Group-4 metals (M4+ = Zr, Ti, Hf) anchored on silica and silica-alumina are reported to be active catalysts for ethylene coupling and hydrogenolysis of paraffins to fuel range hydrocarbons. Density functional theory (DFT) calculations are employed to rationalize their observed activity. We construct atomistic models of metal sites grafted on (111) and (001) surfaces of beta-cristobalite, a silica polymorph. While group-4 ions are isovalently substituted into silica, substitution of Al3+ produces more diversity into the reactive site with the introduction of proximal Brønsted and Lewis acidic sites. We contrast ethylene oligomerization and hydrogenolysis pathways for Group-4 ions on silica and Al-doped silica to probe the synergistic effect of different acid sites on reaction pathways, including Cossee-Arlman chain growth and beta-termination mechanisms. Microkinetic models parameterized on DFT-based rate constants are applied to infer reactivity under experimental conditions and compare predictions with observations. Degree of rate control analysis shows that the steps controlling the rates vary across these sites. The approach is extended to examine the role of charge and of partially filled d-orbitals on reaction pathways for similarly constructed Ga3+, Zn2+, Ni2+, Co2+ sites on silica. A comprehensive set of reaction pathways, including Cossee-Arlman, metallacycle, and proton transfer mechanisms proposed in the literature is evaluated to analyze structure activity-relationships. Results obtained aid in understanding trends across metal ions and factors governing their activity towards hydrocarbon conversion reactions relevant to today's economy based on oil and increasing production of shale gas.