The discovery of high-performance organic photocatalysts for hydrogen evolution remains limited by the vastness of chemical space and the reliance on human intuition for molecular design. Here we present ChemNavigator, an agentic AI system that autonomously derives structure-property relationships through hypothesis-driven exploration of organic photocatalyst candidates. The system integrates large language model reasoning with density functional tight binding calculations in a multi-agent architecture that mirrors the scientific method: formulating hypotheses, designing experiments, executing calculations, and validating findings through rigorous statistical analysis. Through iterative discovery cycles encompassing 200 molecules, ChemNavigator autonomously identified six statistically significant design rules governing frontier orbital energies, including the effects of ether linkages, carbonyl groups, extended conjugation, cyano groups, halogen substituents, and amine groups. Importantly, these rules correspond to established principles of organic electronic structure (resonance donation, inductive withdrawal, $π$-delocalization), demonstrating that the system can independently derive chemical knowledge without explicit programming. Notably, autonomous agentic reasoning extracted these six validated rules from a molecular library where previous ML approaches identified only carbonyl effects. Furthermore, the quantified effect sizes provide a prioritized ranking for synthetic chemists, while feature interaction analysis revealed diminishing returns when combining strategies, challenging additive assumptions in molecular design. This work demonstrates that agentic AI systems can autonomously derive interpretable, chemically grounded design principles, establishing a framework for AI-assisted materials discovery that complements rather than replaces chemical intuition.