3.9.1. Special Case: SSMF3 and F-SAPT Partitioning Analyses for Complexes of CX··· Gly

The SAPT0 interaction energies of 24 pairs (fragment··· Gly), resulting from the SSMF3 fragmentation of the CX, are presented in Table 4 for *al*, *pc*, and *wc* conformers of CX, while the corresponding F-SAPT partitionings are presented in Figure 6. One immediately sees that the resulting interaction energies are completely different for these three cases. Let us analyze these differences in more detail, starting from the *pc* conformer. In this case, the SSMF3-SAPT0 fragmentation energies with the largest absolute values correspond to fragments 7, 8, and 9 (see Figure 7). All these fragments contain the same hydroxy group OH-4, which donates its oxygen atom to a strong H-bond with the hydroxy group of Gly (the 1.78 Å distance between the H-ending of the glycine hydroxy group and the oxygen atom from the OH-4). Removal or addition of the methyl group does not have any influence on this energy, which is equal to −18.5 mH. However, it would be incorrect to attribute this energy to the isolated H-bond since the removal of the phenyl ring with the attached OH-3 group reduces the attraction by as much as 5 mH (see fragment 10). The weaker attraction cannot be simply explained as a lack of the attraction between Gly and Ph-3 or OH-3, because the fragment 11, which possesses the same OH-4 group bound to Gly but additionally has the phenyl ring with the OH-5 group on another side, reduces the attraction with Gly by another 5 mH. Therefore, the relative position of the second unit is crucial. One can presume that for fragments 7 to 9 the interaction of OH-4 with OH-3 plays a role since according to the I-SAPT partitioning (see Table 3) there is a strong intramolecular H-bond between these two groups. From geometrical considerations and

from a more detailed analysis of induction components, one can see that the OH-4 group donates the H atom while the OH-3 group is the H acceptor, which results in shifting more negative charge to oxygen in OH-4 and making it a better H acceptor for the COOH-Gly. An opposite situation arises for the fragment 11, where the OH-4 group accepts the hydrogen atom from the OH-5 group, what makes the O-4 atom less negative, leading to a weakening of the attraction between the OH-4 and the OH-Gly group. The SSMF3 fragmentation is not detailed enough to directly separate contributions from phenyl ring, methylene, or hydroxy groups, but the F-SAPT partitioning of the complex reveals that indeed *(i)* the attraction of the carboxy group of Gly with the OH-4 is the strongest one (−10 mH), *(ii)* there is an additional attraction of COOH-Gly to the OH-3 and Ph-3 groups (−2 mH), which explains why fragment 10, deprived of those groups, shows a weaker attraction, and *(iii)* there is a relatively strong repulsion between COOH and OH-5 (+4 mH), which explains a reduction in attraction for fragment 11. It should be noted that the attraction between the carboxy group of Gly and the OH-4 group is a net result of a balance between several components of similar importance, such as electrostatics, induction, dispersion and exchange. A significant exchange term indicates that electron clouds of these two groups overlap as in the case of covalent bonds, but the magnitude, which is smaller than for typical covalent bonds, classifies this bond as noncovalent. Therefore, the nonzero exchange and other SAPT components signify that the H-bond should exist between some atoms of COOH-Gly and OH-4 (note that according to the IUPAC criteria atoms participating in H-bonds should be close to each other so that the distance between them was smaller than the sum of atomic Van der Waals radii [121]). If the SSMF3 contributions of a range of about −9 mH are analyzed in the same manner (not shown in the figure), a secondary binding is revealed, which can be attributed to the interaction between NH2-Gly and the OH-1 groups with the amino group being the H donor. As it could be guessed from a relatively large distance between the hydrogen of NH2 and oxygen of the OH-1 (2.23 Å) and from the value of the H··· OH-1 angle (143◦), which is quite different from the full angle, this interaction should be quite weak, but nonetheless, it is still composed of nonzero polarization and exchange contribution, which sum up to −4 mH according to F-SAPT, therefore we can still classify it as an H-bond.

**Figure 6.** The F-SAPT interaction energy graph for the Gly amino acid interacting with the *al*-CX (leftmost graph), *pc*-CX (middle graph), and *wc*-CX (rightmost graph). Calixarene functional groups are depicted on the left and those for Gly–on the right. The red (blue) lines denote attraction (repulsion), and their thickness is proportional to the interaction strength.


**Table 4.** The total SAPT0 interaction energies of unfragmented and the SSMF3 fragments for all CX conformers + Gly complex are presented. Energies are in millihartree.

**Figure 7.** The fragments 7 to 11 generated from the SSMF3 partitioning of the *pc*-CX interacting with Gly. The numeration goes row-wise from top left to bottom right. Selected H-bond distances (in Å) are shown in order to identify their placement in the original calixarene.

