Time-dependent picture of the charge-transfer contributions to surface enhanced Raman spectroscopy

We reexamine the Herzberg-Teller theory of charge-transfer contributions to the theory of surface enhanced Raman scattering (SERS). In previous work, the Kramers-Heisenberg-Dirac framework was utilized to explain many of the observed features in SERS. However, recent experimental and theoretical developments suggest that we revise the theory to take advantage of the time-dependent picture of Raman scattering. Results are obtained for molecular adsorption on nanoparticles in both the strong confinement limit and the weak confinement limit. We show that the Herzberg-Teller contributions to the charge-transfer effect in SERS display a resonance at the molecule-to-metal or metal-to-molecule transition while retaining the selection rules associated with normal Raman spectroscopy (i.e., harmonic oscillator, as opposed to Franck-Condon overlaps). The charge-transfer contribution to the enhancement factor scales as Gamma(-4), where Gamma is the homogeneous linewidth of the charge-transfer transition, and thus is extremely sensitive to the magnitude of this parameter. We show that the Herzberg-Teller coupling term may be associated with the polaron-coupling constant of the surface phonon-electron interaction. A time-dependent expression for the Raman amplitude is developed, and we discuss the implications of these results for both metal and semiconductor nanoparticle surfaces.