Energy landscape mappings are performed for two different molecular systems under mechanical loads. Barrier heights are observed to scale as $\Delta U\sim {\delta }^{3∕2}$, where $\delta$ is a residual load. Catastrophe theory predicts that this scaling should arise for vanishing $\delta$; however, this region is irrelevant in physical processes at finite temperature because thermal fluctuations cause the system to cross over the barrier before reaching the small-$\delta$ regime. Surprisingly, we find that the $\Delta U\sim {\delta }^{3∕2}$ scaling is valid far beyond the vanishing $\delta$ regime described by catastrophe theory. We discuss how this scaling will therefore be relevant at finite temperatures and gives corrections to Eyring’s theory for transition rates.

• Received 24 August 2005

DOI:https://doi.org/10.1103/PhysRevE.73.061106