Supplementary Material for the Paper

Supplementary Material for the paper

Water structuring inside the cavities of cucurbit[n]urils (n = 5-8): a quantum-chemical forecast

Tatiana N. Grishaeva1), Alexey N. Masliy, and Andrey M. Kuznetsov

Kazan National Research Technological University, K. Marx St. 68, Kazan, Russian Federation 420015

1) Corresponding author, E-mail:

Comparison of theoretical IR spectra of the (H2O)n@CB[6] inclusion complexes (n=1-6) with experimental spectrum of CB[6] synthesized in aqueous solution

The experimental IR spectrum of CB[6] extracted from the aqueous solution after synthesis was recorded in NIIC SB RAS (Novosibirsk) on a Scimitar FTS 2000 spectrophotometer in KBr tablets. Quantum-chemical calculations of IR spectra of the model (H2O)n@CB[6] inclusion complexes were carried out using the program package Priroda within the PBE density functional with atomic basis set 6-31+G(d,p) for all the atoms. Experimental and theoretical spectra were processed using the software package QitiPlot [1S].

Comparisons of the experimental and theoretical IR spectra were carried out for CB[6] only, which, compared to its homologues, is known to have the highest yield in the synthesis.

As was shown in our study (see main text), the thermodynamically most probable number of the water molecules in the CB[6] cavity is equal to four, and accordingly we first present a comparison between the calculated IR spectrum of the (H2O)4@CB[6] inclusion complex with the experimental one of CB[6].

Fig. S1 Comparison of the experimental IR spectrum of CB[6] (solid line) and theoretical spectrum of the (H2O)4@CB[6] inclusion complex. No frequency scaling factors were applied

Fig. S1 provides a comparison of the experimental IR spectrum of CB[6] and theoretical spectra of the (H2O)4@CB[6] inclusion complex. As can be seen, there are some discrepancies between the positions of the key peaks in the experimental and theoretical spectra. It is known (see, for example [2S,3S]) that such mismatches are typically due to a systematic error of calculation methods, that causes a certain shift in the calculated IR spectrum. In the practice of quantum-chemical calculations, frequency scaling factors have been widely used to partially compensate this error. Specific values of these coefficients depend on the chosen quantum-chemical method and atomic basis set. Currently, one of the constantly updating databases [4S] contains a large number of frequency scaling factors for different combinations of the method and atomic basis sets. Based on the above consideration, for the calculated IR spectra of the (H2O)n@CB[6] inclusion complexes we used the scaling factor of 0.989. This value was recommended in [4S] for the PBE density functional in combination with the atomic basis set 6-31+G(d,p).

Fig. S2 Comparison of the experimental IR spectrum of CB[6] (solid line) and theoretical spectrum of the (H2O)4@CB[6] inclusion complex. Theoretical frequencies of the whole spectrum were scaled by the scaling factor of 0.989

Fig. S2 shows the comparison of the experimental IR spectrum of CB[6] and the calculated spectrum of the (H2O)4@CB[6] complex, modified using this scaling factor for the entire spectrum. This figure demonstrates that the correspondence between the calculated and experimental spectra is much improved in the high-frequency region of the spectrum, although in the low-frequency region the differences become more significant.

The analysis of prior relevant literature data shows that the authors of [5S,6S] faced a similar problem. In their studies they demonstrated that one must use different scaling factors for high- and low-frequency regions of the spectrum. According to the results of [5S], the conventionally used boundary for the dividing of the spectrum lies in the range of 1000-2000 cm-1 and it is chosen individually for each system under study. In our case, this boundary was chosen to account and compensate for the differences in the positions of the characteristic peaks in the experimental and theoretical spectra. Figures S1 and S2 show that this boundary is located approximately in the region of 1650-1700 cm-1.

