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We discuss the susceptibility third-rank tensor for second harmonic andsumfrequency generation, associated with low index surfaces of silicon(Si(001), Si(011) and Si(111)) from two different approaches: the SimplifiedBond-Hyperpolarizablility Model(SBHM) and Group Theory (GT). We show that SBHMagrees very well with the experimental results for simple surfaces because thedefinitions of the bond vectors implicitly include the geometry of the crystaland therefore the symmetry group. However, for more complex surfaces it isshown that one can derive from GT the SBHM tensor, if Kleinman symmetry isallowed.

Simplified Bond Hyperpolarizability Model of Second Harmonic Generation, Group Theory and Neumann's Principle