Exploring Orthogonality between Halogen and Hydrogen Bonding Involving Benzene

The concept of orthogonality between halogen and hydrogen bonding, brought out by Ho and coworkers some years ago, has become a widely accepted idea within the chemists’ community. While the original work was based on a common carbonyl oxygen as acceptor for both interactions, we explore here, by means of M06-2X, M11, ωB97X, and ωB97XD/aug-cc-PVTZ DFT calculations, the interdependence of halogen and hydrogen bonding with a shared π-electron system of benzene. The donor groups (specifically NCBr and H2O) were placed on either or the same side of the ring, according to a double T-shaped or a perpendicular geometry, respectively. The results demonstrate that the two interactions with benzene are not strictly independent on each other, therefore outlining that the orthogonality between halogen and hydrogen bonding, intended as energetical independence between the two interactions, should be carefully evaluated according to the specific acceptor group.

Analysis of crystal structures of halogenated molecules has revealed that XB often acts in a cooperative way with hydrogen bonding (HX) [36][37][38][39]. In particular, Ho and coworkers reported that halogen and hydrogen bonds can be geometrically perpendicular to and energetically independent on each other, when the involved X and H donor atoms interact with the same carbonyl group in protein-ligand complexes [40]. The authors then proposed the concept of XB/HB orthogonality, paving the way for the development of new strategies aimed at the rational design of halogenated ligands as drugs [36].
Prompted by the conclusions obtained by Ho and coworkers on the CO···X/H orthogonality [40], we have considered the possibility to extend this concept to the case where the halogen and hydrogen donor atoms share a common benzene π-electron system as bonding acceptor. In previous studies [41][42][43], we extensively investigated from a theoretical point of view the XB established between a series of halogenated molecules (NCX or PhX where X = F, Cl, Br, I) and the aromatic system of benzene in the T-shaped configuration, an interaction rather ubiquitous in biological systems [44,45]. Here, the more appropriated computational protocols proposed in our previous studies are used to investigate the simultaneous interaction of NCBr and H 2 O, two relatively strong XB and HB donors, respectively, with a common π-electron system of benzene. To this purpose, two geometrical approaches have been examined, that is, a 'double T-shaped' one, where NCBr and H 2 O, both in T-shaped configuration with respect to benzene, point to the ring from opposite sides; and a 'perpendicular' approach, where NCBr and H 2 O lie on the same side of the ring forming a right angle with the center of the ring. Of course, the concept of orthogonality we want here to explore refers uniquely to the energetical independence of the two interactions rather than to the geometrical arrangement of the interacting species, which strictly applies only to the 'perpendicular' approach. To provide solid support to our conclusions, different functionals have been used for this analysis, that is M06-2X, M11, and ωB97X, chosen among the better performing on the basis of our previous investigation on the NCX···π XB [42]. Owing to the demonstrated importance of the dispersion forces, besides the electrostatic ones, in describing the RX···π interaction [42], additional calculations were performed with a DFT-D functional, ωB97XD, which explicitly includes a posteriori dispersion correction.

Double T-Shaped Configuration
The simultaneous formation of XB and HB with benzene, where the respective donors are located on opposite sides with respect to the plane of the ring, represents a quite common motif in organic crystal structures, as denoted by a survey of the Cambridge Structural Database (CSD version 5.42, February 2021) [46]. Up to 962 hits were in fact obtained by searching for organic compounds containing A-X···c(Ph)···H-B fragments (being A and B generic atoms, c(Ph) the geometrical centroid of a phenyl ring, and X = Cl, Br or I) with X···c(Ph) and c(Ph)···H distances in the 3.0-4.0 Å and 2.0-3.0 Å range, respectively, and both A-X···c(Ph) and X···c(Ph)···H angles in the 150 • -180 • range.
