database and after geometry optimization at the *ω*B97XD/def2-TZVP level of theory. E1 is a bond energy based on the Espinosa model, given in kcal \* mol−1. Units of gathered quantities are as follows: electron density, *<sup>ρ</sup>BCP*, is given in *<sup>e</sup>* · *<sup>a</sup>*−<sup>3</sup> <sup>0</sup> atomic units and the Laplacian of electron density, <sup>∇</sup>2*ρBCP*, is in *<sup>e</sup>* · *<sup>a</sup>*−<sup>5</sup> <sup>0</sup> units. VBCP stands for BCP potential energy density and HBCP denotes the energy density at the BCP.


The use of the QTAIM method allowed a qualitative and quantitative description of the interactions between monomers. Bond energies were estimated on the basis of their linear dependence on the potential energy density at the BCP (VBCP) via the Espinosa equation [95]. It can be observed that, in the case of both (D) and (E) dimers, the hydrogen bonds form quasi-rings, which provides structural stabilization. Their formation is indicated by the presence of the ring critical points (RCPs) (marked as small yellow spheres in Figure 7). For the dimer denoted as (D1), the properties at BCPs corresponding to two non-covalent interactions and two covalent bonds: ND-H. . . OA hydrogen bond and the intramolecular F...N contact as well as the ND-H and C=OA bonds were analyzed extensively. Both aforementioned non-covalent interactions can be considered weak, rather electrostatic in nature, since their estimated bond energies lie below 4 kcal \* mol−<sup>1</sup> and their Laplacian and energy density values are positive. Interestingly, when we inspect the data

corresponding to the (D2) dimer, it can be seen that the relaxation of the structure causes the weakening of ND-H covalent bond, the intramolecular F...N interaction (which is not even detected by QTAIM) and the accompanying strengthening of the ND-H. . . OA hydrogen bond. In this case, the character of the ND-H. . . OA is noticeably more covalent, because the corresponding *ρ* and energy density values become larger and lower, respectively (HBCP is indeed very close to zero) [34]. A similar analysis regarding the dimer (E) leads to the same conclusions: the optimization of the examined structures results in the strengthening of the hydrogen bond and the weakening of the corresponding covalent bond of the proton donor. More interesting is the characteristics of the hydrogen bond itself, namely OD-H. . . OA. In both the experimental and the optimized structures ((E1) and (E2)), the HBCP values corresponding to the hydrogen bonds are negative and their bond energies are much larger compared to (D1) and (D2)—for this reason, one can say that they are more covalent in nature than their counterparts, ND-H. . . OA.

**Figure 7.** QTAIM molecular graphs of the studied dimers. Ball and stick model was used for visualization. Bond paths, BCPs and RCPs are presented as green lines and small green and yellow spheres, respectively. Color coding: white—hydrogen, grey—carbon, red—oxygen, blue—nitrogen, yellow—fluorine. (**D1**,**E1**) are the experimental structures, whereas (**D2**,**E2**) are the structures after the relaxation at the *ω*B97XD/def2-TZVP level of theory.
