Determining Absolute Molecular Orientation at Interfaces: A Phase Retrieval Approach for Sum Frequency Generation Spectroscopy

Abstract

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 phase-sensitive 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.

Erratum: “Observation of buried water molecules in phospholipid membranes by surface sum-frequency generation spectroscopy” [J. Chem. Phys. 131, 161107 (2009)]

“…1(c)], rather than the value of -1.4 we concluded in our original manuscript. The retrieved Im[χ (2) ] spectrum appropriately corrected for the nonresonant phase now corresponds well to the results obtained using experimental approaches to determine the Im[χ (2) ] spectrum and are consistent with an intuitive orientation of the interfacial water, with O-D groups pointing "up. "…”

“…2 and the supporting information of Ref. 1, there are certain caveats and boundary conditions that have to be met for the successful application of the maximum entropy method to the analysis of SFG spectra (as opposed, for example, of using the same analysis tool to investigate coherent anti-Stokes Raman scattering spectra 6 ).…”

“…This is equivalent to a multiplication of the retrieved imaginary part by -1, as illustrated in Figs. 1(a) and 1(b), which shows retrieved Im[χ (2) ] spectra without any error phase correction (φ NR = 0). This dependence on the mode of analysis is typical of the fast-Fourier transform (FFT) involved in the analysis routine (and is present in all commercial FFT software we have checked), and was therefore also observed for the surfactants.…”

“…Briefly, the phase correction should meet the following criteria: first of all, for the systems studied here, the Im[χ (2) ] should be negative in the C-H stretch region; second, Im[χ (2) ] ≈ 0 in the regions without resonances; third, the C-H resonances must appear as (negative) peaks in the Im[χ (2) ]…”

Observation of buried water molecules in phospholipid membranes by surface sum-frequency generation spectroscopy

“…We employ vibrational sum-frequency generation ͑VSFG͒ spectroscopy [2][3][4][5] to probe membrane-bound water. Owing to its unique selection rules, VSFG is able to probe the outermost few molecular layers at the surface, where the local symmetry is broken, making it ideal to investigate water molecules near lipid headgroups.…”