Chelate effect and thermodynamics of metal complex formation in solution: a quantum chemical study

The accuracy of quantum chemical predictions of structures and thermodynamic data for metal complexes depends both on the quantum chemical methods and the chemical models used. A thermodynamic analogue of the Eigen-Wilkins mechanism for ligand substitution reactions (Model A) turns out to be sufficiently simple to catch the essential chemistry of complex formation reactions and allows quantum chemical calculations at the ab initio level of thermodynamic quantities both in gas phase and solution; the latter by using the conductor-like polarizable continuum (CPCM) model. Model A describes the complex formation as a two-step reaction: 1. [M(H2O)x](aq) + L(aq) <==>[M(H2O)x], L(aq); 2. [M(H2O)x], L(aq) <==>[M(H2O)(x-1)L],(H2O)(aq). The first step, the formation of an outer-sphere complex is described using the Fuoss equation and the second, the intramolecular exchange between an entering ligand from the second and water in the first coordination shell, using quantum chemical methods. The thermodynamic quantities for this model were compared to those for the reaction: [M(H2O)x](aq) + L(aq) <==>[M(H2O)(x-1)L](aq) + (H2O)(aq) (Model B), as calculated for each reactant and product separately. The models were tested using complex formation between Zn(2+) and ammonia, methylamine, and ethylenediamine, and complex formation and chelate ring closure reactions in binary and ternary UO(2)(2+)-oxalate systems. The results show that the Gibbs energy of reaction for Model A are not strongly dependent on the number of water ligands and the structure of the second coordination sphere; it provides a much more precise estimate of the thermodynamics of complex formation reactions in solution than that obtained from Model B. The agreement between the experimental and calculated data for the formation of Zn(NH(3))(2+)(aq) and Zn(NH(3))(2)(2+)(aq) is better than 8 kJ/mol for the former, as compared to 30 kJ/mol or larger, for the latter. The Gibbs energy of reaction obtained for the UO(2)(2+) oxalate systems using model B differs between 80 and 130 kJ/mol from the experimental results, whereas the agreement with Model A is better. The errors in the quantum chemical estimates of the entropy and enthalpy of reaction are somewhat larger than those for the Gibbs energy, but still in fair agreement with experiments; adding water molecules in the second coordination sphere improves the agreement significantly. Reasons for the different performance of the two models are discussed. The quantum chemical data were used to discuss the microscopic basis of experimental enthalpy and entropy data, to determine the enthalpy and entropy contributions in chelate ring closure reactions and to discuss the origin of the so-called "chelate effect". Contrary to many earlier suggestions, this is not even in the gas phase, a result of changes in translation entropy contributions. There is no simple explanation of the high stability of chelate complexes; it is a result of both enthalpy and entropy contributions that vary from one system to the other.