Perturbed reactivity descriptors: the chemical hardness

A simple framework to study the effects of (small) external perturbations on conceptual density functional theory descriptors is discussed. Based on this, the general expressions recently presented for the perturbed chemical potential are revisited. Additionally, new formulas that take into account the effect of the molecular environment on the chemical hardness are derived. Some consequences of this framework are analyzed in the context of several magnitudes that characterize charge transfer reactions. It is expected that the resulting formulas provide more accurate results when the unperturbed chemical potentials and chemical hardnesses of the reagents are not significantly different between them.