Transition states definition

In reactions at the sulfur atom of a sulfinate ion to form a sulfone, of a sulfoxide to form R3S+—0, or of bisulfite ion to form a sulfonic acid, the fractionally positive sulfur becomes more positively charged in the poly-ionic transition states. Definitive experimental evidence... 

For transition state searches, none of the above updates is particularly appropriate as a positive definite Hessian is not desired. A more usefiil update in this case is the Powell update [16] ... 

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. 

More definitive evidence for the formation of an oxirene intermediate or transition state was presented recently by Cormier 80TL2021), in an extension of his earlier work on diazo ketones 77TL2231). This approach was based on the realization that, in principle, the oxirene (87) could be generated from the diazo ketones (88) or (89) via the oxocarbenes 90 or 91) or from the alkyne (92 Scheme 91). If the carbenes (90) (from 88) and (91) (from 89) equilibrate through the oxirene (87), and if (87) is also the initial product of epoxidation of (92), then essentially the same mixture of products (hexenones and ketene-derived products) should be formed on decomposition of the diazo ketones and on oxidation of the alkyne this was the case. 

That is, terms of the form (1 — jr -I- jr< )/) appear in the denominator for all reactant sites having exchangeable protons and similarly in the numerator for all transition state sites. If there is no change in the fractionation factor for a site, its contribution cancels. If the solvent is a reactant, its term disappears because the solvent fractionation factor is unity by definition. 

Next we turn to the magnitudes of the p constants. Evidently if p = 0, there is no substituent effect on reactivity. Moreover because p = -I-1.000 by definition for the aqueous ionization of benzoic acids, we have a scale calibration of sorts. Wiberg gives examples of p as a measure of the extent of charge development in the transition state. McLennan" has pointed out that p values must first be adjusted for the transmission factor before they can be taken as measures of charge devel-... 

An IRC calculation examines the reaction path leading down from a transition structure on a potential energy surface. Such a calculation starts at the saddle point and follows the path in both directions from the transition state, optimizing the geometry of the molecular system at each point along the path. In this way, an IRC calculation definitively connects two minima on the potential energy surface by a path which passes through the transition state between them. 

Probably the most important development of the past decade was the introduction by Brown and co-workers of a set of substituent constants,ct+, derived from the solvolysis of cumyl chlorides and presumably applicable to reaction series in which a delocalization of a positive charge from the reaction site into the aromatic nucleus is important in the transition state or, in other words, where the importance of resonance structures placing a positive charge on the substituent - -M effect) changes substantially between the initial and transition (or final) states. These ct+-values have found wide application, not only in the particular side-chain reactions for which they were designed, but equally in electrophilic nuclear substitution reactions. Although such a scale was first proposed by Pearson et al. under the label of and by Deno et Brown s systematic work made the scale definitive. 

Dediazoniation does not show a significant solvent isotope effect ( h2o/ d2o = 0.98 0.01 Crossley et al., 1940 Swain et al., 1975 a). This result is definitely not consistent with a mechanism in which charge is built up on oxygen in the rate-limiting transition state, as expected for an ANDN-like process. 

As has been indicated, since there is a ring isotope effect there must be a degree of C-H bond breaking in the transition state of the rate-determining stage. Clearly further work is required in this system before a definitive mechanism can be established for the intramolecular rearrangement. 

When a reaction between two or more molecules has progressed to the point corresponding to the top of the curve, the term transition state is applied to the positions of the nuclei and electrons. The transition state possesses a definite geometry and charge distribution but has no finite existence the system passes through it. The system at this point is called an activated complex. ... 

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