A detailed analysis of the Raman enhancement mechanisms associated with the interaction of a Raman scatterer with a resonant metal cluster: Results for Lin–H2

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Abstract
The results of time dependent Hartree–Fock calculations of frequency dependent polarizability derivatives for H2–Lin clusters (n=2, 4, 6) are presented and analyzed in terms of Raman enhancement mechanisms associated with interaction between H2 and the metal clusters. In these calculations, the width factors associated with unoccupied Hartree–Fock molecular orbitals are chosen so that the cluster polarizabilities are the same as those of bulk metal spheroids of the same size. The calculations are otherwise ab initio, and predict polarizability derivatives whose squares are enhanced by 103–104 for H2–Lin clusters at equilibrium geometries when irradiated at frequencies corresponding to metal cluster excitation energies. These enhancements were found to be reasonably independent of cluster size and vary by factors of 2–4 with H2 adsorption location. The enhancements were found to vary as the inverse fourth power of the excited state widths, and to decrease with increasing adsorbate–metal separation with a complicated functionality which reflects the varying contributions of three different enhancement mechanisms. At relatively large separations, induced polarization effects (i.e., electromagnetic interactions) make a large contribution to the enhancement factor. This is also important near equilibrium, but also important at this location (as well as at large separations) is a mechanism which involves the modulation of the metal orbital energies by the adsorbate vibrational motions. At smaller separations, corresponding to the repulsive region of the H2–Lin interaction potential, a third mechanism becomes dominant which involves the enhanced dipole matrix element derivatives which arise from charge transfer between adsorbate and metal. Symmetry of the electronic states giving rise to the cluster resonances was also found to influence enhancements, with the largest enhancements obtained for excited cluster states which have large overlap with the adsorbate HOMO and LUMO. Extension of these mechanistic interpretations to the description of surface enhanced Raman scattering (SERS) is considered.