Entropy barriers

Pathways through abstraction and addition-elimination mechanisms may lead to the same product channel. However, they will only compete significantly when the energy and entropy barriers (or free energy barriers AG = AH — TAS) for the two mechanisms are comparable. In these cases, they make excellent candidates for multiple pathway studies because several experimental approaches discussed in Section III are suited to detect the competition. 

In some cases presented here, each pathway follows a traditional route through wells and/or over saddle points toward products. In these cases, a competition arises because the rate-limiting energy and entropy barriers of the... 

Zero-Temperature Relaxation. This interpretation rationalizes the aging behavior found in exactly solvable entropy barrier models that relax to the ground state and show aging at zero temperature [190, 191]. At T = 0, the stimulated process is suppressed (microscopic reversibility, Eq. (8), does not hold), and Eq. (204) holds by replacing the free energy of a CRR by its energy, F = E. In these models a region corresponds to just a... 

A. Crisanti and F. Ritort, A glass transition scenario based on heterogeneities and entropy barriers. Philos. Mag. B 82, 143-149 (2002). 

The pentamer of tetrafluoroethene (66) (Scheme 29) is an unusual example of type (96) and reacts readily with nucleophiles [129] (Scheme 65). In contrast, (66) undergoes a remarkable reaction with aqueous triethylamine, producing the dihydrofuran derivative (101) and the process formally involves a direct intramolecular displacement of fluorine from a saturated site and a mechanism has been advanced (Scheme 66) which accounts for the product formed [126]. Understandably, this process is not easily accepted [3, 130] because it has essentially no precedent. Indeed, it is well established that nucleophilic displacement from saturated sites in fluorocarbons occurs only in exceptional circumstances. Consequently, other mechanisms have been advanced, which seem no more convincing [3, 130]. It should be remembered that the major point in favour of the step (100) to (101) (Scheme 66) is that the nucleophile is generated in close proximity to the reaction centre because of the special geometry of this situation. Consequently, much of the otherwise high energy/entropy barrier has already been overcome in this case. 

As we have already mentioned, intramolecular reactions generally proceed faster compared to their intermolecular versions because of the substantial reduction in the entropy barrier. Therefore it is not surprising that intra-... 

From the variable temperature H-NMR spectrum Saunders found = 11.8 kcalmol" and A = 12.3 s for the degenerate rearrangement of bullvalene. The remarkably small probability and entropy barriers to the rearrangements that involve both carbon-carbon bond breaking and making were ascribed both to extremely favourable geometry and to weakness of the bond . These values were amended slightly... 

Molecular modeling of the P-NH" coordinated complex indeed suggests that the proton can point into the /r-electron cloud of the Pd-alkenyl moiety, bringing the proton right to the spot for protonolysis of the palladium-alkenyl bond. This can be seen as lowering the entropy barrier of activation in the protonolysis step. The... 

H.-X. Zhou and R. Zwanzig (1991) A rate process with an entropy barrier. J. Chem. Phys., 94, pp. 6147-6152... 

On the other hand, if P contains several different minima of the energy separated by high-energy (or low-entropy) barriers, then the sample may well include only configurations from one of these regions, selected by choice of the initial configuration. In that case it is imperative to ensure that subsequent simulation will take place in the most populated low-energy area of P. 

The entropy barrier for A and B to make a complex AB is large when there ate a lot of non-ieactive A and B positions, and only a few that lead to formation of the complex. 

---