*3.7. Pristine Calixarenes–Energy Partitioning*

The calix[6]arenes contain six hydroxy groups, which can be oriented in such a way that one hydroxy group serves as a hydrogen donor, and the second one–as a hydrogen acceptor. Additionally, some hydroxy groups play both roles simultaneously. As already noted, for the *pc* conformer all six groups are connected in a way that allows the creation of six H-bonds, while for the *al* and *wc* cases four H-bonds are present. According to Figure 2 in the *al* conformer, the OH-6 group is connected (by its hydrogen ending) to OH-1, which in turn interacts with OH-2 on the left semi-circle of calixarene, and on the right semi-circle, the OH-3 group donates its hydrogen to OH-4, which in turn passes its hydrogen to OH-5. Similarly, for the *wc* conformer two chains of H-bonds are: OH-5 to OH-4 to OH-3 and OH-2 to OH-1 to OH-6. In Table 3, we list interaction energies between hydroxy groups of all six cases of calixarenes obtained from the I-SAPT method. (Note that I-SAPT calculations for the interaction between hydroxy groups from calixarene have also been performed for selected complexes, see the Supplementary Information).

**Table 3.** I-SAPT interaction energies between hydroxy groups for empty calixarenes. The upper triangle presents the BCX case, the bottom triangle–the CX case, energy values for the *al*, *pc*, and *wc* conformers, respectively, are separated by a dash. Energies in millihartree.


The results in Table 3 indicate that the intramolecular OH-OH interactions strictly correspond to the H-bond pattern, i.e., for the *pc* conformer there are six and for the remaining conformers–four interaction energies, which are negative and below 9 mH. A more detailed analysis shows that the largest absolute value of these energies appears for the *pc* case (15 mH), followed by *al* (12 mH), while the energies for the *wc* conformer (9 mH) have the smallest absolute value. This order strictly corresponds to the increasing O··· H distance. It should be noted that the absolute values of interaction energies between the second neighbors (such as OH-3 and OH-5) are larger than for the opposite groups, in full agreement with chemical intuition. An analysis of SAPT components (not shown) reveals that the second-neighbor interaction has a practically pure electrostatic character, while the interaction of the adjacent hydroxy groups contains similarly important contributions from electrostatics, induction, dispersion, and the exchange counterparts. Although a common explanation of the highest stability of the *pc* conformer is the existence of two additional intramolecular H-bonds, a simple addition of the interaction energies, mentioned above, predicts much higher stability than found from the total energies' differences, see Section 3.4. In a fact, much more factors should be accounted for, among which secondary interactions, such as those involving phenyl groups, etc. should play a significant role.

Hydroxy groups in calixarenes reside in a tight neighborhood of other groups, from which the largest phenyl groups are of the highest importance. Since neighboring hydroxy and phenyl groups are placed in different relative orientations, interactions of various types can be obtained. We performed a detailed analysis of I-SAPT components of the hydroxy–phenyl interactions for the *pc* and *al* conformers, and found that the majority of these pairs interact electrostatically. Additionally, the closeness of the H or O ending of the hydroxy group allows us to predict the sign of the electrostatic interaction. For instance, OH groups with the H-ending placed closer to a neighboring Ph group form as a rule the repelling pair (e.g., OH-3 and Ph-4 with the energy of 9 mH, OH-4 and Ph-5 with the energy of 8 mH, OH-5 and Ph-6 with the energy of 2.5 mH, OH-6 and Ph-1 with the energy of 9 mH, and OH-1 and Ph-2 with the energy of 8 mH, for the *al*-CX). If the O-ending is closer to a neighboring Ph group, an attraction pair is formed (e.g., OH-4 and Ph-3 with the energy of −7 mH, OH-5 and Ph-4 with the energy of −8 mH, and OH-2 and Ph-1 with the energy of −7.5 mH for the *al*-CX). The same picture has been found for the *pc*-CX case, where the electrostatic attraction between pairs: OH-6 and Ph-1 with the energy of −9 mH, OH-1 and Ph-2 with the energy of −6 mH, OH-5 and Ph-6 with the energy of −8 mH can be found, while the electrostatic repulsion of the pairs: OH-6 and Ph-5 with the energy of 11 mH, OH-5 and Ph-4 with the energy of 11 mH, OH-1 and Ph-6 with the energy of 10 mH (plus *C*<sup>2</sup> point-group counterparts) reduce the stability of these conformers.

This rule of thumb does not work for neighboring pairs from the first and second semi-circle for the *al* conformers (both CX and BCX), i.e., for OH-6 and Ph-5 (+4 mH for CX and BCX) and OH-2 and Ph-3 (−4.5 mH for CX and −5 mH for BCX). The latter pair is different from all other neighboring hydroxy–phenyl pairs, since in this case the I-SAPT partitioning shows that all energy components are of equal importance and the resulting attraction is a result of a subtle balance of attractive and repulsive components of similar absolute values. Relatively large exchange components signify that electron clouds of both groups significantly overlap, which allows us to identify a weak secondary H-bond of the *π*-type [119,120]. It is especially worth noting that this noncovalent bonding facilitates the elongation of the OH-2 bond towards Ph-3 during the oscillation. We have already noticed in the study of the IR spectra that the frequency corresponding to the OH-2 stretch for the *al* conformers is lower than the OH-5 counterpart on the opposite site of the calixarene, so the behavior of the I-SAPT interaction energies clarifies the mechanism of this red shift.
