Research ArticleChemistry

Isolation of the simplest hydrated acid

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Science Advances  21 Apr 2017:
Vol. 3, no. 4, e1602833
DOI: 10.1126/sciadv.1602833


Dissociation of an acid molecule in aqueous media is one of the most fundamental solvation processes but its details remain poorly understood at the distinct molecular level. Conducting high-pressure treatments of an open-cage fullerene C70 derivative with hydrogen fluoride (HF) in the presence of H2O, we achieved an unprecedented encapsulation of H2O·HF and H2O. Restoration of the opening yielded the endohedral C70s, that is, (H2O·HF)@C70, H2O@C70, and HF@C70 in macroscopic scales. Putting an H2O·HF complex into the fullerene cage was a crucial step, and it would proceed by the synergistic effects of “pushing from outside” and “pulling from inside.” The structure of the H2O·HF was unambiguously determined by single crystal x-ray diffraction analysis. The nuclear magnetic resonance measurements revealed the formation of a hydrogen bond between the H2O and HF molecules without proton transfer even at 140°C.

  • hydrogen fluoride
  • water
  • hydration
  • encapsulation
  • fullerene
  • open-cage fullerene
  • molecular surgery
  • single crystal x-ray analysis
  • NMR


One of the most important chemical processes is dissociation of a Brønsted acid in aqueous media accompanied by proton transfer from the acid to H2O molecules and solvation of the charged fragments (1). This fundamental event plays a key role in myriad chemical reactions and biological phenomena. However, the detailed mechanism of acid dissociation (2, 3) and the nature of protons in an aqueous environment (4, 5) are rather complex, and still remain to be revealed at the distinct molecular level. Hydrogen fluoride (HF) is the smallest acid and has been studied well, mostly in the gas phase, both theoretically and experimentally (6). One extensively discussed issue on HF is the minimum number of H2O molecules that is necessary to solvate an HF molecule resulting in the formation of the solvent-shared ion pair [H3O+(H2O)nF] (3, 7, 8). However, the central obstacle to resolution of this subject includes the difficulty of preparation of any of the possible HF·(H2O)n complexes in a pure form with definite components. This is because the high reactivity of HF and the strong hydrogen bond affinity of H2O often result in the formation of many types of oligomers, which are in equilibrium with others, rendering their separation and isolation almost impossible (9). To understand this fundamental process, it is highly desirable to construct an ideal system that can elucidate the intrinsic nature of the hydrated HF molecule.

To isolate reactive chemical species, the compounds should be located in an inert atmosphere, preventing interaction and/or reaction from the outer environments. These subnano-sized environments can be found inside fullerenes, which are spherical carbon clusters having a hollow cavity. Very reactive chemical species such as metal ions (10, 11), metal clusters (12), and a nitrogen atom (13) have thus far been encapsulated inside fullerenes. These well-defined supramolecular systems have provided opportunities to study the physical and chemical properties of the encapsulated species at the molecular scale and to use them as functional materials (14). However, selectivity in encapsulated species in addition to fullerene cages are difficult to control because of the reliance of most production methods on harsh conditions (12, 14). In contrast, the “molecular surgery” approach can produce molecule-encapsulating fullerenes with almost-perfect selectivities under mild conditions in solution (15). Using this method, endohedral C60 encapsulating a single molecule of H2 (16), He (17), H2O (18), and HF (19) was synthesized.

