  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.
