A first-principle modelling of hydrogen molecular rotation in the outside of carbon nanotubes is presented. Density functional theory (DFT)-based symmetry-adapted perturbation theory (SAPT) is first applied to analyse the influence of the rotation on the dispersion and dispersionless H2-nanotube interaction for both sub- and nanometer-sized tubes. An adsorbate three-dimensional wave-function treatment is then applied to calculate the molecular energy levels of the rotating hydrogen molecule. As a key difference with the H2 located inside the tubes, the SAPT-based analysis indicates a marked influence of a nanotube curvature-induced dipole on the angular-dependent balance of exchange-repulsion, electrostatic, and dispersion contributions for narrow nanotubes. As a result, the landscape of molecular energy levels depends strongly on the diameter of the porous material. In addition, an effective one-dimensional model is proposed to account for the nuclear motion, reproducing full-dimensional approach within less than 1%.