Determining absolute molecular orientation at interfaces : a phase retrieval approach for sum frequency generation spectroscopy

We report a numerical algorithm, the maximum entropy method (MEM), to obtain the absolute phase of the sum frequency signal from vibrational sum frequency generation (VSFG) spectra, without the need for phasesensitive measurements. From the phase of the VSFG susceptibility, we can determine the molecular orientation, i.e., whether molecular groups are pointing «up» or «down», with respect to the interface. Furthermore, with previous knowledge of the nonresonant phase, the real and imaginary parts of second-order susceptibility can also be determined. The phase retrieval algorithm is successfully applied to spectra obtained from three distinct samples: (1) water vibrations of the SiO₂-water interface, (2) methyl vibrations of a dodecanol monolayer on water, and (3) methyl vibrations of self-assembled dodecanethiol monolayers on a gold substrate. These results demonstrate that the approach is applicable to a wide range of spectra, with varying resonance widths and nonresonant background levels. For the SiO₂-water interface at high pH, we find that the water molecules are oriented with their hydrogen atoms toward the surface, and we show that the procedure demonstrated here provides information on the interfacial vibrations that cannot be obtained from a multiresonance fit. For surfactant monolayers, we find, as expected, that the methyl groups point away from the substrate. Possible complications and limitations in determining the phase spectrum of the nonlinear susceptibility using MEM are also discussed.