We used second-order Møller-Plesset perturbation theory to calculate the binding energies of hydrogen molecules to various carbon nanostructures, in an effort to find improved hydrogen storage materials. For the central concave site of corannulene, a new binding geometry was found, with the H2 molecule in a parallel configuration, and an improved corrected binding energy of 9.8 kJ/mol was discovered. We studied the binding of hydrogen to B and Be doped small carbon nanostructures. For B doped corannulene, Kubas binding was observed in a metastable state. For C11 H8Be, a binding energy of 17.5 kJ/mol and, for C16Be2 H8, a binding energy of 12.3 kJ/mol due to Kubas-type non-dissociative adsorption were found. Benzene-B,N-2COOH and pyrazine dicarboxylate were proposed as higher binding energy building blocks for the metal - organic framework materials. For both benzene-B,N-2COOH and pyrazine dicarboxylate, we found low physisorption binding energies.