Quantum theory of surface Raman scattering from adsorbates

Abstract

The Raman spectrum due to vibrational excitations in molecules adsorbed on a solid surface differs from the corresponding molecules in the liquid or the free state in many important aspects. Because of the substrate-molecule interaction, the ground-state electronic charge density distribution, the nature of the electronic excitation spectrum, the modulation behaviour of the modified electronic polarizability due to ionic vibrations, and the ionic fluctuation spectrum including the vibrational mode frequencies of the molecule are no longer the same in the presence of the polarizable substrate as in the case of a free molecule. Besides these intrinsic changes in the system itself, the external optical field at the incident frequency, acting at the site of the adsorbed molecule, is now different than the incident field, and the Stokes scattered field in the radiation zone arising from the adsorbate is modified by the substrate. The last two modifications are purely “electromagnetic” in the sense that they may be important even when the metal-molecule interaction can be neglected either because the bonding is very weak or because their separation distance d is large compared to atomic distances. In suitable situations, the “electromagnetic” modifications contain enhancements of the incident and scattered fields due to resonant excitation of surface-plasmon-polaritons (SPP) in, e.g., metallic substrates. The intrinsic differences arising from interactions at short distances, the so-called “chemical effect”, lead to the changes in the intrinsic electronic and Raman polarizabilities so that the Raman cross sections are enhanced in special situations, including the possibility of new resonance Raman conditions involving the modified single-particle excited charge-transfer states of the coupled system. In this presentation, a simplified model of electronic interactions of a molecule on a solid surface is used to formulate a general theory of surface Raman scattering. It is shown how this theory can take care of both the electromagnetic as well as the chemical modifications in different systems, whether or not there is any net large enhancement in the Raman cross sections. To account for the bonding and tunneling of electrons at the surface, a consistent quantum formulation for the surface Raman scattering becomes absolutely essential to analyse experimental results and distinguish between different mechanisms for the enhancement or otherwise of the Raman cross sections.