Peaked intersection

Figure 6. Two-dimensional (top) and 3D (bottom) representations of a peaked (a) and sloped (b) conical intersection topology. There are two directions that lift the degeneracy the GD and the DC. The top figures have energy plotted against the DC while the bottom figures represent the energy plotted in the space of hoth the GD and DC vectors. At a peaked intersection, as shown at the bottom of (a), the probability of recrossing the conical intersection should be small whereas in the case of a sloped intersection [bottom of ( )l, this possibility should be high. [Reproduced from [84] courtesy of Elsevier Publishers.]...

Ruedenberg s terminology peaked, sloped, and intermediate, as shown in Figure 8. Often the chemically relevant conical intersection point is located along a valley on the excited state potential energy surface (i.e., a peaked intersection). Figure 9 illustrates a two-dimensional model example that occurs in the photochemical trans —> cis isomerization of octatetraene.28 Here two potential energy surfaces are connected via a conical intersection. This intersection... 

Before we conclude our discussion, we note that the INADEQUATE spectrum of caryophyllene oxide contains an uncommon phenomenon worth exploring. Carbons 6 and 7 of caryophyllene oxide nearly overlap in the 13C spectrum with each other and with the C-15 methyl we list their chemical shifts from Table 5.1 as 29.5 and 29.2 ppm. Because they are bonded to one another in caryophyllene oxide, they should show correlation in the INADEQUATE spectrum, but, instead of an AX system, we have an AB system with ZW/ being much less than ten. For this special case, we no longer expect two doublets whose midpoint lies on the diagonal instead, we predict that an AB multiple (see Chapter 3) should fall on the diagonal line itself. This prediction is borne out in Figure 5.19 where we find a cross peak directly below C-6 and C-7, and this cross peak intersects the diagonal line. 

Figure 2.4 Excited-state reaction profiles for (a) sloped and (b) peaked intersections.

We start with a model peaked intersection. In our model structure, there are two equivalent centers labeled 1 and 1 and a third, different, center labeled 2. We consider two states... 

One important point about photochemical reactions is that state switches between excited states occur in the region of topographies such as the peaked intersection region sketched above (Figure 2.4b). To understand the role of conical intersections in state switches, it is useful to compare the two-dimensional picture of Figure 2.6 with the simple one-dimensional model that is normally used to describe this phenomenon, with the help of an avoided crossing. (One dimensional means here that only one nuclear coordinate, the reaction coordinate, is considered.)... 

In our calculated potential energy surfaces, we have shown that the avoided crossing, which is the transition state for ET in Marcus theory, is a region centered on a conical intersection. The topology is similar to the one shown for the model peaked intersection, and in general cases the reaction will take place on the lower surface of the double cone (Figure... 

The general description of the conical intersections for ET goes along the lines used to describe the model peaked intersection in Figure 2.7 and the seam of intersection in... 

In Fig. 7.5 we indicate the slope of the conical intersection [27]. Of course X3 does not appear on these figures. The peaked intersection corresponds to the... 

Fig. 4.6 Cyclic voltammograms of a mediator-producing bacterial suspension fed glucose at time 0 (black line), and after 30 min (red line) and 120 min (green line). Arrows indicate peaks while dashed lines that cross between oxidation and reduction peaks intersect the x-axis at the formal potential of the redox couple. The peak at -170 mV disappeared when bacteria were washed by centrifugation, but the peak at 180 mV never disappeared. There were no peaks observed from sterile medium. [From Rabaey et al. (2004), reprinted with permission of the American Society for Microbiology.]...

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