Matrix formulation of the surface-enhanced Raman optical activity theory.

The previously formulated surface-enhanced SE Raman optical activity ROA theory is based on a multipole electromagnetic field expansion. The field of molecule and colloid particles is induced by the excitation light. Although this semistatic polarization is not the only enhancement mechanism, it provides a good basis for understanding of the phenomenon. However, the mathematical expressions become rather tedious due to the high degree of expansion quadrupole and magnetic dipole and mutual particlemolecule and molecule-particle polarizations. The huge differences between the molecular and colloid polarizabilities make iterative intuitive solutions difficult. Therefore, we propose to rewrite the formulas in a matrix form leading to direct noniterative solutions. This formulation can also be easily extended to multiparticle systems. Particularly, let us consider N polarizable particles, typically a molecule and S colloids N=S+1 . By default, we express variables in local coordinate systems connected with the particle centers. The induced electric and magnetic dipole, and electric quadrupole are, respectively,