Reaction path vector analysis

Figure 11 Analysis of reaction path vector t(s) and gradient for the reaction CH3 - - H2 —> CH4 - - H. (a) Characterization of t(.s) in terms of amplitudes A. j(f y) (see equation 38). (b) Decomposition of the gradient in terms of attractive and repulsive internal forces. Forces corresponding to the internal coordinate that dominates t(s) in a given range of the RP are indicated by thick solid lines...

This analysis is relevant whenever we are at a stationary point corresponding to a minimum. However at a saddle point and along the IRP the motion (in s) along the reaction path is not of small amplitude and hence must be treated differently. Thus we are left with not SN — 6, but only with 3N — 7 vibrational-like motions plus one translational motion along the reaction path. Formally this is done by introducing yet another constraint, namely that the vibrational displacement pi is perpendicular to a vector along the reaction path. The reference vectors become dependent on the RP parameter s. A vector along the path is dsii/ds, and the RP constraint is... 

The analysis of the RP vector t(s) in terms of internal coordinates reveals which geometrical parameter of the reaction complex dominates the direction of the RP, i.e., the path tangent. 

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