Barrierless isomerization

This equation has been used by Sundstrom and coworkers [151] and adapted to the analysis of femtosecond spectral evolution as monitored by the bond-twisting events in barrierless isomerization in solution. The theoretical derivation of Aberg et al. establishes a link between the Smoluchowski equation with a sink and the Schrodinger equation of a solute coupled to a thermal bath. The reader is referred to this important work for further theoretical details and a thorough description of the experimental set up. It is sufficient to say here that the classical link is established via the Hamilton-Jacobi equation formalism. By using the standard ansatz Xn(X,t)= A(X,i)cxp(S(X,t)/i1l), where S(X,t) is the action of the dynamical system, and neglecting terms in once this... 

Aberg, U., Akesson, E., Alvarez, J.-L., Fedchenia, I. and Sundstrom, V. Femtosecond spectral evolution monitoring the bond- twisting event in barrierless isomerization in solution, Chem.Phys., 183 (1994), 269-288... 

Such effects are very clearly demonstrated in the calculation of Jean [25] on a model for barrierless isomerization, intended to capture some of the essential features of isomerization in rhodopsins [17], A 25-fs pulse populates the initial state and Fig. 6 shows the decay of population of that... 

As discussed in Section II.A, Eisenthal and coworkers have studied the related problem of isomerization at liquid-solid interfaces. They used time-resolved second harmonic generation to investigate the barrierless photoisomerization of malachite green at the silica-aqueous interface using femtosecond time-resolved second harmonic generation [26]. They found that the photoisomerization reaction proceeded but was an order of magnitude slower at the water-silica interface than in bulk solution. 

In summary, we may say that the NBO/NRT description of partial proton transfer in the equilibrium H-bonded complex(es) is fully consistent with the observed behavior along the entire proton-transfer coordinate, including the transition state. At the transition state the importance of partial co valency and bond shifts can hardly be doubted. Yet the isomeric H-bonded complexes may approach the TS limit quite closely (within 0.2 kcal mol-1 in the present example) or even merge to form a single barrierless reaction profile (as in FHF- or H502+). Hence, the adiabatic continuity that connects isomeric H-bond complexes to the proton-transfer transition state suggests once more the essential futility of attempting to describe such deeply chemical events in terms of classical electrostatics. 

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). 

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. 

Seitz and East selected five isomeric protonated octane isomers (CgH "1"), all featuring C—H—C or C—H—H 3c-2e bonds for their theoretical studies (ab initio calculations at the MP2/6-3 lG(d) level of theory).847 In most cases, dissociation into ion-molecule complexes was found to be again barrierless. Proton affinities of C—C and C—H bonds are in the range 154—187 kcal mol 1 and 139-150kcalmol-1, respectively. 

The cycloaddition reaction of singlet GeX2 (X = F, Cl) with formaldehyde was studied employing the HF/6-311+G theory.106 The reaction proceeds in two steps barrierless formation of an intermediate complex followed by rate-determining isomerization to form the product. The results were compared with those from other cycloadditions of germylenes and silylenes. 

The presence in the excited state of competing channels that are barrierless or nearly barrierless (see model surface in Figure 4b) is an interesting feature of longer protonated Schiff bases.39-112 Here we characterize the Sj MEPs of both these isomerization processes. 

In Figure 29 we report the two MEPs. Again the structure of such paths is similar to the one of Figure 23 but with a longer energy plateau (from 1 to 3 a.u. (bohr) and from 1 to 5 a.u. for the C2-C3 and C4-C5 isomerization, respectively). The two paths are nearly barrierless with only a small (<1 kcal/mol)... 

An isomerization model in which arguments were presented to show that rhodopsin and bathorhodopsin are interconvertible via a common, barrierless, thermally re-... 

Besides solving the quantum yield enigma, this concept also rationalizes some other results. If rotation is inhibited by, say, structural design as, for instance, in azobenzenophanes or constraint from outside as, for instance, in restricted spaces as in iS-cyclodextrin " or zeolites or in solid matrices or low temperature down to 4 K, then the internal conversion from the (7i,7t ) to the (n,7t ) state provides a virtually barrierless path of isomerization. The fact that the stilbenophane analogue of Tamaoki s azobenzeno-phane shows isomerization does not invalidate this reasoning—the azobenzenes choose the easiest isomerization path. 

The radiationless decay has been investigated by ultrafast polarization spectros-copy [44] and time-resolved fluorescence [45,46]. The results confirm that the radiationless decay occurs by an ultrafast internal conversion, due to intramolecular motion about the bridging bond of the chromophore in the excited state, that the isomerization is nearly barrierless, and that there is only a very weak dependence on medium viscosity, thereby implying that the isomerization occurs by a volume-conserving motion such as a hula twist [47]. 

The reaction heat (at O K) is assumed to be zero (Q = 0),since it follows from an analysis by ROSENPELD et al./195/, which shows that during the reaction a barrierless cis-trans isomerization of retinal in the excited singlet state (S ) of rhodopsin takes place. This conclusion is in agreement with the theoretical calculations of SALEM and BRUCKMANN /196/ and WARSHEL /194/. 

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