Revisiting nuclear tunnelling in the aqueous ferrous-ferric electron transfer

The aqueous ferrous-ferric system provides a classic example of an electron-transfer process in solution. There has been a long standing argument spanning more than three decades around the importance of nuclear tunnelling in this system, with estimates based on Wolynes theory suggesting a quantum correction factor of 65, while estimates based on a related spin-boson model suggest a smaller factor of 7-36. Recently, we have shown that Wolynes theory can break down for systems with multiple transition states leading to an overestimation of the rate, and we suggest that a liquid system such as the one investigated here may be particularly prone to this. We re-investigate this old yet interesting system with the first application of the recently developed golden-rule quantum transition-state theory (GR-QTST). We find that GR-QTST can be applied to this complex system without apparent difficulties and that it gives a prediction for the quantum rate 6 times smaller than that from Wolynes theory. The fact that these theories give different results suggests that although it is well known that the system can be treated using linear response and therefore resembles a spin-boson model in the classical limit, this approximation is questionable in the quantum case. It also intriguingly suggests the possibility that the previous predictions were overestimating the rate due to a break down of Wolynes theory.