Statistical interpretation of enthalpy–entropy compensation

TYPICALLY, enthalpy and entropy estimates from kinetic and equilibrium data are highly correlated, varying in a linear fashion with one another (enthalpy–entropy compensation effect). This effect can be readily explained in most cases simply as a statistical or data handling artefact. The statistical analysis presented here reveals three novel insights. First, the enthalpy and entropy parameter estimates are highly correlated, such that estimated correlation coefficients > 0.95, say, do not imply chemical causation. Second, enthalpy and entropy estimates are distributed by experimental and measurement errors in elliptical probability regions that are very elongated and appear as lines. The slope of such lines is the harmonic mean of the experimental temperatures. Third, estimates of enthalpy and free energy at the harmonic mean of the experimental temperatures are not statistically correlated, so any observed structured variation between these parameter estimates arises from the chemical effect alone. Note that, since the thermodynamic potentials are interrelated by the Maxwell relationships, a correlation between any two potentials can be transformed to give the corresponding correlation between any other two. We now discuss these results to resolve a number of issues concerning a much disputed data set.