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Molecular properties leading to second harmonic generation in chiral media in the electric dipole approximation for the cases of axial and biaxial symmetry are described. The components of the hyperpolarizability tensor that transform like a second-rank pseudotensor (L=2) and a third-rank tensor (L=3) contribute. The sum-over-states quantum formula for the hyperpolarizability is used to illuminate the molecular features necessary for optimizing the second-rank pseudotensor for dipolar molecules including orthogonal moments and high frequency. The example of C_2v, appropriate for Λ-shaped molecules, is examined in more detail. Results of the measurements of these components in representative molecules using hyper-Rayleigh scattering are presented. Two compounds in which the delocalized pi-system is two-dimensional, a camphorquinone derivative and crystal violet are found to exhibit sizable L=2 and L …