Theoretical method for near-field Raman spectroscopy with multipolar Hamiltonian and real-time-TDDFT: Application to on- and off-resonance tip-enhanced Raman spectroscopy.

Tip-enhanced Raman spectroscopy in combination with scanning tunneling microscopy could produce ultrahigh-resolution Raman spectra and images for single-molecule vibrations. Furthermore, a recent experimental study successfully decoupled the interaction between the molecule and the substrate/tip to investigate the intrinsic properties of molecules and their near-field interactions by Raman spectroscopy. In such a circumstance, more explicit treatments of the near field and molecular interactions beyond the dipole approximation would be desirable. Here, we propose a theoretical method based on the multipolar Hamiltonian that considers full spatial distribution of the electric field under the framework of real-time time-dependent density functional theory. This approach allows us to treat the on- and off-resonance Raman phenomena on the same footing. For demonstration, a model for the on- and off-resonance tip-enhanced Raman process in benzene was constructed. The obtained Raman spectra are well understood by considering both the spatial structure of the near field and the molecular vibration in the off-resonance condition. For the on-resonance condition, the Raman spectra are governed by the transition moment, in addition to the selection rule of off-resonance Raman. Interestingly, on-resonance Raman can be activated even when the near field forbids the π-π transition at equilibrium geometry due to vibronic couplings originating from structural distortions.