Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland.
J Chem Phys. 2019 Mar 14;150(10):104107. doi: 10.1063/1.5081108.
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.
我们提出了一种新的量子过渡态理论，用于计算复杂多维体系中费米黄金规则速率。该方法能够考虑电子转移反应中离域、零点能和隧穿的核量子效应。它与瞬时理论有关，但可以通过路径积分采样计算，因此适用于处理溶液中的分子反应。引入了基于能量守恒的约束泛函，以确保对反应速率有贡献的主要路径被采样。我们证明该理论对交叉线性势系统给出了精确结果，并数值表明它对非谐系统也具有准确性。一般来说，将该方法推广到多维系统仍然存在一定的自由度，我们在这里提出的方法在经典极限下是精确的，但通常不严格大小一致。然而，它在多维自旋-玻色子模型中表现良好，甚至对马库斯反转区的速率也给出了很好的预测。