A first set of calculations were performed on dimers of NCBr or H 2 O with benzene (or bz) in T-shaped configuration (see structure (a) in Figures 1 and 2, respectively), with the Br or the H atom, respectively, approaching the center of the ring. The binding energy curves, computed at the M06-2X/aug-cc-PVTZ level of theory, are plotted in Figures 1 and 2 (see Figures S1-S6 for the M11, ωB97X, and ωB97XD binding energy curves and Tables S1-S8 for the ∆E vs. r numerical values). Comparing halogen and hydrogen bonds, the four examined functionals display the same trend in the values of equilibrium distances, r eq , and interaction energies, ∆E XB and ∆E HB for XB and HB, respectively (see Table 1). For both the NCBr·bz and H 2 O·bz optimized dimers, in fact, M06-2X provides the higher ∆E XB and ∆E HB interaction energies, respectively, which correspond to the shorter intermolecular distances. The M11 functional gives the lower interaction energies, with differences in ∆E XB and ∆E HB amounting to 0.35 and 0.42 kcal/mol (i.e., 9.1 and 12.2%), respectively, compared to the M06-2X values. Finally, the ωB97X and ωB97XD functionals provide the longer equilibrium distances and energy values intermediate between the M06-2X and the M11 ones. Comparing the two related ωB97X and ωB97XD hybrid functionals, it is found that the empirical dispersion correction does not provide any significant variation in both equilibrium distances and energies. Interestingly, however, while equilibrium distances of both interactions are slightly elongated when explicitly including dispersion, the corresponding energies undergo different, though very small, variations according to the HB or XB interaction. In the first case, in fact, ∆E increases in magnitude, as generally obtained going from DFT to DFT-D calculations on non-covalently bound systems [47,48], while for the XB interaction the opposite trend is observed, suggesting that dispersion effects are somehow taken into account in the ωB97X functional, too. omers, the RX molecule being slightly out from the perpendicularity with respect to the benzene plane and pointing towards a CC benzene bond rather than to the center of the ring. However, geometry optimization of the NCBr·bz and H2O·bz dimers here examined, performed at the ωB97XD/aug-cc-PVTZ level of theory, results in absolute minima, confirmed by frequency calculations, which are only 0.20 and 0.50 kcal/mol (for XB and HB, respectively) more stable than the constrained T-shaped configuration (see the minimum energy geometries in Figure S7). This denotes a rather flat potential energy surface for the NCBr·bz and H2O·bz interacting systems, indicating that the chosen T-shaped configuration does not represent in any way a too strong assumption affecting the subsequent results.  benzene plane and pointing towards a CC benzene bond rather than to the center of the ring. However, geometry optimization of the NCBr·bz and H2O·bz dimers here examined, performed at the ωB97XD/aug-cc-PVTZ level of theory, results in absolute minima, confirmed by frequency calculations, which are only 0.20 and 0.50 kcal/mol (for XB and HB, respectively) more stable than the constrained T-shaped configuration (see the minimum energy geometries in Figure S7). This denotes a rather flat potential energy surface for the NCBr·bz and H2O·bz interacting systems, indicating that the chosen T-shaped configuration does not represent in any way a too strong assumption affecting the subsequent results.   Finally, it should be noted that the considered T-shaped approach represents a constrained path enabling to uniquely fix the dimers' geometry for subsequent calculations on trimers. As previously reported for RX···π XB systems [41], unconstrained geometry optimization of such dimers leads to a breakdown of the T-shaped geometry of the monomers, the RX molecule being slightly out from the perpendicularity with respect to the benzene plane and pointing towards a CC benzene bond rather than to the center of the ring. However, geometry optimization of the NCBr·bz and H 2 O·bz dimers here examined, performed at the ωB97XD/aug-cc-PVTZ level of theory, results in absolute minima, confirmed by frequency calculations, which are only 0.20 and 0.50 kcal/mol (for XB and HB, respectively) more stable than the constrained T-shaped configuration (see the minimum energy geometries in Figure S7). This denotes a rather flat potential energy surface for the NCBr·bz and H 2 O·bz interacting systems, indicating that the chosen T-shaped configuration does not represent in any way a too strong assumption affecting the subsequent results.
Keeping the optimized dimers fixed in their respective T-shaped energy minima, we then computed the binding energy curves corresponding to the T-shaped approach of either NCBr to bz·H 2 O or H 2 O to bz·NCBr from the opposite site with respect to NCBr or H 2 O, respectively, according to a 'double T-shaped' geometry (see structure (b) in Figures 1 and 2 The results are collected in Table 1 and the binding energy curves obtained by M06-2X calculations are plotted in Figures 1 and 2 (see Figures S1-S6 for the M11, ωB97X, and ωB97XD binding energy curves and Tables S1-S8 for the ∆E vs. r numerical values). It is found that the minimum energy geometry of XB is only slightly perturbed when NCBr interacts with [bz·H 2 O] rather than with bz alone, with elongations lying within the step size used to build up the curves (0.02 Å in the minimum energy region). Even lower elongations are obtained for HB. Considering the interaction energies, however, non-negligible variations are obtained comparing the same interaction in the dimer and in the trimer. For example, looking at the results obtained with the M11 functional, providing the larger variations, ∆E XB decreases in absolute value from −3.48 to −2.90 kcal/mol and ∆E HB from −3.01 to −2.43, with a comparable percentage reduction of 16.7 (∆E XB ) and 19.3% (∆E HB ). These results are confirmed by M06-2X, ωB97X, and ωB97XD calculations, providing percentage reductions of 14.4 (∆E XB ), 16.0% (∆E HB ); 13.6 (∆E XB ), 15.9% (∆E HB ); and 12.8 (∆E XB ), 14.4% (∆E HB ), respectively. The destabilization associated with the trimer formation indicates a strong perturbation of the whole π-electron system of benzene within the dimer, allowing to conclude that XB and HB on either side of benzene are not strictly orthogonal interactions.
