A computational method for Cr 2 O 3 and Cr 3 C 2 has been established based on a systematic investigation of functionals, basis sets and corrections for dispersion, self-interaction and relativistic effects. The suggested method comprises of the PBE functional with Grimme's dispersion correction, the TZ2P basis set with a frozen core of up to 2p for chromium and 1s for oxygen and carbon, and with the zeroth-order regular approximation for relativistic effects, and is in good agreement with experimental results for both bulk crystals and surface structures. Self-interactions have been corrected for by the DFT + U approach, but it still gives band gaps significantly different from the experimental band gap. We have also calculated the adsorption energy of methane on a chromium terminated (0001) Cr 2 O 3 surface, and the significance of dispersion and self-interaction corrections for the adsorption of methane on Cr 2 O 3 was found to be substantial.