Calculation of equilibrium binding constants and cooperativity of Cu(II) mixed solvated complexes formation

A new extension of matrix approach is proposed to calculate the equilibrium constants of coordinated solvent substitution in a metal ion first salvation shell in the mixed solvent system. The proposed method allows reducing the number of independent variables, necessary to calculate the fractions of species in solution. The equilibrium model of MeCN substitution with DMF and DMSO in the presence of Cu(II) ion for the assessment of structure of intermediate species is presented and verified. The distribution diagrams of Cu(II) species in mixed organic solvents have been analyzed using the modified matrix method. The intrinsic equilibrium constants K of the first solvent molecule replacement in the Cu(II) coordination shell and the correction for the mutual influence between the solvent molecules as ligands in the successive complex formation (cooperativity parameter w) in acetonitrile solution have been calculated from the fitting procedure. It is shown that anticooperative substitution of MeCN by donor ligands in the first coordination shell of the Cu(II) ion is always governed by the change of coordination number during the stepwise process.