Chapter 1 Chemical reactivity and the shape function

Conceptual density functional theory (DFT) offers an elegant way to predict and interpretthe outcome of a chemical reaction in terms of the properties of the reactants. The properties of interest are usually response functions with respect to perturbations, with the perturbations of greatest interest being changes in the external potential, in the number of electrons,... capturing the essential chemical characteristics of the relevant reactive agent. Within DFT, the electron density function ρ(r) has always been considered as the (simplest) carrier of information on the system. In recent years, however, the shape function, σ(r) (defined as ρ(r)/N, i.e. the density per particle; N being the number of electrons), has been invoked as an even simpler function characterizing a given system. In this contribution, the properties of this function are reviewed. Its importance for understanding molecular structure and reactivity is highlighted, linking variations in the shape function to more conventional reactivity descriptors in DFT and providing explicit methods for describing chemical reactivity using the shape function only. Applications in the field of atomic and molecular similarity analysis are given, and a shape function-based analogue of Mezey's holographic electron density theorem is discussed.