Transition state for

To detemiine k E) from equation (A3.12.9) it is assumed that transition states with positivefomi products. Notmg that / f = p dqf/dt, where p is the reduced mass of the separating fragments, all transition states that lie within and + dq with positive will cross the transition state toward products in the time interval dt = pj dqf p. Inserting this expression into equation (A3.12.9), one finds that the reactant-to-product rate (i.e. flux) through the transition state for momenPim p is... 

The tenn (E-E ) is tire sum of states at the transition state for energies from 0 to E-E. Equation (A3.12.15) is the RRKM expression for the imimolecular rate constant. 

The classical counterpart of resonances is periodic orbits [91, 95, 96, 97 and 98]. For example, a purely classical study of the H+H2 collinear potential surface reveals that near the transition state for the H+H2 H2+H reaction there are several trajectories (in R and r) that are periodic. These trajectories are not stable but they nevertheless affect strongly tire quantum dynamics. A study of tlie resonances in H+H2 scattering as well as many other triatomic systems (see, e.g., [99]) reveals that the scattering peaks are closely related to tlie frequencies of the periodic orbits and the resonance wavefiinctions are large in the regions of space where the periodic orbits reside. 

Sadeghi R and Skodje R T 1995 Barriers, thresholds and resonances—spectral quantization of the transition state for the collinear D + H2 reaction J. Chem. Phys. 102 193... 

Point B isa ina.xiiiium along the path from A to C (saddle point). I h e forces on th e atom s are also zero for th is structure. Poin t B rep-resentsa transition state for the Iran sforrn atiori of A to C. 

Example Hthanc is stable in the staggered gauche) con formation. The transition state for rotating a methyl group in ethane has the eclipsed con form at ion, A gcom etry optim i/ation start in g from an eclipsed eon formation yields th e tran sition state. 

Noyori "Open" Transition State for non-Chelation Control Aldols... 

The regioselectivity benefits from the increased polarisation of the alkene moiety, reflected in the increased difference in the orbital coefficients on carbon 1 and 2. The increase in endo-exo selectivity is a result of an increased secondary orbital interaction that can be attributed to the increased orbital coefficient on the carbonyl carbon ". Also increased dipolar interactions, as a result of an increased polarisation, will contribute. Interestingly, Yamamoto has demonstrated that by usirg a very bulky catalyst the endo-pathway can be blocked and an excess of exo product can be obtained The increased di as tereo facial selectivity has been attributed to a more compact transition state for the catalysed reaction as a result of more efficient primary and secondary orbital interactions as well as conformational changes in the complexed dienophile" . Calculations show that, with the polarisation of the dienophile, the extent of asynchronicity in the activated complex increases . Some authors even report a zwitteriorric character of the activated complex of the Lewis-acid catalysed reaction " . Currently, Lewis-acid catalysis of Diels-Alder reactions is everyday practice in synthetic organic chemistry. 

Wheland intermediate (see below) as its model for the transition state. In this form it is illustrated by the case mentioned above, that of nitration of the phenyltrimethylammonium ion. For this case the transition state for -nitration is represented by (v) and that for p-substitution by (vi). It is argued that electrostatic repulsions in the former are smaller than in the latter, so that m-nitration is favoured, though it is associated rvith deactivation. Similar descriptions can be given for the gross effects of other substituents upon orientation. 

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 influence of alkyl groups has been attributed to the +/ effect operating primarily at the 0- and />-positions (i), and somewhat less strongly at the m-position by relay. Alternatively, the effect is seen as stabilising the transition states for 0- and />-substitution (ii), more than... 

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. ... 

The transition state for this step involves partial bond formation between tert butyl cation and chloride ion... 

With the potential energies shown on a common scale we see that the transition state for formation of (CH3)3C is the highest energy point on the diagram A reaction can proceed no faster than its slowest step which is referred to as the rate determining step In the reaction of tert butyl alcohol with hydrogen chloride formation of the... 

The major difference between the two mechanisms is the second step The second step m the reaction of tert butyl alcohol with hydrogen chloride is the ummolecular dis sociation of tert butyloxonium ion to tert butyl cation and water Heptyloxonium ion however instead of dissociating to an unstable primary carbocation reacts differently It IS attacked by bromide ion which acts as a nucleophile We can represent the transition state for this step as... 

This behavior stems from the greater stability of secondary compared with primary free radicals The transition state for the step m which a chlorine atom abstracts a hydro gen from carbon has free radical character at carbon... 

FIGURE 5 8 Methyl migration in 1 2 2 tnmethylpropyl cation Structure (a) is the initial second ary carbocation structure (b) is the transition state for methyl migration and structure (c) is the final tertiary carbocation... 

Step 2 The 7C complex rearranges to an organoborane Hydrogen migrates from boron to carbon carrying with it the two electrons m its bond to boron Development of the transition state for this process is shown m 2(a) and its transformation to the organoborane is shown m 2(b)... 

Representation of transition state for migration of carbon from boron to oxygen... 

Table 6 3 shows that the effect of substituents on the rate of addition of bromine to alkenes is substantial and consistent with a rate determining step m which electrons flow from the alkene to the halogen Alkyl groups on the carbon-carbon double bond release electrons stabilize the transition state for bromonium ion formation and increase the reaction rate... 

Peroxy acid and alkene Transition state for oxygen transfer from the OH group of the peroxy acid to the alkene Acetic acid and epoxide ... 

FIGURE 9 5 (a) Curved arrow notation and (b) transition state for electrophilic addition of a hydrogen halide HXto an alkyne... 

FIGURE 10 6 Confor mations and electron delo calization in 1 3 butadiene The s CIS and the s trans con formations permit the 2p or bitalsto be aligned parallel to one another for maxi mum TT electron delocaliza tion The s trans conformation is more stable than the s CIS Stabilization resulting from tt electron de localization is least in the perpendicular conformation which IS a transition state for rotation about the C 2—C 3 single bond The green and yellow colors are meant to differentiate the orbitals and do not indicate their phases... 

Transition state for formation of 3 bromo 1 butene IS of lower energy than transition state for formation of 1 bromo 2 butene... 

HOMO of one ethylene mol ecule and the LUMO of an other do not have the proper symmetry to permit two O bonds to be formed in the same transition state for concerted cycloaddition... 

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