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Single- and bi-atom catalysts (SACs and BACs) exhibit great potential in catalyzing electrochemical nitrogen reduction reaction (NRR) due to their unusual coordination-environment effect of active centers, which unfortunately remains elusive so far. Herein, by applying a descriptor ψ based on the valence-electron number and electronegativity of the catalytic centers, we have systematically studied NRR on SACs and BACs with diverse coordination environments. Our results quantify the elemental type and number of metal atoms and their neighbors at the active centers on the adsorption properties and reactivity of atomic catalysts. This uncovers the pronounced differences and similarities between SACs, homonuclear BACs, and heteronuclear BACs as well as the unique role of N dopant. With these findings, we have also predicted that Ir-N4-SAC and TiMn-N6-BAC as promising candidates for further experimental studies. Therefore, our findings can serve as useful guidelines for developing high-performance catalysts for NRR. [ABSTRACT FROM AUTHOR]