Equi-energetic states

Exciton hopping to the same chromophore and using equi-energetic states depend on dipole-dipole orientation and the interaction distance, Rq-... 

Figure 1. Qualitative behaviour with the gas concentration of the steady-state signal shift (a) and time constant inverse (b) for a pure Langmuir adsorption on a limited amount of equi-energetic adsorption sites over a sensor surface.

In Figure 11 we display two other theoretical structures. The TS structure is the transition state governing the torsional motion of the OH group of phenol between its equi-energetical structures shown in Chart 4. The energy difference between this structure and the 5 o-state phenol molecule determines the torsional barrier as equal to 13 kJmol ... 

Clearly, this indicates that the 3,3-shift transition state has little cyclohexane-1,4-diyl character. This is not unreasonable considering that bond formation in this case must occur with generation of a strained cyclopropane bond so the transition state, no doubt, has much more bisallyl radical character (see Chapter 7, Section 4.1). Indeed, radical stabilizing substituents on the cyclopropane ring bond being broken dramatically increase the rate of the 3,3-shift to the point where the transition state is nearly equi-energetic with starting materials (Scheme 10.35). ... 

The first and simplest mechanism starts with the naked anion and does not take into account the presence of a counter-ion, the anion (Fig. 6). It was originally presented as the mechanism responsible for the formation of the meso dyad (m) stereodefects based on the fact that the transition state geometries before and after a site epimerization are equi-energetic and therefore the assumption is that the activation energy barrier for the site epimerization is be very high. 

This angular dependence of the interaction parameter can be extended by using the rotational isomeric state approximation to calculate the conformer populations. This approach was used to interpret the solid-state spectrum of poly(3-methyl-l-pentene), which in the amorphous state can have either a four-fold right-handed helix or a nearly equi-energetic four-fold left-handed helix. Three of the six ehemical shifts of a right-handed unit differ from the corresponding resonances of a left-handed unit, and these stereochemical differences are observed [35]. 

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