Average local ionization energy: A review

The average local ionization energy $ \overline {\hbox{I}} \left( {\mathbf{r}} \right) $ is the energy necessary to remove an electron from the point r in the space of a system. Its lowest values reveal the locations of the least tightly-held electrons, and thus the favored sites for reaction with electrophiles or radicals. In this paper, we review the definition of $ \overline {\hbox{I}} \left( {\mathbf{r}} \right) $ and some of its key properties. Apart from its relevance to reactive behavior, $ \overline {\hbox{I}} \left( {\mathbf{r}} \right) $ has an important role in several fundamental areas, including atomic shell structure, electronegativity and local polarizability and hardness. All of these aspects of $ \overline {\hbox{I}} \left( {\mathbf{r}} \right) $ are discussed. Figure