Isoenergetic displacements

For an isoenergetic displacement, no secular term appears in the general solution, as is readily obtained from Equations(47),(48) and (49). 

Fig. 7. Energetics of a bimolecular rate process. Top Representation of the potential energy surface along coordinate axes corresponding to the interatomic distance of B-to-C and A-to-B, where incremental displacements along the potential energy axis are shown as a series of isoenergetic lines (each marked by arbitrarily chosen numbers to indicate increased energy of the transition-state (TS) intermediate relative to the reactants). Bottom Typical reaction coordinate diagram for a bimolecular group transfer reaction.

The ground state of an atom is obtained by placing all available electrons in the orbitals in the order of increasing energy, following Hund s rule, when there are isoenergetic orbitals. An excited state is formed when one or several of these electrons are displaced to other orbitals. These states then correspond to one-electron or two-electron , etc., excitations, as illustrated in Figure 3.2. 

REF19 Hobza, P., Sezle, H. L. and Schlag, W. (1996) Potential energy surface for benzene dimer. Results of ab initio CCSD(T) calculations show two nearly isoenergetic structures T-shaped and parallel-displaced, J. Phys. Chem., 100, 18790-18794... 

Surface for the Benzene Dimer. Results of Ah Initio CCSD(T) Calculations Show Two Nearly Isoenergetic Structures T-Shaped and Parallel-Displaced. 

A close analogue of the hydrocarbons are the fluorocarbons. The fluorine atoms are able to induce quadrupolar interactions leading to an isoenergetic double potential minimum displaced approximately 10° from the equatorial configuration. These minima are of considerable significance as they force the molecule to adopt a helical conformation and this structure is retained in the solid phase. Ultrasonic measurements combined with NMR studies of short chain fluorinated hydrocarbons confirm these theoretical predictions and indicate that facile exchange between trans minimum energy states occurs. 

---