*3.4. Stability of Complexes with Amino Acids*

In this study, we are mostly interested in energy partitioning and relative energies; therefore, we do not aim at achieving very accurate interaction energies. Nevertheless, we selected one case (a complex of *pc*-CX with Gly), for which we calculated the interaction energy in two basis sets from a modified Dunning series for the SAPT0, MP2, and SCS-MP2 theories. One of these basis sets, jun-cc-pVDZ, has been used for all other complexes, while the larger one–jun-cc-pVTZ–has been used for the purpose of the CBS study. As expected, the main part of the basis set unsaturation comes from the electron-correlation part of the interaction energy. A difference in the HF interaction energy between both basis sets amounts to 0.7 mH only, while the net dispersion from SAPT0 (E(20) disp <sup>+</sup> <sup>E</sup>(20) exch−disp) is equal to 4.8 mH, a quantity similar to the correlation part of the MP2 and SCS-MP2 interaction

energies, where these differences are equal to 5.0 and 4.1 mH, respectively. If a popular inverse cubic extrapolation formula [98],

$$\mathbf{E}\_{\rm L} = \mathbf{E}\_{\infty} + \frac{\mathbf{A}}{\mathbf{L}^{\Im}} \tag{4}$$

is applied to the correlation part of the interaction energy (with L equal to 2 and 3 for jun-cc-pVDZ and jun-cc-pVTZ, respectively), then the estimated correlation energy decreases by another 1.7 mH for the SCS-MP2 case, so (taking the HF interaction energy on a larger basis) the estimate of the CBS limit of the SCS-MP2 interaction energy for this complex is −21.5 mH, which should be compared with −19.1 mH and −15.6 mH for the jun-cc-pVTZ and jun-cc-pVDZ basis sets, respectively. Therefore, the energetic results in the jun-cc-pVDZ basis set are rather semiquantitative and as a rule of thumb it should be rescaled by approximately <sup>4</sup> <sup>3</sup> to make the estimate for the CBS interaction energy.

The relative stability of both empty calixarenes for three considered conformations and complexes of these conformations with amino acids calculated from their total energies with respect to the lowest conformation are presented in Table 1 and in Figure 4. For empty calixarenes, the *pc* conformer is the most stable for both the CX and BCX cases, which can be explained by two more H-bonds stabilizing the macrocycle structure in comparison to the *wc* and *al* cases. For the *al* and *wc* conformers, the folding of the calixarene macrocycle prevents the creation of H-bonds between the following hydroxy pairs: first with sixth and fourth with third. The order of the *wc* and *al* conformers differs for the CX and BCX cases–in the former case, the *al* conformer has the lower energy, while the opposite is true for the BCX case. It should also be noted that the *wc*-BCX has the energy higher only by 2.4 mH than the *pc*-BCX, while both *al*-CX and *wc*-CX lie over 12 mH higher than the *pc*-CX. Therefore, at standard conditions, one can expect a sizable (about 7%) contribution of the *wc* conformer for the hexa-*p*-*tert*-butylcalix[6]arene, while for the case of calix[6]arene there is only one dominant conformer (*pc*).

The energetic order of complexes of *pc*, *al*, and *wc* calixarenes with amino acids is in most cases different than the pristine series. The energetic sequence is preserved for amino acids: Leu, Phe, Pro, Trp, and Val interacting with CX and only Met, Phe, and Tyr interacting with BCX. If the energetic difference between the highest and the lowest conformers of empty calixarenes with the analogous energetic span of complexes are compared, one can find that this difference becomes smaller (within 2.0 mH or less) for CX interacting with Ala, Gln, GluH, HisD, and Tyr, and for BCX interacting with Ala, Met, and Phe. For these complexes, all types of conformers are accessible under standard conditions. On the other hand, the energy span between conformers becomes larger than for pristine conformers only for one case (Asn) for the CX case and for Asn, AspH, Cys, Gly, HistD, Lys, Ser, and Trp for the BCX one. However, it should be noted that the energy span between conformers of the empty BCX (10.7 mH) is smaller than for the CX (15.8 mH). In general, the addition of large *tert*-butyl groups seems to reduce energetic differences in both pristine calix[6]arenes and their complexes. In several cases, the complexation diminishes the energetic differences for two from three conformers. If access to a specific conformer is desired, the special cases, for which one conformer has much lower energy than the two remaining ones are the most promising in view of potential applications. For complexes with CX especially, often the *al*-CX complexes become energetically more favorable than the *pc* ones. The exceptionally large difference between the *al*-CX complex and *pc* or *wc* ones occurs for the Asn amino acid (16 mH). Other cases include: Gly (8 mH), Ser (10 mH), and Thr (6 mH). The *wc*-CX complexes have the lowest energy for three cases only, but in all of these cases, the differences are very small (2 mH and smaller). The *pc*-CX remains the lowest one for a couple of cases, but only for the complex with Val energetic differences larger than 2.5 mH.

Contrary to the complexes with CX, it is the *wc*-BCX conformer that becomes the lowest energetically for the majority of complexes with amino acids. The situation where the other two conformers lie higher than 4 mH occurs for AspH, Gln, GluH, Gly, HisD, HisE, Ile, Leu, Thr, Trp, and Val. In several cases, two conformers (*wc* and *al*) are almost isoenergetic and lower than *pc*, such as in the case of Asn, Lys, and Ser. Finally, for the Phe amino acid, the differences between all three conformers are less than 2 mH. It should be noted that the *al*-BCX conformer does not become the preferred one for all but one case, which is the complex with Cys. However, even in this case, the next lowest conformer is the *wc* conformer.

Summarizing, the complexation with amino acids tends to modify the energetic order of both CX and BCX conformers, and in several cases, these differences are quite substantial. The extreme differences are seen more often for the unsubstituted calix[6]arene case. One should mention that one important potential application resulting from such a change of energetic order of *pc*, *al*, or *wc* conformers is a possibility of accessing, e.g., the *al*-type conformer for the purpose of chemical reactions with calix[6]arene, which would otherwise be dominated by the *pc* conformer.

**Table 1.** The relative electronic and total energy of both empty calixarenes in three considered conformations, and complexes of these conformations with amino acids with respect to the lowest conformation energy. Energies in millihartree.

