Fermi's golden rule defines the transition rate between weakly coupled states and can thus be used to describe a multitude of molecular processes including electron-transfer reactions and light-matter interaction. However, it can only be calculated if the wave functions of all internal states are known, which is typically not the case in molecular systems. Marcus theory provides a closed-form expression for the rate constant, which is a classical limit of the golden rule, and indicates the existence of a normal regime and an inverted regime. Semiclassical instanton theory presents a more accurate approximation to the golden-rule rate including nuclear quantum effects such as tunneling, which has so far been applicable to complex anharmonic systems in the normal regime only. In this paper, we extend the instanton method to the inverted regime and study the properties of the periodic orbit, which describes the tunneling mechanism via two imaginary-time trajectories, one of which now travels in negative imaginary time. It is known that tunneling is particularly prevalent in the inverted regime, even at room temperature, and thus, this method is expected to be useful in studying a wide range of molecular transitions occurring in this regime.

中文翻译：

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马库斯倒置政权中费米黄金定律的Instanton公式。

费米的黄金法则定义了弱耦合状态之间的跃迁速率，因此可以用来描述包括电子转移反应和光物质相互作用在内的多种分子过程。但是，只有在知道所有内部状态的波函数的情况下才能进行计算，这在分子系统中通常不是这样。马库斯理论为速率常数提供了封闭形式的表达式，这是黄金法则的经典极限，并指出了正常状态和反向状态的存在。半经典瞬时子理论提供了一个更精确的近似黄金定律速率，包括诸如隧道效应之类的核量子效应，迄今为止，它仅适用于正常状态下的复杂非谐系统。在本文中，我们将瞬时方法扩展到倒置状态，并研究周期轨道的属性，该周期轨道通过两个假想时间轨迹描述了隧穿机理，其中之一现在以负假想时间传播。众所周知，即使在室温下，隧穿在倒置方案中也特别普遍，因此，预期该方法可用于研究在该方案中发生的各种分子跃迁。