  The interaction strength of molecular hydrogen and water to carbon
nanomaterials is relevant to, among many applications, hydrogen storage, water
treatment, and water flow. However, accurate interaction energies for hydrogen
and water with carbon nanotubes(CNTs) remain scarce despite the importance of
having reliable benchmark data to inform experiments and to validate
computational models. Here, benchmark fixed-node diffusion Monte Carlo (DMC)
interaction energies are provided for hydrogen and water monomers, inside and
outside a typical zigzag CNT. The DMC interaction energies provide valuable
insight into molecular interactions with CNTs in general, and are also expected
to be particularly relevant to gas uptake studies on CNTs. In addition, a
selection of density functional theory (DFT) exchangecorrelation(xc)
functionals and force field potentials that ought to be suitable for these
systems, is compared. An unexpected variation is found in the performance of
DFT van der Waals (vdW) models in particular. An analysis of the peculiar
discrepancy between different vdW models indicates that medium-range
correlation (at circa 3 to 5 \r{A}) plays a key role inside CNTs, and is poorly
predicted by some vdW models. Using accurate reference information, this work
reveals which xc functionals and force fields perform well for molecules
interacting with CNTs. The findings will be valuable to future work on these
and related systems, that involve molecules interacting with low-dimensional
systems.
