A discrete interaction model/quantum mechanical method for simulating surface-enhanced Raman spectroscopy.

We have derived and implemented analytical gradients for the discrete interaction model/quantum mechanics (DIM/QM) method. DIM/QM combines an atomistic electrodynamics model with time-dependent density functional theory and thus enables modeling of the optical properties for a molecule while taking into account the local environment of a nanoparticle's surface. The DIM/QM analytical gradients allow for geometry optimizations, vibrational frequencies, and Raman spectra to be simulated for molecules interacting with metal nanoparticles. We have simulated the surface-enhanced Raman scattering (SERS) spectra for pyridine adsorbed on different sites of icosahedral nanoparticles with diameters between 1 and 8 nm. To describe the adsorption of the pyridine molecule onto the metal surface, we have implemented a coordination-dependent force field to differentiate the various local surface environments. We find that the DIM/QM method predicts geometries and frequencies that are in good agreement with full QM simulations and experiments. For the simulated SERS spectra of pyridine, we find a significant dependence on the adsorption site and the size of the metal nanoparticle. This illustrates the importance of accounting for the local environment around the molecule. The Raman enhancement factors are shown to roughly mirror the magnitude of the nanoparticle's local field about the molecule. Because the simulated nanoparticles are small, the plasmon peaks are quite broad which results in weak local electric fields and thus modest Raman enhancement factors.