Gradient fields of potential energy surfaces

Abstract

While contour plots provide conceptual pictures of potential energy surfaces and exhibit their critical points, quantitative determinations of critical points and reaction paths as well as dynamical calculations require a knowledge of the gradient fields. The corresponding orthogonal trajectory maps are more complex than contour maps, but they provide 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 orthogonal trajectory bundles with gradient extremals. The analysis leads to the distinction between eight different kinds of such gradient extremal channels. The most important ones are the streambeds and ridges, the former being typical conceptual prototypes of reaction channels, the latter being prototypes of reaction barriers. Gradient extremal channels emanate from second order critical points in the directions of all normal modes, but they do not necessarily follow along the entire reaction path of any one reaction. They can also exist unrelated to critical points. The conclusions are exemplified on a number of model potential energy surfaces.