Chapter 5 Understanding and using the electron localization function

Electron localization function (ELF) helps in understanding the empirical concept of electron localization, specially the pair electron localization in the spirit of Lewis structures. This chapter discusses the principal ingredients involved in the ELF and their relation with chemical concepts. A brief comparison of the ELF with other theoretical related tools, like the atoms in molecules model of Bader is discussed and also presents elementary concepts from the mathematical theory of topological analysis. One important characteristic of the ELF is its numerical stability with respect to the theoretical level at which the electron density and the molecular orbitals are calculated. One of the first and most direct applications of the ELF is to the explanation and confirmation of the valence shell electron pair repulsion model of Gillespie. The ELF has emerged as a powerful tool to understand in a qualitative way the behavior of the electrons in a nuclei system. It is possible to explain a great variety of bonding situations ranging from the most standard covalent bond to the metallic bond. The ELF is a well-defined function with pragmatic characteristic. It does not depend on the method of calculation or on the basis set used. Its application to understand new bond phenomenon is already well documented and it can be used safely. Its relationship with the Pauli Exclusion Principle has been carefully studied and its consequence to understand the chemical concept of electron pair is also been discussed in the chapter.