The outstanding amplification observed in surface-enhanced Raman scattering (SERS) is due to several enhancement mechanisms, and standing out among them are the plasmonic (PL) and charge-transfer (CT) mechanisms. The theoretical estimation of the enhancement factors of the CT mechanism is challenging because the excited-state coupling between bright plasmons and dark CT states must be properly introduced into the model to obtain reliable intensities. In this work, we aim at simulating electrochemical SERS spectra, considering models of pyridine on silver clusters subjected to an external electric field E⃗ that represents the effect of an electrode potential V_el. The method adopts quantum dynamical propagations of nuclear wavepackets on the coupled PL and CT states described with linear vibronic coupling models parametrized for each E⃗ through a fragment-based maximum-overlap diabatization. By presenting results at different values of E⃗, we show that indeed there is a relation between the population transferred to the CT states and the total scattered intensity. The tuning and detuning processes of the CT states with the bright PLs as a function of the electric field are in good agreement with those observed in experiments. Finally, our estimations for the CT enhancement factors predict values in the order of 10⁵ to 10⁶, meaning that when the CT and PL states are both in resonance with the excitation wavelength, the CT and PL enhancements are comparable, and vibrational bands whose intensity is amplified by different mechanisms can be observed together, in agreement with what was measured by typical experiments on silver electrodes.

中文翻译：

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用于表面增强拉曼散射的线性振动耦合方法：量化电荷转移增强机制

表面增强拉曼散射 (SERS) 中观察到的出色放大是由于多种增强机制所致，其中最突出的是等离子体 (PL) 和电荷转移 (CT) 机制。 CT机制增强因子的理论估计具有挑战性，因为必须将亮等离子体激元和暗CT状态之间的激发态耦合适当地引入模型中以获得可靠的强度。在这项工作中，我们的目标是模拟电化学 SERS 光谱，考虑银簇上的吡啶模型受到外部电场E ⃗ 的影响，该电场代表电极电势V _el的影响。该方法采用核波包在耦合 PL 和 CT 状态上的量子动力学传播，并通过基于片段的最大重叠解绝化对每个E ⃗ 进行参数化的线性振动耦合模型进行描述。通过呈现不同E ⃗值的结果，我们表明转移到 CT 状态的总体与总散射强度之间确实存在关系。具有明亮 PL 的 CT 状态作为电场函数的调谐和失谐过程与实验中观察到的结果非常一致。最后，我们对 CT 增强因子的估计预测值约为 10 ⁵至 10 ⁶，这意味着当 CT 和 PL 状态均与激发波长共振时，CT 和 PL 增强具有可比性，并且振动带的通过不同机制放大的强度可以一起观察到，这与银电极上的典型实验测量的结果一致。