Method to Derive Restoring Forces of Strained Molecules from Kinetic Measurements

We report a method to estimate the restoring force of a constrained small molecule and relate changes in its reactivity to this force. Restoring force is a size-invariant measure of molecular strain and offers a conceptual framework to bridge studies of macromolecular reactions by force spectroscopies with those of strained small molecules. We illustrate our method by showing that E stiff stilbene (1,1'-Delta-biindan) with up to 700 pN of force along its C6,C6' axis is accessible by photoisomerization. It reverts thermally to the Z isomer with tau(1/2) approximately 100 ms, probably long enough to be useful for microscale actuation. The quantum yield of photoisomerization and the activation barrier of thermal isomerization of constrained stiff stilbene increase sharply as the restoring force decreases.