Cluster-Continuum Calculations of Coordination Structures and Formation Constants for Aqueous Cadmium Halide Complexes

This study investigates the coordination structures and formation constants of cadmium halide complexes (CdX_<i>n</i>(H₂O)_{(CN-<i>n</i>)}^{(2-<i>n</i>)+}, X = F, Cl, Br, and I; <i>n</i> = 1, 2, 3, and 4; and CN = 3, 4, 5, and 6) using a quantum-chemical cluster-continuum model. By comparing the relative energies of 24 different coordination structures for each category of CdX_<i>n</i>(H₂O)_{(CN-<i>n</i>)}^{(2-<i>n</i>)+} (X = F, Cl, Br, and I), it is found that all four types of complexes prefer low-coordination structures, primarily existing in tri- or tetra-coordination. In calculating the solvation energy of halide ions using different thermodynamic cycle methods, it is found that the cluster cycle yields results closer to experimental values than the monomer cycle. Halide ions with high electronegativity and small radii require more water molecules to form stable solvation structures. In complex formation constant (log <i>K</i>) calculations, the log <i>K</i> values from monomer cycles are generally larger than those from the cluster cycles. The accuracy of log <i>K</i> estimation is jointly affected by the thermodynamic cycle type, the solvation characteristics of the halide ion, and the entropy change of the reaction. Accurate log <i>K</i> determination for cadmium halide complexes is enabled by the "cluster-size-matching" approach. This work aids in predicting the coordination structures of heavy metal-halide complexes, especially offering a feasibility reference for thermodynamic cycle methods in calculating their thermodynamic parameters.