*2.3. Energy of HBs with Fluorine*

Ligand–receptor complexes are stabilized by various intermolecular forces, such as strong HBs (O···H–O, N···H–O, N···H–N), weak HBs (O···H–C, S···H–N), XBs, πstacking, salt bridge, amide stacking, cation-π, and hydrophobic interactions and others [17]. Fluorine-containing HBs, especially those with hydroxyl and amine donors, are not common in biological systems (Figures 3 and 4). Therefore, it is important to determine the strength and geometric preferences of these HBs in biological systems. In this study, we attempted to evaluate the nature and energetic dependencies of HBs with fluorine in the theoretical background by performing quantum chemical calculations using small molecular systems extracted from ligand–biomolecule crystals (O–H, N–H, +N–H, and C–H were only considered to be HB donors). We determined the energy of HBs with fluorine found in crystal structures by applying three different methods as follows: (1) Diff—energy was calculated as the difference between the energy of the interacting molecules and the sum of the energies of isolated species calculated in Gaussian; (2) QTAIM—energy was calculated at BCP in AIMAll software; and (3) ETS—energy was calculated between two interacting molecules using the ETS-NOCV scheme implemented in ADF software.

At first, a simple statistical analysis was performed on the data obtained from the three approaches using the correlation coefficient and Pearson test in R (Supplementary Tables S1 and S2). The results of the analysis indicated the highest correlation between Diff and ETS methods (*p* < 0.05, correlation coefficient ~1) because they consider the energy of the entire system and approximately 70% of the calculated energy accounts for the same nature of interaction (attractive/repulsive). Additionally, the correlation decreased for stronger interactions (Supplementary Tables S1 and S2) due to the fact that the Diff method is intended for weak and medium HBs; strong HBs result in geometry distortion of the interacting molecules, which decreases the accuracy of the evaluation of the HB itself [18]. The energies of HBs calculated by QTAIM did not correlate with those determined by the remaining methods, since this method takes only isolated L–R interaction and neglects long-range interactions occurring between the atoms from separated fragments.

The distribution of calculated interaction energies for all selected complexes for a given type of HB with fluorine and method is illustrated in Figure 5. For HBs with Fal, the interaction energy calculated by QTAIM varied between 0 and −1.2 kcal/mol (the

weakest HBs were found for Fal··· H–O, with an energy value of −0.64 kcal/mol). For Fal··· H–C HBs, the energy was (−0.69 kcal/mol). The strongest HBs (~−0.8 kcal/mol) were observed for Fal··· H–N (no significant difference was noted between Fal··· H–N HB and Far··· H–N<sup>+</sup> HB) (Figure 5A). The energy range determined by the Diff method was also between 0 and –1.2 kcal/mol, while the energy determined by the ETS method ranged from 0 to −8 kcal/mol (Figure 5A). Additionally, the Diff method indicated that the charge-assisted Fal··· H–N+ was the weakest HB (−0.70 kcal/mol), while Fal··· H–N HB was stronger (−0.96 kcal/mol). Unlike Diff, the results of the ETS method showed that the charge-assisted Fal··· H–N+ HB was the stronger (−5.11 kcal/mol), while Fal··· H–N HBs were weaker than Fal··· H–O HBs (−2.28 and −2.46 kcal/mol, respectively) (Figure 5A). For HBs with Far, a different trend was noted in the QTAIM method than for HBs with Fal, where the strongest HBs had OH as a donor (−0.94 kcal/mol). The Far··· H–N HBs were found to be slightly weaker with median energy values of ~–0.7 kcal/mol (for +NH and NH donors), and the weakest was Far··· H–C HB (−0.62 kcal/mol) (Figure 5B). A comparison of Diff and ETS methods revealed a similar trend as in the case of Fal—the Diff method indicated that the Far··· H–N+ HB was the weakest (−0.8 kcal/mol), while the ETS method indicated it as the strongest interaction (−5.3 kcal/mol) (Figure 5B). The QTAIM method showed that F··· H–O HBs with Far were stronger than those with Fal, while HBs with other donors were found at a similar energy level. However, it should be emphasized that both Diff and ETS methods revealed higher stabilization energy for HBs with Far compared to HBs with Fal.

