Local hardness: An application to electrophilic additions

Links among the Fukui potential, the alchemical hardness and the local hardness of an atom in a molecule

This paper presents a brief summary of the difficulty that resides in the definition of the elusive concept of local chemical hardness. We argue that a definition of local hardness should be useful to a reactivity principle and not just as a mere definition. We then continue with a formal discussion about the benefits and difficulties of using the Fukui potential, which is interpreted as an alchemical derivative (alchemical hardness), as descriptor of local hardness of molecules. Computational evidence shows that the alchemical hardness is at least as good a descriptor as the combination of other two well-stabilized descriptors of local hardness, such as the Fukui function and grand canonical local hardness. Although our results are auspicious for the alchemical hardness as descriptor of local hardness, we finish by calling the attention of the community on the importance of discussing the raison d'être of a local hardness function and its main characteristics. We suggest that an axiomatic construction of local hardness could be they way of constructing a local hardness which is both useful and free of arbitrariness.

Local chemical potential, local hardness, and dual descriptors in temperature dependent chemical reactivity theory

From the definition of a local chemical potential, well-behaved expressions for the local hardness and the dual descriptors are derived.

Revisiting the definition of local hardness and hardness kernel

Local hardness is redefined following similar rules to those of local softness. The new concept describes chemical trends correctly.

An information-theoretic resolution of the ambiguity in the local hardness

A definition of the local hardness, suitable for application in the local hard/soft acid/base principle, is derived by applying information theory.

Do the local softness and hardness indicate the softest and hardest regions of a molecule?

In this work, we will show that the largest values of the local softness and hardness do not necessarily correspond to the softest and hardest regions of the molecule, respectively. Based on our results, we will argue that it is more useful to interpret the local softness and the local hardness as functions that measure the "local abundance" or "concentration" of the corresponding global properties. This new point of view helps reveal how and when these local reactivity indices are most useful.