Molecular surgery can also be applied to fullerene C70 despite difficulties in characterization of products due to low symmetry. Reflecting the larger inner space in C70 compared to C60 (20, 21), two small molecules were introduced inside open-cage C70 derivatives to afford the corresponding doubly encapsulating endohedral C70s after restoration of the cage, that is, (H2)2@C70 (22) and (H2O)2@C70 (23), respectively. Previously, we reported two open-cage C70 derivatives, α-13mem (24) and β-13mem (Fig. 1A) (23), both having a 13-membered ring opening with the same functional groups. These compounds were synthesized by a three-step reaction starting from the addition of a pyridazine derivative to the α- and β-bonds of C70, with total yields of 22 and 2%, respectively. Both openings were enlarged in situ into the 16-membered ring as their C60 analog (18). The opening of α-16mem is smaller than that of β-16mem, evidenced by the fact that only a trace amount of H2O was introduced inside α-16mem, whereas an H2O molecule was entrapped almost quantitatively inside β-16mem. Density functional theory (DFT) calculations also supported the smaller size of α-16mem (23). Taking advantage of the efficient synthetic yield of α-13mem, we envisioned that α-13mem would be more suitable as a starting material for novel endohedral C70s. Because the size of HF is smaller than that of H2O (25), we studied encapsulation of HF into α-13mem with initial intention to synthesize HF@C70. Here, we report facile synthesis of HF@C70, as well as unprecedented formation of (H2O·HF)@C70 and H2O@C70, using α-13mem as a key compound despite the small size of the opening for the insertion of H2O.

Fig. 1 Molecular surgery for the synthesis of endohedral fullerene C70s.

(A) Two open-cage C70 derivatives α-13mem and β-13mem obtained from the initial addition of a pyridazine derivative to the α-bond and β-bond of C70 followed by stepwise cleavages of the C=C double bonds. The openings of α-13mem and β-13mem are enlarged in situ by dehydration to afford α-16mem and β-16mem. The opening size of α-16mem is too small for H2O insertion, whereas that of β-16mem is large enough. (B) Insertion of the guest molecules (G = HF, H2O·HF, and H2O) into α-13mem and synthesis of HF@C70, (H2O·HF)@C70, and H2O@C70 by closure of the opening via two-step reactions.

As shown in Fig. 1B, after optimization of the conditions (vide infra), the high-pressure treatment of α-13mem in the presence of 0.5 equivalence of 70% (w/w) HF in pyridine (HF-Py) (26) and a trace amount of water was conducted in chlorobenzene under 9000 atm at 120°C for 18 hours to afford guest-encapsulating α-13mem (G@α-13mem; G = HF, H2O·HF, and H2O) in 40% isolated yield after purification with column chromatography. The filling factors of the guests inside α-13mem were determined by the proton nuclear magnetic resonance (1H NMR) analysis: 32% HF@α-13mem, 11% (H2O·HF)@α-13mem, 27% H2O@α-13mem, and 30% empty α-13mem, respectively. After collecting the products from several batches, closing of G@α-13mem via two-step reactions, without considerable loss of the encapsulated species, gave the corresponding endohedral C70s, that is, expected HF@C70, and unprecedented (H2O·HF)@C70 and H2O@C70 (figs. S8 to S15).

We confirmed that HF encapsulation into α-16mem did not take place in chlorobenzene under ambient pressure at 110°C, in contrast to the case for the open-cage C60 (25). Thus, the high-pressure conditions were found to be critical, where the guest species are forced to be “pushed from outside” of the opening of α-16mem. The experimental conditions and results are summarized in Table 1. Upon checking the time dependence (entries 1 to 4), the filling factor of HF appeared to almost reach a plateau after 14 hours, whereas that of H2O·HF increased slowly and that of H2O was developed rapidly at around 14 hours. These observations suggested stepwise formation of G@α-16mem, that is, HF@α-16mem followed by (H2O·HF)@α-16mem and then H2O@α-16mem. To prevent a high degree of decomposition of the starting materials and the products, a reduced amount of HF-Py at slightly higher temperature gave the better chemical yield of G@α-13mem (entry 5). As described previously by Zhang et al. (23, 24), H2O encapsulation did not occur in the absence of HF (entry 6), showing only that pushing from outside was not an effective method of inserting H2O inside α-16mem. Among the products obtained from entries 1 to 5, (HF)2@α-13mem and (H2O)2@α-13mem were not detected.

