We derive a Hierarchical Equations of Motion (HEOM) description of nonadiabatic Herzberg-Teller type coupling effects and of non-Condon effects in a system of electronic transitions interacting with intra- and inter-molecular vibrational modes. We point out analogies between the auxiliary density operators (ADOs) of the hierarchy and the terms arising from explicit description of the vibrational modes in the Hamiltonian. In comparison with the standard formulation of HEOM, our equations contain additional connections between ADOs in the hierarchy scheme, which account for the dependence of the nonadiabatic coupling elements on the vibrational coordinates. We compare absorption spectra calculated with our HEOM methodology and with explicit treatment of vibrational DOF for a dimer system in the strong resonance coupling regime. Furthermore, we show that for sufficiently strong excitonic coupling, the corresponding effects in linear absorption spectra of vibronic dimers can be captured very well by the concept of effective Huang-Rhys factors.

我们导出了非绝热Herzberg-Teller型耦合效应和非过渡效应与分子内和分子间振动模式相互作用的系统中的非绝热Herzberg-Teller型耦合效应的运动分层方程（HEOM）。我们指出了层次结构中的辅助密度算子（ADO）与由哈密顿量中的振动模态的显式描述引起的术语之间的类比。与HEOM的标准公式相比，我们的方程式在层次结构方案中包含ADO之间的其他连接，这说明了非绝热耦合元素对振动坐标的依赖性。我们比较了用我们的HEOM方法和在强共振耦合条件下对二聚体系统的振动自由度进行显式处理所计算出的吸收光谱。此外，