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Derivation has been made of the expressions of surface vibrational sum-frequency generation(SVSFG). The results include (a) the vibrational selection rule, (b) the expressions of the susceptibility tensors at the surfaces composed of functional groups with C3v and C2v local symmetry, (c) the formulas of the SFG tensor components which apply specifically to the vibrational resonance with the CH stretching modes of methyl and methylene groups, and (d) the interference effect by the nearby Fermi resonance band. Changes introduced by the slight distortion of C3v symmetry into Cs symmetry have also been discussed. Sample calculations have been made of the SVSFG of the CH stretch modes of oriented CH3 groups.
Hirose et al. (Wed,) studied this question.