The theoretical insights on the mechanism for Fe-N4 improving the HCOOH dissociation on Pd13/Gra

•The Pd13/Fe-N-Gra exhibits high activity for the decomposition of formic acid.•The Pd13/Fe-N-Gra catalyst shows higher activity for CO2 production than Pd13/Gra.•The deformation of Pd13 will improve the selectivity for CO production.•The Fe-N-C site can keep the electron of Pd13 to prevent its deformation.