Revealing the intrinsic relation between heteroatom dopants and graphene quantum dots as a bi-functional ORR/OER catalyst

•The unbiased comparison between nitrogen, boron, sulfur, and phosphorous for graphene quantum dot reveal the intrinsic nature of dopants in ORR/OER reactions.•intrinsic bond strength index (IBSI) is proposed to regulate the adsorption energy of key intermediates.•Nitrogen is identified as the most effective dopant for ORR/OER.•A reactivity map is provided to screen potential effective bifunctional catalysts.