Development of quadrupole susceptibility automatic calculator in sum frequency generation spectroscopy and application to methyl C-H vibrations

Sum frequency generation (SFG) spectroscopy has been established as a powerful interface probe technique based on the electric dipole approximation, while possible signals of quadrupole and bulk origin have also been known for a long time. In this work, we developed a computational tool, namely, Qsac (quadrupole susceptibility automatic calculator), to evaluate the comprehensive contributions of the dipole/quadrupole and interface/bulk in the arbitrary vibrational bands of SFG spectra. The calculations of relevant susceptibility terms are performed on the basis of the theory of energy representation using quantum chemical calculation and molecular dynamics simulation, which allows for semi-quantitative comparison among these terms on the same footing. We applied the Qsac to the methyl C-H stretching bands of organic molecules and found a general trend that the weak asymmetric bands are more sensitive to the bulk contribution than the symmetric ones. The phases of interface and bulk terms tend to cancel in the asymmetric band, which results in the reduced band intensity in the SFG spectra.