Table 1 Encapsulation of HF, H2O·HF, and H2O inside α-13mem under the high-pressure conditions of 9000 atm in the chlorobenzene solution.
View this table:

Our experiments considered the insertion mechanisms of HF, H2O·HF, and H2O (as shown in Fig. 2). Because the size of the opening of α-16mem, which was generated in situ from α-13mem by eliminating a water molecule from the bis(hemiketal) moiety, is not large enough for water to pass through, insertion of a smaller HF initially takes place by pushing from outside to give molecular complex A. In earlier work, Gan et al. (27) reported that encapsulated H2O inside an open-cage C60 was pulled out by attractive interaction with fluorine atom being present outside the opening, resulting in the release of the H2O. Taking into consideration the similar attractive interaction of the encapsulated HF and the H2O near the opening, the H2O should be introduced into α-16mem by the assist of “pulling from inside,” shown as B, to yield C. Then, positional exchange of the lower HF and the upper H2O occurs to afford D. DFT calculations at the M06-2X/6-31G(d) level showed that the required energy for the positional exchange of the HF and H2O in C is 20.8 kcal/mol (tables S3 to S5), which should be possible to occur under the applied conditions. Finally, the resulting HF near the opening escapes to form E. During the cooling process, addition of a water molecule regenerates the α-13mem cage to furnish G@α-13mem.

Fig. 2 Insertion mechanism of HF, H2O·HF, and H2O into α-16mem with the synergestic effects of pushing from outside by high-pressure conditions and pulling from inside by attractive interaction of HF with the outer H2O.

Because of the complexities in the structures of H2O clusters and hydrated HF, it is very difficult to evaluate energy profiles including A, B, D, and E by DFT studies. In the case of the gas-phase stabilization energy calculated at the MP2/6-311++G(3pd,3df) level, H2O·HF gains more energy (7.3 kcal/mol) than HF dimer (3.9 kcal/mol) and H2O dimer (3.8 kcal/mol) (tables S8 to S15). This stability is considered to play an important role for the formation of C. However, we needed to study another possibility that the presence of an acid would change the solvated structures of HF and H2O before encapsulation to result in facile encapsulation of H2O. Although a high-pressure treatment in the presence of HCl-Py, instead of HF-Py, under the same conditions was conducted, the resulting products obtained in 64% isolated yield were found to contain only a small amount of H2O@α-13mem (1.8% filling factor). These results strongly support the hypothesis that both pushing and pulling effects are necessary to achieve encapsulation of H2O·HF inside α-13mem in a remarkably high yield compared with the doubly encapsulating C70s reported so far (22, 23).

After closure of the openings (Fig. 1B), the high-performance liquid chromatography (HPLC) analysis of the products displayed three peaks corresponding to empty C70, a mixture of HF@C70 and H2O@C70, and (H2O·HF)@C70 (as shown in Fig. 3A). The monoencapsulating HF@C70 and H2O@C70 appeared at almost the same retention time regardless of the encapsulated species. In contrast, facile separation of (H2O·HF)@C70 as a pure form was achieved in a preparative scale, showing clear differences caused by the double encapsulation. By the atmospheric pressure chemical ionization mass analysis (APCI MS), we detected (HF)2@C70 before elution of (H2O·HF)@C70, albeit in only a trace amount (fig. S16).

Fig. 3 Properties of (H2O·HF)@C70.

(A) HPLC trace of reaction products after the complete closure of the opening. The HPLC was equipped with the Cosmosil Buckyprep column (4.6ϕ × 250 mm) eluted with toluene at 50°C. 1H NMR (500 MHz) spectra in CDCl3/CS2 (1:1) at 25°C of (B) a mixture of HF@C70 and H2O@C70, and (C) pure (H2O·HF)@C70. (D) Single crystal x-ray structure of (H2O·HF)@C70 with thermal ellipsoids at the 50% level, with cocrystalized nickel(II)octaethylporphyrin. Solvent molecules and hydrogen atoms were omitted for clarity. (E) Detailed x-ray structure of the encapsulated H2O·HF complex. The H atom between O and F was refined, whereas the other two H atoms were geometrically fixed. (F) Calculated structure of (H2O·HF)@C70 at the ONIOM-(MP2/6-311++G(3df,3pd):M06-2X/6-31G(d)). Only the encapsulated species were shown. Calculated structures at the MP2/6-311++G(3df,3pd) of (G) a free HF and (H) a free H2O·HF.

