Prediction of confinement entropy of gas binding in the solid-state is made challenging by quantum mechanics of electronic motion, and the statistical mechanics of molecular vibrations, each requiring the scaling of an exponential wall in computational complexity. Light nuclei like hydrogen are particularly susceptible to such over-simplifications in the treatment of molecular motion. We present here a quantum coupled vibrational Hamiltonian sampled with a range-separated hybrid meta GGA functional particularly adroit at capturing short-range metal-ligand interactions which also describes frustrated translations and torsions of molecular hydrogen bound to an open metal (Vanadium (II)) site in a metal-organic framework. Our formulation is a form-agnostic discrete variable representation (DVR) which may be used to sample arbitrary molecular PESs and may be constructed from uncoupled mode Hamiltonians. Our findings posit a solution in bridging the gap between accurate electronic structure and statistical mechanics in the prediction of the confinement entropy of industrially relevant gases within nanoporous frameworks.

Confinement entropy from quantum coupling of frustrated translations and rotations: Molecular hydrogen bound to a vanadium (II) site in a MOF

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