Hydrogen Molecules inside Fullerene C70: Quantum Dynamics, Energetics, Maximum Occupancy, And Comparison with C60

摘要

Recent synthesis of the endohedral complexes of C₇₀ and its open-cage derivative with one and two H₂ 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 H₂ molecules in C₇₀ and C₆₀, which are highly quantum mechanical. Diffusion Monte Carlo (DMC) calculations were performed for up to three para-H₂ (p-H₂) molecules encapsulated in C₇₀ and for one and two p-H₂ molecules inside C₆₀. 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-H₂ molecules and of the spatial distribution of two p-H₂ molecules in the cavity of C₇₀. The energy of the global minimum on the intermolecular potential energy surface (PES) is negative for one and two H₂ molecules in C₇₀ but has a high positive value when the third H₂ is added, implying that at most two H₂ molecules can be stabilized inside C₇₀. By the same criterion, in the case of C₆₀, only the endohedral complex with one H₂ molecule is energetically stable. Our results are consistent with the fact that recently both (H₂)_n@C₇₀ (n = 1, 2) and H₂@C₆₀ were prepared, but not (H₂)₃@C₇₀ or (H₂)₂@C₆₀. The ZPE of the coupled T−R motions, from the DMC calculations, grows rapidly with the number of caged p-H₂ molecules and is a significant fraction of the well depth of the intermolecular PES, 11% in the case of p-H₂@C₇₀ and 52% for (p-H₂)₂@C₇₀. Consequently, the T−R ZPE represents a major component of the energetics of the encapsulated H₂ molecules. The inclusion of the ZPE nearly doubles the energy by which (p-H₂)₃@C₇₀ is destabilized and increases by 66% the energetic destabilization of (p-H₂)₂@C₆₀. 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 H₂ content.