In 1982 Perdew, Parr, Levy and Balduz showed that the dependence of the energy (E) in the number of electrons (N) is constituted by a series of straight-lines interconnecting integer electrons number energy values. Consequently, second and higher order derivatives of the E vs N profile, commonly connected with chemical concepts as the chemical hardness, are mathematically ill-defined. As an alternative, Parr and Pearson considered that the energy dependence with respect the number of electrons can be approximated through a smooth quadratic interpolation. Regardless of its lack of rigorousness, the parabolic approximation has proven to be an adequate model to develop theoretical concepts (as the Parr and Pearson hardness or the Morell’s dual descriptor), useful to predict the chemical reactivity of the species. By exploring the explicit temperature-dependence of the Helmholtz free energy (A) and of the (average) electronic energy with respect to the number of electrons, we show that at finite temperature conditions, where the entropic contribution is non-negligible, is the Helmholtz free energy the one that resembles to a parabolic function in the number of electrons. Our results show that there exist a unique temperature value for which the curvature and the minimum of the A vs N profile, are numerically equivalent to those observed for the Parr and Pearson parabolic interpolation.

The parabolic interpolation is justified by thermodynamics

255th National Meeting (2018)

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.