Reaction pathways hypersurfaces

Some Remarks on Reaction Pathways. So far, hypersurface calculations with close correlation to (spectroscopic) molecular data have been considered. Outside the potential minima, the uncer-... 

This last example again demonstrates the usefulness of correlating hypersurface calculations as closely as possible to measurement data although methyl and vinyl nitrenes, which by chemical intuition seem to be reasonable intermediates, do not have to occur necessarily along the reaction pathway (36,39), the predictions stimulated an experiment, which otherwise - due to the hazardous starting material (38) - hardly would have been carried out. 

Stable adsorption complexes are characterized by local minima on the potential energy hypersurface. The reaction pathway between two stable minima is determined by computation of a transition state structure, a saddle point on the potential energy hypersurface, characterized by a single imaginary vibrational mode. The Cartesian displacements of atoms that participate in this vibration characterize movements of these atoms along the reaction coordinate between sorption complexes. 

Horsley et a/.164 have determined a reaction pathway for the geometrical isomerization of cyclopropane by a calculation and search of the full 21-dimensional hypersurface The calculations were performed using a minimal basis set of STO s in a modified SCF calculation using the restricted Hartree-Fock formalism suggested by Nesbet.165 In the region of the trimethylene diradical, a 3 x 3 configuration interaction calculation was included. 

Fig. 7 3D representation of the B3LYP hypersurface of the isomerization of 2 +. Each contour line corresponds to 3 kcal/mol. The reaction pathway shown in Fig. 5 is indicated in bold. 

Furthermore, interesting properties may be deduced either directly from the potential energy hypersurface of the system under consideration or by solving the nuclear equation. So, for example, a careful analysis of the function Uo of the ground state of a supermolecule allows us to determine not only equilibrium and transition structures but also reaction pathways at 0 K. 

The authors concede that the P value obtained from their model is several times larger than what can be expected on the basis of the standard C-0 stretching frequency and the reduced mass for a relatively large acetal. The discrepancy was attributed to the fact that the apparent slope, revealed by the one-dimensional model, is a projection of the reaction pathway across an energy hypersurface and depends on the vantage point of the observer, that is, on the choice of the plane of projection. 

The ideal diradical has a AV of 2 and two atoms have a AV value near 1. whereas the AV will be small. In a zwitterion AK will be close to or greater than 2 and AK will be negligibly small. This classification can be particularly useful for the determination of the reaction mechanism in polymerization reactions, but can also be applied to excited states, intermediates on excited hypersurfaces. Another useful application is the monitoring of breaking and forming of bonds along a reaction pathway. 

Summarizing facts and speculations despite the crudeness of the model chosen, the relative thermal stcibilities of both isomers, FSSF and F2SS are correctly reproduced by the CNDO hypersurface calculations, and also the surprising likeness of their ionization patterns (33-35). Whatever the real isomerization pathway may be, the chances for the experimentalist to ever isolate the molecules H2S=S and Cl2S=S under normal reaction conditions are predicted to be close to zero - another recommendation to avoid futile experimental efforts by precalculating hypersurfaces. 

Figure 17 indicates that it is not valid to describe these structures in terms of the Berry pathway at all. The considerable deviation of points about the reaction coordinate for structures close to the trigonal bipyramid may indicate that the energy hypersurface does not rise sharply in a direction perpendicular to the reaction coordinate in this region of space. In addition, it has been shown [37] that 5-coordinate complexes may lie on a reaction coordinate involving attack by a ligand on a 4-coordinate centre. This means that 5-coordinate complexes are not always ideally suited for this form of analysis, and deviations from the theoretical rearrangement pathways may be attributable to alternative dissociative pathways. 

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