*3.2. Pristine calixarenes–IR Spectra*

The simulated harmonic IR spectra of three forms of calix[6]arene and hexa-*p*-*tert*butylcalix[6]arene, together with a complete list of frequencies and intensities are presented in the Supplementary Information. Studies of smaller molecules containing the hydroxy groups, such as, e.g., studies of phenol and its complexes with water and ammonia [113] or a study of water dimer IR spectrum [114] with respect to basis sets, anharmonicity and couplings, etc., show that harmonic stretching frequencies are blue-shifted by 100–150 cm−<sup>1</sup> in these cases, so one expects a similar shift of the calculated O–H stretching frequencies for calixarenes.

From IR spectra presented in Figures in the Supplementary Information one can see that there is a group of high-intensity frequencies above 3000 cm−<sup>1</sup> for all the cases. The *pc* conformer is characterized by just one high-intensity composite peak, while for the remaining conformers, this peak is shifted to higher frequencies of about 3500 cm−<sup>1</sup> and one finds an additional lower peak (or two peaks for *al*) at even higher energies. For the BCX case, an additional bunch of peaks appears at about 3000 cm−1, which is well separated from the first group, and whose intensity is comparable to the previously discussed group for the *al* and *wc* conformers. Let us first focus on the highest vibrational frequencies, which turn out to be related to hydroxy group stretching. The six highest frequencies for the *wc* and *al* conformers correspond to various O-H stretching patterns, as can be expected for six OH groups. Since these frequencies span from about 3300 cm−<sup>1</sup> up to about 3700 cm−1, and the C-H stretching modes start from about 3100 cm−1, the stretching modes for O-H and C-H do not mix. A different situation arises for the *pc* conformer. The highest frequency (3270 and 3280 cm−<sup>1</sup> for CX and BCX, respectively) is much lower than for the *al* and *wc* conformers, and the examination of mode characters for consecutive frequencies reveals only the five highest ones are dominated by the O-H stretching. The "missing" sixth mode can be found at 3115 cm−<sup>1</sup> for the BCX, separated from five OH-stretch frequencies mentioned above by several C-H stretching modes. The situation is even more complicated for the CX case, where instead of one missing mode dominated by the O-H stretch one finds three nearly degenerate modes of frequency 3099 cm−1. They can be described as a simultaneous symmetric stretch of all present O-H bonds mixed with various patterns of C-H stretches, where the C-H bonds come from the phenyl groups. The replacement of the hydrogen atom in the *para* position by the *tert*-butyl group leads to a distortion of this mixing, which results in the absence of such mode combinations in the BCX case.

All the five highest frequencies of *pc* correspond to concerted stretching motions, i.e., involving simultaneously all six O-H bonds. They differ by the pattern of the motions, and, e.g., for the highest energetic mode there is–quite understandably – the alternate motion (when odd O-H bonds stretch then even ones shrink). More precisely, one can differentiate several patterns of these motions and–as usual in such cases–more nodes in the wave function mean higher energy. To this end, if we start counting the O-H bonds as in Figure 2, then the pattern corresponding to the highest frequency is the alternating one: (+,−,+,−,+,−), then the next highest is partially alternate (+,− −,++,+,− −,++), followed by more and more symmetrical patterns, such as (++,−,−,++,−,−), (++,−,− −,− −,+,++), and (++,++,+,− −,− −,−), whereby doubled plus or minus signs try to catch the increased amplitude of the motion. Finally, as discussed above, the expected totally symmetric case, i.e., (+,+,+,+,+,+), is mixed with C−H stretching motions for the CX case.

The lowering of spatial symmetry, as in the case of the *al* conformer, leads to a decoupling of the O-H stretch modes. Their highest two frequencies correspond to the stretching of a single O-H bond (for the OH-5 and OH-2 groups, respectively). The same two OH groups are involved in the two highest modes for the *wc* case. In all these cases, the high-frequency vibration corresponds to the OH group, which is involved in the H-bond as an electron donor only (i.e., through the oxygen ending), while the hydrogen atom does not participate in the H-bond because of the geometry hindrance. As a result, the O-H bond is not weakened by the H-bond and no red shift is observed in the IR spectrum. For the *wc* case there are two such high-energy (about 3700 cm<sup>−</sup>1) vibrations, one corresponding to a simultaneous stretch and another–to an alternate stretch of the OH-2 and OH-5 groups. It should be noted that values of these frequencies are similar to water stretching frequencies [114], or to the stretching frequency of the hydroxy group in phenol [113]. However, for the *al* conformer (for both unsubstituted and substituted calixarenes) one of these high-energy vibrations becomes lower by approximately 100 cm−1. This fact can be explained by a weak attractive interaction of the hydroxy group with the phenyl ring. Such interactions were reported and studied for the prototypical models of benzene with one or two water molecules in Ref. [115]. We will go back to this topic in Section 3.7.

