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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 the 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 the predictions of unphysical reaction pathways, while 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. [ABSTRACT FROM AUTHOR]

We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths and find that two such paths dominate the expression. For symmetric barriers, these two paths join together to describe the semiclassical instanton periodic orbit. However, for asymmetric barriers, one of the two paths takes an unphysically low energy and dominates the expression, leading to order-of-magnitude errors in the rate predictions. Nevertheless, semiclassical instanton theory remains accurate. We conclude that semiclassical instanton theory can be obtained directly from the semiclassical limit of the quantum instanton only for symmetric systems. We suggest a modification of the quantum instanton approach which avoids sampling the spurious path and thus has a stronger connection to semiclassical instanton theory, giving numerically accurate predictions even for very asymmetric systems in the low temperature limit. [ABSTRACT FROM AUTHOR]

We propose a new quantum transition-state theory for calculating Fermi's golden-rule rates in complex multidimensional systems. This method is able to account for the nuclear quantum effects of delocalization, zero-point energy, and tunneling in an electron-transfer reaction. It is related to instanton theory but can be computed by path-integral sampling and is thus applicable to treat molecular reactions in solution. A constraint functional based on energy conservation is introduced which ensures that the dominant paths contributing to the reaction rate are sampled. We prove that the theory gives exact results for a system of crossed linear potentials and show numerically that it is also accurate for anharmonic systems. There is still a certain amount of freedom available in generalizing the method to multidimensional systems, and the suggestion we make here is exact in the classical limit but not rigorously size consistent in general. It is nonetheless seen to perform well for multidimensional spin-boson models, where it even gives good predictions for rates in the Marcus inverted regime. [ABSTRACT FROM AUTHOR]