**1. Introduction**

Calixarenes are phenolic-based macrocycles consisting of repeated units of phenol and hydrocarbon groups, which have attracted a lot of attention in recent years owing to their ability to form host–guest complexes for hydrophobic guests, in particular, in the context of their biological and pharmaceutical potential [1–3]. Experimentally known calixarenes usually contain between four and eight phenol units [4]. The simplest calixarene, calix[4]arene, consists of four phenol groups connected through methylene links ( – CH2 – ). A theoretical study of the stability of smaller calix[3]arenes [5] revealed strong structure stress, which disappears only when one more phenol ring is added to the macrocycle. A known feature of calixarenes is their ability to form inclusion complexes in one conformation and release the guest molecule after the conformation change. Such adducts, which are examples of intermolecular complexes, are being studied as possible drug carriers [6–8], models of enzyme active centers [4], the base for supramolecular catalysts [9,10], building elements of nonlinear optics structures [11], structures binding metal ions [5,12] and their clusters [13], and as chemosensors [14–16]. Furthermore, the modification of the calixarenes' basic core and both upper and lower rims extended the range of their applications towards becoming anticancer drugs [17–19], antimicrobial agents [17,20–25], and sensitizers for photodynamic therapy [26].

The smallest stable calixarene is known to have four conformations, which can be unanimously described by just listing relative orientations of the phenol groups with respect to the macroring, i.e., since each phenol ring can assume either upward (*u*) or

**Citation:** Masoumifeshani, E.; Chojecki, M.; Rutkowska-Zbik, D.; Korona, T. Association Complexes of Calix[6]arenes with Amino Acids Explained by Energy-Partitioning Methods. *Molecules* **2022**, *27*, 7938. https://doi.org/10.3390/ molecules27227938

Academic Editor: Miroslaw Jablonski

Received: 23 September 2022 Accepted: 9 November 2022 Published: 16 November 2022

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downward (*d*) position relative to this ring, one finds four possibilities, denoted as *cone* (*uuuu*), *partial cone* (*uuud*), *1,2-alternate* (*uudd*), and *1,3-alternate* (*udud*)–in parenthesis, the arrangement of adjacent phenol rings has been listed. This classification turns out to be insufficient for larger calixarenes, where additional degrees of freedom result from more variants of orientations of phenol rings with respect to their left and right neighbors. In order to characterize these calixarene conformers, Ugozzoli and Andreetti [27] proposed to represent a conformation of calix[*n*]arene through a list of *n* pairs of conformational parameters, defined as dihedral angles between a phenol ring and a plane defined by two C-C bonds originating from a linker carbon atom towards phenol groups. Formally these angles are calculated as dihedral angles *C*1*C*2*C*3*C*<sup>4</sup> (*φ*) and *C*2*C*3*C*4*C*<sup>5</sup> (*χ*), see Figure 1 for numbering of carbon atoms. Additionally, a "top side" of calixarene is defined in Ref. [27], and the order of (*φ*, *χ*) descriptors is set to be counterclockwise with respect to the top. For all cases considered in the present paper, the simplest definition of the top side applies, i.e., it is the side with the highest number of phenolic oxygen atoms. Some of these conformations are more stabilized by hydrogen bonds (H-bonds) between the hydroxy groups than others. Moreover, the cavity size and the rim properties differ significantly in various conformers. The conformations described above are in dynamic equilibrium, which is related to the possibility of rotation around the bonds bridging the individual phenol units. This rotation may be blocked by the introduction of large substituents into the aromatic rings, which will form a steric hinge within the upper edge of the calixarene ring (opposite to the hydroxyl groups) [28]. Other factors affecting the possibility of rotation of phenol units are: temperature and solvents. The availability of conformers in a finite temperature is governed by their energetic stability differences according to the Boltzmann law, while polar or nonpolar solvents can either preferably bind with the polar hydroxy groups of calixarenes or–on the opposite–stabilize conformers for which hydroxy groups can be hidden inside the hole creating the intramolecular H-bond network(s).

**Figure 1.** Dihedral angles between adjacent aryl groups of a calixarene. The first dihedral angle is defined through atoms 1–4, and the second one–through atoms 2–5.

