Analysis of solvent effects on the Cu-catalyzed azide-alkyne cycloaddition reaction via three-dimensional reference interaction site model self-consistent field method and solvation free energy decomposition

The reaction rate of the Cu-catalyzed azide-alkyne cycloaddition (CuAAC) exhibits a unique solvent dependence that cannot be rationalized by solvent polarity alone; the reaction proceeds faster in glycerol, followed by water, and then CH₂Cl₂. In the present study, this characteristic solvent dependence is elucidated in detail using the three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) method, which combines quantum chemical calculation of the solute and statistical mechanical description of the solvent molecules. It is found that the calculated free energy profiles in the three solvents are consistent with the experimental results. A decomposition analysis of the relative solvation free energy in the rate-determining step reveals that the energetic contribution arising from solute-solvent electrostatic interactions is substantial in water, whereas the entropic contribution caused by associative reaction plays a dominant role in glycerol. The latter attenuates the destabilization of solute electronic energy, resulting in the greatest stabilization of the transition state in glycerol.