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The Wolynes theory of electronically nonadiabatic reaction rates [P. G.Wolynes, J. Chem. Phys. 87, 6559 (1987)] is based on a saddle pointapproximation to the time integral of a reactive flux autocorrelation functionin the nonadiabatic (golden rule) limit. The dominant saddle point is on theimaginary 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 obtainedfrom an imaginary time path integral calculation. However, if $\lambda_{\rmsp}$ lies outside this range, as it does in the Marcus inverted regime, thepath integral diverges. This has led to claims in the literature that Wolynestheory cannot describe the correct behaviour in the inverted regime. Here weshow how the imaginary time correlation function obtained from a path integralcalculation can be analytically continued to $\lambda_{\rm sp}<-\beta/2$, andthe continuation used to evaluate the rate in the inverted regime. Comparisonswith exact golden rule results for a spin-boson model and a more demanding(asymmetric and anharmonic) model of electronic predissociation show that thetheory it is just as accurate in the inverted regime as it is in the normalregime.

Analytic continuation of Wolynes theory into the Marcus inverted regime