Energies of Transition States

Calculate activation energies for the three Diels-Alder reactions (energy of transition state - sum of energies of reactants). Which reaction has the smallest energy barrier Which has the largest energy barrier Do your results parallel the measured relative rates of the same reactions (see table at left) ... 

In many cases the most interesting results of a computational study are the relative energies of transition states and intermediates because they determine the reaction mechanism. In this section we will try to outline when improved active-site geometries can be expected to have important effects on relative energies. 

Data for the 4-chlorophenyl derivative were obtained at three temperatures (Table A4.1). At the lower temperatures, the rate acceleration is greater because the transition state binding is strengthened more than the substrate binding. The data may be analysed to elicit the enthalpic and entropic contributions to the free energy of transition state stabilization, obtainable from the variation of AGrs(=AHyS TAS s) with temperature (Table 2). If desired, the data may be further dissected since, from (9),... 

As seen in Table 2, A//yS = 9.42 kcal mol-1 and AAxS = 13.9 e.u., and so the free energy of transition state stabilization (approximately 5 kcal mol-1) results from a favourable enthalpy change, partly offset by an unfavourable entropy change. A similar situation pertains to binding of the substrate also (Table 2). Thus, the similarity between transition state binding and substrate binding, pointed out above from the correlation of p/fTS with pKs, is evident in thermodynamic parameters as well. 

Since molecular mechanics cannot be used to calculate the energy of transition states, suitable models were adopted. These models are extremely similar to the Jt-olefin complex with an orientation of the growing chain rather similar to that adopted when a a-agostic interaction is present. They were often called pre-insertion intermediates because the insertion transition state could be reached from these intermediates with a minimal displacement of the reacting atoms. 

Tab. 16.1 Calculated relative energies of transition states and products for the cyclization of 10.

Quantum chemical calculations need not be limited to the description of the structures and properties of stable molecules, that is, molecules which can actually be observed and characterized experimentally. They may as easily be applied to molecules which are highly reactive ( reactive intermediates ) and, even more interesting, to molecules which are not minima on the overall potential energy surface, but rather correspond to species which connect energy minima ( transition states or transition structures ). In the latter case, there are (and there can be) no experimental structure data. Transition states do not exist in the sense that they can be observed let alone characterized. However, the energies of transition states, relative to energies of reactants, may be inferred from experimental reaction rates, and qualitative information about transition-state geometries may be inferred from such quantities as activation entropies and activation volumes as well as kinetic isotope effects. 

Experiments cannot tell us what transition states look like. The fact is that transition states cannot even be detected experimentally let alone characterized, at least not directly. While measured activation energies relate to the energies of transition states above reactants, and while activation entropies and activation volumes, as well as kinetic isotope effects, may be invoked to imply some aspects of transition-state structure, no experiment can actually provide direct information about the detailed geometries and/or other physical properties of transition states. Quite simply, transition states do not exist in terms of a stable population of molecules on which experimental measurements may be made. Experimental activation parameters provide some guide, but tell us little detail about what actually transpires in going from reactants to products. 

As elaborated in Chapter 1, the proper way to anticipate the outcome of a kinetically-controlled reaction is to compare the energies of transition states leading to the different possible products. 

Finally, although this will not be of direct concern to us here, the use of outer d-orbitals in reducing the energy of transition states in reactions of compounds of elements belonging to the second row of the periodic table has often been proposed. 

Atomization energy helicene in eV Atomization energy of transition state in eV Racemization energy (eV) ... 

The Hammett equation is an LFER that can be demonstrated as follows for the case of rate constants. For an unsubstituted reactant, as a reference reactant, the free energy of transition state complex (TSC) is ... 

The orbital interactions discussed above not only govern the energy of ground state conformations or configurations but can also modulate the energy of transition states and, therefore, the reactivity of compounds. In conformationally constrained systems it has been observed that orbital overlap can affect the nucleophilicity and basicity of unshared electron pairs. The basicity differences of the amines shown in Scheme 2.11 [39] can, for instance, be interpreted as a result of a more or less efficient overlap between vicinal rrC-N and rr c x orbitals, where X represents an electron-withdrawing group. 

Stereoelectronic effects can have a profound effect on the ground-state structure of molecules, and can often help to explain counter-intuitive conformational preferences or spectroscopic features. Their effect on the energy of transition states is, however, less straightforward to predict. As stated by the Curtin-Hammett principle [75] (Section 1.4), reactions will proceed via energetically unfavorable conformers if these are more reactive (as is often the case) than better stabilized conformers. In such instances ground-state stabilization of certain conformers or the weakening of bonds by hyperconjugation will not necessarily be predictive for the outcome of a reaction. 

Probably the major contribution of computational chemistry is the determination of the structures and energies of transition states, which considerably expands our understanding of reaction mechanisms. 

S. S. Shaik, E. Duzy, A. Bartuv, J. Phys. Chem. 94, 6574 (1990). The Quantum Mechanical Resonance Energy of Transition States An Indicator of Transition State Geometry and Electronic Structure. 

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