[en] The catalytic effect of calcium on nitric oxide (NO) heterogeneous adsorption with carbon was investigated through a first-principles calculation on pristine and calcium decorated graphene models, respectively. Compared with the classical polycyclic carbon model, new graphene computational models with periodical boundary conditions are better in simulating the characteristics of solid phase carbon. The adsorption of a single NO molecule on the pristine graphene surface is physical, but it is dramatically enhanced by the calcium as the absolute value of binding energy E_b increases from 19.34 kJ/mol to 206.02 kJ/mol. In order to investigate the influence of the concentration of NO molecules, the adsorption of clusters containing two and three molecules were examined. On pristine graphene surface, E_b increases with the number of NO molecules, however, on calcium decorated one, E_b demonstrates reverse tendency. This significant difference derives from the distinct mechanisms: van der Waals interaction among the NO molecules plays a crucial role in the adsorption of NO on the pure graphene surface, while the electron transfer from the 4s- and 3d orbitals of calcium to the 2p orbitals of nitrogen and oxygen atoms contributes to the catalytic effect of calcium. - Highlights: • Periodical graphene model is proposed for the NO adsorption with carbon. • The catalytic effect of Ca is studied by Ca-decorated graphene model. • The binding energy of NO cluster on carbon increases due to the van der Waals force. • Charges in 4s and 3d orbitals of Ca transfer to NO and increase the binding energy.