Method for evaluating vibrational mode assignments in surface-bound cyclic hydrocarbons using sum-frequency generation

A method is proposed and tested in which vibrational sum frequency generation (SFG) spectra are assigned to vibrational modes in cyclic hydrocarbon species at transparent oxide surfaces. This method is especially effective for identifying asymmetric C-H stretches which are particularly difficult to assign in cyclic hydrocarbons because they have frequencies similar to those of overtones and Fermi resonances, and because multiple nondegenerate asymmetric C-H stretches occur. The ratios between SFG signal intensities in two different experimental polarization combinations are compared to the predicted values assuming local C_2v symmetry for an asymmetric CH₂ stretching vibration. By applying this method to silica surfaces containing covalently linked cyclopropyl, cyclobutyl, cyclopentyl, and cyclopentenyl groups with fixed orientations, and benchmarking to published gas phase spectra, the observed SFG peaks are assigned to either (1) isolated asymmetric stretches of CH₂ groups possessing local C_2v symmetry, (2) motions of CH bonds coupled throughout the molecule not possessing local C_2v symmetry, or (3) symmetric stretching or other C-H stretching motions. The SFG spectra of the less-strained five-membered rings contain peaks that - based on polarization ratios - correspond to isolated asymmetric stretches. For these species, the results contradict a full-molecule normal mode description of molecular vibrations.