Effects of reorientation in vibrational sum-frequency spectroscopy

Vibrational sum-frequency spectroscopy (VSFS) has become a widely used tool for studying molecules at interfaces. While VSFS data are often interpreted in terms of static structure, Wei and Shen demonstrated that orientational dynamics that occur on the time scale of vibrational dephasing can influence the strength of the VSFS signal (Wei, X.; Shen, Y. R. Phys. Rev. Lett. 2001, 86, 4799). In this report, we consider the orientational averages relevant to VSFS under different polarization conditions in terms of the infrared transition dipole and the Raman tensor when the infrared and Raman transitions are simultaneous and when they are separated by a delay that is greater than the orientational correlation time. We examine specific cases of orientational averaging that apply to commonly studied functional groups. This analysis makes possible the identification of the circumstances under which reorientation should be taken into account when using VSFS to determine molecular orientation at interfaces.