  We describe a path-integral molecular dynamics implementation of our recently
developed golden-rule quantum transition-state theory (GR-QTST). The method is
applied to compute the reaction rate in various models of electron transfer and
benchmarked against exact results. We demonstrate that for systems exhibiting
two or more transition states, rates computed using Wolynes theory [P. G.
Wolynes, J.\ Chem.\ Phys.\ 87, 6559 (1987)] can be overestimated by orders of
magnitude, whereas the GR-QTST predictions are numerically accurate. This is
the case both at low temperature, where nuclear tunneling makes a considerable
contribution, and also in the classical limit, where only GR-QTST rigorously
tends to the correct result. Analysis shows that the saddle-point approximation
employed by Wolynes theory is not valid in this case, which results in
predictions of unphysical reaction pathways, whilst the energy constraint
employed by GR-QTST resolves this problem. The GR-QTST method is also seen to
give accurate results for a strongly anharmonic system by sampling
configurations around the instanton pathway without making the semiclassical
approximation. These promising results indicate that the GR-QTST method could
be an efficient and accurate approach for simulating electron-transfer
reactions in complex molecular systems.
