Linear vibronic coupling approach for surface-enhanced Raman scattering: quantifying the charge-transfer enhancement mechanism

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 Vel. 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.