Transition state, symmetric

Gershinsky G and Poliak E 1995 Variational transition state theory application to a symmetric exchange in water J. Chem. Phys. 103 8501... 

Symmetrical transition states are the lowest energy eon figuration w ithin th at syrn m etry. If a geometry optim i/ation starts off with in that sym m etry, th en th e calcu latio n can fin d th e trail sition state. 

Evans and co-workers investigated the effect of a number of -symmetric bis(oxazoline) ligands on the copper(II)-catalysed Diels-Alder reaction of an N-acyloxazolidinone with cyclopentadiene. Enantiomeric excesses of up to 99% have been reported (Scheme 3.4). Evans et al." suggested transition state assembly 3.7, with a square planar coordination environment around the central copper ion. In this scheme the dienophile should be coordinated predominantly in an cisoid fashion in... 

Symmetrical transition states are the lowest energy configuration within that symmetry. If a geometry optimization starts off within that symmetry, then the calculation can find the transition state. 

Furthermore, the situation becomes even worse for an asymmetric potential like that in (3.18), because at low temperature nearly the entire period p is spent on dwelling in the potential well (see appendix A), so that lim -oo < >ins = 0- In other words, unless the potential is strictly symmetric, the transition state position x tends to the minimum of the initial state It is natural to expect that the centroid approximation will work well when x does not deviate too far from x. To summarize, the centroid method is an instructive way to describe in a unique TST-like manner both the high [T > T ) and fairly low [T < T ) temperature regions, but it does not give a reliable estimate for k. ... 

Let us now turn to the surfaces themselves to learn the kinds of kinetic information they contain. First observe that the potential energy surface of Fig. 5-2 is drawn to be symmetrical about the 45° diagonal. This is the type of surface to be expected for a symmetrical reaction like H -I- H2 = H2 -h H, in which the reactants and products are identical. The corresponding reaction coordinate diagram in Fig. 5-3, therefore, shows the reactants and products having the same stability (energy) and the transition state appearing at precisely the midpoint of the reaction coordinate. 

Let us now consider a chemical reaction whose initial and final states are different. Then the potential energy surface will not be symmetrical. This geological analogy will be helpful Suppose the valleys are formed by erosion. Then the valley that has eroded faster (or for a longer time) will be both deeper and longer than the less eroded valley, with the necessary consequence that the saddle between the two valleys is shifted toward the shallower valley. Figure 5-4 shows such a surface on which the reactant valley is longer and deeper than the product valley clearly the transition state is located closer to the final state than to the initial state as a result of this disparity in stabilities. 

Now consider the position of the proton in the transition state, that is, the extent to which the proton has been transferred from A to B. First suppose H is equidistant from A and B in the transition state. Then the symmetric stretch consists of A and... 

If the proton is not equidistant between A and B, it will undergo some movement in the symmetric stretching vibration. Isotopic substitution will, therefore, result in a change in transition state vibrational frequency, with the result that there will be a zero-point energy difference in the transition state. This will reduce the kinetic isotope effect below its maximal possible value. For this type of reaction, therefore, should be a maximum when the proton is midway between A and B in the transition state and should decrease as H lies closer to A or to B. 

To account for the course of this reaction theoretical calculations of the coordination of ketomalonate 37 to copper(II) and zinc(II) have revealed that the six-membered ring system is slightly more stable than the five-membered ring system (Scheme 4.30). The coordination of 37 to catalyst (l )-39 shows that the six-membered intermediate is C2-symmetric with no obvious face-shielding of the carbonyl functionality (top), while for the five-membered intermediate (bottom) the carbonyl is shielded by the phenyl substituent. Calculations of the transition-state energy for the reaction of the two intermediates with 1,3-cyclohexadiene leads to the lowest energy for the five-membered intermediate this approach is in agreement with the experimental results [45]. 

The hetero-Diels-Alder reaction of formaldehyde with 1,3-butadiene has been investigated with the formaldehyde oxygen atom coordinated to BH3 as a model for a Lewis acid [25 bj. Two transition states were located, one with BH3 exo, and one endo, relative to the diene. The former has the lowest energy and the calculated transition-state structure is much less symmetrical than for the uncatalyzed reaction shown in Fig. 8.12. The C-C bond length is calculated to be 0.42 A longer, while the C-0 bond length is 0.23 A shorter, compared to the uncatalyzed reac-... 

Mechanistically the 1,3-dipolar cycloaddition reaction very likely is a concerted one-step process via a cyclic transition state. The transition state is less symmetric and more polar as for a Diels-Alder reaction however the symmetry of the frontier orbitals is similar. In order to describe the bonding of the 1,3-dipolar compound, e.g. diazomethane 4, several Lewis structures can be drawn that are resonance structures ... 

Although the above work showed that for the symmetrization reaction (and its reverse reaction) the mechanism is SE2 with two steps of dissimilar rate, a symmetrical transition state (XLIII),... 

The reaction of RHgX with HgX2, another exchange,23 can be accounted for by a symmetric transition state... 

Does the transition state composition for the RCS, [S04 H20], really follow from Eq. (8-48) Indeed, from Eq. (8-35), that is exactly the case. There is no indication in this circumstance that a chain mechanism operates. [Keep in mind, however, that this example is fictional, in that Eq. (8-47) is not important compared with Eq. (8-38).] Fractional-order dependences are not necessarily indicative of chains when the reagent is symmetric, like S20 , although the particular examples presented do happen to feature chain mechanisms. 

What we have shown here is the fact that large inverse values can be obtained for the Br2 addition to a "normal" olefin which should pass through a symmetrical, or nearly so, transition state. Of course, more work involving other systems would be beneficial in assessing the scope and limitation of the use of the a-deuterium kie s in mechanistic studies of Br2 and Br3 reactions with olefins. 

This rearrangement, which accounts for the scrambling, is completely stereospecific.The rearrangements probably take place through a nonplanar cyclobutyl cation intermediate or transition state. The formation of cyclobutyl and homoallylic products from a cyclopropyl-methyl cation is also completely stereospecific. These products may arise by direct attack of the nucleophile on 58 or on the cyclobutyl cation intermediate. A planar cyclobutyl cation is ruled out in both cases because it would be symmetrical and the stereospecificity would be lost. 

The chemical reactions through cyclic transition states are controlled by the symmetry of the frontier orbitals [11]. At the symmetrical (Cs) six-membered ring transition state of Diels-Alder reaction between butadiene and ethylene, the HOMO of butadiene and the LUMO of ethylene (Scheme 18) are antisymmetric with respect to the reflection in the mirror plane (Scheme 24). The symmetry allows the frontier orbitals to have the same signs of the overlap integrals between the p-or-bital components at both reaction sites. The simultaneous interactions at the both sites promotes the frontier orbital interaction more than the interaction at one site of an acyclic transition state. This is also the case with interaction between the HOMO of ethylene and the LUMO of butadiene. The Diels-Alder reactions occur through the cyclic transition states in a concerted and stereospecific manner with retention of configuration of the reactants. 

The frontier orbital interaction is forbidden by the symmetry for the dimerization of ethylenes throngh the rectangular transition state. The HOMO is symmetric and the LUMO is antisymmetric (Scheme 25a). The overlap integrals have the opposite signs at the reaction sites. The overlap between the frontier orbitals is zero even if each overlap between the atomic p-orbitals increases. It follows that the dimerization cannot occur throngh the fonr-membered ring transition states in a concerted and stereospecfic manner. 

The dienophiles may be treated in an analogous manner. For a substituted dienophile reacting with a symmetric diene through transition state 6, we may write... 

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