Transition state multiple

The inner multiple integral is the transition state s density of states at energy , and also the numerator in... 

Chesnavich W J, Bass L, Su T and Bowers M T 1981 Multiple transition states in unimolecular reactions a transition state switching model. Application to C Hg" J. Chem. Rhys. 74 2228—46... 

Song K and Chesnavich W J 1989 Multiple transition states in chemical reactions variational transition state theory studies of the HO2 and HeH2 systems J. Chem. Rhys. 91 4664-78... 

Hammes-Schiffer S and Tully J C 1995 Nonadiabatic transition state theory and multiple potential energy surfaces molecular dynamics of infrequent events J. Chem. Phys. 103 8528... 

Miller W H 1983 Symmetry-adapted transition-state theory and a unified treatment of multiple transition states J. Phys. Chem. 87 21... 

Miller first used Eq. (7-41) to correlate multiple variations, and this approach has more recently been subjected to considerable development. Many cross-interaction constants have been evaluated multiple regression analysis is one technique, but Miller and Dubois et ah discuss other methods. Lee et al. consider Pxy to be a measure of the distance between groups x and y in the transition state... 

The ortho effect may consist of several components. The normal electronic effect may receive contributions from inductive and resonance factors, just as with tneta and para substituents. There may also be a proximity or field electronic effect that operates directly between the substituent and the reaction site. In addition there may exist a true steric effect, as a result of the space-filling nature of the substituent (itself ultimately an electronic effect). Finally it is possible that non-covalent interactions, such as hydrogen bonding or charge transfer, may take place. The role of the solvent in both the initial state and the transition state may be different in the presence of ortho substitution. Many attempts have been made to separate these several effects. For example. Farthing and Nam defined an ortho substituent constant in the usual way by = log (K/K ) for the ionization of benzoic acids, postulating that includes both electronic and steric components. They assumed that the electronic portion of the ortho effect is identical to the para effect, writing CTe = o-p, and that the steric component is equal to the difference between the total effect and the electronic effect, or cts = cr — cte- They then used a multiple LFER to correlate data for orrAo-substituted reactants. 

State Multiplicity Symr Modern Terminology netry Mulliken s Terminology Transition... 

For reactions of A-acyliminium ions with alkenes and alkynes one has to distinguish between A-acyliminium ions locked in an s-trans conformation and those which (can) adopt an s-cis conformation. The former type reacts as a (nitrogen stabilized) carbocation with a C —C multiple bond. Although there are some exceptions, the intramolecular reaction of this type is regarded as an anti addition to the 7t-nucleophile, with (nearly) synchronous bond formation, the conformation of the transition state determining the product configuration. 

How can one formulate a mechanism for a chain reaction when the rate law does not provide the composition of the transition state The process is an inexact one, but this guidance may be helpful. Factor the rate law mentally into components that suggest the multiplication of one reagent by one intermediate. Thus, for Eqs. (8-20)-(8-23), we might rewrite Eq. (8-24) to read... 

Many reactions involve multiple transition states, each with an associated change in free energy. For these reactions, the ovetaU AG teptesents the sum of all of the free energy changes associated with the fotmation and decay of all of the ttansition states. Therefore, it is not possible to infer from the overall AG the number or type of transition states through which the reaction proceeds. Stated another way overall thermodynamics tells us nothing about kinetics. 

Figure 12 (from the chapter Exploring Multiple Reaction Paths to a Single Product Channel ). Two-dimensional cut through the potential surface for fragmentation of the transition state [OH CH3 ] complex as a function of the CF bond length and the FCO angle. All other coordinates are optimized at each point of this PES. Pathway 1 is the direct dissociation, while pathway 2 leads to the hydrogen-bonded [CH3OH F ] structure. The letter symbols correspond to configurations shown in Fig. 11. Reprinted from [63] with permission from the American Association for the Advancement of Science.

In the case of n-butene isomerization it was demonstrated (Figure 2) that the ideal micro-pore topology led to retardation of the C8 dimer intermediate and that the catalyst based on the ferrierite structure was close to optimal in this respect [1). For selective isodewaxing a one-dimensional pore structure which constrained the skeletal isomerization transition state and thereby minimized multiple branching such as the SAPO-11 structure was found to meet these criteria. Clearly, these are ideal systems in which to apply computational chemistry where the reactant and product molecules are relatively simple and the micro-porous structures are ordered and known in detail. 

The X-ray structure of the dibromine complex with toluene (measured at 123 K) is more complicated, and shows multiple crystallographically independent donor/acceptor moieties [68]. Most important, however, is the fact that in all cases the acceptor shows an over-the-rim location that is similar to that in the benzene complex. In both systems, the acceptor is shifted by 1.4 A from the main symmetry axis, the shortest Br C distances of 3.1 A being significantly less than the sum of the van der Waals radii of 3.55 A [20]. Furthermore, the calculated hapticity in the benzene/Br2 complex (x] = 1.52) is midway between the over-atom (rj = 1.0) and over-bond (rj = 2.0) coordination. In the toluene complex, the latter varies from rj = 1.70 to 1.86 (in four non-equivalent coordination modes) and thus lies closer to the over-bond coordination model. Moreover, the over-bond bromine is remarkably shifted toward the ortho- and para-carbons that correspond to the positions of highest electron density (and lead to the transition states for electrophilic aromatic bromination [12]). Such an experimental location of bromine is in good agreement with the results of high level theoretical... 

Although fccat is a composite rate constant, representing multiple chemical steps in catalysis, it is dominated by the rate-limiting chemical step, which most often is the formation of the bound transition state complex ES from the encounter complex ES. Thus, to a first approximation, we can consider kCM to be a first-order rate constant for the transition from ES to ES ... 

The intramolecular rearrangement of allylic boranes (Eq. 5) clearly involves a multiple boron-carbon bond in the transition state (45), as the boron 2pz-orbital interacts with the 7r-bonding MO. 

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