Franck-Condon Theory of Quantum Mechanochemistry

The spectroscopic Franck-Condon (FC) principle is extended to mechanochemistry. If the external force is applied rapidly (the sudden-force regime), then the transition between the potential energy surface and the force-modified potential energy surface is analogous to the optical electronic transition. Such a transition produces a nonequilibrium ensemble of vibrationally excited molecules. This excess of vibrational energy is another activation source in addition to the well-known reaction barrier modulation by the external force. In the same time, the nonequilibrium vibrational distribution implies nonstatistical kinetics of a mechanochemical transformation. Mechanochemical FC principle thus provides a conceptual picture for the sudden-force mechanochemistry and opens possibilities for quantitative calculations of the mechanochemical rates and mechanisms. Here we use it to compute the dissociation rates of a model diatomic molecule and to explain the selectivity in mechanochemical bond breaking in n-butane. The approach is predicted to be relevant for large-magnitude external forces, applied instantaneously. Otherwise, the excess vibrational energy will dissipate due to intramolecular vibrational redistribution and interaction with environment.