Marcus–Levich–Jortner (MLJ) theory is one of the most commonly used methods for including nuclear quantum effects in the calculation of electron-transfer rates and for interpreting experimental data. It divides the molecular problem into a subsystem treated quantum-mechanically by Fermi’s golden rule and a solvent bath treated by classical Marcus theory. As an extension of this idea, we here present a “reduced” semiclassical instanton theory, which is a multiscale method for simulating quantum tunneling of the subsystem in molecular detail in the presence of a harmonic bath. We demonstrate that instanton theory is typically significantly more accurate than the cumulant expansion or the semiclassical Franck–Condon sum, which can give orders-of-magnitude errors and, in general, do not obey detailed balance. As opposed to MLJ theory, which is based on wavefunctions, instanton theory is based on path integrals and thus does not require solutions of the Schrödinger equation nor even global knowledge of the ground- and excited-state potentials within the subsystem. It can thus be efficiently applied to complex, anharmonic multidimensional subsystems without making further approximations. In addition to predicting accurate rates, instanton theory gives a high level of insight into the reaction mechanism by locating the dominant tunneling pathway as well as providing similar information to MLJ theory on the bath activation energy and the vibrational excitation energies of the subsystem states involved in the reaction.

中文翻译：

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Marcus-Levich-Jortner理论的半经典瞬子公式。

Marcus–Levich–Jortner（MLJ）理论是在计算电子传输速率和解释实验数据中包括核量子效应的最常用方法之一。它将分子问题分为费米黄金定律量子力学处理的子系统和经典马库斯理论处理的溶剂浴。作为该思想的扩展，我们在这里提出一种“简化的”半经典瞬子理论，这是一种在存在谐波浴的情况下模拟分子细节中子系统的量子隧穿的多尺度方法。我们证明，瞬时量理论通常比累积扩展或半经典的弗兰克-康登总和要精确得多，后者可以给出数量级的误差，并且通常不遵循详细的平衡。与MLJ理论相反，基于波函数的瞬时子理论基于路径积分，因此不需要Schrödinger方程的解，甚至不需要子系统内基态和激发态电势的全局知识。因此，它可以有效地应用于复杂的非谐多维子系统，而无需进行进一步的近似。除了预测准确的速率外，瞬子理论还可以通过确定主导的隧穿路径来深入了解反应机理，并提供与MLJ理论类似的有关浴液活化能和涉及到的子系统状态的振动激发能的信息。反应。瞬时理论基于路径积分，因此不需要Schrödinger方程的解，甚至不需要子系统内基态和激发态电势的全局知识。因此，它可以有效地应用于复杂的非谐多维子系统，而无需进行进一步的近似。除了预测准确的速率外，瞬子理论还可以通过确定主导的隧穿路径来深入了解反应机理，并提供与MLJ理论类似的有关浴液活化能和涉及到的子系统状态的振动激发能的信息。反应。瞬时理论基于路径积分，因此不需要Schrödinger方程的解，甚至不需要子系统内基态和激发态电势的全局知识。因此，它可以有效地应用于复杂的非谐多维子系统，而无需进行进一步的近似。除了预测准确的速率外，瞬子理论还可以通过确定主导的隧穿路径来深入了解反应机理，并提供与MLJ理论类似的有关浴液活化能和涉及到的子系统状态的振动激发能的信息。反应。