Potential energy nondegenerate

Our object of interest is a many electron finite system (such as an atom, molecule, cluster etc.), having, by assumption, a nondegenerate ground state (GS) (this assumption will be removed in Sects. 4.4 and 5). The numter of electrons N and the electron-nuclei potential energy v(r) = Ve (r) (the so-called external potential) are given and common for all schemes to be discussed. The GS energy qs aod the GS wave function Vqs of the system can be found from a variational principle as... 

Figure 18 Representation of the potential energy surfaces involved in photoionization from a nondegenerate ground state of a molecule to a Jahn-Teller active state of a molecular ion. The distortion coordinate is the Jahn-Teller active vibration. The vertical arrows represent the most probable transitions...

The model Hamiltonian of Section II captures some of the essential features of the electronic and vibrational structure of polyatomic molecules, like benzene and 5ym-triazine, that have both nondegenerate and degenerate, Jahn-Teller active, electronic levels. In this section interference experiments are described which will be sensitive to the geometric phase development accompanying adiabatic nuclear motion on either of the electronic potential energy surfaces in the Jahn-Teller pair. 

Now consider the splitting of the potential energy surface for nontotaUy symmetric (i.e., E in Ds ) displacements of the nuclei. For such geometries the symmetry is lower, and in general the electronic states become nondegenerate (e.g., 0 82 in C2v) instead of being doubly degenerate E in D3/,). Thus,... 

Let us consider the term in (3) which is linear in Q. At any maximum or minimum in the potential energy curve, dEldQ=0 and therefore the integral must be identically zero, independent of symmetry. At all other points this term must be the dominant one, since Q is small. If yo belongs to a degenerate S5mmetry species E or T), the term usually leads to the first-order Jahn-Teller effect, which removes the degeneracy. Since this is not important in the present context, we will assume that y>o is nondegenerate. 

---