Transition State Species and Chemical Reactions

The theoretical challenge of characterizing the bonding of a molecular or supramo-lecular species becomes considerably more complex when the species undergoes chemical reaction. A primary goal of chemical theorists is to elucidate the macroscopic reaction thermodynamics and kinetics in terms of elementary reactions that compose the mechanism of overall chemical transformation. Such elementary reactions are typically of unimolecular 

Discovering Chemistry With Natural Bond Orbitals, First Edition. Frank Weinhold and Clark R. Landis. 2012 John Wiley Sons, Inc. Published 2012 by John Wiley Sons, Inc. 

Despite their central role in chemical reaction theory, TS species challenge conventional structural characterization by experimental means. Modern ab initio methods therefore provide a uniquely valuable source of detailed TS information that can significantly advance understanding of chemical reactivity. Given the fact that accurate TS wavefunctions and IRC profiles are now routinely available for a variety of chemical reactions, our aim is to extend NBO/NRT-based analysis techniques to characterize TS and other IRC species in simple Lewis structural and resonance theoretic terms, analogous to those found useful for equilibrium species. 

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Chapter 10 Transition State Species and Chemical Reactions... 

Chapter 10 Transition State Species and Chemical Reactions ------------------------------------------//O-I0.2—--------------------... 

Let us define a reaction coordinate s, joining reactants (s < 0) to products (s > 0), and a transition state with a fixed value of s, that is, with one degree of freedom less than a stable molecule (Figure 6.1). It is possible to derive TST from one fundamental assumption there is a quasi-equilibrium between the transition-state species (formed from the reactants) and the reactants themselves. The quasi-equilibrium state is characterised by the equilibrium between the reactants and the transition-state species, and by the fact that the concentration of these species does not vary with their disappearance to the products. This quasi-equilibrium offers a method to calculate the concentration of transition-state species using chemical equilibrium theories, and the dynamics problem is transformed into an equilibrium problem, with a known solution. 

A postulated reaction mechanism is a description of all contributing elementary reactions (we will call this the kinetic scheme), as well as a description of structures (electronic and chemical) and stereochemistry of the transition state for each elementary reaction. (Note that it is common to mean by the term transition state both the region at the maximum in the energy path and the actual chemical species that exists at this point in the reaction.)... 

We have just discussed several common strategies that enzymes can use to stabilize the transition state of chemical reactions. These strategies are most often used in concert with one another to lead to optimal stabilization of the binary enzyme-transition state complex. What is most critical to our discussion is the fact that the structures of enzyme active sites have evolved to best stabilize the reaction transition state over other structural forms of the reactant and product molecules. That is, the active-site structure (in terms of shape and electronics) is most complementary to the structure of the substrate in its transition state, as opposed to its ground state structure. One would thus expect that enzyme active sites would bind substrate transition state species with much greater affinity than the ground state substrate molecule. This expectation is consistent with transition state theory as applied to enzymatic catalysis. 

The quantitative prediction of the stereochemistry of a chemical reaction by strain energies requires knowledge of the reaction mechanism, i.e., the selective intermediates and/or transition states involved, and an accurate force field for the transient species. As discussed above, these are two demanding problems and so far there are no reports of studies in this area that have used molecular mechanics for quantitative predictions at the same level of accuracy as for conformational analyses. The application of empirical force field calculations to the design of asymmetric transformations clearly is a worthy task, and some examples of studies in this area have been discussed above. On the basis of two examples we will now discuss some general aspects highlighting the limitations of the qualitative considerations emerging horn molecular mechanics calculations for the interpretation and support of assumed reaction pathways. 

The reaction course for addition of the singlet EH2 and EF2 species with E = C to Sn to ethylene has been investigated with quantum chemical methods by Sakai87. The author calculated also the transition states for the addition reactions. A related work by Boatz et al. reported about the reactions of EH2 and EF2 (E = C to Sn) with acetylene yielding metallacyclopropenes88. The results of both studies are discussed below in the section on reaction mechanisms . 

More importantly, a molecular species A can exist in many quantum states in fact the very nature of the required activation energy implies that several excited nuclear states participate. It is intuitively expected that individual vibrational states of the reactant will correspond to different reaction rates, so the appearance of a single macroscopic rate coefficient is not obvious. If such a constant rate is observed experimentally, it may mean that the process is dominated by just one nuclear state, or, more likely, that the observed macroscopic rate coefficient is an average over many microscopic rates. In the latter case k = Piki, where ki are rates associated with individual states and Pi are the corresponding probabilities to be in these states. The rate coefficient k is therefore time-independent provided that the probabilities Pi remain constant during the process. The situation in which the relative populations of individual molecular states remains constant even if the overall population declines is sometimes referred to as a quasi steady state. This can happen when the relaxation process that maintains thermal equilibrium between molecular states is fast relative to the chemical process studied. In this case Pi remain thermal (Boltzmann) probabilities at all times. We have made such assumptions in earlier chapters see Sections 10.3.2 and 12.4.2. We will see below that this is one of the conditions for the validity of the so-called transition state theory of chemical rates. We also show below that this can sometime happen also under conditions where the time-independent probabilities Pi do not correspond to a Boltzmann distribution. 

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