The slightly greater destabilization of HB with respect to XB in the presence of the other perturbing interaction on the other side of benzene should be imputed to the here considered NCBr·bz XB, which is slightly stronger (by 0. 40 Figures 1 and 2, respectively). A quite different behavior is observed for the halogenbonded and the hydrogen-bonded trimers (see Table 1, Figures 1, 2 and S1-S6 for the M06-2X, M11, ωB97X, and ωB97XD binding energy curves, respectively, and Tables S1-S8 for the ∆E vs. r numerical values). In fact, looking again at the M11 results, calculations provide a much stronger reduction of the XB interaction energy with respect to that computed for the HB one, with percentage reductions equal to 24.7 (∆E XB ) and 14.6% (∆E HB ). Similarly, M06-2X, ωB97X, and ωB97XD calculations provide percentage reductions of 21.9 (∆E XB ), 12.0% (∆E HB ); 20.4 (∆E XB ), 12.1% (∆E HB ); 18.9 (∆E XB ), 11.0% (∆E HB ), respectively. Such results can be explained by considering that the π-electron system of benzene is perturbed in a greater extent by the stronger NCBr·bz XB with respect to the weaker H 2 O·bz HB.

Perpendicular Configuration
To explore the configuration where both NCBr and H 2 O molecules lie on the same side of the benzene ring, perpendicular to each other, preliminary M06-2X/aug-cc-PVTZ calculations have been performed on the halogen-and hydrogen-bonded dimers with benzene, aimed at establishing the constrained path of minimum energy towards the center of the ring. Binding energy curves were calculated by moving either NCBr or the interacting OH group along the line through the center of the ring and forming a 45 • angle with the benzene plane. Both approaches where the projection of the line on this plane crosses one carbon atom or the center of a CC bond (see Figures S8 and S9, respectively) have been examined. Moreover, in the case of the hydrogen-bonded dimer, the non-interacting hydrogen atom was directed either inward or outward with respect to the benzene ring. As shown in Table S9, the more stable approach was found to be along the center of a CC bond for both dimers, with the non-interacting H atom of water outwards with respect to the benzene ring (see structure (a) in Figures 3 and 4 for the NCBr·bz and H 2 O·bz dimers, respectively). Such an approach was then chosen for all the subsequent calculations.    As expected, the resulting ∆E values (see Table 2, Figures 3, 4 and S10-S15 for the M06-2X, M11, ωB97X, and ωB97XD binding energy curves, respectively, and Tables S10-S17 for the ∆E vs. r numerical values) are lower than those computed for the T-shaped configuration, because such a 'bent' approach is even farther, compared to the T-shaped one, from the minimum energy path (see Figure S7). However, it is interesting to note that XB is now slightly less stable (by 0.17, 0.20, 0.13, and 0.25 kcal/mol according to the M06-2X, M11, ωB97X, and ωB97XD functional, respectively) than HB, differently from what derived for the T-shaped configuration. Such a result could be explained by the greater directionality of XB with respect to HB, due the more restricted positive region of the electrostatic potential on the halogen atom, compared to that hemispherically distributed around the hydrogen atom [49]. In the present approach, the NCBr molecule is then more affected, with respect to H 2 O, by being quite far from the minimum energy path.  Compared with the results obtained on dimers in T-shaped configuration, the higher interaction energies are obtained with the ωB97X functional, while M11 still provides the lower ΔE values (see Table 2). Moreover, the examined functionals provide much more different interaction energies despite rather similar equilibrium distances. The variations from the ωB97X values to the M11 ones amount to 0.68 (ΔEXB) and 0.61 (ΔEHB) kcal/mol, corresponding to 27.5 and 23.5% reductions with respect to the higher ωB97X values. Such discrepancies are much higher than those (9.1 and 12.2%) determined for the T-shape approach. Considering that, in the two different approaches, we are dealing with the same molecules in different orientations, it may be hypothesized that the larger discrepancies observed for the bent dimers could be ascribed to the fact that this orientation is more outside, with respect to the T-shaped configuration, the minimum energy one, implying a stronger angular dependent energy bias [50].  