Challenges in predicting Δ_rxnG in solution: The chelate effect

Gibbs energies for reactions involving aqueous ions are challenging to predict due to the large solvation energies of such ions. A stringent test would be the ab initio reproduction of the aqueous-phase chelate effect, an entropic effect in reactions of very small enthalpy changes. This paper examines what is required to achieve such a reproduction for the paradigmatic reaction M(NH₃)₄ ²⁺ + 2 en → M(en)₂ ²⁺ + 4 NH₃ (en = 1,2-ethylenediamine), for which Δ_rxnG* and Δ_rxnH* are -2.3 and +1.6 kcal mol^-1, respectively, if M = Zn. Explicit solvation via simulation was avoided in order to allow sufficiently accurate electronic structure models; this required the use of continuum solvation models (CSMs), and a great deal of effort was made in attempting to lower the relative errors of Δ_solvG*[M(NH₃)₄ ²⁺] vs Δ_solvG*[M(en)₂ ²⁺] from the CSMs available in Gaussian software. CSMs in ADF and JDFTx software were also tested. A uniform 2.2 kcal mol^-1 accuracy in Δ_rxnG* for all three metal-atom choices M = {Zn, Cd, Hg} was eventually achieved, but not from any of the known CSMs tested, nor from cavity size reoptimization, nor from semicontinuum modeling: post facto solvation energy corrections [one per solute type, NH₃, en, M(NH₃)₄ ²⁺, M(en)₂ ²⁺] were needed. It is hoped that this study will aid (and encourage) further CSM development for coordination-complex ions.