In the theory of condensed-phase spectroscopy, local field effect is of general importance to account for intermolecular electrostatic interactions. The present paper extends the microscopic treatment of local field effects on the sum frequency generation (SFG) spectroscopy to incorporate quadrupole interactions, since their roles have been increasingly recognized in the SFG spectroscopy. The extended theory involves some corrections to the conventional formulas of the nonlinear susceptibilities in both the interface and bulk regions, including the χIQB term. Fresnel transformations for the interface and bulk susceptibilities are rigorously applied, which implies inseparability of the interface and bulk signals in PSS and PPP cases. We examined the influence of the corrections with quantitative calculations of the susceptibilities, including dipolar and quadrupolar interactions.
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