Electronic transport properties of single-molecule junctions have been widely measured by several techniques, including mechanically controllable break junctions, electromigration break junctions or by means of scanning tunneling microscopes. In parallel, many theoretical tools have been developed and refined for describing such transport properties and for obtaining numerical predictions. Most prominent among these theoretical tools are those based upon density functional theory. In this review, theory and experiment are critically compared and this confrontation leads to several important conclusions. The theoretically predicted trends nowadays reproduce the experimental findings quite well for series of molecules with a single well-defined control parameter, such as the length of the molecules. The quantitative agreement between theory and experiment usually is less convincing, however. { Two main sources for the quantitative discrepancies can be identified: Experimentally, the atomic structure of the junction typically realized in the measurement is not well known, so that simulations rely on plausible scenarios. In theory, correlation effects can be included only in approximations that are difficult to control for experimentally-relevant situations. Therefore, one typically expects a qualitative agreement with present modeling tools; encouragingly, in exceptional cases also a quantitative agreement has already been achieved.} For further progress, benchmark systems are required that are sufficiently well-defined by experiment to allow quantitative testing of the approximation schemes underlying the theoretical modeling. Several key experiments can be identified suggesting that the present description may even be qualitatively incomplete in some cases. Such key experimental observations and their current models are also discussed here, leading to several suggestions for extensions of the models towards including dynamic image charges, electron correlations, and polaron formation.

中文翻译：

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单分子电子传输的进展与挑战

单分子结的电子输运性质已通过多种技术进行了广泛测量，包括机械可控的断裂结，电迁移断裂结或通过扫描隧道显微镜。同时，已经开发和完善了许多理论工具来描述这种传输特性并获得数值预测。这些理论工具中最突出的是那些基于密度泛函理论的工具。在这篇综述中，理论与实验进行了严格的比较，这种对抗导致了一些重要的结论。如今，理论上预测的趋势很好地再现了一系列具有单个明确定义的控制参数（例如分子的长度）的分子的实验结果。但是，理论与实验之间的定量协议通常不太令人信服。{可以找到两个主要的定量差异来源：实验上，通常在测量中实现的结的原子结构并不为人所知，因此模拟依赖于可能的情况。理论上，相关效应只能包含在与实验相关的情况下难以控制的近似值中。因此，人们通常期望与现有的建模工具在质量上达成一致。令人鼓舞的是，在特殊情况下，也已经达成了定量协议。}为了取得进一步的进展，需要通过实验充分定义基准系统，以便对基于理论模型的近似方案进行定量测试。可以确定几个关键实验，这表明在某些情况下本说明在质量上甚至可能是不完整的。这里还将讨论这些关键的实验观察结果及其当前模型，从而为该模型的扩展提供了一些建议，包括动态图像电荷，电子相关性和极化子形成。