Nonlinear, four-wave mixing vibrational spectroscopies are commonly used to probe electron–vibration coupling in isotropic media. Most of these methods rely on infrared and/or Raman transitions, but methods involving hyper-Raman transitions are also possible. Hyper difference frequency generation (HDFG) spectroscopy is an underdeveloped four-wave mixing vibrational spectroscopy based upon both infrared absorption and hyper-Raman scattering transitions. Despite several experimental reports on HDFG, its spectroscopic properties have not been fully explored. To this end, we investigate the selection rules and behavior of HDFG spectroscopy as an upconverted infrared spectroscopy and as a probe of vibronic coupling in molecular systems. We discuss the similarities between HDFG, a four-wave mixing technique, and vibrational sum frequency generation (vSFG) spectroscopy, a three-wave mixing technique. vSFG and HDFG appear to provide similar output intensities, making HDFG feasible for vSFG practitioners. HDFG is shown to be a sensitive probe of vibronic coupling in bulk systems and provides an alternative method to investigate electronic-nuclear coordinate correlations.
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