Many theoretical and experimental studies exist for calixarenes, especially for the smallest calix[4]arenes, see, e.g., Refs. [29–31]. Studies of larger calixarenes, calix[6]arenes and calix[8]arenes as reported in Refs. [29,32,33] and [29,34,35], respectively, revealed that in the majority of cases, the cone conformation is the most stable. This finding can be explained by the creation of intramolecular H-bonds, as proposed by Gassoumi et al. [29] after a density-functional theory (DFT) study with several functionals for six- and eightmember unsubstituted calixarenes, while Furer et al. [32,34] arrived at the same conclusion for heavily substituted calix[*n*]arenes, *n* = 6, 8, with adamantane and *tert*-butyl serving as substituents.

Inclusion complexes with calixarenes were objects of several studies, too. For instance, Puchta et al. [36] examined the possibility of the binding of small molecules such as CH3NH2 and CH3CN by calix[4]arenes by employing a simple DFT functional and a small basis set as an extension of the nuclear magnetic resonance (NMR) studies. They found that no proper inclusion complexes are created since the most favorable position

of the guest molecules would be on the outer part of the edge. The binding energy was small (5 kcal/mol), but one should take into account that the utilized functional and basis set were not optimal for such an investigation. It should be also noted that Puchta et al. observed a proton transfer from the host species after binding of CH3NH2. In another study Galindo-Murillo et al. [6] examined the applicability of calix[*n*]arenes (where *n* = 4, 5, 6, 8) as hosts for 3-phenyl-1H-[1]benzofur[3,2-c]pyrasol (GTP). Their DFT calculations (with a better B97-D functional) showed that the most promising GTP carriers are the two largest calixarenes, which can be attributed to the existence of a large enough space inside the host molecule and to the presence of hydrogen bondings between the host and guest. The stabilizing role of a partial charge transfer (CT) between GTP and calixarene has also been noted in this work.

The usability of calix[4]rene and calix[4]resorcinarene and their derivatives to host a zoledronate acid molecule has been studied by Jang et al. [37] with DFT plus a dispersion correction (DFT+D), where the cone conformer of calixarene has been used. It turned out that the adduct contains a guest attached to the upper ring edge of the calixarene and that the inclusion of this guest causes only modest changes in the cavity of the host. If calixarene is modified with the sulfone groups or with phosphone ones, their cavities become notably wider, while the bottom remains mostly rigid, as it is stabilized by the intramolecular H-bonds. Further analysis of electronic structures shows that *π*–*π* interactions play a decisive role in the binding between the host and the guest. The number of H-bonds is important for the relative stability of similar complexes, e.g., the binding with calix[4]resorcinarene is stronger than that of the sulfonated calix[4]arene. In another study performed by Kryuchkova et al. [38], it has been found that calix[4]arenes modified by the R2PO groups can ligate up to two cobalt complexes with the nitrate ions. The smallest calix[4]arenes were also studied as carriers of small gas molecules, such as H2, O2, N2, H2O, CO2, NH3, H2S, N2O, HCN, SO2 [39], if the lower rim of the host has been methylated, either fully or in part. The calculations, performed with the DFT+D approach, revealed that one can modify the selectivity of calixarenes through their methylation. Very recently, a theoretical study on the docking of insulin on calixarenes have appeared, where the CHARMM force field has been applied to determine the preferred amino acids docking to substituted calixarenes [40]. Other investigations of docking on calixarenes have been performed, e.g., in Refs. [41,42].

