Proton dynamics in a single H₂O confined in a Buckyball

Using a density functional theory approach with the B3LYP and PBE0 functionals and the 6-G31(d,p) basic set, we simulate the partial vibrational spectra of isolated H₂O and C₆₀ molecules, of a periodic H₂O structure (ice XI) and of a single H₂O molecule encaged in a buckyball (H₂O@C₆₀). A very significant result of the H₂O@C₆₀ calculation is that the C-atoms of the hosting fullerene lattice (which for pure C₆₀ are subjected to a vibrational frequency spectrum that terminates at ∼ 1600 cm⁻¹) were found to participate in the high frequency modes at ∼ 3800 cm⁻¹ of the H₂O guest, indicating a coupling between the modes of the two sub systems. The effect of temperature between 5 and 300 K on the atomic kinetic energies, Ke(X) (X = C,O,H) were also deduced. The calculated Ke(C) in C₆₀ using B3LYP was found to be in better agreement with experiment than that of PBE0. Surprisingly, the zero point Ke(H) in the hydrogen bonds (HBs) free H₂O@C₆₀, as well as its T-dependence, were found to be nearly the same as those of the HBs containing condensed bulks of H₂O, namely ice and liquid water. This result is at variance with that of other H₂O confining systems measured using deep inelastic neutron scattering, where anomalous Ke(H) values were generically observed. An attempt to understand this behavior is made in view of the observed coupling between the caged H₂O modes and those of the C₆₀ host.