Trenins George, Richardson Jeremy O
Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland.
J Chem Phys. 2022 May 7;156(17):174115. doi: 10.1063/5.0088518.
Fermi's golden rule (GR) describes the leading-order behavior of the reaction rate as a function of the diabatic coupling. Its asymptotic (ℏ → 0) limit is the semiclassical golden-rule instanton rate theory, which rigorously approximates nuclear quantum effects, lends itself to efficient numerical computation, and gives physical insight into reaction mechanisms. However, the golden rule by itself becomes insufficient as the strength of the diabatic coupling increases, so higher-order terms must be additionally considered. In this work, we give a first-principles derivation of the next-order term beyond the golden rule, represented as a sum of three components. Two of them lead to new instanton pathways that extend the GR case and, among other factors, account for effects of recrossing on the full rate. The remaining component derives from the equilibrium partition function and accounts for changes in potential energy around the reactant and product wells due to diabatic coupling. The new semiclassical theory demands little computational effort beyond a GR instanton calculation. It makes it possible to rigorously assess the accuracy of the GR approximation and sets the stage for future work on general semiclassical nonadiabatic rate theories.
费米黄金规则（GR）描述了反应速率作为非绝热耦合函数的主导阶行为。其渐近（ℏ→0）极限是半经典黄金规则瞬子速率理论，该理论严格近似核量子效应，便于进行高效数值计算，并能对反应机制给出物理洞察。然而，随着非绝热耦合强度的增加，仅靠黄金规则本身就变得不够了，因此必须额外考虑高阶项。在这项工作中，我们对黄金规则之外的下一阶项进行了第一性原理推导，该项表示为三个分量的和。其中两个分量导致了新的瞬子路径，扩展了GR情形，除其他因素外，还考虑了再穿越对全速率的影响。其余分量源自平衡配分函数，并考虑了由于非绝热耦合导致的反应物和产物阱周围势能的变化。新的半经典理论除了GR瞬子计算外几乎不需要额外的计算量。它使得严格评估GR近似的准确性成为可能，并为未来关于一般半经典非绝热速率理论的工作奠定了基础。