The 1H NMR analysis is a powerful tool to study the structure and dynamics of the isolated H2O·HF. As shown in Fig. 3B, a signal of the singly encapsulated H2O at −27.1 parts per million (ppm) [500 MHz; CDCl3/CS2 (1:1), 25°C] coincides with that of our previous report for H2O@C70 synthesized from different synthetic routes (23), showing strong shielding effects due to C70 cage (22, 23). A doublet corresponding to the singly encapsulated HF was observed at −25.0 ppm with a coupling constant JHF = 507 Hz, whose value is almost the same as that of HF@C60 (19). The 1H NMR of (H2O·HF)@C70 displayed a singlet at −25.3 ppm corresponding to the H2O in addition to a doublet at −17.5 ppm corresponding to the HF. It is noteworthy that both chemical shifts are downfield-shifted compared with those of H2O@C70 and HF@C70, indicating more positive charges on the protons due to the formation of a hydrogen bond. The shifted value for the HF (Δδ +7.5) is larger than that of the H2O (Δδ +1.8), demonstrating that this molecular complex adopts the structure H2O·HF, in which the oxygen works as a hydrogen bond acceptor, rather than HF·H2O, in which the fluorine works as the acceptor. In addition, the smaller value of the coupling constant JHF = 443 Hz also supports the structure H2O·HF, the value being close to those of HF in diethyl ether and dimethyl sulfoxide solutions, JHF = 464 and 410 Hz, respectively (28). Hence, we concluded that this is the simplest hydrated acid. Upon heating the solution in ortho-dichlorobenzene-d4 (ODCB-d4), no change in the spectral shape was observed even at 140°C, revealing that no proton transfer takes place between the H2O and HF on the NMR time scale.

The structure of (H2O·HF)@C70 was unambiguously determined by the single-crystal x-ray diffraction analysis for the crystals containing nickel(II) octaethylporphyrin and solvent molecules, with almost the same unit cell constants as those of empty C70 (29) and H2O@C70 (23). As shown in Fig. 3D, the O and F atoms of the H2O·HF were observed inside the C70 located on the porphyrin. It is the first example of the x-ray structure for doubly encapsulating C70. Here, in contrast to the x-ray structure of H2O@C70 with dynamic disorder on the position of the O, the O and F in this study did not show any dynamic or positional disorder, demonstrating the perfect alignment of the H2O·HF. Reflecting its dense encapsulation, the averaged longer axis of the C70 cage [7.931(1) Å] was elongated by 0.20% compared with that of H2O@C70 [7.915(1) Å]. The distance between the O and F was 2.438(2) Å (Fig. 3E). It should be mentioned that the position of H between O and F was experimentally determined and refined, showing a distance of 1.39(4) and 1.05(4) Å, respectively. Thus, H2O·HF was found to adopt such structure as the proton of HF forms a liner hydrogen bond to the oxygen of H2O, which is in good agreement with the 1H NMR results.

To obtain deeper insights, the structure of (H2O·HF)@C70 was optimized at the ONIOM (our own n-layered integrated molecular orbital and molecular mechanics)-(MP2/6-311++G(3pd,3df):M06-2X/6-31G(d)) level (Fig. 3F). The calculated structure was found to reproduce well the x-ray structure, showing a distance of 2.496 Å between O and F as well as 0.15% elongation of the cage. Then, an HF molecule and a molecular complex H2O·HF, in free forms in a gas phase, were calculated at the MP2/6-311++G(3pd,3df) level (Fig. 3, G and H). Comparison of the calculated structures of (H2O·HF)@C70 with free H2O·HF demonstrated that the O–F (2.496 Å) and O–H (1.542 Å) distances are shorter by 5.5 and 9.6%, respectively, whereas the H–F bond is longer by 2.1%. These data supported the hypothesis that a contact ion character described as H3O+·F slightly appears by compression of the H2O and HF inside the limited space. The positional exchange of the H2O and HF was not detected at room temperature because the 13C NMR of (H2O·HF)@C70 displayed nine signals due to its C5v symmetry (fig. S14), in contrast to the averaged D5h symmetry of H2O@C70 and HF@C70 with dynamic motion of the encapsulated species.

