Relative contributions of Franck-Condon to Herzberg-Teller terms in charge transfer surface-enhanced Raman scattering spectroscopy

We have theoretically modeled charge transfer (CT) surface enhanced raman scattering (SERS) spectroscopy using pyridine bound to a planar Ag-6 metal nanocluster. CT states were determined by natural transition orbital hole-particle plots and CT distance D-CT and the amount of charge transferred q(CT) indices. We first consider a resonance Raman (RR) model based on the Albrecht approach and calculate the ratio of the Herzberg-Teller (HT) B or C term to the Franck-Condon (FC) A term for a totally symmetric a(1) vibrational mode exciting in the lowest energy CT state. Using a dimensionless upper limit to the displacement factor = 0.05 in the FC term based on the examination of overtones in experimental spectra and a calculated HT coupling constant h(CT) = 0.439 eV/angstrom (amu)(1/2) in the HT term, we calculated the scattering ratio of the HT to FC intensities as 147. This example indicated that for totally symmetric modes, the scattering intensity would all come from HT scattering. To further verify this result, we used the general time-dependent-RR formulation of Baiardi, Bloino, and Barone with the adiabatic Hessian model to calculate the FC, the Frank-Condon and Herzberg-Teller (FCHT), and the HT terms for pyridine in the C-2v Ag-6-pyridine complexes. For all cases we studied with pyridine in two orientations either parallel or perpendicular to the planar Ag-6 cluster, the HT terms, FCHT + HT, dominate the FC term in the CT RR spectrum. These results indicate that for CT SERS, the intensity of all the totally and non-totally symmetric vibrational modes should come from the HT effect.