Gold catalysis enables selective chemical transformations with catalytic activity tunable through ligand selection. This study uses the density functional theory (DFT) to explore the impact of phosphine ligands (PR3) on gold(I)-catalyzed alkyne-alkene cyclobutene formation. We analyze the following key steps: (i) PR3-Au+ complexation, (ii) alkyne binding, (iii) alkene binding, (iv) C-C coupling transition state, (v) cyclobutene formation transition state, and (vi) cyclobutene dissociation. Molecular electrostatic potential (MESP) analysis provided a deeper understanding of electronic effects and revealed a strong correlation between the change in MESP at the gold nucleus (ΔNVAu+) upon complex formation with various ligands and the corresponding complexation energy, as well as between the change in MESP at the alkyne carbon (ΔVC) and the C-C coupling step activation barrier. This establishes MESP as a powerful tool for understanding ligand influence on catalysis. Our findings suggest that electron-donating phosphine ligands, combined with electron-withdrawing alkyne substituents, enhance catalyst turnover, promote cyclobutene product dissociation from the gold(I) complex, and facilitate catalyst regeneration. Solvent effects also play a crucial role. Bulky XPhos, JohnPhos, and CyJohnPhos ligands enhance gold(I) catalysis via steric protection, electron donation, and catalyst regeneration efficiency. In conclusion, this study provides insights into ligand effects in gold(I)-catalyzed cyclobutene formation, guiding future catalyst design.