Returning to the *pc* conformer of the CX, one can detect several characteristic IR peaks at lower frequencies. An examination of these cases shows that some of them belong to the O-H bending (either in-plane or out-of-plane with respect to the phenyl ring), while others are C-H bending from phenyl or breathing Kekule modes of phenyl rings. Similar peaks appear for the *al* and *wc* conformers, but they differ in intensities and exact positions of peaks, allowing us, in principle, to recognize which conformer has been measured.

For the hexa-*p*-*tert*-butylcalix[6]arene case, additional strong features around 3000 cm−<sup>1</sup> should be attributed to multiple C-H stretching modes of methyl groups, which together form a *tert*-butyl group. Usually, several C-H bonds are simultaneously involved in these vibrations. Stretching frequencies of methylene bridges are of a similar energy range, so they contribute to these composite peaks as well.

### *3.3. Complexes with Amino Acids–Geometries*

### 3.3.1. Dihedral Angles of Calixarenes

Before we analyze the binding (docking) sites for amino acids, let us first systematically analyze modifications of the calixarene macrocycle upon complexation with help of dihedral angles between selected carbon atoms between calixarene units. The values of the dihedral angles are defined through carbon atoms as indicated in Figure 1 together with the standard nomenclature for the considered calixarene conformers are listed in the Supplementary Information for both CX and BCX types. One should note that for each linking methylene group two angles are defined with the convention that the dihedral angle denoted as R*n*aR*m* has two carbon atoms from the R*n* ring, while R*n*bR*m* has two carbon atoms from the R*m* ring in its definition. The numbering for dihedral angles corresponds to the numeration presented in Figure 2.

Let us first analyze the pristine calixarenes. At the beginning, one should note that *pc*, *al*, and *wc* conformers can be distinguished by distinct sign patterns of the dihedral angles, which are: (± ∓ ± ± ∓±) for *pc*, (∓ = ∓± = ±) for *wc*, and (∓ ∓ ± ± ∓∓) for *al* (the ± symbol here denotes that first from two dihedral angles around a given methylene group is positive and the second negative, ∓–the opposite, while = denotes that both angles are negative). Secondly, because of the *C*<sup>2</sup> point-group symmetry within the *pc* and *wc* conformers for the CX, the second half of the dihedral angles is identical to the first half. No such exact symmetry exists in the *al* conformed; however, as noted above, there is an approximate correspondence between two parts of the *al* conformer and in an ideal case the *k*th angle from the table would correspond to the negative of the (12 − *k*)th angle. The same resemblances can be also found for the *pc* with the majority of differences of the order of a few degrees for the CX. For the hexa-*p*-*tert*-butylcalix[6]arene conformers, no exact point symmetry exists because of the presence of *tert*-butyl groups, but the same approximate resemblance is nevertheless preserved, confirming a small influence of the substitution on the macroring shape. It should be emphasized that no case has been found during geometry optimization where the complexation would modify the geometry of the calixarene to such an extent that the conformer became unrecognizable, although in a couple of cases the sign pattern is not preserved anymore.

In order to make the analysis of numerical values of the dihedral angles more complete, we compare them to two model molecules, which are also built from two phenol groups connected through the methylene linker. The geometry optimization of these molecules has been performed on the same level as for calixarenes. The simplest molecule of this type is diphenylmethane, for which the corresponding dihedral angles are equal to −62◦ and 118◦. It turns out that there are indeed pairs (R*n*aR*m*,R*n*bR*m*), which resemble this pattern, but only for the *pc* conformer such a correspondence holds for all six pairs, while for the *al* and *wc* cases at least two angles are much smaller (by about 10–20◦), so here other factors, such as hydroxy groups' interaction, should play a decisive role. In order to examine this issue in more detail, we likewise performed a geometry optimization for several conformers for the 2,2 -dihydroxydiphenylmethane molecule, which is the simplest molecule with two hydroxyphenyl groups connected with the methylene linker. Only one of these conformers has an intramolecular H-bond and the creation of this bond is gratified by the highest stability. The corresponding pair of dihedral angles for this H-bonded conformer is (−76◦,101◦), which corresponds quite accurately to all the pairs of the *pc* conformer and to four from six pairs of the *al* and *wc* conformers. The 2,2 -dihydroxydiphenylmethane conformer, which resembles the most the dihedral angles for the fifth and sixth ring of *al* and *wc* (and, because of symmetry, also for the second and third ring of *wc*) has two hydroxy groups separated by the CH2 group, but they still point towards each other as an attempt to create an H-bond. It can be seen that although the distance between the corresponding oxygen and hydrogen is too large for effective creation of the H-bond (4.4 Å), it is still 0.3 Å smaller than for the *wc* conformer, i.e., one can say that these hydroxy groups are placed less optimally in the *wc* calixarene. One can also see this by a comparison of dihedral angles, which differ by as much as 22◦ when comparing *wc* to 2,2 -dihydroxydiphenylmethane. For the *al* case no such strains are observed. In order to fully describe the *al* conformer, one more local minimum of 2,2 -dihydroxydiphenylmethane should be used, which has the corresponding pair of angles equal to (−19◦,117◦).