**Figure 5.** Box plots showing the distribution of the stabilization energy for HBs containing fluorine bonded to an (**A**) aliphatic or (**B**) aromatic carbon. A comparison is made for the individual donor groups (OH, +NH, NH, and CH) as well as the calculation approaches used (Diff, QTAIM, and ETS).

The hydroxyl donor occurs in the side chains of three amino acid—tyrosine (TYR), threonine (THR), and serine (SER). The phenolic hydroxyl group (TYR) is significantly more acidic (pKa of about 9.8 in polypeptides) than the aliphatic hydroxyl group (SER or THR, pKa ~13.6) [19]. In addition, Graton et al. found in an analysis of the PDB repository that the distances and angle of HBs with a hydroxyl group decreased in the order THR > SER > TYR, which suggests that TYR forms the stronger HBs [20]. In the present study, the results obtained by the QTAIM method revealed that for Fal (Figure 6A), the energy of HBs does not depend on the F··· H–O angle, as the highest values were observed in the whole range of the analyzed angles. Instead, the energy of Fal··· H–O HBs closely correlated with the distance, as observed in the case of conventional hydrogen bonding. It should be mentioned that the QTAIM method showed higher energy for F··· H–O HBs

with aromatic fluorine than for HBs with aliphatic fluorine (Figure 6). Most of the F··· H–O HBs with distances shorter than 2.75 Å are repulsive (Figure 6), which shows that despite the stabilizing nature of the F··· H–O HB itself, the interacting fragments have a positive energy contribution (repulsive character). This effect may be due to the interaction of the neighboring atoms, or high positive kinetic energy. All three methods showed that the highest stabilizing energies (red squares in Figure 6) were in the range of 2.85–3.45 Å (for both fluorine) and 150◦–120◦ for Fal and 145◦–120◦ for Far, suggesting that these are the optimal ranges of geometric parameters for F··· H–O HBs. The analysis of the selected crystal structures did not show any significant differences between the F··· H–O HBs of attractive and repulsive nature. The only differentiating factor identified was the F···O distance (Figure 6).

**Figure 6.** HB energy maps generated based on Diff, QTAIM, and ETS calculations of interaction energy between OH donor and fluorine attached to (**A**) an aliphatic fragment and (**B**) an aromatic ring for specific geometric parameters. The areas for which the highest stabilizing energy was observed in all three methods are marked with a red square.

Among amino acids, three (ARG, LYS, HIS) have additional amino groups. The side chain of arginine (ARG) is amphipathic because at physiological pH it contains a positively charged guanidine group (pKa = 12.48). Another amphipathic amino acid is lysine (LYS), the side chain of which contains a positively charged primary amine group at the end of the long hydrophobic carbon tail (pKa = 10.53). Histidine (HIS) contains an imidazole side chain. His pKa is 6, above which one of the two protons is missing (in physiological pH, histidine has two tautomers). Since it is difficult to automatically protonate the appropriate nitrogen atom of histidine which forms an F··· H–N<sup>+</sup> HB, we calculated the energy of <sup>F</sup>··· H–N+ HB only for LYS and ARG (Figure 7). The QTAIM calculations showed that the energy of Fal··· H–N+ and Fal··· H–O HBs was similar. Additionally, F··· H–N<sup>+</sup> was found to be strongly influenced by the distance between F···N and not by the angle (Figure 7) (as noticed for F··· H–O HBs). A similar trend for both aliphatic and aromatic F was observed for F··· H–N<sup>+</sup> HBs, but the highest interaction energy was mostly localized at higher values of the Far···H–N+ angle (Figure 7). For aliphatic fluorine, the range of geometric parameters

in which the three methods indicated the strongest Fal···H–N+ HBs was 140◦–120◦ and 2.85 –3.45 Å (as for F··· H–O HB). In the case of Far, two ranges of geometric parameters were distinguished: (1) 170◦–150◦ and 3.0–3.6 Å; and (2) < 120◦ and 2.4–3.6 Å. Due to its large volume, the guanidine group interacts not only with fluorine directly but also with neighboring atoms. Therefore, the energy calculated by Diff and ETS methods might be overestimated.

