Molecular orbitals second-order reactions

Richard Bader was among the earliest of workers to realize the importance of electron density in providing an understanding of chemistry. Early on he was led to formulate the first symmetry rule governing a chemical reaction in answer to the question of how the electron density changes in response to a motion of the nuclei. This rule, termed the pseudo- or second-order Jahn-Teller effect, provides the theoretical underpinnings of frontier molecular orbital theory and is still widely used in discussions of reaction mechanisms and molecular geometries. 

Most aquatic oxidation reactions are attributable to well-defined chemical oxidants. As a result, model systems can be designed where second-order rate constants can be determined precisely for families of organic congeners. The comparatively high quality of these data allows mechanistic models of electron transfer to describe aquatic oxidations of environmental interest. Kinetic studies of these processes have produced many QSARs, mostly simple empirical correlations with common convenient descriptors such as the Hammett constant (a), half-wave oxidation potential ( j/2)> energies of the highest occupied molecular orbital ( HOMO), or rate constants for other oxidation reactions as descriptors (Canonica and Tratnyek, 2003). Their predictive power has lead to engineering applications in water treatment and remediation. 

Oxidation rate constant k, for gas-phase second order rate constants, kon for reaction with OH radical, k os with NOj radical and koj with O3 or as indicated, data at other temperatures see reference photooxidation half-life of 0.24-2.4 h in air for the gas-phase reaction with OH radical, based on the rate of disappearance of hydrocarbon due to reaction with OH radical (Darnall et al. 1976) k < 0.8 M s for the reaction with ozone in water at pH 2 and 20-23°C (Hoignd Bader 1983) koH = (13.6 1.3) X cm molecule s at 298 K (Wallington et al. 1988a Atkinson 1989) kojj = (14.4 1.5) X 10 2 cm molecule s at 298 2 K (relative rate method, Nelson et al. 1990) koe(calc) = 11.67 X 10 cm molecule s (molecular orbital calculations, Klamt 1996)... 

There is much evidence for this mechanism, similar to that discussed for ester hydrolysis. A molecular-orbital study on the mechanism of amide hydrolysis is available. In certain cases, kinetic studies have shown that the reaction is second order in OH, indicating that 94 can lose a proton to give Depending on the nature... 

Although sophisticated electronic structure methods may be able to accurately predict a molecular structure or the outcome of a chemical reaction, the results are often hard to rationalize. Generalizing the results to other similar systems therefore becomes difficult. Qualitative theories, on the other hand, are unable to provide accurate results but they may be useful for gaining insight, for example why a certain reaction is favoured over another. They also provide a link to many concepts used by experimentalists. Frontier molecular orbital theory considers the interaction of the orbitals of the reactants and attempts to predict relative reactivities by second-order perturbation theory. It may also be considered as a simplified version of the Fukui function, which considered how easily the total electron density can be distorted. The Woodward-Hoffmann rules allow a rationalization of the stereochemistry of certain types of reactions, while the more general qualitative orbital interaction model can often rationalize the preference for certain molecular structures over other possible arrangements. 

The basic idea of this theory can be suimnarized in the form of a sinq>le rule expressing the condition for an easy course of reaction by the requirement of the maximal positive overlap between the highest occupied molecular orbital HOMO and the lowest unoccupied molecular orbital LUMO. The practical use of this simple rule can be again best demonstrated by concrete exaitq)les. The sinqrlest situation is in the case of cycloadditions where the role of frontier orbitals is played by the HOMO of the first and the LUMO of the second component. In order to demonstrate the practical use of the above simple criterion let us analyze first the well known case of the Diels-Alder reaction. The situation is in this case depicted by the following Scheme. As can be seen from this scheme, the nodal structure of frontier orbitals is in this case favorable for the positive overlap in the regions of newly created bonds so that the reaction is allowed. 

Using rate constants derived from reaction of H2A and HA" with [Co(ox)3] and [Fe(phen)3], comparisons of the Marcus-derived one-electron potentials for H2A /H2A and HA /HA" with molecular orbital calculations for the homo energy confirm the greater reactivity of HA" over H2A. It is pointed out that the Marcus-derived potential for HA /HA", 0.85-1.0 V, is greater than the best available measurement for this parameter, 0.68 V. The self-exchange rate for ascorbate radical is lO -lO" M s" and indicates a considerable barrier to electron transfer. The ascorbate radical A also has a high intrinsic barrier to electron transfer, and detection of second-order kinetics in the decomposition of A" suggests a dimerization step with subsequent acid catalysis. 

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