Using different density function methods, we examined the transformation processes from the physisorption state (state P) to the chemisorption state (state C) of a H-2 molecule in a pristine fullerene C-20 and a B-doped fullerene C19B system, models of hydrogen-storage solid materials. We explored the precise potential energy surfaces (PES) for the transformation process by fully optimizing all the stationary points including the stable points and the transition states without any restriction. Our results demonstrate that both the two transformation processes could undergo transition states. We anticipate that the results obtained in the present Letter are helpful to understand the adsorption mechanism of the H-2 molecule in solid materials. (C) 2011 Elsevier B.V. All rights reserved.