Reaction hypersurface

Alternatively one can make use of No Barrier Theory (NBT), which allows calculation of the free energy of activation for such reactions with no need for an empirical intrinsic barrier. This approach treats a real chemical reaction as a result of several simple processes for each of which the energy would be a quadratic function of a suitable reaction coordinate. This allows interpolation of the reaction hypersurface a search for the lowest saddle point gives the free energy of activation. This method has been applied to enolate formation, ketene hydration, carbonyl hydration, decarboxylation, and the addition of water to carbocations. ... 

The exact form of the pre-exponential factor A (see Chapter 5) is still being debated from the preceding considerations it is apparent that we must distinguish two cases If the reaction is adiabatic, the pre-exponential factor will be determined solely by the dynamics of the inner and outer sphere if it is nonadiabatic, it will depend on the electronic overlap between the initial and final state, which determines the probability with which the reaction proceeds once the system is on the reaction hypersurface. 

When a reaction is adiabatic, the electron is transferred every time the system crosses the reaction hypersurface. In this case the preexponential factor is determined solely by the dynamics of the inner-and outer-sphere reorganization. Consequently the reaction rate is independent of the strength of the electronic interaction between the reactant and the metal. In particular, the reaction rate should be independent of the nature of the metal, which acts simply as an electron donor and acceptor. Almost by definition adiabatic electron-transfer reactions are expected to be fast. 

Here we are using reactants to mean the molecular system involved in the chemical reaction at any point on the reaction hypersurface. 

Accurate solutions forth reaction hypersurface (three atoms)... 

ACCURATE SOLUTIONS FOR THE REACTION HYPERSURFACE (THREE ATOMS )... 

Figure 1. Representative slice through the reaction hypersurface for deuterium exchange for a reactant with an unfilled valence shell, showing the binding energy of the intermediate and the reaction exoergicity. ...

Investigation of reaction surfaces and reaction hypersurfaces If the translational motion of the reaction complex couples with other LAMs of the complex, the RP can be sharply curved in the regions with strong coupling. The actual trajectory of the reaction complex deviates far from the RP and a correct dynamic description can only be achieved if the reaction valley is extended to a minimum energy reaction surface or hypersurface, which embeds all LAMs. Calculations needed to describe the reaction (hyper) surface can become rather expensive and, therefore, this approach is limited to... 

In the following section we present an overview of the theoretical calculations. The succeeding sections report reaction hypersurfaces for each of the chemical species. In the case of hydrogen nitroxide, we also report simplified rate coefficient estimates in a discussion of the recombination of hydrogen and nitrogen oxide. 

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