Relative free energies of activation

Fig. 28 Nucleophilic ring opening of cyclic dimethylammonium ions [38], Free energies of activation relative to ring-size 6 against cycloalkane strain-energies. Energy units kcal mol"1. (Reproduced with permission from Di Vona et al., 1985)...

The free energy of activation at the QCISD(T)/6-31 H-- -G(d,p) level amounts to 21.1 kcal/mol. According to the authors, the large electron density redistribution arising upon cyclization makes it necessary to use extended basis sets and high-order electron correlation methods to describe the gas-phase thermodynamics, which indicates clearly the gas-phase preference of the azido species. However, the equilibrium is shifted toward the tetrazole as the polarity of a solvent is increased. For instance, SCRF calculations (e = 78.4) yield a relative free energy of solvation with respect to the cw-azido isomer of —2.4 kcal/mol for the tmns-zziAo compound and of —6.8 kcal/mol for the tetrazole isomer. At a much lower level, the... 

The importance of solvation on reaction surfaces is evident in striking medium dependence of reaction rates, particularly for polar reactions, and in variations of product distributions as for methyl formate discussed above and of relative reactivities (18,26). Thus, in order to obtain a molecular level understanding of the influence of solvation on the energetics and courses of reactions, we have carried out statistical mechanics simulations that have yielded free energy of activation profiles (30) for several organic reactions in solution (11.18.19.31. ... 

Formation of a relatively stable carbocation is important in an SnI reaction => low free energy of activation (AGJ) for the slow step of the reaction. 

Figure 7.7 Free-energy diagrams for the formation of carbocations from protonated tertiary, secondary, and primary alcohols. The relative free energies of activation are tertiary < secondary primary.

In the example of the anodic oxidation of A, if aA = 1, the overpotential causes a Gibbs free energy change of the reactant state relative to the transition state, without altering the free energy of activation of the product state. Thus, the reactant A must... 

Another method for evaluating carbocation stability involves the measurement of solvolysis rates (14,45). Typically, the transition state of the rate-determining step in SN1 reactions is assumed to closely resemble the intermediate ion pair, on the basis of the Hammond postulate (46). Thus, the free energy of activation for this reaction, AG, reflects the relative thermodynamic stabilities of the intermediate carbocations. 

These results suggested examination of the buttressing effect in bromo compounds, so 1,2,3,4-tetrabromo- and l-bromo-9-(l,l-dimethyl-2-phenylethyl)-triptycenes were prepared. As expected, the tetrabromo compound had a relatively low barrier of 35.1 kcal/mol at 500 K. In contrast, the free energy of activation for rotation of the monobromo compound was 39.2 kcal/mol. The difference amounts to 4.1 kcal/mol (151). The reverse buttressing effect can be large if the substituents concerned are large. 

The relative rates of solvolysis of camphene hydrochloride and t-butyl chloride indicate that the free energy of activation is 5 kcal mole higher with the latter compound. This might be attributed either to non-classical stabilization of the camphenyl transition state... 

Pi)Ay /Rr. Thus, In 2 = (3000 - l)Ay /(82.05 X 298) = 5.7 cm. This exercise indicates that reaction rate is relatively insensitive to pressure changes if Ay is small. See Transition-State Theory Expressed in Thermodynamic Terms Gibbs Free Energy of Activation Enthalpy of Activation Entropy of Activation lUPAC (1979) Pure Appl. Chem. 51, 1725. 

E Initial kinetic energy of relative motion of reactants Electric vector of light A G° per mole Standard Gibbs free energy of activation... 

Fig. 11 Unimolecular decomposition pathways of 2-oxepinoxy radical (1). The relative free energies (298 K, kcal/mol) at the B3LYP/ 6-311 + G(d,p)//B3LYP/6-31G(d) level are shown for each intemiediate relative to 1, and each free energy of activation is relative to the reactant for that specific step, [courtesy of Michael Fadden (J Phys Chem A 2000 104 8121-8130) Reprinted with permission of J Phys Chem A.]...

Table 4 Comparison of reaction pathway energetics (kcal/mol) for benzylperoxy radical and 2-picolinylperoxy radical at 298 K, via B3LYP/6-311+G //B3LYP/6-31G. Numbers refer to pathways depicted in Fig. 18. All enthalpies and free energies are relative to the peroxy radical (2) when preceded by TS, the relative data are the enthalpy and free energies of activation...

Relative Free Energies of Activation of Olefins in Type II Photosensitized Oxygenation Reactions... 

---