Title: Analytic continuation of Wolynes theory into the Marcus inverted regime,
Abstract: 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 $t_{\rm sp}=i\lambda_{\rm sp}\hbar$, and provided
$\lambda_{\rm sp}$ lies in the range $-\beta/2\le\lambda_{\rm sp}\le\beta/2$,
it is straightforward to evaluate the rate constant using information obtained
from an imaginary time path integral calculation. However, if $\lambda_{\rm
sp}$ 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 $\lambda_{\rm sp}<-\beta/2$, and
the continuation used to evaluate the rate in the inverted regime. Comparisons
with exact golden rule results for a spin-boson model and a more demanding
(asymmetric and anharmonic) model of electronic predissociation show that the
theory it is just as accurate in the inverted regime as it is in the normal
regime.