Transition states types

No catalyst has an infinite lifetime. The accepted view of a catalytic cycle is that it proceeds via a series of reactive species, be they transient transition state type structures or relatively more stable intermediates. Reaction of such intermediates with either excess ligand or substrate can give rise to very stable complexes that are kinetically incompetent of sustaining catalysis. The textbook example of this is triphenylphosphine modified rhodium hydroformylation, where a plot of activity versus ligand metal ratio shows the classical volcano plot whereby activity reaches a peak at a certain ratio but then falls off rapidly in the presence of excess phosphine, see Figure... 

In the alkylation of benzene with long-chain a-olefins (Ce, Cg, C12, etc ), the large-pore zeolites mordenite, beta-zeolite, and ZSM-12 favor the less bulky 2-phenyl isomers. HY and rare-earth-Y produce a mixture of other -alkylbenzene isomCTS. Shiqie selectivity is attributed here to both product- and restricted transition state type selectivities [76]. 

The importance of transition state-type selectivity was first demonstrated by Csic-sery. In the reaction of 1-methyl — 2-ethylbenzene over mordenite, the amounts of 1,3-dimethyl — 5-ethylbenzene and 1 -methyl — 3,5-dimethylbenzene were very small where the 1,3,5-trialkylbenzenes are the main components at equilibrium. It was concluded that symmetrical trialkylbenzenes cannot form in the pores of H-mordenite too little space is available for diphenylmethane-type intermediates in transition states leading to symmetriccd isomers. The other trialkylbenzene isomers can form because their transition states are smtiller. 

The gas-phase thermal elimination of 2,2-diethoxypropane provided ethanol, acetone, and ethylene, while 1,1-diethoxycyclohexane yielded 1-ethoxycyclohexene and ethanol. " The elimination reactions are homogeneous, unimolecular, and follow a first-order rate law. Theoretical calculations using DPT methods demonstrated that the elimination reactions of 2,2-diethoxypropane and 1,1-diethoxycyclohexane proceed through a concerted nonsynchronous four-membered cyclic transition state type of mechanism for which elongation of the C-O bond is a rate hmiting factor. The intermediate product of 2,2-diethoxypropane elimination, 2-ethoxypropene, further decomposes through a concerted cyclic six-membered cychc transition state. 

It may be iisefiil to mention here one currently widely applied approximation for barrierless reactions, which is now frequently called microcanonical and canonical variational transition state theory (equivalent to the minimum density of states and maximum free energy transition state theory in figure A3,4,7. This type of theory can be understood by considering the partition fiinctions Q r ) as fiinctions of r similar to equation (A3,4.108) but with F (r ) instead of V Obviously 2(r J > Q so that the best possible choice for a... 

Variational RRKM calculations, as described above, show that a imimolecular dissociation reaction may have two variational transition states [32, 31, 34, 31 and 36], i.e. one that is a tight vibrator type and another that is a loose rotator type. Wliether a particular reaction has both of these variational transition states, at a particular energy, depends on the properties of the reaction s potential energy surface [33, 34 and 31]- For many dissociation reactions there is only one variational transition state, which smoothly changes from a loose rotator type to a tight vibrator type as the energy is increased [26],... 

Adopting the view that any theory of aromaticity is also a theory of pericyclic reactions [19], we are now in a position to discuss pericyclic reactions in terms of phase change. Two reaction types are distinguished those that preserve the phase of the total electi onic wave-function - these are phase preserving reactions (p-type), and those in which the phase is inverted - these are phase inverting reactions (i-type). The fomier have an aromatic transition state, and the latter an antiaromatic one. The results of [28] may be applied to these systems. In distinction with the cyclic polyenes, the two basis wave functions need not be equivalent. The wave function of the reactants R) and the products P), respectively, can be used. The electronic wave function of the transition state may be represented by a linear combination of the electronic wave functions of the reactant and the product. Of the two possible combinations, the in-phase one [Eq. (11)] is phase preserving (p-type), while the out-of-phase one [Eq. (12)], is i-type (phase inverting), compare Eqs. (6) and (7). Normalization constants are assumed in both equations ... 

A simple VB approach was used in [75] to describe the five structures. Only the lowest energy spin-pairing structures I (B symmehy) of the type (12,34,5 were used (Fig. 21). We consider them as reactant-product pairs and note that the transformation of one structure (e.g., la) to another (e.g., Ib) is a thr ee-electron phase-inverting reaction, with a type-II transition state. As shown in Figure 22, a type-II structure is constructed by an out-of-phase combination of... 

Type-n structures are formally the out-of-phase transition states between two type-I structures, even if there is no measurable banier. 

The key to the correct answer is the fact that the conversion of one type-V (or VI) structures to another is a phase-inverting reaction, with a 62 species transition state. This follows from the obseiwation that the two type-V (or VI) stiucture differ by the spin pairing of four electrons. Inspection shows (Fig. 28), that the out-of-phase combination of two A[ structmes is in fact a one,... 

