The electrochemical conversion of CO₂ into value-added products represents a promising route toward a circular carbon economy; however, its efficiency and selectivity are highly dependent on the choice of catalyst. In this work, we computationally investigate the electrochemical reduction of CO₂ to formic acid (HCOOH) using a series of N-heterocyclic compounds as molecular catalysts. Density Functional Theory (DFT) calculations were performed to determine the reaction barrier heights for this conversion. Among the tested catalysts, imidazole exhibited the lowest barrier (14.3 kcal/mol), outperforming pyridine (17 kcal/mol), a well-established benchmark catalyst. To further optimize catalytic performance, we employed a Genetic Algorithm (GA) framework in which each generation of candidate molecules was evaluated based on computed barrier heights. The most promising catalysts were iteratively selected for refinement. Through this approach, we identified five N-heterocyclic derivatives with barrier heights below 15 kcal/mol, demonstrating significantly improved activity compared to literature-reported systems. These findings underscore the potential of GA-driven computational strategies to accelerate the discovery of efficient molecular catalysts for sustainable CO₂ utilization.