Symmetry characterization in molecular multiphoton spectroscopy

In this paper it is shown how simple application of irreducible tensor calculus provides a powerful method for the symmetry characterization of a wide range of multiphoton transitions in solids, liquids or gases. These methods provide for a systematic classification of distinct symmetry classes for any multiphoton process and facilitate devising suitable polarization studies for spectroscopic application. General results for multiphoton processes up to and including those involving four-photon interactions are presented in the tables for all the common molecular and crystallographic point groups. A new symmetry class labelling scheme is also introduced. Applications are illustrated by reference to two-, three- and four-photon absorption, resonance and non-resonance Raman scattering and hyper-Raman scattering. Whilst the examples principally involve electric dipole coupling, it is demonstrated how the effects of higher multipoles may be incorporated into the results.