Simple Valley Floor Line

We assiime a chemical reaction along a valley path crossing a saddle 

The potential energy E(x, X2) is defined by taking the CN diatom fixed on the x -axis with the zero point in the center of mass, and taking pure (x, X2) Cartesian coordinates to describe the migration of the H-atom around the CN kernel. 

Let us choose a point (x, X2) near the valley floor line of E in the configuration space of the coordinates, and let us expand the PES up to the second order 

we turn our attention to an equipotential line, for instance, as a function y2=y2(yi)/ which leads through the energy E =E(x, X2). We 

corresponds to the radius of the curve, and its center is M=(-G /A, -G2/A22) We note that, away from the stationary points, the higher order terms are more important and the harmonic curve (6) can give only a crude imagination of the valley structure. Nevertheless, we can treat some special cases (cf.Fig.3). The point (Y-itY-y) (0 0) is the initial point of the curve other interesting points are y at y = i/ ii 

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