Extension of instanton theory includes tunneling effects in electron transfer rate calculations
Extension of instanton theory includes tunneling effects in electron transfer rate calculations lead image
In the normal Marcus regime, electron transfer rates can be calculated without the inclusion of tunneling. However, there also exists a Marcus inverted regime, in which the driving force of a system is larger than its reorganization energy.
Because tunneling is known to have a large effect on electron transfer in the inverted regime, its exclusion leads to results orders of magnitude smaller than expected. Eric Heller and Jeremy Richardson extended instanton theory to include the optimum tunneling pathway in the inverted regime, which was previously thought to be impossible.
Describing the reaction in the normal regime using instanton theory requires simulating the system’s reactants and products at two different temperatures. Because it is so asymmetric, the inverted regime requires one of the temperatures to be negative – a nonphysical result and a problem.
“When molecules have negative temperatures, they actively search out high-energy states,” said Richardson. “If you ask for the optimal tunneling pathway for the molecule at negative temperatures, it goes wild and runs to infinity and back.”
By instead expressing negative temperature as negative time, the team demonstrated the system can be represented by a periodic orbit of two imaginary time trajectories, one traveling backward. Thus, the proper tunneling pathway is determined by requiring a molecule to find the optimal path when at positive temperatures and the worst path at negative temperatures.
This new method can be used to calculate accurate electron transfer rates in regions where tunneling effects cannot be ignored.
“It could be that many reactions, which take place in our labs or even our bodies, only take place because of quantum tunneling,” Richardson said.
Source: “Instanton formulation of Fermi’s golden rule in the Marcus inverted regime,” by Eric R. Heller and Jeremy O. Richardson, Journal of Chemical Physics (2020). The article can be accessed at https://doi.org/10.1063/1.5137823 .
