Sum frequency generation (SFG) spectroscopy is a powerful experimental technique to probe surface structures. This paper presents a new theoretical mode of nonempirical analysis of SFG spectra for interfacial structures, which considerably generalizes our previous effort (Chem. Phys. 2000, 258, 371), which involved several empirical elements. The method is based on a time correlation function for the frequency-dependent hyperpolarizability, which can be straightforwardly evaluated via molecular dynamics simulations and which explicitly takes into account, for example, intramolecular vibrations and electronic polarization. The new theory is capable of precisely describing a number of factors significant for the spectrum, such as the dielectric local field correction, vibrational dephasing, inter/intramolecular vibrational coupling, etc., and is fairly nonempirical and rigorous, within the dipole approximation. The results for the water-vapor interface reproduce the experimental spectra fairly well, although with some discrepancies; possible reasons for these are suggested.