A Statistical Mechanical Perspective on Linear Free Energy Relationships
David M. Ford, Department of Chemical Engineering, Texas A&M University, TAMU 3122, College Station, TX 77843-3122
Consider a family of related molecules, such as a series of small organic molecules with systematic perturbations on the molecular structure or a series of proteins with different primary structures. When each member of the family is subjected to the same thermodynamic change process, such as chemical reaction, physical association, solvation, adsorption, or protein folding, the resulting enthalpy and entropy changes are frequently correlated across the family. Furthermore, the statistical correlation is often quite linear, resulting in the term “linear free energy relationship.” Both positive correlations (compensation) and negative correlations (anti-compensation) between delta_H and delta_S have been observed in the literature under various experimental contexts. Many examples have been demonstrated to be statistical artifacts, but some appear to be genuine signatures of the perturbations in molecular characteristics. In particular, recent claims in the literature state that compensation is a general feature of bimolecular associations arising from weak intermolecular interactions. We employ a statistical mechanical framework to predict the magnitude and direction of enthalpy-entropy correlation in bimolecular association. The theory links the macroscale thermodynamic correlation to the relationship between the intermolecular potential parameters. Using a harmonic approximation to the Lennard-Jones model and potential parameters taken from the literature, we show examples of both compensation and anti-compensation for gas-phase self-association among five homologous series. Furthermore, an aggregate presentation of data for 48 different chemical species shows no correlation in either direction, for the case of self-association in a dilute gas phase.