Simulations of the hydrogen storage capacities of activated carbons require an accurate treatment of the interaction of a hydrogen molecule physisorbed on the graphitic-like surfaces of nanoporous carbons, which is dominated by the dispersion interactions. These interactions are described accurately by high level quantum chemistry methods such as the Coupled cluster method with single and double excitations and a non-iterative correction for triple excitations (CCSD(T)), but those methods are computationally very expensive for large systems and massive simulations. Density functional theory (DFT) based methods that include dispersion interactions are less accurate, but computationally less expensive. Calculations of the volumetric hydrogen storage capacities of nanoporous carbons, simulated as benzene and graphene slit-shaped pores, have been carried out, using a quantum-thermodynamic model of the physisorption of H-2 on surfaces and the interaction potential energy curves of H-2 physisorbed on benzene and graphene obtained using the CCSD(T) and second order Moller-Plesset (MP2) methods and the 14 most popular DFT-based methods that include the dispersion interactions at different levels of complexity. The effect of the dispersion interactions on the DFT-based volumetric capacities as a function of the pressure, temperature and pore width is evaluated. The error of the volumetric capacities obtained with the quantum -thermodynamic model and each method is also calculated and analyzed. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.