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.