ABSTRACT
A new strategy, recently reported by us to develop local and linear (nonlocal) counterparts of global response functions, is applied to study the local behavior of the global softness and hardness reactivity descriptors. Within this approach a local counterpart is designed to identify the most important molecular fragments for a given chemical response. The local counterpart of the global softness obtained through our methodology corresponds to the well-known definition of local softness and, in agreement with what standard conceptual chemical reactivity in density functional theory dictates, it simply reveals the softest sites in a molecule. For the case of the local hardness, we obtain two expressions that lead to different information regarding the values of the hardness at the different sites within a chemical species. The performance of these two proposal were tested by comparing their corresponding atom-condensed values to experimentally observed reactivity trends for electrophilic attack on benzene and ethene derivatives.
ABSTRACT
This reply complements the comment of Guégan 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.