Effects of tunnelling and asymmetry for system-bath models of electron transfer

Abstract

We apply the newly derived nonadiabatic golden-rule instanton theory to asymmetric models describing electron-transfer in solution. The models go beyond the usual spin-boson description and have anharmonic free-energy surfaces with different values for the reactant and product reorganization energies. The instanton method gives an excellent description of the behaviour of the rate constant with respect to asymmetry for the whole range studied. We derive a general formula for an asymmetric version of Marcus theory based on the classical limit of the instanton and find that this gives significant corrections to the standard Marcus theory. A scheme is given to compute this rate based only on equilibrium simulations. We also compare the rate constants obtained by the instanton method with its classical limit to study the effect of tunnelling and other quantum nuclear effects. These quantum effects can increase the rate constant by orders of magnitude.

Nonadiabatic quantum transition-state theory in the golden-rule limit. II. Overcoming the pitfalls of the saddle-point and semiclassical approximations

“…Instanton theory is thus seen to describe this tunneling effect very accurately, as expected from previous work, 20 and shows good agreement with the exact results, with only a 5% error mostly emanating from the harmonic approximation to the reactant partition function.…”

“…It can be defined in a similar way to the ring-polymer versions given above with N = 1 and λ = 0 and can also be calculated with a δ-TI approach similar to Eq. (20). Finally, we shall also employ the semiclassical instanton method as described in Ref.…”

“…Like the original version, [39][40][41] the golden-rule instanton theory can also be efficiently evaluated in the ring-polymer formulation, 19 and has been benchmarked on system-bath models and shown to give accurate predictions for electron-transfer rates. 20 However, although the theory is applicable to anharmonic systems, as the semiclassical limit only treats fluctuations to second order, it is equivalent to performing a local harmonic approximation, which cannot be used successfully in atomistic solvent environments.…”

Perspective: Ring-polymer instanton theory

“…However, both anharmonic and tunneling effects are accurately treated by the new theory. 103 Reactions such as proton-coupled electron transfer are also nonadiabatic but do not occur in the golden-rule limit. For these, a more general approach is needed which correctly gives the limiting cases in both the strong-and weak-coupling regimes.…”

Instanton formulation of Fermi’s golden rule in the Marcus inverted regime

“…In this paper, we propose an extension of the semiclassical instanton method 45,49,50 for the inverted regime in the goldenrule limit. The rate expression in the inverted regime is derived by analytic continuation of the formula in the normal regime, leading to a one-shot method which requires no extrapolation of results collected in a different regime.…”