Intrinsic free energy barriers

Among catalysts I-IV, which predominantly catalyze the generation of cyclodimer products, the overall lowest intrinsic free-energy barrier of 20.5 kcal mol-1 (AG nt) for 2a -> 8a appears for catalyst IV with L = P(OPh)3, where both electronic and steric factors are seen to assist the formation of VCH to a similar amount. Reductive elimination involves a higher intrinsic barrier (AG nt) for catalysts bearing moderately bulky, donor phosphines,... 

Relationships having the same form as eq 14 can also be written for the enthalpic and entropic contributions to the intrinsic free energy barriers (10). Provided that the reactions are adiabatic and the conventional collision model applies, eq 14 can be written in the familiar form relating the rate constants of electrochemical exchange and homogeneous self-exchange reactions (13) ... 

AGrxn = 0 [44]. The intrinsic free energy barrier AGl, which provides a reference barrier height, can be analytically expressed as [3]... 

We now turn to the isotope dependence of the FER, which will be important for the discussion of KIEs in Section 10.2.3. This dependence arises from the components AGIq and a of the FER. The isotope dependence of the intrinsic free energy barrier AGl, given by Eq. (10.4) is, as is apparent in Fig. 10.8(a), due solely to the difference in the H and D ZPEs... 

Endicott s group has measured and made an extremely detailed analysis of rate and equilibrium constants for transmethylation between various cobalt N4-macrocyclic systems (see Table 7.6 and accompanying structures). The reactions are first order in each reagent. Rates can vary by 10 (even for the back reactions where AG < 0). AG is analyzed into components, intrinsic free energy barriers to transmethylation being small for cobalt corrin and large for sterically hindered neutral macrocyclic complexes. Estimates for C0-CH3 bond energies are between 33 and 48 kcal mol the bond is stabilized by unsaturation in the N4 macrocycle, but is also very sensitive to stereochemistry. 

An intrinsic free energy of activation, which would exist if the reactants and products had the same AG° This is a kinetic part, called the intrinsic barrier AG ,... 

Overall, steric and electronic factors, which are seen to be small, are found to work in opposite directions and, to some degree, cancel each other out. Consequently, the intrinsic free activation barriers and reaction free energies (AG nt, AG nt), respectively, span a small range for catalysts I-IV and differ by less than l.Okcalmol-1. Thus, oxidative coupling represents the one process (beside allylic isomerization, cf. Section 5.3) among all the critical elementary steps of the C8-cyclodimer channel, that is least influenced by electronic and steric factors. 

It also is important to note that the aforementioned treatments of free-energy barriers refer only to weak-overlap reactions. This corresponds to the curve PAS in Fig. 1, where the transition-state energy is essentially unaffected (at least in a specific manner) by the proximity of the metal surface. When these reactant-electrode interactions become sufficiently strong and specific, marked decreases in both the inner- and outer-shell intrinsic barriers can be anticipated. This is discussed further in Sects. 3.5.1 and 4.6. 

In the framework of the assumption that the free-energy barrier is dependent on the two terms intrinsic barrier and the free energy of rearrangement (see above) one should consider the effect of steric factors on each component. Here only the intrinsic barrier steric effects will be discussed. 

This is the equation of Marcus, where AGq is the intrinsic kinetic energy barrier, i.e., the free energy of activation when AG->0. This barrier is given by... 

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