Computationally predicting reverse intersystem crossing (RISC) rates is important for designing new thermally activated delayed fluorescence (TADF) materials. We report a method that can quantitatively predict RISC rates by explicitly considering the spin-vibronic coupling mechanism. The coupling element of the spin-vibronic Hamiltonian is obtained by expanding the spin-orbit and the non-Born-Oppenheimer terms to second order and is then brought into the Golden Rule rate under the Condon approximation. The rate equation is solved directly in the time domain using a correlation function approach. The contributions of the first-order direct spin-orbit coupling and the second-order spin-vibronic coupling to an RISC rate can be quantitatively analyzed in a separate manner. We demonstrate the utility of the method by applying it to a representative TADF system, where we observe that the spin-vibronic portion is substantial but not dominant especially with a relatively small triplet-singlet energy gap. Likewise, our method may elucidate the physical background of efficient nonradiative transitions from the lowest triplet to a higher lying singlet in other purely organic TADF systems, and it will be of great utility toward designing new such molecules.

中文翻译：

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热活化延迟荧光系统中逆系统间交叉速率定量预测的自旋振动模型。

通过计算预测反向系统间交叉（RISC）速率对于设计新的热激活延迟荧光（TADF）材料非常重要。我们报告了一种方法，可以通过明确考虑自旋振动耦合机制来定量预测RISC率。通过将自旋轨道项和非Born-Oppenheimer项扩展到二阶，可以得到自旋振动哈密顿量的耦合元素，然后在Conden近似下将其转化为黄金定律率。使用相关函数方法在时域中直接求解速率方程。一阶直接自旋轨道耦合和二阶自旋振动耦合对RISC速率的贡献可以以单独的方式进行定量分析。通过将其应用到代表性的TADF系统，我们证明了该方法的实用性，在该系统中，我们观察到自旋振动的部分很大但不占优势，尤其是在三重态-单重态能隙相对较小的情况下。同样，我们的方法可以阐明在其他纯有机TADF系统中从最低的三重态到较高的单重态的有效非辐射跃迁的物理背景，它将对设计新的此类分子具有极大的实用性。