Mechanisms of Ligand Exchange Reactions, A Quantum Chemical Study of the Reaction UO₂²⁺(Aq) + HF(Aq) → UO₂F⁺(Aq) + H⁺(Aq)

The thermodynamics and the reaction mechanism for the reaction UO₂²⁺(aq) + HF(aq) → UO₂F⁺(aq) + H⁺(aq) in water solution has been studied using quantum chemical methods. The solvent was modeled using the polarized medium method (CPCM) with additional water molecules in the second coordination sphere of the complexes studied. The overall reaction was divided into three steps that were analyzed separately. The quantum chemical study was made on the reaction step [UO₂(H₂O)₅²⁺],HF(H₂O)_n → [UO₂F (H₂O)₄⁺],H₃O⁺ (H₂O)_n, with n = 1 and 2, where the species in the second coordination sphere are located outside the square brackets. The formation of the precursor complex and dissociation of the successor complex were described by the Fuoss equation. The geometry of the different precursor and successor complexes was in good agreement with known bond distances, and strong F- - -H- - -O, and/or O- - -H- - -O hydrogen bonds are an important structure element in all of them. The Gibbs energy, enthalpy, and entropy of reaction was calculated using the electronic energy at the MP2 level in the solvent, with thermal functions calculated at the SCF/B3LYP levels using the gas-phase geometry. The calculated Gibbs energy of reaction for n = 2 at 298.15 K was −35 kJ/mol at the HF and −25 kJ/mol at the B3LYP level after correction for a known systematic error in the HF bond energy; this compares favorably with the experimental value, −11 kJ/mol. The ligand exchange mechanism was explored by identification of a transition state where HF from the second sphere enters the first coordination sphere in an associative reaction. It was not possible to identify the same transition state from the successor side, indicating that the reaction mechanism consists of at least two steps. We suggest that the rate determining step is the entry of HF from the second to the first coordination sphere, with practically no bond-breaking as indicated by the small change in the H−F distance between precursor and transition state. This suggestion is supported by the experimentally observed reverse H/D isotope effect. The quantum chemical activation energy ΔU^≠ was 34 kJ/mol, close to the experimental activation enthalpy ΔH^≠ = 38 kJ/mol.