De novo design of enzymes or small-molecule catalysts requires the accurate geometries of the transition states of reactions to be catalyzed. Remarkably little is known about structures of the transition states of even simple reactions, for example ligand displacements at Si, P and S or at transition metals. Although at present one can compute transition state of essentially any small-molecule reaction, the challenge is to validate such calculations against the experiment. The importance of solvation in these reactions makes quantum-chemical calculations of their transition states difficult. Since a transition state is not a stable structure, its geometry cannot in general be probed directly by spectroscopy. Instead, experimental validation of transition-state computations traditionally relies on reproducing enthalpies of activation or stereochemical effects of a reaction. Because enthalpy of activation is a difference of energies of two structures (reactant and the transition state), it is simple to get the correct activation enthalpy from a pair of incorrect structures, through error cancellation. On the other hand, the large number of variable that control the stereochemical outcome of reactions and often small (<kT) energy differences between the competing pathways make computational studies of stereochemical effects one of the most challenging areas of computational chemistry.
The geometry of the transition state can be inferred by measuring the rates as a function of the force exerted on the reactant along its various molecular axes (see figure). If the distortion doesn't affect the intrinsic reactivity much, then any acceleration of the reaction is due to conformational relaxation of the non-reacting parts of the distorted molecule only along the restoring force vector. In this case the lowering of the reaction barrier relative to an unstrained reactant equals the product of the restoring force, f, and the elongation of the reactive moiety along the force vector, Δl. The slope of the linear plot of the log of the measured rate vs. the calculated restoring force gives the dimension of the transition state along one molecular axis. Repeating such measurements for the same reactant strained along different molecular axes would give a nearly complete 3D structure of the transition state.
We develop such molecular rulers based on the macromolecule-free form of force spectroscopy to validate the calculated transition state structures of fundamental classes of chemical reactions, including catalytically-relevant transition-metal chemistries.
- Force increases reaction rate proportionally to the change in the dimension of the reacting moiety along the force vector. By applying force along different axis of the reacting moiety and measuring the resultant rate enhancements it becomes possible to determine the 3D structure of the transition state. The rate enhancements will be largest when the force acts along the internuclear distances (blue in the figure) that elongate the most during the reaction, whereas applying force along axes whose dimensions do not change will have little or no kinetic effect (red).