The Concept of the Potential Energy Surface

The potential energy surface (PES) is a central concept in computational chemistry. A PES is the relationship – mathematical or graphical – between the energy of a molecule (or a collection of molecules) and its geometry. The Born−Oppenheimer approximation says that in a molecule, the nuclei are essentially stationary compared to the electrons. This is one of the cornerstones of computational chemistry because it makes the concept of molecular shape (geometry) meaningful, makes possible the concept of a PES, and simplifies the application of the Schrödinger equation to molecules by allowing us to focus on the electronic energy and add in the nuclear repulsion energy later; this third point, very important in practical molecular computations, is elaborated on in Chap. 5 . Geometry optimization and the nature of transition states are explained.