  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. This scaling will therefore be relevant at
finite temperatures, and can be the basis for corrections to standard rate
theoretic approaches.
