Enhancing catalyst activity of two-dimensional C$_4$N$_2$ through doping for the hydrogen evolution reaction

This study investigates the structural, electronic, and catalytic properties of pristine and doped C$_4$N$_2$ nanosheets as potential electrocatalysts for the hydrogen evolution reaction. The pristine C$_{36}$N$_{18}$ nanosheets exhibit limited HER activity, primarily due to high positive Gibbs free energies ($>$ 2.2 eV). To enhance catalytic performance, doping with B, Si, or P at the nitrogen site was explored. Among these systems, B-doped C$_{36}$N$_{17}$ nanosheets exhibit the most promising catalytic activity, with a Gibbs free energy close to zero ($\approx -0.2$ eV), indicating efficient hydrogen adsorption. Band structure, projected density of states, charge density, and Bader charge analyses reveal significant changes in the electronic environment due to doping. While stacking configurations (AA$'$A$''$ and ABC) have minimal effect on catalytic performance, doping -- particularly with B -- substantially alters the electronic structure, optimizing hydrogen adsorption and facilitating efficient HER. These findings suggest that B-doped C$_{36}$N$_{17}$ nanosheets could serve as efficient cocatalysts when combined with metallic materials, offering a promising approach to enhance catalytic efficiency in electrocatalytic and photocatalytic applications.