  We take the golden-rule instanton method derived in the previous paper
[arXiv:1509.04919] and reformulate it using a ring-polymer approach. This gives
equations which can be used to compute the rates of electron-transfer reactions
in the nonadiabatic (golden-rule) limit numerically within a semiclassical
approximation. The multidimensional ring-polymer instanton trajectories are
obtained efficiently by minimization of the action. In this form, comparison
with Wolynes' quantum instanton method [P. G. Wolynes, J. Chem. Phys. 87, 6559
(1987)] is possible and we show that our semiclassical approach is the
steepest-descent limit of this method. We discuss advantages and disadvantages
of both methods and give examples of where the new approach is more accurate.
