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Methane pyrolysis provides a scalable alternative to conventional hydrogen production methods, avoiding greenhouse gas emissions. However, high operating temperatures limit economic feasibility on an industrial scale. A major scientific goal is, therefore, to find a catalyst material that lowers operating temperatures, making methane pyrolysis economically viable. In this work, we derive a model that provides a qualitative comparison of possible catalyst materials. The model is based on calculations of adsorption energies using density functional theory. Thirty different elements were considered. Adsorption energies of intermediate molecules in the methane pyrolysis reaction correlate linearly with the adsorption energy of carbon. Moreover, the adsorption energy increases in magnitude with decreasing group number in the $d$-block of the periodic table. For a temperature range between 600 and 1200 K and a normalized partial pressure range for $\mathrm{H_2}$ between $10^{-1}$ and $10^{-5}$, a total of eighteen different materials were found to be optimal catalysts at least once. This indicates that catalyst selection and reactor operating conditions should be well-matched. The present work establishes the foundation for future large-scale studies of surfaces, alloy compositions, and material classes using machine learning algorithms.