Atomistic polarization model for Raman scattering simulations of large metal tips with atomic-scale protrusions at the tip apex.

Tip-enhanced Raman spectroscopy (TERS) has recently been developed to push the spatial resolution down to single-chemical-bond scale. The morphology of the scanning tip, especially the atomistic protrusion at the tip apex, plays an essential role in obtaining both high spatial resolution and large field enhancement at the Ångström level. Although it is very difficult to directly characterize the atomistic structures of the tip, the Raman scattering from the apex's own vibrations of the metal tip can provide valuable information about the stacking of atoms at the tip apex. However, conventional quantum chemistry packages can only simulate the Raman scattering of small metal clusters with few atoms due to huge computational cost, which is not enough since the shaft of the tip behind the apex also makes significant contributions to the polarizabilities of the whole tip. Here we propose an atomistic polarization model to simulate the Raman spectra of large metal tips at subwavelength scales based on the combination of the atomistic discrete dipole approximation model and the density functional theory. The atomistic tip with different sizes and stacking structures is considered in its entirety during the calculation of polarizabilities, and only the vibrational contributions from the tip apex are taken into account to simulate the Raman spectra of the tip. The Raman spectral features are found to be very sensitive to the local constituent element at the tip apex, atomic stacking modes, and shape of the tip apex, which can thus be used as a fingerprint to identify different atomistic structures of the tip apex. Moreover, our approaches can be extended to the metal tips with sub-wavelength sizes, making it possible to consider both the large scale and the atomistic detail of the tip simultaneously. The method presented here can be used as a basic tool to simulate the Raman scattering process of the metal tips and other nanostructures in an economic way, which is beneficial for understanding the roles of atomistic structures in tip- and surface-enhanced spectroscopies.