Compared with the results obtained on dimers in T-shaped configuration, the higher interaction energies are obtained with the ωB97X functional, while M11 still provides the lower ∆E values (see Table 2). Moreover, the examined functionals provide much more different interaction energies despite rather similar equilibrium distances. The variations from the ωB97X values to the M11 ones amount to 0.68 (∆E XB ) and 0.61 (∆E HB ) kcal/mol, corresponding to 27.5 and 23.5% reductions with respect to the higher ωB97X values. Such discrepancies are much higher than those (9.1 and 12.2%) determined for the T-shape approach. Considering that, in the two different approaches, we are dealing with the same molecules in different orientations, it may be hypothesized that the larger discrepancies observed for the bent dimers could be ascribed to the fact that this orientation is more outside, with respect to the T-shaped configuration, the minimum energy one, implying a stronger angular dependent energy bias [50]. We then computed the binding energy curves corresponding to the perpendicular approach, on the same side of the benzene ring, of either NCBr to bz·H 2 O or H 2 O to bz·NCBr, keeping the dimers fixed in their respective energy minima (see structure (b) in Figures 3 and 4 for the NCBr·bz and H 2 O·bz dimers, respectively). As obtained for the double T-shaped configuration, the minimum energy geometry for both interactions is only slightly perturbed when NCBr or H 2 O interact with the dimer rather than with  Table 2). However, the corresponding interaction energies undergo even larger variations compared with those obtained for the double T-shaped approach: according to M11, M06-2X, ωB97X, and ωB97XD calculations, ∆E XB

Materials and Methods
DFT geometry optimizations were performed by constraining the interacting molecules to the prefixed (T-shaped and double T-shaped; bent by 45 • with respect to the benzene plane and perpendicular) geometries on the basis set superposition error (BSSE)-free potential energy surface. The distance of the Br or H atom from the center of the ring was varied from either 1.8 to 6.0 Å (T-shaped approaches) or 3.3 to 4.7 Å (perpendicular approaches with NCBr) or 2.4 to 3.8 Å (perpendicular approaches with H 2 O) with 0.1 Å step except for the region of minimum energy where the step size was reduced to 0.02 Å. Calculations were performed with the range-separated or long-range corrected GGA functional ωB97X [51], the hybrid meta-GGA functional M06-2X [52], and the range-separated hybrid meta-GGA functional M11 [53]. They were chosen based on their optimal performance to reproduce both interaction energies and geometry of benchmark CCSD(T)/CBS values, according to our previous studies [41,42]. Additional calculations were performed with ωB97XD [54] to check the effect of explicitly including dispersion corrections into the ωB97X functional. For these latter calculations, slightly reduced ranges of distances, including the minima, have been explored. In all cases, a large pruned integration grid (99 radial shells and 590 angular points per shell) was used to avoid artifacts associated with numerical integration procedures, as evidenced by previous investigation on the sensitivity of functionals to the size of the integration grid [55]. All calculations were performed with the aug-cc-PVTZ basis set, using the Gaussian 16 Revision A suite of programs [56].

Conclusions
The interdependence between halogen bonding and hydrogen bonding with a common π-electron system of benzene has been investigated by DFT calculations, using as donor molecules NCBr and H 2 O, respectively. Four different functionals, selected among the best performing based on previous investigation on the RX···π XB, namely M06-2X, M11, ωB97X, and ωB97XD, have been used to build up binding energy curves for both dimeric (i.e., NCBr·bz and H 2 O·bz) and trimeric (i.e., NCBr·[bz·H 2 O] and H 2 O·[bz·NCBr]) units. Two different configurations of the donor molecules with respect to benzene have been explored, i.e., a double T-shaped and a perpendicular one, where NCBr and H 2 O point towards the center of the ring from either opposite sides or the same side, perpendicularly to each other, respectively. In both cases, comparison between the interaction energies at the equilibrium distances computed for the trimers and the corresponding dimers indi-cates, for all the adopted functionals, that the two interactions cannot be considered strictly orthogonal, in particular as far as the perpendicular approach is concerned.