Figure 31 shows the proposed Longuet-Higgins loop for the cyclopentadienyl cation. It uses the type-VI Ai anchors, with the type-VII B structures as transition states between them. This situation is completely analogous to that of the radical (Fig. 23). Since the loop is phase inverting, a conical intersection should be located at its center—as required by the Jahn-Teller theorem.

IlyperChem supplies two differeiii types or algorithms for transition state search eigenvector I ollowing and synchronous transit (linear and quadratic search ). 

Transition state theory calculations present slightly fewer technical difficulties. However, the accuracy of these calculations varies with the type of reaction. With the addition of an empirically determined correction factor, these calculations can be the most readily obtained for a given class of reactions. 

Dewar s treatment of transition state structure, using reactivity numbers, has the logical defect that in the intermediate kinds of transition states for which it provides evidence the electron localisation is only partial. However, in obtaining the values of the reactivity numbers (which are approximate localization energies), the process of localization is considered to be complete thus, values of parameters which strictly are relevant only to the Wheland type of transition state are incorporated into a different model. ... 

The best-known equation of the type mentioned is, of course, Hammett s equation. It correlates, with considerable precision, rate and equilibrium constants for a large number of reactions occurring in the side chains of m- and p-substituted aromatic compounds, but fails badly for electrophilic substitution into the aromatic ring (except at wi-positions) and for certain reactions in side chains in which there is considerable mesomeric interaction between the side chain and the ring during the course of reaction. This failure arises because Hammett s original model reaction (the ionization of substituted benzoic acids) does not take account of the direct resonance interactions between a substituent and the site of reaction. This sort of interaction in the electrophilic substitutions of anisole is depicted in the following resonance structures, which show the transition state to be stabilized by direct resonance with the substituent ... 

Streitwieser pointed out that the eorrelation whieh exists between relative rates of reaetion in deuterodeprotonation, nitration, and ehlorination, and equilibrium eonstants for protonation in hydrofluorie aeid amongst polynuelear hydroearbons (ef. 6.2.3) constitutes a relationship of the Hammett type. The standard reaetion is here the protonation equilibrium (for whieh p is unity by definition). For eon-venience he seleeted the i-position of naphthalene, rather than a position in benzene as the referenee position (for whieh o is zero by definition), and by this means was able to evaluate /) -values for the substitutions mentioned, and cr -values for positions in a number of hydroearbons. The p -values (for protonation equilibria, i for deuterodeprotonation, 0-47 for nitration, 0-26 and for ehlorination, 0-64) are taken to indieate how elosely the transition states of these reaetions resemble a cr-eomplex. 

A different explanation of the high 0 -ratios is based on the view, for which there is some evidence, that in a transition state for substitution which resembles the Wheland intermediate in structure there is a larger positive charge at the - than at the o-position. Substituents of the present type would therefore stabilise the transition state more from the 0-than from the -position. ... 

Another quantitative approach to the reactivity of thiazole (381) in reactions involving a cationic transition state, though not exactly of the electrophilic substitution type, deserves to be mentioned here because of... 

Free-radical reactivity of thiazole has been calculated by semiempirical methods, and results free valence and localization energy) have been compared with experimental data. For mono- and dimethylthiazoles the radical localization energy of the unsubstituted position may be correlated with the logarithm of experimental reactivity (180, 200). The value of the slope shows that a Wheland-type complex is involved in the transition state. 

Step 2 of the mechanism m Figure 6 12 is a nucleophilic attack by Br at one of the carbons of the cyclic bromonium ion For reasons that will be explained m Chapter 8 reactions of this type normally take place via a transition state m which the nude ophile approaches carbon from the side opposite the bond that is to be broken Recall mg that the vicinal dibromide formed from cyclopentene is exclusively the trans stereoisomer we see that attack by Br from the side opposite the C—Br bond of the bromonium ion intermediate can give only trans 1 2 dibromocyclopentane m accordance with the experimental observations... 

Reactions of this type are rather rare and seem to proceed in a stepwise fashion rather than by way of a concerted mechanism involving a single transition state... 

The bond highlighted m yellow is the peptide bond ) Pencyclic reaction (Section 10 12) A reaction that proceeds through a cyclic transition state Period (Section 1 1) A honzontal row of the penodic table Peroxide (Section 6 8) A compound of the type ROOR Peroxide effect (Section 6 8) Reversal of regioselectivity oh served m the addition of hydrogen bromide to alkenes brought about by the presence of peroxides m the reaction mixture... 

Potential energy diagram (Section 4 8) Plot of potential en ergy versus some arbitrary measure of the degree to which a reaction has proceeded (the reaction coordinate) The point of maximum potential energy is the transition state Primary alkyl group (Section 2 13) Structural unit of the type RCH2— in which the point of attachment is to a pnmary carbon... 

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