Interestingly, the replacement of hydroxy groups by hydrogens and reoptimization of the resulting hydrocarbons leads to a complete distortion of semi-circles in the *al* and *pc* cases, while the *wc* conformer does not change so dramatically. Therefore, for the former two cases, the intramolecular H-bonds play a pivotal role in the stability of the molecule. Differences between dihedral angles and the corresponding angles for 2,2 -dihydroxydiphenylmethane can serve as an indicator of the intramolecular strain. One can see that for pristine calixarenes these differences are small for most angles, which supports the conclusion about the general stability of these conformers. Only for a few angles are these differences larger than 10◦, such as, e.g., the angles between third and fourth (and symmetrically: first and sixth) rings for the *pc* case, first and second for the *al* and R2bR3 (and symmetrically: R5bR6) for the *wc* conformers of calix[6]arene. The substitution of hydrogens with the *tert*-butyl substituent leads to the largest strains for the *pc*-BCX case (two-digit differences for eight out of twelve angles, with the largest change of 28◦). For *wc*-BCX conformer, the same R2xR3 (*x* means in the following both *a* and *b*) angles show differences of 10◦ and −13◦, and the smallest differences with respect to the 2,2 -dihydroxydiphenylmethane conformers are found for the *al*-BCX conformer (−11◦ for R1bR2). The largest distortion for the *pc* case can be easily explained by the fact that in this case, all *tert*-butyl groups reside on the same bottom side of the calixarene macroring, so an adaptation of this ring should be performed to avoid repulsion between the *tert*-butyl groups.

The analysis of geometrical changes in calixarenes caused by the complexation can be performed at best by making a comparison between these angles for the pristine calixarenes and angles for calixarenes within complexes. On average, these changes are again quite small and become significantly larger only for a couple of angles (most often these are the angles R2bR3 and R5bR6 for *pc*, R2aR3 and R4bR5 for *al*, and R2bR3 and R5bR6 for *wc*). The presence of *tert*-butyl groups makes the calixarene backbone more rigid for the *wc* and *pc* conformers, since the average change for the BCX is smaller than for the CX. This rigidness can be explained by the fact that the *tert*-butyl groups cannot be easily moved in space because they start to overlap, and this problem is especially severe when all these groups reside on the same side of calix[6]arene (i.e., for the *pc* and to some extent for the *wc* cases). For several amino acids, the distortion of one or more dihedral angles is quite significant, which indicates a larger geometry modification of the calixarene and possibly larger deformation energy. Especially for complexes with the *wc* conformer of CX for the majority of cases, one angle is modified by more than 30◦. The only amino acids for which there is no such large distortion are: AspH, Cys, Gln, GluH, Lys, and Pro. For the *al* conformer, such a large distortion occurs for two cases only (HisE and Pro), while other large distortions are at most 20–22◦ (for Cys, Gln, Gly, Ile, and Thr). For the *pc* conformer changes are even smaller: only for two cases the largest discrepancy amounts to 20◦ (for Asn and GluH) and is smaller for the remaining cases. A comparison to the BCX complexes leads to a conclusion that the largest differences for the *wc* conformers are much smaller than for the unsubstituted counterpart–only for two cases the difference is larger than 20◦ (HisE and Trp). For the *al*-BCX conformer, there are two cases of distortion larger or close to 30◦ (Tyr and Phe). Finally, for the *pc* case there is one case of a change close to 20◦ (for HisE), while the other largest discrepancies are much smaller (about 15◦ for several cases, but usually–a one-digit number). Therefore, the overall conclusion is that the substitution with *tert*-butyl groups hinders geometry modifications under complexation in the majority of complexes.
