We investigate the Kubas-type attraction of dihydrogen onto Ca adatoms and validity of approximated density functionals for such problems. Dihydrogens can be bound to Ca adatom sites only when the Ca adsorption configurations stabilize the 3d orbitals. When the valency of the Ca site is dominated by the 4s orbital, the binding strength of dihydrogens is negligible. For such cases, exchange functional adopted in the popular density-functionals can possibly lead to an over-stabilization of the dihydrogen binding states. We show that marginally activated graphene surfaces can induce such stabilization of the 3d-orbital states of the adsorbed Ca. (C) 2011 Elsevier B.V. All rights reserved.