*3.3. Theoretical DFT Study*

To analyze and understand the different modes of interaction observed in the solid state of the cocrystals, a density functional theory (DFT) study at the PBE0-D3/def2TZVP level of theory was carried out. The recurrent motifs observed in the solid-state X-ray structures are analyzed herein, focusing on the calculation of the individual H-bond energies and also the unconventional stacking interactions in compounds **1** and **3** that include the H-bonded arrays as described below.

Figure 7 shows the molecular electrostatic potential (MEP) surfaces of all coformers (pyridylcarboxamides and mandelic acid) studied in this work. The MEP surface analysis is useful to investigate the electron-rich and electron-poor regions of the crystal coformers. It can be observed that the most positive region corresponds to the H-atom of carboxylic acid (+58 kcal/mol) in mandelic acid followed by the H-atoms of the carboxamide groups. These are more positive in nicotinamide and isonicotinamide due to the influence of the aromatic H-atom in *ortho* (+52 and +53 kcal/mol for nicotinamide and isonicotinamide, respectively). Moreover, the most negative regions correspond to the O-atoms of the carboxamide group (ranging from −38 to −43 kcal/mol). The MEP values are also large and negative at the O-atom of the carboxy group in mandelic acid and the aromatic N-atom of nicotinamide and isonicotinamide rings (ranging from −30 to −35 kcal/mol). Finally, the MEP is slightly less negative at the aromatic N-atom of picolinamide (−17 kcal/mol) and hydroxyl group of mandelic acid (−27 kcal/mol). This analysis provides evidence that the carboxy group of mandelic acid is the strongest H-bond donor and the O-atom of the carboxamide group the best H-bond acceptor.

**Figure 7.** MEP surfaces of picolinamide (**a**), nicotinamide (**b**), isoniconitamide (**c**) and mandelic acid (**d**) at the PBE0-D3/def2-TZVP level of theory. Isosurfaces plotted using 0.001 a.u. The energies at selected points of the surface are indicated in kcal/mol.

The hydrogen bond and formation energies of the assemblies were estimated using the QTAIM method and the value of the Lagrangian kinetic G(r) contribution to the local energy density of electrons at the critical point (CP). The dissociation energy of each individual H-bonding interaction was estimated using the approach proposed by Vener et al. [40], which was specifically developed for HBs (Energy = 0.429 × G(r) at the bond CP).

Figure 8 represents the distribution of bond CPs and bond paths for the tetrameric assembly observed in the picolinamide–mandelic acid cocrystal exhibiting a network of H-bonds. The existence of a bond CP and bond path connecting two atoms is a universal indication of an interaction [41]. The QTAIM analysis of the tetrameric assembly represented in Figure 8a shows the presence of appropriate bond CPs (red spheres) and bond paths connecting the N/O-atoms to the H atoms in the H-bonding interactions. Moreover, several ring CPs (yellow spheres) also emerge upon complexation due to the formation of supramolecular rings. The distribution also shows the existence of weak C–H··· O interactions between one aromatic C–H group and the hydroxyl O-atom of the mandelic acid. The dissociation energy of the tetrameric assembly is large (39.7 kcal/mol), thus confirming the importance of this H-bonding network. Figure 8b also includes the individual energy of each H-bond that is indicated in blue next to the bond CP that characterizes each H-bond. In agreement with the MEP analysis, the H-bonds involving the carboxy

group as H-bond donor (O–H···O) are the strongest (11.0 and 7.8 kcal/mol). Moreover, several structure-guiding motifs are observed in the solid state structure of compound **1**. These are *R*<sup>2</sup> <sup>2</sup>(8) and *<sup>R</sup>*<sup>4</sup> <sup>4</sup>(8), involving only the carboxy and carboxamide groups, In addition, a *R*<sup>2</sup> <sup>2</sup>(10) motif is also important, where the pyridine N-atom and the hydroxyl groups participate in addition to the dominant carboxy and carboxamide groups. We also evaluated energetically the formation of a different tetrameric assembly where two *R*<sup>2</sup> <sup>2</sup>(8) motifs are stacked (see Figure 8c) in an antiparallel fashion. The binding energy computed as a dimerization energy of two *R*<sup>2</sup> <sup>2</sup>(8) motifs is −9.7 kcal/mol, thus revealing the strong nature of this unconventional π-stacking interaction. The NCIplot index analysis is represented in Figure 8c, showing large and green (meaning attractive interaction) isosurfaces located between the carboxy and carboxamide groups of both crystal coformers, thus suggesting that the interaction involves the π-system of both groups (πCOOH···πCONH2). The NCI isosurface is dark blue for the OH···O and light blue for the NH···O H-bonds of the *<sup>R</sup>*<sup>2</sup> <sup>2</sup>(8) motifs, thus confirming the strong nature of the OH···O bonds in line with the QTAIM dissociation energy and the MEP surface analysis.