The molecular complex H2O·HF should have a polarity, which could affect the properties of the outer C70 cage. In the 13C NMR spectra, the chemical shifts of the cage carbons near the H2O are smaller than those near the HF, indicating the polarity of (H2O·HF)@C70, which was shown by the gauge-independent atomic orbital (GIAO) calculations (fig. S17). However, this polarity was not obvious on reduction potentials determined by cyclic voltammetry (CV) in ODCB, the first reduction potentials for (H2O·HF)@C70 and empty C70 being −1.04 and −1.06 V versus a ferrocene/ferrocenium couple (fig. S18). The ultraviolet-visible (UV-vis) absorption in toluene is almost superimposable with that of empty C70 (fig. S19). The infrared (IR) bands for the HO–H and F–H bonds were not observed, probably due to the shielding effects of the cage, which was the same for H2O@C60 (18), HF@C60 (19), and H2O@C70 (23). However, interesting suppression of the characteristic IR bands of C70 was observed for HF@C70 and (H2O·HF)@C70 (fig. S20).

In summary, the simplest hydrated HF was isolated in a confined subnano space by the use of molecular surgical methods. Compared with the doubly encapsulating C70s reported so far, a high efficiency of the encapsulation was achieved because of the synergetic effects of pushing from outside by the high-pressure conditions and pulling from inside with an attractive interaction of the encapsulated HF with the outer H2O, which was supported by the stepwise formation of HF@C70, followed by (H2O·HF)@C70 and then H2O@C70. The NMR studies revealed the rigid structure of the H2O·HF without hydrogen exchange. The single crystal x-ray analysis and theoretical calculations showed the closer contact of the oxygen with the hydrogen of HF compared with that of free H2O·HF.



The 1H, 13C, and 19F NMR measurements were performed with the JEOL JNM-ECA 500 and JNE-ECA 600 instruments. The NMR chemical shifts were reported in parts per million with reference to residual protons, carbons, and fluorine of CDCl3 (δ 7.26 ppm in 1H NMR, δ 77.0 ppm in 13C NMR), tetrahydrofuran (THF-d8) (δ 67.57 ppm in 13C NMR), and hexafluorobenzene (C6F6) (δ 164.90 ppm in 19F NMR). The APCI MS spectra were measured on a Bruker micrOTOF-Q II. High-pressure experiments were conducted by using the Hikari Koatsu high-pressure apparatus HR15-B3. The HPLC was performed with a Cosmosil Buckyprep column (4.6φ × 250 mm) for analytical purpose and the same columns (two directly connected columns; 20φ × 250 mm) for preparative purpose. CV was conducted in an ALS Electrochemical Analyzer Model 620C using a three-electrode cell with a glassy carbon working electrode, a platinum wire counter electrode, and a Ag/0.01 M AgNO3 reference electrode. UV-vis spectra were recorded with a Shimadzu UV-3150 spectrometer. The IR spectra were collected by using a Thermo Fisher Scientific Magna 550 FT-IR spectrometer equipped with a Harrick Scientific VRA reflection attachment (30). The detector was a liquid nitrogen–cooled mercury-cadmium-telluride detector with a modulation frequency of 60 kHz. The number of accumulation was 1000, and the wavenumber resolution was 4 cm−1. Fullerene C70 was purchased from SES Research Co. Triisopropyl phosphite was purchased from Tokyo Chemical Industry Co. Ltd. Hydrogen fluoride pyridine was purchased from Sigma-Aldrich. The open-cage C70 derivative α-13mem was prepared according to a previous report (24).