**Figure 7.** HB energy maps generated based on Diff, QTAIM, and ETS calculations of interaction energy between positively charged NH donor and fluorine attached to (**A**) an aliphatic fragment and (**B**) an aromatic ring for specific geometric parameters. The areas for which the highest stabilizing energy was observed in all three methods are marked with a red square.

Interestingly, the analysis of crystal structures with F··· H–N<sup>+</sup> HBs showed that for F··· N+ distances of <2.8 Å, almost 70% of HBs exhibited a destabilizing character. Moreover, the interaction of positively charged nitrogen with the CF3 group, with a partial positive charge on the carbon atom, is often repulsive (Figure 7).

The F··· H–N HBs were found almost four times more frequently in PDB than F··· H– O HBs (Figures 3 and 4). The energies of F··· H–N HBs were calculated for all amino acids, except for arginine and lysine as these amino acids contain positively charged nitrogen atoms. Furthermore, whether the nitrogen atom was in the main chain or the side chains (ASN, GLN) was not considered in the analysis. The energies of F··· H–N HBs determined by the QTAIM method showed no significant differences between Fal and Far. In addition, it must be noted that energy is inversely proportional to the HB distance and does not depend on the F··· H–N angle (Figure 8). However, since the nitrogen atom was mostly present in the main chain, and was thus adjacent to different atoms, the energies calculated by Diff and ETS methods mostly had a destabilizing nature, which might be due to steric effects. On the other hand, for Fal, the areas where the energies were found to be high and exhibited a stabilizing character had a narrow range of 150◦–125◦ and 2.4–3.45 Å, while for Far the areas were within the range of geometric parameters (165◦–135◦ and 2.85–3.75 Å) (Figure 8). The analysis of selected crystal structures showed no significant differences between the systems with attractive energy and repulsive energy (Figure 8).

**Figure 8.** HB energy maps generated based on Diff, QTAIM, and ETS calculations of interaction energy between NH donor and fluorine attached to (**A**) an aliphatic fragment and (**B**) an aromatic ring for specific geometric parameters. The areas for which the highest stabilizing energy was observed in all three methods are marked with a red square.

The F··· H–C HBs were found to be the most abundant in biological systems (Figures 3 and 4). The interaction energies calculated by the QTAIM method showed that Fal··· H–C HBs are stronger than Far··· H–C HBs. In addition, the interactions with an HB distance of <2.7 Å showed a destabilizing character (Figure 9). The results produced by Diff and ETS methods were quite divergent, and it is difficult to find any constant trend. Interestingly, the results obtained from all three methods indicate that HBs with Fal are stronger than those with Far (Figure 9). The energetically favorable HBs with Fal had an angle of 155◦–145◦ and a distance of >2.7 Å, while HBs with Far had an angle of 160◦–120◦ and a distance of >2.85 Å (red squares in Figure 9). The analysis of selected crystal structures showed that F··· H–C HBs mostly exhibited a stabilizing character for distances longer than 3 Å (Figure 9).

Analysis of the ETS-NOCV decomposition results showed that for uncharged donors (OH, NH, CH) the contribution of Coulomb energy term has the greatest impact on the stabilization energy of HBs with fluorine, while for NH<sup>+</sup> the XC energy term has the largest contribution. The reason for the destabilizing nature of the shorter HBs with fluorine may be due to the high value of the kinetic energy contribution (Figure S2). To determine the significance of HBs with fluorine, the density maps of geometric parameters of HBs found in the PDB repository (Figures 3 and 4) were compared with the corresponding HB energy maps (Figures 6–9). The proposed areas (red squares) of favorable geometric parameters with the highest energy values did not match with the most occupied areas of geometric parameters. This suggests that HBs with fluorine do not play a significant role in the stabilization of the L–R system and are often formed under unfavorable geometric parameters.

**Figure 9.** HB energy maps generated based on Diff, QTAIM, and ETS calculations of interaction energy between CH donor and fluorine attached to (**A**) an aliphatic fragment and (**B**) an aromatic ring for specific geometric parameters. The areas for which the highest stabilizing energy was observed in all three methods are marked with a red square.
