Funnel pericyclic

F. Pericyclic Minima (Funnels) and Their Open-Chain Counterparts... 

The global term pericyclic funnel will be used to refer to the funnel or funnels in the S surface that occur at the critically heterosymmetric biradicaloid geometries reached near the halfway point along the path of a thermally forbidden pericyclic reaction, and the minima in S, that are encountered along one-dimensional cuts along reaction paths that miss the conical intersections (in particular, those along high-symmetry paths, which pass... 

The results of model 20 x 20 Cl calculations on H4 led to the proposal (Gerhartz et al., 1977) that the [2 + 2J and x[2s -I- 2J processes proceed through the same pericyclic funnel in the S, state. This has been supported by recent more realistic calculations (Olivucci et al., 1993, 1994b), and the two processes are therefore best discussed together. 

The D state with its pericyclic funnel is not related to the four low-energy ionic states. It originates from a mixing of the triplet-triplet annihilation wave function with totally symmetric higher excited configurations and... 

From Example 6.4 it can be seen that the molecule may also end up in a minimum or funnel in S, or T, that is further away from the geometry of the starting species. This then corresponds to a nonspectroscopic minimum or funnel (Figure 6.3, minimum 0 such as the pericyclic funnel of the anthracene dimerization in Figure 6.7, or even to a spectroscopic minimum of another molecule or another conformer of the same molecule (Figure 6.3, minimum i). Reactions of the latter kind can sometimes be detected by product emission (Figure 6.3, path j). (Cf. Example 6.5.)... 

Pericyclic minima and funnels that can be easily predicted by means of correlation diagrams are of great importance in concerted pericyclic photoreactions. However, there may be additional minima and barriers on the excited-state surfaces that affect or even determine the course of the photoreaction. 

Finally, in a remarkable series of recent papers, Bernard , Olivucci, Robb and their collaborators (1990-1994) demonstrated that the S -S touching actually is not avoided even in the low-symmetry case of real organic molecules, and they confirmed the earlier conjectures by computing the actual geometries of the funnels (conical intersections) in the S, surface at a reasonable level of ab initio theory. They also pointed out that still additional reactions can proceed through the same pericyclic funnel, such as the cis-trans isomerization of butadiene. 

Sections 6.2.1.1 and 6.2.1.2 describe the pericyclic funnel in more detail for two particularly important and illuminating examples the cycloaddition of two ethylene molecules and the isomerization of butadiene. We rely heavily on the results of recent ad initio calculations (Bernardi et al., 1990a Olivucci et al., 1993). 

Figure 6.13. Pericyclic funnel region of ethylene dimerization, showing two equivalent conical intersections corresponding to 1,3 and 2,4 diagonal interactions and the transition slate region at rectangular geometry (a = 0). The curves shown for a = 0 correspond to the van der Lugt-Oosterhoff model (by permission from Klessinger, 1995),...

Figure 6.15. r-Orbital interactions in butadiene a) planar geometry, p AOs, b) high-symmetry disrotatory pericyclic geometry, peripheral interactions along the perimeter, and c)-f) geometries of two equivalent funnels diagonal interactions are shown in c) and d) peripheral interactions in e) and f). 

According to Figure 6.17, the height of the barrier between the excimer minimum and the pericyclic funnel depends both on their depths and on the relative placement of the two excited-state surfaces S and D. The depth of the diagonally distorted pericyclic funnel is determined by the nature of the biradical its dependence on molecular structure, on the head-to-head and head-to-tail orientation of the components, and on reaction medium can be discussed using the principles outlined in Section 4.4.1. 

It is probably reasonable to assume that the excited-state motion is initially dominated by the slope of the B and A surfaces, which points in the disrotatory way and toward the diagonally-bonded pericyclic funnel, and to assume that the acquired momentum is kept after the jump to Sq. This would point in the direction of bicyclobutane. Unless the surface jump occurs right at the cone tip, it generates an additional momentum in the Xj direction, that is, along the y perturbation coordinate, toward cyclobutene and the original as well as cis-trans isomerized butadiene. Whether further facile motions on... 

Photodimerization often involves an excimer that can be treated as a su-permolecule. (Cf. Section 6.2.3.) Then, the state correlation diagram for the singlet process (Figure 7.27a) ordinarily calls for a two-step return from S, to So along the concerted reaction path. First, an excimer intermediate E is formed. Second, a thermally activated step takes the system to the diagonally distorted pericyclic funnel P" (cf. Section 4.4.1), and the return to So that follows is essentially immediate. The reaction will be stereospecific and concerted in the sense that the new bonds form in concert. However, it will not be concerted in the other sense of the word, in that it involves an intermediate E. ... 

There may well be systems in which the excimer minimum occurs in the S2 rather than the S, surface (Figure 7.27b). The approach to the pericyclic funnel P on S, may then be barrierless, and an excimer intermediate will... 

Figure 7.27. Schematic representation of the state correlation diagram for a ground-state-forbidden pericyclic reaction with an excimer minimum E a) at geometries well before the pericyclic funnel P is reached, and b) at geometries similar to those of P. ...

Finally, it should be remembered that excimer minima E and pericyclic funnels P of different energies can result if different mutual arrangements of the reactants can lead to cycloaddition, as indicated in Scheme 3 in Section 6.2.3. The related issues of regio- and stereoselectivity of singlet photocycloaddition are dealt with in Section 7.4.2. 

It is likely that [2 + 2] and x[2 + 2] cycloadditions proceed through the same type of diagonally distorted pericyclic funnel (Section 4.4.1) with a preservation of the diagonal interaction, and eventual production of two di-... 

Many factors must be considered to explain these facts, not least the relative stabilities of the various possible excimers or exciplexes and the accessibility of the pericyclic funnels. (Cf. Scheme 3 in Section 6.2.3.) In addition, the geometrical structure at the funnel and the ground-state relaxation pathways originating in the decay region determine which products will be formed. 

The formation of head-to-tail dimers such as those of 9-substituted anthracenes and similar species can be rationalized by the conjecture that in this case it is not the most favorable excimer that determines the stereochemical outcome of the reaction but rather, the most readily reached peri-cyclic funnel. This can be understood if the effect of substituents on the pericyclic funnel is first considered at the simple two-electron-two-orbital model level (3x3 Cl, Section 4.3.1). The discussion of cyclodimerization of an olefin is restricted to the four orbitals directly involved in the reaction. 

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