**4. Conclusions**

Three calix[6]arene and hexa-*p*-*tert*-butylcalix[6]arene conformers and their most stable complexes with amino acids were studied with DFT+D, SSMF, MP2, SCS-MP2, SAPT0, and F-SAPT methods.

The *pc* (pinched-cone) conformer is the most stable for the pristine calix[6]arene and hexa-*p*-*tert*-butylcalix[6]arene. A ring of six H-bonds strongly stabilizes the calixarene pinched-cone shape, with a strength of the H-bond of about −15 mH, according to the I-SAPT analysis. This ring partially closes the top of the calixarene molecule. No significant differences between calix[6]arene and hexa-*p*-*tert*-butylcalix[6]arene stability of the *pc* conformer have been found. The *wc* (winged-cone) and *al* (alternate) conformers each have two triples of hydroxy groups connected by H-bonds, which are weaker than for the *pc* case (−10 mH and −12 mH).

The energetic order of complexes with the same amino acid usually differs from the stability order of empty calixarene conformers. The interaction energy order is different too, which can be attributed to deformations, which strongly depend on the conformer and on the amino acid type. The absolute values of interaction energies of the *pc* conformers are about two times smaller than those for the *wc* and *al* ones, indicating that because of the more stable structure the *pc* conformer is less prone to interact with polar molecules such as amino acids. No molecule was able to penetrate inside the *wc* conformer, while for other conformers both inclusion and outer complexes are found as the lowest complex conformers.

Systematic molecular fragmentation is proven to reproduce the interaction energy of the complexes with good accuracy. Especially the dispersion energy (i.e., electroncorrelated part of the interaction energy) is well suited to be treated by the SSMF3 approach. The examination of individual contributions to the interaction energy calculated *via* the SSMF3 method is useful to select those parts of the calixarene molecule, which are of major importance for the interaction. By a difference analysis of two or more such fragments, more information can be obtained about the nature of the interaction, such as, e.g., about the cooperative or anti-cooperative interaction of the major binding site with neighboring functional groups or about a subtle dependence of the sign of such effects on the relative position of these groups.

A partition of the SAPT interaction energy into components and – simultaneously–into contributions from pairs of functional groups with help of the F-SAPT approach, gives a plethora of information about the strength and nature of interactions between these groups. Depending on the relative importance of the electrostatic, first-order exchange, and effective induction and dispersion contributions with respect to the total interaction energy of the pair, we propose a preliminary classification of the interactions into: (i) typical H-bonds; (ii) H-bonds with a dispersion flavor; (iii) H-bonds with an aryl ring as the hydrogen acceptor; (iv) dispersion-dominated, and finally; (v) electrostatic-dominated interactions, depending on ratios of SAPT components with respect to the total interaction energy between these

two groups. The characteristic feature of H-bonds is a high ratio of first-order exchange, which is a prerequisite of the effective overlap of the electron clouds.

After pair interactions are classified according to their strength and origin, one can single out cases, for which two or more such interactions are of similar importance. Numerous such cases arise in this study because of multiple candidates for binding sites for both calixarenes and amino acids. Especially interesting among them are those inclusion complexes for which the confinement effect plays a role in stabilization.

Finally, smaller-than-expected stability of some complexes can be explained by the existence of pair interactions that are weakly bound or which repel each other because of an inadequate alignment of the interacting pair.

The picture of the binding between the studied calixarenes and the amino acids is not simple and unequivocal. Therefore, it was not possible to find a clear tendency in the studied set of complexes. However, the analysis of data reveals that irrespectively of the type of the amino acid its NH2 group and, to a lesser extent also the COOH group, participate in the calixarene-amino acid binding and that they can form H-bonds of various strengths and geometries, as described in more detail above. Further, in the case of His, a large contribution comes from the interaction of its imidazole ring. This ring can participate both in the H-bond formation through its nitrogen atoms, as well as in the *π*-*π* stacking interactions. The latter is also very well developed and plays a decisive role in the case of the binding of Phe. Surprisingly, the indole ring of Trp contributes less to the overall binding. The amino acids possessing the OH group (Ser, Thr, and Tyr) involve this entity to form relatively strong H-bonds with the calixarenes hosts. Finally, the contribution of the SH entity is also seen in the case of the Cys complexes.

This study shows that the I- and F-SAPT approaches are very useful to elucidate the nature of inter- and intramolecular noncovalent bindings. Additionally, they can be used to refine explanations or other phenomena, such as the lowering of the IR frequency for the *al*-CX, which–as revealed by the I-SAPT analysis–resulted from the noncovalent attractive interaction between hydroxy and phenyl groups of different calixarene units.

**Supplementary Materials:** The following are available at https://www.mdpi.com/article/10.3390/ molecules27227938/s1, Figure S1: Amino acids as guest molecules used in this study, Figures S2–S9: IR spectra of calixarenes, Figures S10–105: The F-SAPT partitioning graphs, Tables S1 and S2: Dihedral angles for complexes of calixarenes, Table S3: I-SAPT interaction energies al-CX, Tables S4–S9: A comparison of the SSMF3 fragmentation scheme with the unfragmented results for supermolecular and SAPT0 interaction energies for amino acid and calixarene complex, Table S10: The SAPT0 energy components, SAPT0 and HF interaction energies, MP2 and SCS-MP2 electron-correlated parts of the interaction energies for BCX+amino acid complexes, Table S11: The electronic and total energy of both empty calixarenes in three considered conformations, and complexes of these conformations with amino acids, Tables S12–S17: Percent errors of the SSMF3 fragmentation scheme in respect to unfragmented results for amino acid+calixarene complex, Tables S18–S23: A complete list of frequencies and intensities of calixarenes, Tables S24–S26: The total SAPT0 interaction energies of unfragmented and the SSMF3 fragments for BCX+Gly complex, Table S27: The accuracy of the SSMF3-HF(b) and SSMF3-MP2(b) electric dipole moments and dipole static polarizabilities for three conformers of calix[6]arene, Table S28: The F-SAPT partitioning for selected CX+amino acid pairs with their classification, Table S29: The F-SAPT partitioning for selected BCX+amino acid pairs with their classification, Table S30: Interaction of hydroxy groups of the BCX calixarene with and without the presence of Gly as calculated with the I-SAPT method. FSAPT\_h-sub.ods, F-SAPT partitioning for complexes with calix[6]arene; FSAPTz\_b-sub.ods, F-SAPT partitioning for complexes with hexa-*p*-*tert*-butylcalix[6]arene; xyz\_files.zip, Cartesian coordinates of studied systems.

**Author Contributions:** Conceptualization, T.K. and D.R.-Z.; methodology, M.C., T.K. and E.M.; software (SSMF program), E.M.; validation, T.K. and D.R.-Z.; formal analysis, T.K., M.C., E.M.; investigation, E.M., M.C., T.K.; writing–original draft preparation, M.C., T.K., D.R.-Z.; writing review and editing, T.K., D.R.-Z., E.M. and M.C.; visualization, E.M., T.K., M.C.; supervision, T.K.; project administration, T.K.; resources, T.K.; funding acquisition, T.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Science Centre of Poland through grant 2017/27/B/ST4/02699. This research was supported by PCSS infrastructure and PRACE-6IP 823767, MNISW DIR/WK/2016/18.

**Data Availability Statement:** Data is contained within the article or supplementary material

**Conflicts of Interest:** The authors declare no conflict of interest.
