The general topology of potential energy surfaces

In this chapter, we will first discuss the general topology of potential energy surfaces that have been calculated for elementary chemical reactions. Second, we will consider the solution of the electronic Schrodinger equation with a focus on analytical results and elementary concepts rather than detailed computational procedures. 

1 These three coordinates have in fact already been separated out of Eq. (1.6). 

For direct reactions a single saddle point is found on the path from reactants to products, with potential energy valleys extending in the directions of separate reactants and products see Fig. 3.1.1. 

A saddle point is a stationary point on the multidimensional potential energy surface. It is a stable point in all dimensions except one, where the second-order derivative of the potential is negative (see Appendix E). The classical energy threshold Eci or barrier height of the reaction corresponds to the electronic energy at the saddle point relative to the electronic energy of the reactants. 

The energy threshold of a reaction corresponds to the minimum relative translational energy that must be supplied to the reactants in order to produce products. This energy threshold will differ from the classical barrier height, even when the reac- 

---