Density functional theory insights into the solvent effect on the binding energies of Cd²⁺ in functionalized MOFs

The clean-up of cadmium-contaminated waters is a significant environmental issue, and metal-organic frameworks (MOFs) have been shown to be effective adsorbents with great potential. Yet, the basic principles driving Cd²⁺ binding in multiple solvent environments remain enigmatic and hinder rational adsorbent design. In this work, the solvent effects on the binding energies of Cd²⁺, referring to (M = -NH₂, -OH, -COOH, and -NO₂), are systematically investigated using DFT in four solvents (water, ethanol, methanol, and acetonitrile). Using the SMD implicit solvation model and the M06-2X functional with def2-TZVP basis set, we demonstrate that solvent polarity significantly affects binding thermodynamics, with aqueous systems demonstrating 68-72% weaker binding than acetonitrile. With binding energies of -156.8 kcal mol^-1 (water), -187.3 kcal mol^-1 (ethanol), -181.4 kcal mol^-1 (methanol), and -198.5 kcal mol^-1 (acetonitrile), the carboxyl-functionalized MOF exhibits exceptional performance in all solvents. Protic solvents (1.18-1.24|e|) exhibit greater charge transfer than aprotic acetonitrile (0.94-1.08|e|), according to natural bond orbital analysis. This is explained by hydrogen bonding networks stabilizing charge-separated coordination states. Predictive relationships for mixed-solvent industrial wastewater applications are established by the significant linear correlation between binding energies and inverse solvent polarity (R ² = 0.96-0.98). These results directly address the pressing need for efficient cadmium remediation technologies in a variety of aqueous-organic media by offering crucial theoretical guidance for the design of solvent-adaptive MOF adsorbents optimized for particular industrial effluent compositions.