**Figure 8.** (**a**) AIM distribution of bond and ring critical points (green and yellow spheres, respectively) and bond paths obtained for the H-bond assembly of compound **1**. The dissociation energies of the H-bonds using the G(r) values are indicated next to the bond CPs. (**b**) AIM distribution of bond and ring critical points (green and yellow spheres, respectively) and bond paths obtained for the H-bonding *R*<sup>2</sup> <sup>2</sup>(8) motif. (**c**) NCIplot index analysis of the π-stacked tetramer. |RGD| isosurface 0.5, density cutoff 0.04 a.u., color range: −0.04 a.u. ≤ (signλ2) ρ ≤ 0.04 a.u.

For compounds **2a** (JILZOU01) and **2b** (JILZOU), a similar study was performed, where we selected a representative tetrameric assembly for each one including the most important interactions and motifs. The QTAIM analyses are shown in Figure 9, where each H-bond is characterized by a bond CP connecting the O/N-atoms to the H-atoms. Similar to **1**, the distribution shows the existence of weak C–H··· O interactions between H-atoms of nicotinamide ring and the O-atoms of the hydroxyl groups in **2a** or carboxamide group in **2b**. Moreover, a recurrent *R*<sup>2</sup> <sup>2</sup>(7) motif is observed in both compounds where the carboxy group of the mandelic acid forms a strong OH···Npy H-bond (8.4 and 10.4 kcal/mol in **2a** and **2b**, respectively) combined with a much weaker C–H···O H-bond (2.6 and 1.7 kcal/mol in **2a** and **2b**, respectively). In **2a**, a *R*<sup>2</sup> <sup>2</sup>(9) motif is observed where the hydroxyl group of mandelic acid establishes a moderately strong H-bond (5.7 kcal/mol) with the carboxamide group of the coformer. An interesting *R*<sup>2</sup> <sup>2</sup>(8) motif is observed in **2b** involving the carboxamide groups (4.5 kcal/mol each H-bond) and leading to the formation of a self-assembled

dimer. The formation energies of the selected tetramers are similar (24.6 kcal/mol in **2a** and 26.9 kcal/mol in **2b**).

In compound **3**, the tetrameric assembly shown in Figure 10a was analyzed, where the isonicotinamide molecule forms self-assembled dimers via two equivalent N–H···O bonds (*R*<sup>2</sup> <sup>2</sup>(8) motif) with a total dissociation energy of 10.4 kcal/mol. In addition, the recurrent *R*<sup>2</sup> <sup>2</sup>(8) motif described above in **2a** and **2b** is also observed in **3** with a dissociation energy of 13.8 kcal/mol, thus revealing that the combination of the strong OH···H and weak CH···O H-bonds is energetically favored over the two symmetric NH···O H-bonds between the carboxamide groups. This tetrameric assembly, which presents a very large dissociation energy (37.0 kcal/mol) self-assembly, forming π-stacking octamers in the solid state, as represented in Figure 10b. The NCIplot index analysis shows a much extended isosurface that embraces the whole assembly and explaining the large dimerization energy (−27.3 kcal/mol). The isosurfaces clearly show that the H-bonded arrays are also involved in the stacking interaction, as previously observed in the literature [42]. Actually, it has been demonstrated that the formation of H-bonded arrays is energetically enhanced over aromatic surfaces [43].

**Figure 10.** (**a**) AIM distribution of bond and ring critical points (green and yellow spheres, respectively) and bond paths obtained for the H-bonding assembly of compound **3**. The dissociation energies of the H-bonds using the G(r) values are indicated next to the bond CPs. (**b**) NCIplot index analysis of the π-stacked octamer. |RGD| isosurface 0.5, density cutoff 0.04 a.u., color range: −0.04 a.u. ≤ (signλ2) ρ ≤ 0.04 a.u.

Table 3 summarizes the interaction energies for the H-bonding assemblies represented in Figures 8–10 computed using the supramolecular approach (BSSE corrected) and estimated using Verner's equation. In general, there is a good agreement between the BSSE corrected energies and those derived from QTAIM, giving reliability to Verner's approach. In some cases, such as the pentameric assembly of compound **1** (Figure 8a) and the tetramer of compound JILZOU (Figure 9b), the interaction energies are greater (in absolute value) than the formation energies derived from the QTAIM approach. This is due to an extra stabilization in those assemblies caused by van der Waals forces and other long-range interactions due to the approximation of the bulk of the molecules. In any case, the H-bonding interactions are clearly dominant.

**Table 3.** Interaction energies of the HB assemblies derived from the supramolecular approach (BSSE corrected) and derived from the QTAIM (EBSSE and ΣEHB, respectively) in kcal/mol at the PBE0-D3/def2-TZVP level of theory.

