Linear Combination of Atomic Orbitals

Abstract

The Linear Combination of Atomic Orbitals (LCAO) approximation is fundamental to many of our current models of chemistry. Both the vast majority of the calculational programs that we use, be they ab initio, density functional, semiempirical molecular orbital, or even some sophisticated force-fields, and our qualitative understanding of chemistry are based on the concept that the orbitals of a given molecule can be built from the orbitals of the constituent atoms. We feel comfortable with the π-HOMO (Highest Occupied Molecular Orbital) of ethylene depicted as a combination of two carbon p-orbitals, as shown in Fig. 2.1, although this is not a very accurate description of the electron density of this Molecular Orbital (MO). The use of the π-Atomic Orbitals (AOs), however, makes it easier to understand both the characteristics of the MO itself and the transformations that it can undergo during reactions.