11 - Topological Analysis of Electron Density—Quantum Theory of Atoms in Molecules

Abstract

Quantum theory of atoms in molecules (QTAIM) developed by Bader and collaborators, which relies on quantum observables such as electron density and energy density, is able to answer some fundamental questions related to chemical bonding such as the definition of atom within a molecule, natural way to distribute the electrons in a molecule, and the identification of atomic space within the molecular volume. These and related issues have been taken up in this chapter. Instead of developing its mathematical theory, which treats atom as an open quantum system and is quite involved, we have tried to understand some of the basic concepts of QTAIM from the viewpoint of its applications to structural issues. The chapter starts with topological analysis of electron density and defines terms like maximum electron density (MED) path, first and second derivatives of the electron density, critical points (nuclear, bond, ring, and cage), etc., and describes their characteristics. It then explains with suitable examples, topological characterization of chemical bond through parameters such as electron density at bond critical point (BCP) and bond order, bond radius of an atom and bond path length, bond path angles and bond ellipticity, etc. While using energy density for bond characterization, the concepts of Schrödinger kinetic energy, gradient kinetic energy and the basin, surface, and total potential energies have been introduced and atomic and local forms of the virial theorem developed. Energy densities at BCP are then correlated with chemical binding. At the end of the chapter, several applications of QTAIM to problems in molecular structural analysis, chemical reaction studies, the formation of hydrogen bonds, H⋯H bonds, and van der Waals intermolecular bonds have been taken up as illustration.