Barrierless processes

Equation (5.86c), written as a strict equality, may also be taken to define the NRT transition state as an alternative to (and slightly different from) the usual definitions based on energetic, saddle-point-curvature, or density-of-states criteria. Note that this NRT alternative definition can be employed for non-IRC choices of reaction coordinate, and remains valid even in the case of barrierless processes (such as many ion-molecule or radical-recombination reactions) for which the reaction profile does not exhibit an energy maximum as in Fig. 5.52. The NRT definition is practically identical to the usual saddle-point definition of the transition state in the present examples. 

Model computational studies aimed at understanding structure-reactivity relationships and substituent effects on carbocation stability for aza-PAHs derivatives were performed by density functional theory (DFT). Comparisons were made with the biological activity data when available. Protonation of the epoxides and diol epoxides, and subsequent epoxide ring opening reactions were analyzed for several families of compounds. Bay-region carbocations were formed via the O-protonated epoxides in barrierless processes. Relative carbocation stabilities were determined in the gas phase and in water as solvent (by the PCM method). 

The protonated epoxides, i.e. the oxonium ions, could not be characterized as minima on the respective potential energy surfaces, as in every case the epoxide ring opened by a barrierless process upon O-protonation. Charge delocalization maps are shown in Figure 9, and some selected NPA-derived charges for the carbocations are displayed in Table 4. 

Steric factors are often responsible for skeletal isomerization in ion-radical states. The simple example in Scheme 6.31 illustrates the effect of steric congestion on activation energy of this kind of isomerization and depicts the transition of 2,2,3,3-tetramethylmethylenecyclopropane into 1,1,2,2-tetramethyltrimethylenemethane cation-radical. The rearrangement is brought about by one-electron oxidation of the substrate and represents an entirely barrierless process. Interestingly, methylenecy-clopropane (bearing no methyl groups) is protected from such a spontaneous collapse by a barrier of 7.4 k J mol l (Bally et al. 2005). 

Now, another possibility is to consider what would happen if one lowered the overpotential sufficiently. Then one gets what is shown in Fig. 9.33(c), which some workers (Krishtalik) have called barrierless processes because the transfer between the initial and final state becomes simply the heat of the reaction. 

In n-hexane, a similar band with a maximum at around 384 nm was observed with a comparably fast risetime, so that one can conclude that the photoinduced charge-transfer process in this fluorinated derivative is a quasi-barrierless process in both polar and non-polar solvents. Preliminary DFT calculations indicate that in vacuum DMABN-F4 is nonplanar in the ground state in contrast to DMABN [7]. The fact that the observed CT state absorption spectrum is blue-shifted compared to that of DMABN and of the benzonitrile anion radical (Fig. 3) might be an indication that the equilibrium geometry of the CT state of DMABN-F4 is different from that of the TICT state of DMABN or might be due to the influence of the four fluorine atoms. 

To summarize, Jean shows that coherence can be created in a product as a result of nonadiabatic curve crossing even when none exists in the reactant [24, 25]. In addition, vibrational coherence can be preserved in the product state to a significant extent during energy relaxation within that state. In barrierless processes (e.g., an isomerization reaction) irreversible population transfer from one well to another occurs, and coherent motion can be observed in the product regardless of whether the initially excited state was prepared vibrationally coherent or not [24]. It seems likely that these ideas are crucial in interpreting the ultrafast spectroscopy of rhodopsins [17], where coherent motion in the product is directly observed. Of course there may be many systems in which relaxation and dephasing are much faster in the product than the reactant. In these cases lack of observation of product coherence does not rule out formation of the product in an essentially ballistic manner. 

Both steps are spin-allowed and exothermic reactions. A scan of the N4 potential energy surface at the CAS(12,12)/cc-pVTZ level indicated that a perpendicular approach of N(2D) towards the molecular plane of 15 is most favorable for formation of 1. This can also be rationalized from an analysis of the occupied orbitals in the two species. According to the computed dissociation pathway at the MRCI-SD(Q)/cc-pVTZ//CAS(15,12/cc-pVTZ level, 1 can be formed from 15 and N(2Z>) (Eq. 2) in a near barrierless process, as is expected for a radical recombination reaction. However, the scan of the potential energy surface shows that the reaction channel is rather narrow and that two N2 molecules is likely to be formed in a competing process. 

The rotational triple energy minima about C - C single bonds follows directly from the tetrahedral geometry of saturated carbon centers [16], yet was not proven experimentally until 1936 [17]. In practice, the energy barrier to rotation around a C - C single bond is so low (ca. 3 kcalmol x) that this is an effectively barrierless process at room temperature. To achieve some kind of control over rotation about a chemical bond it is necessary to raise that energy barrier. This has typically been achieved by increasing the steric demand in the proximity of the bond around which we want to control rotation. 

Thus these preliminary studies on the temperature dependence support our earlier proposal (Oevering et al., 1987) that in the lower homologues of l(n) photoinduced charge-separation occurs as a virtually barrierless process. 

The first channel is a barrierless process, whereas the second one has a tight transition state. The key structures and the energy diagram obtained at the G2M (CC5)//PW91PW91/6-311+G(3df) leve are shown in Fig. 16. 

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