We present periodic DFT calculations for studying the effect of a rutile-TiO2(110) support on the interaction of H with a metal atom M, M=K to Zn. For some metals, the surface support gives a decrease of the M-H interaction strength as usually associated with SMSI. On the contrary for others, we show that the M-H interaction is enhanced by the presence of the support. Both M-H and M- support interactions are strong when each of them is associated with a strongly exothermic transfer of at least one electron, requesting the transfer of at least two electrons. (C) 2013 Elsevier B.V. All rights reserved.