Nonadiabatic Tunnelling
Nonadiabatic rate theory
In nonadiabatic reactions, we have two potential energy surfaces, reactant R and product P, and we wish to calculate the rate to transfer from R to P. Instead of computing the overlaps of quantum-mechanical wave functions in R and P, which is tedious, costly, and often times not even possible for real systems, we reformulate the rate as an integral over the so-called flux-correlation function whose complex argument we often split into real (t) and imaginary times (τ).
As before, the flux-correlation function can be expressed as a path
integral, which is approximated by locating an optimal tunnelling path,
the so-called instanton, with contributions from both the R and P
states. Physically, this amounts to the instanton travelling on the
reactant surface for some imaginary time before crossing over to the
product surface and travelling there until a full orbit of length ℏβ is completed.
We have derived and applied this theory not just in the Marcus normal regime, but also for the inverted regime, where it allows for an interesting interpretation in terms of antimolecules moving backwards in imaginary time.
Recently, we found it necessary to extend this theory to account for branch-point singularities which may appear in the flux-correlation function, thus introducing more complex-analysis concepts to deform the integration contour around the branch cut.
Applications
Instanton theory in the non-adiabatic regime highlights heightened quantum mechanical effects showcasing orders-of-magnitude increase in various chemical reactions. For instance it has revealed how tunnelling causes a 23 orders of magnitude increase in the rate of singlet oxygen deactivation and how molecules behave when they pass through a conical intersection! More recently we have been successful in showing the change in mechanistic behaviour of carbenes at low temperatures.
We are always on the hunt for new types instanton as well as interesting reactions for which the mechanism is not yet clear.
