GRADIENT FIELDS OF POTENTIAL-ENERGY SURFACES

While contour plots provide conceptual pictures of potential energy su rfaces and exhibit their critical points, quantitative determinations of critical points and reaction paths as well as dynamical calculation s require a knowledge of the gradient fields. The corresponding orthog onal trajectory maps are more complex than contour maps, but they prov ide additional insights. They are found to contain certain frequently occurring structural elements and these patterns are here examined. It is shown that many of them result from local confluences of orthogona l trajectory bundles with gradient extremals. The analysis leads to th e distinction between eight different kinds of such gradient extremal channels. The most important ones are the streambeds and ridges, the f ormer being typical conceptual prototypes of reaction channels, the la tter being prototypes of reaction barriers. Gradient extremal channels emanate from second order critical points in the directions of all no rmal modes, but they do not necessarily follow along the entire reacti on path of any one reaction. They can also exist unrelated to critical points. The conclusions are exemplified on a number of model potentia l energy surfaces.