Biradical minima

The results for the carbon-oxygen attack are summarized schematically in Figure 7.38. The excited-state branch of the reaction path terminates in a conical intersection point at a CO distance of 177 pm before the biradical is fully formed (cf. Figure 7.37a). Thus the system can evolve back to the reactants or produce a transient C,C-biradical intermediate that is isolated by small barriers (< 3 kcal/mol) to fragmentation (TS,) or to rotation and ring closure to oxetane (TS2). The singlet and triplet biradical minima are essentially coincident. 

Figure 12.10. Potential-energy functions of the S0 state, the locally excited 1 hit states of guanine and cytosine, the lowest1 rnr state, and the tt-jt charge-transfer state of the WC conformer (a), the conformer B (b), and the conformer C (c) of the CG dimer. The PE functions have been calculated along the linear-synchronous-transit proton-transfer reaction path from the S0 minimum to the biradical minimum. Insets show the potential-energy function of the locally excited 1mr state of guanine calculated along the minimum-energy path for stretching of the NH bond...

The combination is in this case an out-of-phase one (Section I). This biradical was calculated to be at an energy of 39.6 kcal/mol above CHDN (Table ni), and to lie in a real local minimum on the So potential energy surface. A normal mode analysis showed that all frequencies were real. (Compare with the prebenzvalene intermediate, discussed above. The computational finding that these species are bound moieties is difficult to confimi experimentally, as they are highly reactive.)... 

A direct observation of a triplet state of substituted trimethylene biradical has recently been claimed.84) This is in good agreement with the prediction 104,105) that the lowest excited state of cyclopropane will have an energy minimum at a geometry in which one C—C bond is broken. 

Kinetic observations suggest that of the four species, the biradicals 14b and 14b, and the bicyclic hydrocarbons 28 and 29, the triplet biradical 14b is the global energy minimum. Thus, the two related full-valency molecules 28 and 29 both have a negative bond dissociation energy (BDE). 

The calculations showed an apparent preference for the inversion of configuration in the reaction, for which the PES had a very distinct local minimum corresponding to a biradical. It was suggested that an experimental observation of a preference for inversion of configuration at the migrating carbon should not be taken as definitive evidence against a biradical mechanism. The dynamics effect may make mechanistic discussion by means of product analyses less straightforward. 

Figure 15-4. The energy of the Sj state of cytosine (left) and uracil (right) as a function of the C4C5C6N] dihedral angle. EOM-CCSD(T) values are shifted uniformly upward by the amount indicated in the figure. The insert shows the side view of the structure of the minimum of the biradical state of cytosine. (Reprinted with permission from Refs. [10] and [11].)...

Figure 15-9. CIS and CC2/cc-pVDZ potential-energy profiles of the lowest energy tttt state of TMC as a function of CC-d V.C dihedral angle (left panel). CC2/cc-pVDZ potential-energy profiles of the 1 tttt" and biradical states of cytosine (right panel). The number (330 cm-1) refers to the energy barrier (CC2) for the state switch from the tttt minimum to the biradical state. The dihedral angle at the ground-state minimum is 0°. (Reprinted with permission from Ref. [23].)...

Their results are shown in Fig. 8-5, from which the following MFEs could be obtained (1) For each of the compounds with 8 < n < 11, the intensity (7(B)//(0T)) decreased with increasing B from 0 T, attained a minimum value at the minimum field (Smin), and started to increase with increasing B from Smin- (2) Because the singlet exciplex is in equilibrium with the singlet biradical as shown by process (8-2f), the observed MFEs should be due to the LCM and the observed Bmin values correspond to the Blc ones. These Bmin values are very similar to the Bmax ones obtained from the intensity (Et(B)) of the transition absorption due to A as listed in Table 8-1. (3) For each of the compounds with n > 12, the intensity... 

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. 

A schematic representation of the surfaces for the carbon-carbon attack is shown in Figure 7.39. The very flat region of the S surface (barriers of the order of I kcal/mol) corresponds to the C.O-biradical. The biradical has a CC bond length of 156 pm and corresponds to a conical intersection geometry in the case of the singlet, and to a minimum in the case of the triplet. Thus for the singlet photochemistry the decay to So occurs close to the products, and the reaction appears to be concerted. Since, however, the formation of the singlet biradical is also possible from the same funnel, a certain fraction of photoexcited reactant can evolve via a noncon-certed route. 

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