Computational methods

All calculations were conducted with Gaussian 09 packages (31). The structures were optimized at the M06-2X/6-31G(d), MP2/6-311++G(3df,3pd), and ONIOM-(MP2/6-311++G(3df,3pd):M06-2X/6-31G(d)) levels without any symmetry assumptions (32). For the ONIOM method, the MP2 method was applied for the endohedral species and the M06-2X method was used for the fullerene cage. All structures including the stationary states and the transition states were confirmed by the frequency calculations at the same level. The calculated 1H NMR and 13C NMR chemical shifts were obtained at the GIAO-B3LYP/6-311G(d,p) level using the optimized structures at the ONIOM or M06-2X methods with a reference of tetramethylsilane calculated at the GIAO-B3LYP/6-311G(d,p)//M06-2X/6-31G(d) level. The isotropic chemical shifts were calculated for protons (32.3196 ppm) and carbons (185.7282 ppm).


Supplementary material for this article is available at

Supplementary Text

fig. S1. 1H NMR [500 MHz; CDCl3/CS2 (1:1)] spectrum of a mixture of HF@α-13mem, (H2O·HF)@α-13mem, H2O@α-13mem, and empty α-13mem.

fig. S2. 13C NMR (151 MHz; THF-d8) spectrum of a mixture of HF@α-13mem, (H2O·HF)@α-13mem, H2O@α-13mem, and empty α-13mem.

fig. S3. 19F NMR [470 MHz; CDCl3/CS2 (1:1)] spectrum of a mixture of HF@α-13mem, (H2O·HF)@α-13mem, H2O@α-13mem, and empty α-13mem.

fig. S4. 1H NMR [500 MHz; CDCl3/CS2 (1:1)] spectrum of a mixture of HF@α-13mem, (H2O·HF)@α-13mem, H2O@α-13mem, and empty α-13mem obtained under the optimized conditions (Table 1, entry 5).

fig. S5. 1H NMR (500 MHz; CDCl3) spectrum of a mixture of HF@α-8mem, (H2O·HF)@α-8mem, H2O@α-8mem, and empty α-8mem.

fig. S6. 13C NMR (151 MHz; CDCl3) spectrum of a mixture of HF@α-8mem, (H2O·HF)@α-8mem, H2O@α-8mem, and empty α-8mem.

fig. S7. 19F NMR (470 MHz; CDCl3) spectrum of a mixture of HF@α-8mem, (H2O·HF)@α-8mem, H2O@α-8mem, and empty α-8mem.

fig. S8. 1H NMR [500 MHz; CDCl3/CS2 (1:1)] spectrum of a mixture of HF@C70 and H2O@C70 (1:1).

fig. S9. 19F NMR [470 MHz; CDCl3/CS2 (1:1)] spectrum of a mixture of HF@C70 and H2O@C70 (1:1).

fig. S10. Recycling HPLC profiles for separation of HF@C70 and H2O@C70.

fig. S11. 1H NMR [151 MHz; CDCl3/CS2(1:1)] spectrum of the purified HF@C70.

fig. S12. 13C NMR [151 MHz; CDCl3/CS2 (1:1)] spectrum of the purified HF@C70.

fig. S13. 1H NMR [500 MHz; CDCl3/CS2 (1:1)] spectrum of the purified (H2O·HF)@C70.

fig. S14. 13C NMR [151 MHz, CDCl3/CS2 (1:1)] spectrum of the purified (H2O·HF)@C70.

fig. S15. 19F NMR [470 MHz; CDCl3/CS2 (1:1)] spectrum of the purified (H2O·HF)@C70.

fig. S16. APCI MS spectra (negative ionization mode) of (HF)2@C70 and its theoretical isotopic patterns.

fig. S17. CV of (H2O·HF)@C70 and empty C70 in ODCB with 0.1 M n-Bu4NBF4 at a scan rate of 20 mV s−1.

fig. S18. UV-vis spectra of (H2O·HF)@C70 and empty C70 in toluene.

fig. S19. IR reflection-absorption spectra on a gold substrate of empty C70, HF@C70, and (H2O·HF)@C70.

fig. S20. The calculated 1H NMR for (H2O·HF)@α-13mem′ and (HF·H2O)@α-13mem′ obtained at the GIAO-B3LYP/6-311G(d,p)//M06-2X/6-31G(d).

