Toward computation of bulk quadrupolar signals in vibrational sum frequency generation spectroscopy

Theoretical expressions for the bulk quadrupolar contributions in the vibrational sum frequency generation (SFG) spectra are presented for computational purposes. The quadrupolar terms, consisting of resonant and nonresonant components to the infrared frequency, are described by the energy representation and the time-dependent representation, which are extension of our previous SFG theories [A. Morita and J.T. Hynes, Chem. Phys. 258 (2000) 371, J. Phys. Chem. B 106 (2002) 673]. The present formulas are readily incorporated in molecular dynamics calculations of the bulk SFG signals as well as the surface signals.