General studies of the stability of calixarenes usually do not delve into the nuances of the nature of differences between various conformers and/or complexes with calixarenes. It is usually assumed in the literature that binding properties of calixarenes can be explained by the interactions of the CH-*π*, *π*-*π*, and ion-*π* types [2,43], but–to our knowledge–no systematic studies exist, which would explain the variety of properties of calixarene conformers and their complexes through the application of energy partitioning approaches in order to classify interaction types and to estimate their relative strength. Therefore, in this paper, we would like to fill this gap and present such partitioning analyses resulting from Symmetry-Adapted Perturbation Theory (SAPT) [44,45], Functional-group SAPT (F-SAPT) [46,47], and our recent modification of Systematic Molecular Fragmentation (SMF) [48], described in Refs. [49,50] and denoted as Symmetrized SMF (SSMF). Our study will include a systematic search for the H-bonds and other bonding types within the complexes. The recent redefinition of the H-bond is presented in Ref. [51], and numerous investigations concerning various types of H-bonds have been performed, including "unusual" ones (dihydrogen bonds, bonds including unusual hydrogen donors–such as, e.g., C–H, or unusual hydrogen acceptors–such as, e.g., benzene ring, or inverted H-bonds, etc.), see, e.g., Refs. [52–59]. Such investigations have been performed for other complexes with SAPT (see, e.g., Ref. [52]) or F-SAPT methods [46,47]. Additionally, applications of the SMF to intermolecular interaction energy partitionings or comparisons of F-SAPT and SMF approaches are missing in the literature.

We selected standard amino acids as potential guests and calix[6]arenes as hosts for our study because of the biochemical importance and a wide variety of binding sites of potential

guests, which result from hydrophobic, polar, aliphatic, aromatic, etc. groups attached to the amino acid moiety, while the choice of larger calix[6]arenes instead of calix[4]arenes was dictated by the existence of a bigger cavity, in which larger molecules are able to fit. Therefore, the selected set of intermolecular complexes is expected to provide examples of noncovalent bonds of different types and strengths and to show the competition of various bonds under steric constraints, resulting from the existence of a cavity. An additional feature, which will be tracked in this study, is the confinement effect resulting in the enhancement of the attraction. Such cases, reported many times for endohedral complexes of fullerenes [60], appear if a guest molecule has an optimal size for a given cavity and can be attracted from many sides, while a larger molecule starts to feel a repulsion from the cavity wall, and finally a smaller molecule is attracted mostly by one side of the cavity or–if placed in the center–is attracted less strongly because of too large a distance between the guest and the closest atoms of the host. The calixarenes selected for this study are: unsubstituted calix[6]arene and hexa-*p*-*tert*-butylcalix[6]arene, where the latter has been added in order to examine how obstacles created by spatially large nonpolar groups modify host–guest interactions. The *tert*-butyl group is one of the smallest and one of the most popular groups of this type and it is frequently used to decorate calixarene molecules [61]. In the following, these two species will be abbreviated as CX and BCX, respectively.

In the literature, one finds reports on the use of calixarenes for recognition of amino acids [62–72]. The critical review of the available data enabled general observations on amino acid complexation by calixarenes. Usually, the ability to bind these small guests decreases in the order: calix[6]arene > calix[8]arene > calix[4]arene [70,73]. The binding process is controlled by hydrogen bonding, van der Waals, cation–*π*, and *π* –*π* stacking interactions [70]. The strength of the interaction depends strongly on the chemical character of the amino acid and the substituents introduced to the pristine calixarene scaffold. Stone et al. [73] studied the formation of complexes of calixarenes with amino acids with matrix-assisted laser desorption/ionization coupled with mass spectrometer (MALDI-MS) technique. They demonstrated that calix[6]arenes substituted by esters form stable complexes with amino acids which are bound mostly by cation–*π* interactions and hydrogen bondings. The native calix[6]arenes, on the contrary, do not form complexes stable enough in the gas phase to withstand a relatively energetic process of MALDI. Among the association complexes, one finds both: (i) outer-sphere ones, in which amino acids are located outside the pocket created by the phenyl rings (see, e.g., Ref. [66]); and (ii) typical host– guest structures, where the amino acid molecules are buried inside the calixarene cavity (see, e.g., results of Oshima et al. [74] for complexes between hydrophobic amino acids and calix[6]arenes modified by carboxylic groups). Due to the small size of the interacting moieties, often one calixarene species accommodates only one amino acid molecule, but the ratio increases while increasing the size of calixarene. Douteau-Guével and co-workers demonstrated by the microcalorimetry method that calix[6]arene sulfonates form weak 1:1 complexes with Lys and Arg in water [75]. The same stoichiometry was also determined for the host–guest type of binding of Trp by calix[6]arene carboxylic acid derivative [76]. The 1:1 and 1:2 complexes are found in the case of calix[8]arenes [77].
