Path-integral methods for non-adiabatic reaction rates

This thesis discusses recent progress in the development of path-integral methods for non-adiabatic reaction rates in large-scale atomistic simulations. Electronically non-adiabatic reactions are important in a wide range of phenomena, including electron transfer in DNA, enzymatic oxygenation reactions, and the function of light-emitting diodes. Imaginary-time path integrals provide an ideal way to simulate these complex condensed phase reactions, as they are both linearly scaling and capable of accurately describing zero-point energy and tunnelling. The thesis begins by considering methods for calculating reaction rates in systems that are not fully in either the adiabatic or non-adiabatic limits. Recent work in this area is reviewed, before two new approaches are introduced. The first of these, the non-adiabatic quantum instanton (NAQI), generalises Wolynes theory (valid in the non-adiabatic limit) and the projected quantum instanton (valid in the adiabatic limit) to arbitrary values of electronic coupling. The second approach is a simple formula for interpolating between the results of golden-rule and Born-Oppenheimer rate calculations. This formula can immediately be applied to calculate reaction rates in condensed phase reactions, by combining it with pre-existing path-integral methods in each limit. Following this, the thesis focusses on the calculation of reaction rates in the golden-rule limit. Again, two new approaches are introduced. The first is an implementation of Wolynes theory which can be used to numerically analytically continue Wolynes theory into the Marcus inverted regime. The second is an alternative path-integral method called the linear golden-rule (LGR) approximation, a size consistent modification of the recently proposed GR-QTST. LGR overcomes the known deficiencies of Wolynes theory, and can be directly applied to calculate reaction rates in the inverted regime. The thesis concludes with a fully atomistic simulation of aqueous ferrous-ferric electron transfer, which addresses recent questions about the nature of the tunnelling in this system.