Abstract: A thorough theoretical exploration of microscopic mechanism for effect of sodium (Na) on nitric oxide (NO) heterogeneous reduction by char was performed based on density functional theory with consideration of London dispersion interaction. Calculation results show that the Na atom could migrate at edge of char and prefers to be incorporated into a five-atom ring forming a pentagon with 174.2 kJ/mol released. A strong electrostatic attraction between the Na atom and carbon atoms at the edge is found by reduced density gradient analysis. Electrons transfer from the Na atom to char, resulting in electron rearrangement on char. It is the most stable mode for adsorption of the first NO molecule when O atom in NO molecule is adjacent to the Na atom. The doping of Na could promote adsorption of the first NO molecule, but has little effect on that of the second NO molecule. The intrinsic reaction coordinate calculations and Mayer bond order analyses suggest that the Na atom affects heterogeneous reduction through "oxidized-reduced" cycle via "combination-separation" with the O atom. Desorption of N₂ molecule is the rate-determining step in the whole reaction channel. The canonical variational theory was used for kinetic analyses, considering the tunneling effect along the reaction coordinate with Wigner method. It is found that the reaction is accelerated by doping Na atom. Although the addition of Na would not significantly reduce activation energy of the rate-determining step, but would increase activation sites at the edge of char.