Correlation between Equilibrium Constant and Stabilization Energy: A Combined Approach Based on Chemical Thermodynamics, Statistical Thermodynamics, and Density Functional Reactivity Theory

Abstract

In the present work, an attempt is made to establish the correlation between equilibrium constant and stabilization energy [ΔESE(AB)] generated from density functional reactivity theory (DFRT). The reactions chosen here are of type A + B ⇌ AB (i.e., adduct formation type) between an electron acceptor, A, and an electron donor, B. The representative acceptors are methyltrioxorhenium (MTO) and substituted benzaldehydes whereas donors are 26 mono- and bidentate ligands (having N-donors) and semicarbazide. The trends of experimentally generated equilibrium constant (K) values match with those of ΔESE(AB) in most of the cases, both in gas phase as well as in solvent. Justification of this reliable correlation is provided analytically using the expressions of standard Gibbs free energy of reaction (i.e., ΔrGθ) and the stabilization energy expression generated by DFRT. A further analytical explanation (albeit not very rigorous) is provided through statistical thermodynamics showing how equilibrium constant (K) is related to ΔESE(AB) for reactions of the type A + B ⇌ AB, where either A or B is a common species.