Hydrogen molecules inside fullerene C70: quantum dynamics, energetics, maximum occupancy, and comparison with C60.

Recent synthesis of the endohedral complexes of C(70) and its open-cage derivative with one and two H(2) molecules has opened the path for experimental and theoretical investigations of the unique dynamic, spectroscopic, and other properties of systems with multiple hydrogen molecules confined inside a nanoscale cavity. Here we report a rigorous theoretical study of the dynamics of the coupled translational and rotational motions of H(2) molecules in C(70) and C(60), which are highly quantum mechanical. Diffusion Monte Carlo (DMC) calculations were performed for up to three para-H(2) (p-H(2)) molecules encapsulated in C(70) and for one and two p-H(2) molecules inside C(60). These calculations provide a quantitative description of the ground-state properties, energetics, and the translation-rotation (T-R) zero-point energies (ZPEs) of the nanoconfined p-H(2) molecules and of the spatial distribution of two p-H(2) molecules in the cavity of C(70). The energy of the global minimum on the intermolecular potential energy surface (PES) is negative for one and two H(2) molecules in C(70) but has a high positive value when the third H(2) is added, implying that at most two H(2) molecules can be stabilized inside C(70). By the same criterion, in the case of C(60), only the endohedral complex with one H(2) molecule is energetically stable. Our results are consistent with the fact that recently both (H(2))(n)@C(70) (n = 1, 2) and H(2)@C(60) were prepared, but not (H(2))(3)@C(70) or (H(2))(2)@C(60). The ZPE of the coupled T-R motions, from the DMC calculations, grows rapidly with the number of caged p-H(2) molecules and is a significant fraction of the well depth of the intermolecular PES, 11% in the case of p-H(2)@C(70) and 52% for (p-H(2))(2)@C(70). Consequently, the T-R ZPE represents a major component of the energetics of the encapsulated H(2) molecules. The inclusion of the ZPE nearly doubles the energy by which (p-H(2))(3)@C(70) is destabilized and increases by 66% the energetic destabilization of (p-H(2))(2)@C(60). For these reasons, the T-R ZPE has to be calculated accurately and taken into account for reliable theoretical predictions regarding the stability of the endohedral fullerene complexes with hydrogen molecules and their maximum H(2) content.