Barriers partners

The change in the inner-sphere structure of the reacting partners usually leads to a decrease in the transition probability. If the intramolecular degrees of freedom behave classically, their reorganization results in an increase in the activation barrier. In the simplest case where the intramolecular vibrations are described as harmonic oscillators with unchanged frequencies, this leads to an increase in the reorganization energy ... 

Reactions in solution proceed in a similar manner, by elementary steps, to those in the gas phase. Many of the concepts, such as reaction coordinates and energy barriers, are the same. The two theories for elementary reactions have also been extended to liquid-phase reactions. The TST naturally extends to the liquid phase, since the transition state is treated as a thermodynamic entity. Features not present in gas-phase reactions, such as solvent effects and activity coefficients of ionic species in polar media, are treated as for stable species. Molecules in a liquid are in an almost constant state of collision so that the collision-based rate theories require modification to be used quantitatively. The energy distributions in the jostling motion in a liquid are similar to those in gas-phase collisions, but any reaction trajectory is modified by interaction with neighboring molecules. Furthermore, the frequency with which reaction partners approach each other is governed by diffusion rather than by random collisions, and, once together, multiple encounters between a reactant pair occur in this molecular traffic jam. This can modify the rate constants for individual reaction steps significantly. Thus, several aspects of reaction in a condensed phase differ from those in the gas phase ... 

In this simplest type of addition reaction, a single interaction site at one of the partners can react with two possible sites of the other partner (Scheme 12.2). In general, two modes of attack (k —> i or k —> j) will have different reaction barrier introducing different kinetics and regioselectivity. 

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Extreme cases were reactions of the least stabilized, most reactive carbene (Y = CF3, X = Br) with the more reactive alkene (CH3)2C=C(CH3)2, and the most stabilized, least reactive carbene (Y = CH3O, X = F) with the less reactive alkene (1-hexene). The rate constants, as measured by LFP, were 1.7 x 10 and 5.0 X lO M s, respectively, spanning an interval of 34,000. In agreement with Houk s ideas,the reactions were entropy dominated (A5 —22 to —29e.u.). The AG barriers were 5.0 kcal/mol for the faster reaction and 11 kcal/ mol for the slower reaction, mainly because of entropic contributions the AH components were only —1.6 and +2.5 kcal/mol, respectively. Despite the dominance of entropy in these reactive carbene addition reactions, a kind of de facto enthalpic control operates. The entropies of activation are all very similar, so that in any comparison of the reactivities of alkene pairs (i.e., ferei)> the rate constant ratios reflect differences in AA//t, which ultimately appear in AAG. Thus, car-benic philicity, which is the pattern created by carbenic reactivity, behaves in accord with our qualitative ideas about structure-reactivity relations, as modulated by substiment effects in both the carbene and alkene partners of the addition reactions. " Finally, volumes of activation were measured for the additions of CgHsCCl to (CH3)2C=C(CH3)2 and frani-pentene in both methylcyclohexane and acetonitrile. The measured absolute rate constants increased with increasing pressure Ayf ranged from —10 to —18 cm /mol and were independent of solvent. These results were consistent with an early, and not very polar transition state for the addition reaction. 

The boat-boat (417) and the twist-boat-boat (418) have low torsional strains but severe non-bonded repulsions, which, as usual, are transferred to internal angle strains. However, heteroatoms can modify these repulsions and certain transannular interactions can drastically reduce them. Even so, the boat-boat family is relatively unimportant as its energy is calculated to be quite high (12 kj mol-1) in cyclooctane. It probably serves as an intermediate for certain conformational interconversions of the boat-chair, especially when the twist-boat-chair pseudorotation itinerary is of high energy. In cyclooctane the boat-boat and its twisted partner have nearly the same energies and are not separated by a significant barrier. 

At sufficiently high pressure, kum is typically independent of pressure. The high-pressure limit of the rate constant will be denoted kunji00. Intermolecular collisions of C with other C molecules or with other chemical species present in the gas provide the energy needed to surmount the barrier to reaction, such as the breaking of a bond. The partner in such collisions will be genetically denoted M. 

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

Suppose that there is an energetic barrier e that must be overcome for a reaction to occur, for example, the energy needed to break a critical chemical bond. The translational energy of the relative velocity of the collision partners is available to surmount the reaction energy barrier. We consider a simple picture called the line-of-centers model of reactive collisions. In this model only the velocity directed along the line-of-centers between the two molecules at the point of collision is effective in overcoming the barrier to reaction. 

Electronic transitions are optically forbidden only for large intemuclear distances r. For finite r, dipole transitions to the X 2 ground state are possible. They give rise to the well-known Hopfield continuum and 600-A emission and absorption bands.86 Only those collision partners that surmount the barrier of the ungerade potential are likely to radiate. The cross section for light emission65 is typically 10-4 A2, which is much too... 

It is commonly assumed, therefore, that solvent reorganization will dominate electron transfer kinetics and that the reorganization energy in the same medium will be constant within a series of closely related redox partners. With a value of 2.4 kcal/mole for solvent reorganization (as obtained by Rehm and Weller (7) for fluorescence quenching of a series of arenes by substituted anilines in a polar medium) the curve shown in Fig. 2 is obtained. It is clear that substantial solvent-dependent barrier to electron exchange can be encountered. 

By examination of the stereochemical consequences of decarboxylation, Cram and Haberfield8 obtained evidence for internal return of carbon dioxide to the carbanion, affecting the stereochemical outcome of these reactions. It is reasonable to consider that the barrier for the combination of the carbanion and carbon dioxide may be comparable to or lower than that for diffusion, in which case the reverse reaction will be a kinetically significant component in the overall rate of reaction. In such a case, a catalyst cannot deal with the direction of the reaction -if it lowers the transition state energy for the forward reaction, conservation of energy demands that it also lower the barrier for the reverse reaction. The energy for addition of the carbanion to carbon dioxide is also inherent. The reaction should occur readily if the reaction partners have reduced entropy. 

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