Reaction Paths and Transition States

Theory may play two particularly important roles in rationalizing and predicting chemical reaction dynamics. As noted in the last section, the first step to understanding the dynamical behavior of a complex chemical system is breaking down the overall system into its constituent elementary processes. From a theoretical standpoint, the likely importance of various processes may be qualitatively assessed from the potential energy surfaces of putative reactions. Reactions with very high barriers will be less likely to play an important role, while low-barrier reactions will be more likely to do so. 

Moreover, the PES helps to define the scope of each elementary reaction. Thus, for instance, a bimolecular condensation that involves the formation of two new bonds between the reacting species may either proceed in a concerted fashion, with only a single predicted TS structure, or it may proceed as a stepwise process with two TS structures the stepwise process is really two elementary reactions - first a condensation and then a unimolecular rearrangement. 

Returning to kinetics, while theory can be advantageously used to decompose a complex system into its constituent series of elementary reactions, we have not yet described any relationship between a theoretical quantity associated widi die individual elementary reactions and their forward and reverse rate constants. It is axiomatic diat reactions widi high-energy 

TS structures must proceed more slowly than reactions with low-energy TS structures, but a more quantitative analysis requires that we invoke more sophisticated models describing the relationship between the properties of the activated complex and kinetics. Of such models, die most versatile is tfansition-state theory (TST). 

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Komaromi, I., Tronchet, J. M. J. Quantum Chemical Reaction Path and Transition State fora Model Cope (and Reverse Cope) Elimination. J. Phys. Chem. A 1997, 101, 3554-3560. 

Important initial Reaction Paths and Transition States of the Chemically Activated PhOO Adduct... 

One of the most important concepts in chemistry is catalysis. The development of effective catalysts requires knowledge of reaction paths and transition state structures. An important component in the future of physical chemistry, therefore, is the application of principles in reaction dynamics to the development of new materials with useful catalytic properties. I beheve that the remarriage of physical chemistry and materials science will provide many years of excitement and discovery to come. 

On the experimental side, the chemical dynamics on the state-to-state level is being studied via molecular-beam and laser techniques [2]. Alternative, and complementary, techniques have been developed in order to study the real-time evolution of elementary reactions [3]. Thus, the time resolution in the observation of chemical reactions has increased dramatically over the last decades. The race against time has recently reached the ultimate femtosecond resolution with the direct observation of chemical reactions as they proceed along the reaction path via transition states from reactants to products. This spectacular achievement was made possible by the development of femtosecond lasers, that is, laser pulses with a duration as short as a few femtoseconds. In a typical experiment two laser pulses are used, a pump pulse and a probe... 

Computational catalysis can make substantial contributions to these issues because it allows for a comparison of the rates of elementary reaction steps proposed for various mechanistic reaction paths. By use of computations, it is also possible to relate surface structure with the relative stabilities of various reaction intermediates and transition states. 

Embedded quantum/classical calculations were used to study the epoxidation reaction of styrene catalyzed by Mn-porphyrins. Optimized geometries were obtained for the Mn-porphyrin, reaction intermediates, and transition state structures along the proposed reaction path. A polarizable continuum model (PCM) was used to study solvent effects, with dichloromethane as the solvent. While it has been shown previously that the concerted intermediate between the oxidized porphyrin and the alkene is the lowest energy configuration, a transition state to directly form the concerted intermediate without the prior formation of a radical could not be found. A stepwise mechanism, in which a radical intermediate is formed before the concerted intermediate, is proposed. 

M.C. Milletti. Currently, he is a Graduate Student at Wayne State University under the direction of H.B. Schlegel. His research interests include the development of new methods for reaction path following, transition state optimization and the application of electronic structure theory to organometallic and inorganic chemistry. 

Coupled-cluster Theory Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Geometry Optimization 1 Geometry Optimization 2 Mixed Quantum-Classical Methods Mpller-Plesset Perturbation Theory Rates of Chemical Reactions Reaction Path Following Transition State Theory Unimolecular Reaction Dynamics. 

The situation in ketones with relatively small alkyl groups (e.g., 3-propanone) is similar to that of esters (Scheme 2.11). The reaction paths via transition states 48a and 48b (ethyl instead of OR ) with a slight preference for 48b, so that the trans-enolate forms in a moderate excess over the cis-diastereomer. It can be taken as a confirmation of Ireland s model that the sterically more demanding base LTMP enhances the 1,3-diaxial repulsion in 48a, so that the formation of trans-enolates is preferred (Table 2.1, entries 14 vs. 15). The fact that bases of similar bulkiness but different electronic properties, LTMP and lithium (trimethylsilyl)anilide, lead to the opposite stereochemical outcome (entries 15 vs. 17) has been explained by the assumption that the weaker sUylamide base prefers a late expanded Ireland transition state. The stronger base lithium A-f-butyl(trimethylsilyl)amide with similar steric demand leads predominantly to the cis-enolates, in accordance with Ireland s closed transition-state model. If ketones with sterically demanding substituents in the a -position, as in 2,2-dimethyl-3-(trimethylsilyloxy)-4-hexanone... 

Scheme 31.10 Proposed catalytic paths with reaction intermediates and transition states computationally for the t-proline/imidazole-catalyzed formation of (R)-32. Free energy (kj mo - ) calculated at 0°C at the...

Figure 5,30 reprinted from Chemical Physical Letters, 194, Fischer S and M Karplus. Conjugate Peak Refinement An Algorithm for Finding Reaction Paths and Accurate Transition States in Systems with Many Degrees of Freedom. 252-261, 1992, with permission from Elsevier Science. 

Aj ala P Y and H B Schlegel 1997. A Combined Method for Determining Reaction Paths, Minima and Transition State Geometries. Journal of Chemical Physics 107 375-384. 

When the addition and elimination reactions are mechanically reversible, they proceed by identical mechanistic paths but in opposite directions. In these circumstances, mechanistic conclusions about the addition reaction are applicable to the elimination reaction and vice versa. The principle of microscopic reversibility states that the mechanism (pathway) traversed in a reversible reaction is the same in the reverse as in the forward direction. Thus, if an addition-elimination system proceeds by a reversible mechanism, the intermediates and transition states involved in the addition process are the same as... 

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