For the *al*-CX··· Gly complex, there exists much more important terms since the Gly molecule resides in the *al* cavity, and in Figure 8, we present only those fragments, which are the most relevant to the discussion below. The important fragments can be segregated into those corresponding to the binding to the NH2-Gly and COOH-Gly sites and–contrary to the *pc* case–these two sets are of similar importance. The most attractive contributions for the first and second sites come from fragments 1 and 13 and amount to −25 and −26 mH, respectively. Fragments 1 to 3 have an H-bond between the OH-2 and NH2 groups, while fragments 13 to 15–between OH-5 and COOH. Similarly, as in the *pc*-CX case above, the removal of the phenyl ring with the hydroxy group, serving as a

hydrogen donor in the intramolecular H-bond, reduces the interaction energy by about 7 mH (fragments 2 and 14). However, contrary to the *pc*-CX case, the addition of the *n* + 1th calixarene unit (number 3 for the fragment 3 and number 6 for the fragment 15) does not lead to a further reduction in attraction. Quite the opposite, a small rise of the attraction (by 3-4 mH) is observed in comparison to fragments 2 and 14. The geometry analysis shows that these additional phenyl and hydroxy groups are more twisted in comparison to the *pc* case, so that the creation of the H-bond between OH-2 and OH-3 or between OH-5 and OH-6 is prevented, and such bonds would weaken the negative character of the O-2 and O-5 atoms. What remains to be explained is the increase in the attraction for fragment 3 in comparison to fragment 2 (and for fragment 15 in comparison to 14). Since these fragments differ by other phenyl plus hydroxy groups, one (or both) of these groups should be responsible for this phenomenon. Because of the limitations of the SSMF3 partitioning, the explanation of this fact should be postponed till the F-SAPT analysis is made. Now let us move to a complementary view of the F-SAPT partitioning. As expected, there is a strong (−14 mH) binding between the OH-2 and NH2 groups. Surprisingly, the interaction between OH-5 and COOH amounts to −3.5 mH only, but the carboxy group is strongly attracted to the Ph-5 group (−11.5 mH). All F-SAPT components, including the exchange one, are significant for the COOH··· Ph-5 interaction; therefore, the F-SAPT analysis reveals the existence of the untypical H··· *π* H-bond. Such interactions were reported, e.g., in molecules containing aromatic rings with those with the S-H bond [122]. Another candidate for the H··· *π* H-bond would be the H atom from the NH2 group interacting with the Ph-3 group. However, in this case, the total interaction energy is close to zero, which is a result of a perfect cancellation of several contributions of similar magnitude (the electrostatics of −3 mH and dispersion of −4 mH are counterbalanced by the large exchange component). The question remains why fragments 2 and 3 differ in attraction by as much as 4 mH. A perusal of the F-SAPT partitioning table reveals that this difference is due to the electrostatic attraction (−4 mH) between the Ph-3 and COOH groups. Finally, a similar difference for fragments 14 and 15 can be explained by the net attraction to the OH-6 group (−2.5 mH).

**Figure 8.** The fragments 1 to 3 and 13 to 15 generated from the SSMF3 partitioning of the *al*-CX interacting with Gly. The numeration goes row-wise from top left to bottom right.

The most important contributions from the SSMF3 partitioning for the *wc*-CX··· Gly complex provide interaction energies of about −22 to −24 mH (see two representative fragments 3 and 7 in Figure 9) and have in common the H-bond between the OH-3 and NH2 with the latter group as the H acceptor (the H··· N bond of 1.67 Å). As in the previous cases,

this energy cannot be attributed to this one H-bond only, since, e.g., fragment 6 containing this H-bond attracts the Gly molecule weaker by 8 mH. The geometry considerations allow us to point to a possible additional interaction with the OH-2 group for fragment 3 since the O··· H distance in this case is equal to 2.10 Å, that is, the amino group of Gly donates its hydrogen to create a weak H-bond. The mechanism of an increased attraction in case of the fragment 7 is different: here the intramolecular H-bond between the OH-3 and OH-4 groups makes the O-3 oxygen less negative, thus allowing the H-3 to interact more strongly with the nitrogen from the amino group. Not shown in the figure are fragments 15 to 17, for which two interactions: between the amino group and OH-5 (the NH2 as H donor) and between the carboxy group and OH-6 (COOH as the H acceptor) can be guessed from the geometry considerations. The F-SAPT partitioning confirms these predictions. First, a strong interaction between the OH-3 and NH2 groups has been obtained with this method (−13 mH). There are also three weak H-bonds (again recognized by the significance of all SAPT components, including exchange): between OH-6 and COOH (−4 mH), OH-5 and NH2 (−3 mH), and OH-2 and NH2 (−2 mH). The latter interaction is too weak to explain a difference between the attraction from fragments 3 and 6, but the F-SAPT provides the additional strong attraction of a purely electrostatic type between the OH-2 and carboxy group (−4 mH) to fill this gap.

**Figure 9.** The fragments 3, 6, and 7 generated from the SSMF3 partitioning of the *wc*-CX interacting with Gly. The numeration goes from left to right.

Summarizing, all three cases of the interaction with the simplest Gly amino acid provide different mechanisms for secondary stabilizing interactions, which would be difficult to elucidate just from the analysis of the total energies.
