Analytic continuation of Wolynes theory into the Marcus inverted regime

The Wolynes theory of electronically nonadiabatic reaction rates [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] is based on a saddle point approximation to the time integral of a reactive flux autocorrelation function in the nonadiabatic (golden rule) limit. The dominant saddle point is on the imaginary time axis at t_sp=iλ_spℏ, and provided λ_sp lies in the range -β/2≤λ_sp≤β/2, it is straightforward to evaluate the rate constant using information obtained from an imaginary time path integral calculation. However, if λ_sp lies outside this range, as it does in the Marcus inverted regime, the path integral diverges. This has led to claims in the literature that Wolynes theory cannot describe the correct behaviour in the inverted regime. Here we show how the imaginary time correlation function obtained from a path integral calculation can be analytically continued to λ_sp<-β/2, and the continuation used to evaluate the rate in the inverted regime. Comparison with exact golden rule results for a spin-boson model and a more demanding (asymmetric and anharmonic) model of electronic predissociation shows that the theory is just as accurate in the inverted regime as it is in the normal regime.