Faculty and Staff Publications

Document Type

Article

Publication Date

6-21-2010

Abstract

Understanding energy landscapes is a major challenge in chemistry and biology. Although a wide variety of methods have been invented and applied to this problem, very little is understood about the actual mathematical structures underlying such landscapes. Perhaps the most general assumption is the idea that energy landscapes are low-dimensional manifolds embedded in high-dimensional Euclidean space. While this is a very mild assumption, we have discovered an example of an energy landscape which is nonmanifold, demonstrating previously unknown mathematical complexity. The example occurs in the energy landscape of cyclo-octane, which was found to have the structure of a reducible algebraic variety, composed of the union of a sphere and a Klein bottle, intersecting in two rings.

Publisher

American Institute of Physics

Publication Title

The Journal Of Chemical Physics

ISSN

0021-9606

Volume

132

Issue

234115

First Page

1

Last Page

7

DOI

10.1063/1.3445267

Language (ISO)

English

Included in

Mathematics Commons

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