Single-site heterogeneous catalysts (SSHC) have received increasing attention due to their well-defined active sites and potentially high specific activity. Detailed computational studies were carried out on a set of potential SSHC's, i.e., silica supported metal ions, to investigate the reactivity of these catalysts with H-2 as well as to evaluate the performance of density functional theory (DFT) methods in conjunction with triple-zeta quality basis sets (i.e., cc-pVTZ) on reaction energetics. The ions considered include 4d and 5d metals as well as several post-transition metal ions. A representative cluster model of silica is used to calculate reaction free energies of the metal hydride formation that results from the heterolytic cleavage of H-2 on the M-O bond. The hydride formation free energy is previously shown to be strongly correlated with the catalytic activity of such catalysts for alkene hydrogenation. ONIOM calculations (CCSD(T)//MP2) are used to assess the accuracy and reliability of the MP2 results and it is found that MP2 is a suitable level of theory for gauging the performance of DFT functionals. The performance of various DFT functionals is assessed relative to MP2 results and it is found that the wB97xd and PBEO functionals have the lowest standard deviation (STD) value while the MN12SX and PBE functionals have the lowest mean absolute deviation (MAD) values. The B3LYP functional is shown to have similar MAD and STD values as the top performing functionals. Potential active SSHC's for exergonic hydrogen activation predicted in this study include mostly late and post transition metal ions, i.e., Au3+, pd(2+), pt(4+), pd(4+), Ir4+, Hg2+, Rh3+, pb(4+), Tl3+, In+3, Ir3+, Os4+, Cd2+, Ru2+, and Ga3+. This study provides important guidance to future computational studies of such catalyst systems.