fig. S21. The calculated 1H and 13C NMR for (H2O·HF)@C70, HF@C70, and H2O@C70, at the GIAO-B3LYP/6-311G(d,p)//ONIOM-(MP2/6-311++G(3df,3pd):M06-2X/6-31G(d)).

fig. S22. X-ray structure of (H2O·HF)@C70.

table S1. Optimized geometry for (H2O·HF)@α-13mem′ at the M06-2X/6-31G(d).

table S2. Calculated 1H and 13C chemical shifts for (H2O·HF)@α-13mem′ obtained at the GIAO-B3LYP/6-311G(d,p)//M06-2X/6-31G(d).

table S3. Optimized geometry for (HF·H2O)@α-13mem′ at the M06-2X/6-31G(d).

table S4. Calculated 1H and 13C chemical shifts for (HF·H2O)@α-13mem′ obtained at the GIAO-B3LYP/6-311G(d,p)//M06-2X/6-31G(d).

table S5. Optimized geometry for (H2O·HF)@α-16mem′ at the M06-2X/6-31G(d).

table S6. Optimized geometry for (HF·H2O)@α-16mem′ at the M06-2X/6-31G(d).

table S7. Transition state for the positional exchange of the inner HF and H2O inside α-16mem′ at the M06-2X/6-31G(d).

table S8. Optimized geometry for HF@C70 at the ONIOM-(MP2/6-311++G(3df,3pd):M06-2X/6-31G(d)).

table S9. Calculated 1H and 13C chemical shifts for HF@C70 obtained at the GIAO-B3LYP/6-311G(d,p)//ONIOM-(MP2/6-311++G(3df,3pd):M06-2X/6-31G(d)).

table S10. Optimized geometry for (H2O·HF)@C70 at the ONIOM-(MP2/6-311++G(3df,3pd):M06-2X/6-31G(d)).

table S11. Calculated 1H and 13C chemical shifts for (H2O·HF)@C70 obtained at the GIAO-B3LYP/6-311G(d,p)//ONIOM-(MP2/6-311++G(3df,3pd):M06-2X/6-31G(d)).

table S12. Optimized geometry for HF at the M06-2X/6-31G(d).

table S13. Optimized geometry for HF at the MP2/6-311++G(3pd,3df).

table S14. Optimized geometry for HF dimer at the MP2/6-311++G(3pd,3df).

table S15. Optimized geometry for H2O at the M06-2X/6-31G(d).

table S16. Optimized geometry for H2O at the MP2/6-311++G(3pd,3df).

table S17. Optimized geometry for H2O dimer at the MP2/6-311++G(3pd,3df).

table S18. Optimized geometry for H2O·HF at the M06-2X/6-31G(d).

table S19. Optimized geometry for H2O·HF at the MP2/6-311++G(3pd,3df).

table S20. Transition state for the proton exchange between HF and H2O at the M06-2X/6-31G(d).

table S21. Transition state for the proton exchange between HF and H2O at the MP2/6-311++G(3pd,3df).

table S22. Crystal data and structure refinement for (H2O·HF)@C70.

table S23. Atomic coordinates (×104) and equivalent isotropic displacement parameters (Å2 × 103).

table S24. Bond lengths (Å) and angles (º).

table S25. Anisotropic displacement parameters (Å2 × 103).

table S26. Hydrogen coordinates (× 104) and isotropic displacement parameters (Å2 × 103).

table S27. Torsion angles (º).

References (33, 34)

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Funding: Financial support was provided by the Japan Society for the Promotion of Science KAKENHI Grant Numbers JP23241032, JP15K13641, JP15H0093, JP15H00939, and JP15J09612. The NMR measurements were supported by the Joint Usage/Research Center at the Institute for Chemical Research, Kyoto University. Author contributions: Y.M. conceived and designed the projects. R.Z. performed most of the experimental works and theoretical calculations and wrote the paper, supported by M.M. and A.W. The IR measurements were performed by T.S. and T.H. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data available related to this paper may be requested from the authors. Metrical parameters for the structure of (H2O·HF) @C70 is available free of charge from the Cambridge Crystallographic Data Center under reference number CCDC-1513130.

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