Local and non-local chemical potential and hardness: a grand canonical ensemble approach.

Context: The formulation of conceptual density functional theory in the grand canonical ensemble provides a theoretical framework that allows one to establish additional insights about the response functions that characterize this approach. In particular, through this procedure, one can establish the local counterpart of the chemical potential which, when integrated over all the space, leads to the global quantity and the local counterpart of the hardness that not only provides a function free of ambiguities, but also generates through its integration over all the space the well-defined value of the global quantity given by the difference of the vertical first ionization potential and electron affinity. In the present work, the non-local counterpart of these local reactivity descriptors is derived making use of the Fukui kernel descriptor previously developed by us.