*3.5. Complexes with Amino Acids–Interaction Energies*

Interaction energies of the calixarene complexes with amino acids are presented for SAPT0, MP2, and SCS-MP2 methods in Figure 5. We treat the SCS-MP2 results as the most accurate since the scaling of the MP2 same- and opposite-spin energies, which make up the SCS-MP2 model, is devised [117,118] to reproduce the CCSD(T) correlation energy. The MP2 and SAPT0 results are consistently lower than SCS-MP2, but the interaction energies for all three methods follow the same global trend, as can be seen in Figure 5, where for a given conformer, the lines connecting interaction energies for various amino acids obtained with the same method look similar for SAPT0, MP2, and SCS-MP2. In particular, the *pc* conformer is the least prone to making a strong binding with amino acids, while the remaining conformers provide more attractive contributions (with a slight advantage of *al*). Since the F-SAPT and I-SAPT partitioning schemes utilize the preceding SAPT0 calculations, the consistency of SAPT0 and SCS-MP2 results should be especially emphasized in view of the reliability of further F/I-SAPT analyses. It is also interesting to note that on average the

BCX complexes have lower interaction energies than the CX ones. A general analysis of the SAPT contributions shows that indeed the mean SAPT0 interaction energy for the BCX complexes is about 6 mH lower than this for the CX complexes, and the main contribution to this difference is due to the effective dispersion (10 mH lower), while the more repulsive first-order exchange contribution partially counterweights the additional attractive effect coming from electron correlation.

**Figure 4.** Relative total and electronic energies for complexes with three conformers of calix[6]arene and hexa-*p*-*tert*-butylcalix[6]arene. Energies are in millihartree.

The analysis of Figure 5 leads to the conclusion that the largest attraction appears for the Asn and Gln amino acids for the *al*-CX conformer and for Asn for the *al*-BCX, and for Ala and (again) Asn for the *pc*-CX and *pc*-BCX, respectively. On the other hand, in the case of the *wc* conformer, it is the HisD amino acid, which shows the most attractive interaction for the CX, while the Lys molecule exhibits the largest attraction for the BCX.

The comparison of the SSMF3 interaction energies with the standard (unfragmented) ones, which is presented in Table 2 for the calix[6]arene (the analogous table for hexa*p*-*tert*-butylcalix[6]arene has been moved to the Supplementary Information) shows that the SSMF3 approach (see Equation (3)) quite accurately reproduces interaction energies for investigated complexes. The first study of the applicability of SSMF3 for the interaction energies [50] revealed that the electron-correlation contribution is well reproduced by the SSMF3, while the accuracy of the HF part depends on the distance between the interacting molecules. The present study supports these conclusions, i.e., the electron-correlation parts of the SCS-MP2 interaction energies for complexes with the CX are reproduced with a mean percent error of 1.7%, with the largest absolute error of 3.7%. The electrostatic and first-order exchange SAPT0 contributions are obtained with good accuracy (the mean percent errors of 0.6% and 0.2%, and maximum ones 2.7% and 0.8%), while the most problematic component is the second-order induction (the mean percent error of 3.2%, but the maximum error is as large as 18%). One should note, however, that large percent errors for induction appear for those cases, for which this component is small with respect to other components (the largest error appears for the *pc*-CX with Met, where the second-order induction and dispersion contribute with −8.6 mH and −26.9 mH, respectively). The second-order dispersion, i.e., the pure electron-correlation effect, is reproduced quite accurately for all the cases (the mean and maximum errors of

1.2% and 2.0%, respectively). For the hexa-*p*-*tert*-butylcalix[6]arene complexes, similar error ranges occur, e.g., the maximum absolute errors for the electrostatic and firstorder exchange are equal to 2.3% and 0.9%, and again the highest error arises for the second-order induction, but anyway, the maximum error is more than twice smaller (7.9%). The second-order SAPT0 dispersion is reproduced with a stable mean error of about 2% and the maximum error of 2.8%. The accuracy of the electron-correlated contributions from the MP2 and SCS-MP2 theories are of the same range as for the dispersion. Therefore, the comparison of the SSMF3-SAPT0 and SAPT0 results, as well as SSMF3-(SCS-MP2) and SCS-MP2 allows us to make a conclusion that in the region of a minimum of the intermolecular potential energy hypersurface the SMF-based methods give quite accurate results. Note that in the case of large percentage errors for the HF interaction energy, the energy itself is close to zero. This conclusion is important in view of our perspective applications of SSMF3 in the analysis of energy partitioning among functional groups.

**Figure 5.** Trends in interaction energies for complexes with three conformers of calix[6]arene and hexa-*p*-*tert*-butylcalix[6]arene. Energies are in millihartree.


*Molecules* **2022**, *27*, 7938

**Table 2.** The SAPT0 energy

components,

 SAPT0 and HF

interaction

 energies,

 MP2 and SCS-MP2

electron-correlated

 parts of the

interaction


**Table 2.** *Cont.*
