Chapter 2: Conceptual Development Centred on the Shapes and Topological Features of Potential Surfaces

This chapter focuses on the shapes and topological features of computed potential energy surfaces. We will use cartoons derived from elementary valence bond (VB) theory. The central idea is that electronically excited states are VB isomers of the ground state, i.e. the bonds and/or charges are in different places. Excited state reactivity involves radiationless decay or a nonadiabatic transition at a conical intersection. Thus we will explore the theory of conical intersections in this chapter. The discussion will be focused on the shapes of conical intersections, formulated in terms of three distinguished co-ordinates: X₁ and X₂, the space of the cone, and X₃ a third coordinate. We will use VB theory to rationalize the shapes of such conical intersections and to understand the behavior of the electronic wavefunction, including the phase change, as one does a circuit of the conical intersection. Finally, when the potential surface is plotted against X₃ and X_1/2, a vector chosen from the plane X₁ and X₂, then the conical intersection appears as a seam. We will show that this seam has maxima and minima and that reactivity can be controlled by the place where the reaction path crosses the seam.