Potential energy surfaces surface atom reaction paths

FIGURE 13.21 The contours of a potential energy surface for the reaction between a hydrogen atom and a bromine molecule. The atoms have been constrained to approach and depart in a straight line. The path of lowest potential energy (blue) is up one valley, across the pass—the saddle-shaped saddle point (see inset)—and down the floor of the other valley. The path shown in red would take the atoms to very high potential energies. 

For large systems (systems with more than four atoms) it is necessary to use methods which reduce the coordinate space for which we have to know the potential energy surface. Since chemical reactions are at most three or four-center reactions, the obvious partitioning is to treat the motion of the three or four atoms defining the reaction center by some of the methods described and the remaining motion using a small-amplitude description identical to the one used in the reaction path Hamiltonian method. In the... 

Figure 1.1 Contour line plot of a potential energy surface (PES) for reaction between three identical atoms (A, B, C) based on that for the H + Hj. The diagram also shows the minimum energy path (MEP) and the critical dividing line (S ). The axes are skewed so that a trajectory can be visualised as the motion of a single mass point across this PES.

It seems worthwhile to examine critically this transcription of the Slater method into the standard absolute reaction rate theory. In the simple unimolecular bond break, it does appear reasonable that the coordinate q between the tvfo atoms A and B must reach and go beyond a critical extension q0 in order that decomposition takes place. In Slater s calculations account is taken of the different energies involved in stretching q to q0. In regarding q as the mode of decomposition in the transition state method, one must, however, first look at the potential energy surface. The decomposition path involves passage over the lowest possible barrier between reactants and products. It does not seem reasonable to assume that this path necessarily only involves motion of the atoms A and B at the activated complex. Possibly, a more reasonable a priori formulation in a simple decomposition process would be to choose q as the coordinate which tears the two decomposition fragments apart. Such a coordinate would lead roughly to the relation... 

Figure 4. Qualitative potential energy surfaces cross sections along the reaction path of the Y atom insertion reaction into methane. Schematic correlation diagram for doublet states.

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