Methane is a highly stable molecule, with strong CH bonds, and hence difficult to activate. Thus, finding efficient pathways for the direct oxidation of methane is immensely important. This study explores Group 13 (triel, E) element hydroxide and amide complexes as well as larger “round” and “oblate” E4O6 cluster models for methane activation. Modeling several compounds using density functional theory, it was discovered that heavier Group 13 tris-hydroxide and tris-amide catalysts are more thermodynamically and kinetically favorable for methane activation. Interestingly, for Group 13 E4O6 cluster models there were no clear periodic trends, and these models produced significantly lower reaction free energies and activation barriers than the tris-hydroxide/amide models. Furthermore, the cluster model calculations revealed that the shape/structure of the surface greatly impacted reaction free energies and activation barriers. These findings thus shed light on potential energetically favorable catalysts for methane functionalization for the utilization of natural gas resources.