  Metal-organic frameworks show both fundamental interest and great promise for
applications in adsorption-based technologies, such as the separation and
storage of gases. The flexibility and complexity of the molecular scaffold
poses a considerable challenge to atomistic modeling, especially when also
considering the presence of guest molecules. We investigate the role played by
quantum and anharmonic fluctuations in the archetypical case of MOF-5,
comparing the material at various levels of methane loading. Accurate path
integral simulations of such effects are made affordable by the introduction of
an accelerated simulation scheme and the use of an optimized force field based
on first-principles reference calculations. We find that the level of
statistical treatment that is required for predictive modeling depends
significantly on the property of interest. The thermal properties of the
lattice are generally well described by a quantum harmonic treatment, with the
adsorbate behaving in a classical but strongly anharmonic manner. The heat
capacity of the loaded framework - which plays an important role in the
characterization of the framework and in determining its stability to thermal
fluctuations during adsorption/desorption cycles - requires, however, a full
quantum and anharmonic treatment, either by path integral methods or by a
simple but approximate scheme. We also present molecular-level insight into the
nanoscopic interactions contributing to the material's properties and suggest
design principles to optimize them
