A microscopic basis for the global appearance of energy landscapes

It is shown that the appearance of a multidimensional potential energy surface, or potential energy landscape, can be related to the form of the interatomic or intermolecular potential. Catastrophe theory enables us to describe how the geometry of the surface changes with parameters in the potential, and provides universal scaling relations that explain, for example, the asymmetric reaction profiles observed for systems bound by long-range forces. The principal result is an unexpected connection between barrier heights, path lengths, and vibrational frequencies, with applications to a wide variety of problems in chemical physics, ranging from Hammond's postulate in organic chemistry, to the relaxation dynamics of complex systems such as glasses and biomolecules.