Reply to the Comment on Revisiting the definition of local hardness and hardness kernel' by C. Morell, F. Guegan, W. Lamine, and H. Chermette, Phys. Chem. Chem. Phys., 2018, 20, DOI: 10.1039/C7CP04100D

This reply complements the comment of Guegan et al. about our recent work on the revision of the local hardness and the hardness kernel concepts. Guegan et al. analyze our work using a Taylor series expansion of the energy as a functional of the electron density, to show that our procedure opens a new way to define local descriptors. In this contribution we show that the strategy we followed for the local hardness and the hardness kernel is even more general, and that it can be used to derive from a global response function its corresponding local and non-local counterparts by: (1) requiring that the integral over one of the two variables that characterizes the non-local function leads to the local function, and that the integral over the local function leads to the global response index, and (2) assuming that the global and local functions are related through the electronic density, by making use of the chain rule for functional derivatives.