We review the many-body Green's function Bethe–Salpeter equation (BSE) formalism that is rapidly gaining importance for the study of the optical properties of molecular organic systems. We emphasize in particular its similarities and differences with time-dependent density functional theory (TD-DFT), both methods sharing the same formal (N⁴) computing time scaling with system size. By comparison with higher level wavefunction based methods and experimental results, the advantages of BSE over TD-DFT are presented, including an accurate description of charge-transfer states and an improved accuracy for the challenging cyanine dyes. We further discuss the models that have been developed for including environmental effects. Finally, we summarize the challenges to be faced so that BSE reaches the same popularity as TD-DFT.

中文翻译：

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Bethe–Salpeter化学方程式：与TD-DFT的关系，应用和挑战

我们回顾了多体格林函数Bethe–Salpeter方程（BSE）形式主义，该形式对研究分子有机系统的光学性质正迅速变得重要。我们特别强调其与时变密度泛函理论（TD-DFT）的异同，两种方法共享相同的形式（N ⁴）计算系统规模的时间比例。通过与基于更高水平波函数的方法和实验结果进行比较，提出了BSE优于TD-DFT的优点，包括对电荷转移状态的准确描述以及对具有挑战性的花菁染料的改进准确性。我们将进一步讨论已开发的包括环境影响的模型。最后，我们总结了要面对的挑战，以使BSE达到与TD-DFT相同的知名度。