Based on this reasoning, we used the first scaling factor for the region of frequencies <1700 cm-1 while the second scaling factor was used for the region of frequencies >1700 cm-1 . For the low-frequency region of the spectrum (<1700 cm-1) we have calculated the first scaling factor using the least squares method. It was obtained the value of 1.0246. For the high-frequency region (>1700 cm-1), the value of 0.989 has been used (see above).

Fig. S3 Comparison of the experimental IR spectrum of CB[6] (solid line) and theoretical spectrum of the (H2O)4@CB[6] inclusion complex. Theoretical frequencies were scaled by the scaling factors of 1.0246 and 0.989 for the regions <1700 cm-1 and >1700 cm-1, correspondingly

Fig. S3 illustrates the comparison of the experimental IR spectrum of CB[6] with the calculated spectrum of the (H2O)4@CB[6] complex corrected using two scaling factors mentioned above. As can be seen, the introduction of a second scaling factor significantly improves the agreement in the positions of the main peaks of the experimental and theoretical spectra at lower frequencies. In general, we can make a conclusion that a convincingly good agreement between the theoretical and experimental data can be observed for the entire spectral region.

Finally, in Figures S4-S9 we present the experimental IR spectrum of CB[6] and compare it with the theoretical spectra for (H2O)n@CB[6] inclusion complexes with varying numbers of water molecules n (n=1-6) inside the cavity.

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Fig. S4 Comparison of the experimental IR spectrum of CB[6] (solid line) and theoretical spectrum of the H2O@CB[6] inclusion complex. Theoretical frequencies were scaled by the scaling factors of 1.0246 and 0.989 for the regions <1700 cm-1 and >1700 cm-1, correspondingly

Fig. S5 Comparison of the experimental IR spectrum of CB[6] (solid line) and theoretical spectrum of the (H2O)2@CB[6] inclusion complex. Theoretical frequencies were scaled by the scaling factors of 1.0246 and 0.989 for the regions <1700 cm-1 and >1700 cm-1, correspondingly

Fig. S6 Comparison of the experimental IR spectrum of CB[6] (solid line) and theoretical spectrum of the (H2O)3@CB[6] inclusion complex. Theoretical frequencies were scaled by the scaling factors of 1.0246 and 0.989 for the regions <1700 cm-1 and >1700 cm-1, correspondingly

Fig. S7 Comparison of the experimental IR spectrum of CB[6] (solid line) and theoretical spectrum of the (H2O)4@CB[6] inclusion complex. Theoretical frequencies were scaled by the scaling factors of 1.0246 and 0.989 for the regions <1700 cm-1 and >1700 cm-1, correspondingly

Fig. S8 Comparison of the experimental IR spectrum of CB[6] (solid line) and theoretical spectrum of the (H2O)5@CB[6] inclusion complex. Theoretical frequencies were scaled by the scaling factors of 1.0246 and 0.989 for the regions <1700 cm-1 and >1700 cm-1, correspondingly

Fig. S9 Comparison of the experimental IR spectrum of CB[6] (solid line) and theoretical spectrum of the (H2O)6@CB[6] inclusion complex. Theoretical frequencies were scaled by the scaling factors of 1.0246 and 0.989 for the regions <1700 cm-1 and >1700 cm-1, correspondingly

These figures demonstrate that when the number of water molecules in the CB[6] cavity increases, the agreement between the calculated and experimental spectra is qualitatively improved. However, for (H2O)5@CB[6] and (H2O)6@CB[6] despite a good agreement with experiment in the high-frequency region of the spectrum, in the low-frequency region there appears a discrepancy in positions of the main peaks compared with the experimental spectrum for CB[6] and the theoretical one for (H2O)4@CB[6].

In our opinion, the agreement between experiment and theory for the IR spectrum of (H2O)4@CB[6] is considerably better compared with the spectra of (H2O)n@CB[6] for other numbers n of water molecules in the cavity. This finding may serve as a confirmation of the conclusion about the most probable number of H2O molecules within CB[6] equals to 4; this conclusion was made by us based on the thermodynamic estimates discussed in more detail in the main text of the paper.

References

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