Molecular and surface hyperpolarizability of oriented chromophores of low symmetry

In chromophores of low symmetry, including chiral species, modeling calculations generally do not produce the most convenient set of coordinates for evaluating the molecular second order nonlinear polarizability tensor beta((2)). By referencing the internal coordinate axes with respect to a single, dominant transition, the number of significant electric-dipole allowed beta((2)) tensor elements can be reduced from 18 in second harmonic generation (SHG) to at most 3, with the complete removal of all chiral elements. This coordinate transformation reduces the complexity of SHG measurements of oriented chiral systems to a level consistent with chromophores of significantly higher symmetry and provides a straightforward approach for extracting orientation information from polarization measurements.