Challenges in predicting ΔrxnG in solution: The chelate effect

Abstract

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)42+ + 2 en → M( en)22+ + 4 NH3 ( en = 1,2-ethylenediamine), for which ΔrxnG* and ΔrxnH* 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 ΔsolvG*[M(NH3)42+] vs ΔsolvG*[M( en)22+] 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 ΔrxnG* 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)42+, M( en)22+] were needed. It is hoped that this study will aid (and encourage) further CSM development for coordination-complex ions.