Theoretical Modeling of Plasmon-Enhanced Raman Images of a Single Molecule with Subnanometer Resolution

Under local plasmonic excitation, Raman images of single molecules can now surprisingly reach subnanometer resolution. However, its physical origin has not been fully understood. Here we report a quantum-mechanical description of the interaction between a molecule and a highly confined plasmonic field. We show that when the spatial distribution of the plasmonic field is comparable to the size of the molecule, the optical transition matrix of the molecule becomes dependent on the position and distribution of the plasmonic field, resulting in a spatially resolved high-resolution Raman image of the molecule. The resonant Raman image reflects the electronic transition density of the molecule. In combination with first-principles calculations, the simulated Raman image of a porphyrin derivative adsorbed on a silver surface nicely reproduces its experimental counterpart. The present theory provides the basic framework for describing linear and nonlinear responses of molecules under highly confined plasmonic fields.