Reaction paths, potential energy surfaces principles

The accurate description of a chemical reaction requires detailed knowledge of its potential energy surface (PES). In principle Bom-Oppenheimer PESs can be theoretically obtained using a grid of PES points, but in practice it is not possible because of the drastic increase in computer resources, even for small systems. The alternative way is to find stationary points (minima, maxima and saddle points) and to estimate characteristics of the PES along the reaction path. 

The determination of the specific sites at which the interaction between two chemical species is going to occur, is of fundamental importance to determine the path and the products of a given reaction. In principle, from a theoretical viewpoint, one should calculate the potential energy surface associated with the interacting species, to obtain the reaction coordinate that allows one to establish the path followed by the reacting molecules to reach the transition state and the final products. However, in practice, this procedure may be very complicated and, in general, it may not necessarily lead one to obtain simple chemically significant information to establish the behavior of a family of molecules with respect to a family of reactants. Thus, over the years, chemists have developed intuitive concepts and simple theories that have allowed them to understand the behavior of molecules under different circumstances, their reactive sites, and possible reaction mechanisms. 

The study of reaction paths, in DFT, is not a new 1114,115. Thus we have chosen to explore the potential energy surfaces (PES) introducing the possibility to rationalize the results through the computations of the global hardnesses along the whole reaction path, with the aim to verify if, for the studied processes, the maximum hardness principle (MHP) 53 is satisfied. 

These considerations illustrate the general tendency of S surfaces to have minima at unsymmetrical geometries. The T surface has a similar tendency, for different reasons, and it is probably fair to say that in photochemical reactions, the unsymmetrical reaction paths are the ones normally followed. In spite of this, most illustrations of potential energy curves in the literature and in this book are for symmetrical paths, since these are much easier to calculate or guess. It is up to the reader of any of the theoretical photochemical literature to keep this in mind and to correct for it the best he or she can, using the principles outlined in this chapter. 

There is one path between reactants and products that has a lower energy maximum than any other this is the pathway that the reaction will follow. The line in a two-dimensional potential energy plot represents this lowest-energy pathway. It represents a path across an energy surface describing energy as a function of the spatial arrangement of the atoms involved in the reaction. The principle of microscopic reversibility arises directly from transition. state theory. The same pathway that is traveled in the forward direction of a reaction will be traveled in the reverse direction ... 

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