Transition state theory , development reaction pathways

While it is true that once there is confidence that the correct mechanism has been identified that transition state theory will usually yield a reasonable description of the energetics, it is also true that ignorance of the correct pathway can lead to results that are completely misleading. As a result, work has concentrated on important new developments in the area of determining the relevant reaction pathways in complex systems. In particular, sophisticated techniques have been set forth that are aimed at uncovering the optimal reaction pathway in cases where intuition does not suffice as a guide. 

Hsu et al. [6] state that lumped kinetic models developed by the top-down route have limited extrapolative power . To remedy this situation, many researchers have developed complex reaction schemes based on chemical first principles that involve thousands of chemical species. We can classify them into mechanistic models and pathway models. Mechanistic models track the chemical intermediates such as ions and free radicals that occur in the catalytic FCC process. Transition state theory helps in quantifying the rate constants involved in adsorption, reaction and desorption of reactant and product species from the catalyst surface. Froment and co-workers [19] have pioneered the use of such models in a refinery context and have developed a model for catalytic cracking of vacuum gas oil (VGO). Hsu et al. [6] claim that using this method is challenging because of its large size and reaction complexity. 

The four-membered cyclic transition state is not allowed by orbital symmetry theory and parity rules. It requires inversion of configuration at the a-carbon and trans addition to the alkene by a conrotatory process, which is sterically impossible [261,263]. The six-membered transition state is allowed by parity rules, but the relative contributions of this pathway and that by unimolecular ionization depends on their relative rate constants and therefore their free energies of activation. Since the transition state of electrophilic addition to alkenes proceeds with a very late transition state requiring an electrophile with a highly developed charge, covalent species are not sufficiently polarized to react directly with alkenes. Thus, the reaction should occur in two steps rather than by a concerted addition [264],... 

As discussed in previous sections, the committor is the ideal reaction coordinate in the sense that it exactly quantifies how far a reaction has proceeded. This concept also provides the basis for transition path theory (TPT) [33,278], a probabilistic framework developed by Vanden-Eijnden and collaborators to study the statistical properties of rare event trajectories. In TPT, isocommittor surfaces, i.e., surfaces on which all points have the same conunittor value, play a prominent role. Trajectories initiated from any point of an isocommittor surface have the same probability to reach the final rather than the initial state first. It can be shown [31] that the distribution of points where reactive trajectories pierce a given isocommittor surface is identical to the equiUbrium distribution confined to that surface. From the committor and the equilibrium distribution one can determine the distribution of reactive trajectories, so-called reaction tubes, which contain entire reaction pathways with high probabUity, as well as the reaction rates, providing useful statistical information about the reaction mechanism. 

Besides the two most well-known cases, the local bifurcations of the saddle-node and Hopf type, biochemical systems may show a variety of transitions between qualitatively different dynamic behavior [13, 17, 293, 294, 297 301]. Transitions between different regimes, induced by variation of kinetic parameters, are usually depicted in a bifurcation diagram. Within the chemical literature, a substantial number of articles seek to identify the possible bifurcation of a chemical system. Two prominent frameworks are Chemical Reaction Network Theory (CRNT), developed mainly by M. Feinberg [79, 80], and Stoichiometric Network Analysis (SNA), developed by B. L. Clarke [81 83]. An analysis of the (local) bifurcations of metabolic networks, as determinants of the dynamic behavior of metabolic states, constitutes the main topic of Section VIII. In addition to the scenarios discussed above, more complicated quasiperiodic or chaotic dynamics is sometimes reported for models of metabolic pathways [302 304]. However, apart from few special cases, the possible relevance of such complicated dynamics is, at best, unclear. Quite on the contrary, at least for central metabolism, we observe a striking absence of complicated dynamic phenomena. To what extent this might be an inherent feature of (bio)chemical systems, or brought about by evolutionary adaption, will be briefly discussed in Section IX. 

It would be an advantage to have a detailed understanding of the glass transition in order to get an idea of the structural and dynamic features that are important for photophysical deactivation pathways or solid-state photochemical reactions in molecular glasses. Unfortunately, the formation of a glass is one of the least understood problems in solid-state science. At least three different theories have been developed for a description of the glass transition that we can sketch only briefly in this context the free volume theory, a thermodynamic approach, and the mode coupling theory. 

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