Internal free-energy barrier

In the i r-acetyl-7-azabicyclo[2.2.1]heptadiene derivative (12), restricted rotation about the N-CO bond makes the bridgehead hydrogen atoms at C-1 and C-4 nonequivalent, so that they give rise to two equal intensity signals in the NMR spectrum.N-Acetyl- and N-nitroso-7-azabicyclo[2.2.1]heptanes [(35) and (38)] show the same effect. From the coalescence temperatures (>50°) the free energy barriers to internal rotation were calculated to be 17.4, 17.1, and 16.5 kcal mole for 12,35, and 38, respectively. These values are slightly lower than those measured for analogous acyclic amine derivatives, A,A-dimethylaceta-mide and N,N,-dimethylnitrosamine, respectively. 

The distinction between kinetic and thermodynamic stability is important and is explained by the concept of the free energy of activation necessary to convert the substrate to its transition state. In order for the substrate to form products, its internal free energy must exceed a certain value i.e., it must surmount an energy barrier. The energy barrier is that of the free energy of the transition state, AG. The transition-state theory of reaction rates introduced by H. Eyring relates the rate of the reaction to the magnitude of AG. ... 

The barriers just described were calculated with 1-methylorotic acid (11) as a reference point to model the uncatalyzed reaction in solution. However, the computed free-energy barriers for decarboxylation of zwitterions 4b and 6b are 8.4 and 7.6 kcal mol-1, respectively. This difference of 0.8 kcal mol-1 is significantly smaller than the 6 kcal mol-1 difference calculated by Lee and Houk for the 2-protonation and 4-protonation pathways. This discrepancy arises from an internal hydrogen bond (12) between the Nl-H and the carboxylate that artificially stabilizes the 02-protonated zwitterion 4a, and renders its corresponding decarboxylation barrier too high. When the Nl-H is replaced by a methyl, the hydrogen bond is removed, and the ylide and carbene mechanisms become closer in energy nonetheless, 4-protonation is still favored. 

Crystallization in a sheared melt can also be described by the formalism introduced in the previous subsection in which the internal coordinate represents the coordinates of the center of mass of the crystallites and their number of monomers. The main influence of the flow on crystallization kinetics is to modify the free energy barrier, which is given by... 

Geometric mean approximation, 29 Germane barrier of internal rotation, 391 Gibbs, free energy, 30 function, 20... 

Table A4.6 gives the internal rotation contributions to the heat capacity, enthalpy and Gibbs free energy as a function of the rotational barrier V. It is convenient to tabulate the contributions in terms of VjRTagainst 1/rf, where f is the partition function for free rotation [see equation (10.141)]. For details of the calculation, see Section 10.7c.

Ito and his co-workers (51) noticed that an adduct (14) of tropone with iV-ethoxycarbonylazepine appeared to undergo slow internal rotation by H NMR, the barrier at 83°C being 18.3 kcal/mol. As was discussed earlier, the ethoxy-carbonyl group gives a lower barrier than those of acetyl and formyl derivatives. Indeed, by changing the /V-substitutent from ethoxycarbonyl to acetyl, the barrier was raised to 20.0 kcal/mol. The formyl derivative showed a barrier to rotation of 23.0 kcal/mol at 20°C. It was possible to isolate a pure Z isomer and a nearly pure E isomer of the formyl derivative (15) by TLC. The free energy of activation... 

The description of the chain dynamics in terms of the Rouse model is not only limited by local stiffness effects but also by local dissipative relaxation processes like jumps over the barrier in the rotational potential. Thus, in order to extend the range of description, a combination of the modified Rouse model with a simple description of the rotational jump processes is asked for. Allegra et al. [213,214] introduced an internal viscosity as a force which arises due to a transient departure from configurational equilibrium, that relaxes by reorientational jumps. Thereby, the rotational relaxation processes are described by one single relaxation rate Tj. From an expression for the difference in free energy due to small excursions from equilibrium an explicit expression for the internal viscosity force in terms of a memory function is derived. The internal viscosity force acting on the k-th backbone atom becomes ... 

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