A systematic quantum chemical analysis was conducted on dimethyl-4-(4-hydroxy-2-oxo-2H-chromen-3-yl)-5-phenyl-1-(p-tolyl)-1H-pyrrole-2,3-dicarboxylate. Molecular geometry was optimized using DFT simulations at the B3LYP/6-31G level and HF techniques. Theoretical structural parameters were confirmed with experimental data using RMSD analysis. Electronic characteristics were investigated using MEP mapping and NBO analysis, which revealed important donor-acceptor interactions. As were Fukui functions and dual descriptors, Mulliken analysis was used in reactivity investigations. The compound demonstrated promising reactivity with the HOMO-LUMO energy gap via TD-DFT methods, indicating good electronic conductivity. Molecular docking simulations with target protein receptors showed strong binding affinity (docking score = -8.7 kcal/mol), suggesting potential therapeutic applications. Advanced electronic density analysis using RDG calculations, ELF, and LOL research confirmed the stability of key intramolecular interactions. Gaussian software was used to calculate thermodynamic properties (ΔG°, ΔH°, ΔS°, heat capacity, and activation energy) and indicated favourable reaction spontaneity. This extensive theoretical analysis sheds light on the compound's structural, electrical, and biological properties, adding to our understanding of the coumarin derivative.