Fermi resonance as a means to determine the hydrogen-bonding status of two infrared probes

The C[double bond, length as m-dash]O/C[triple bond, length as m-dash]N stretching vibration arising from a carbonyl/nitrile functional group in various molecular systems has been frequently used to assess, for example, local hydrogen-bonding interactions, among other applications. However, in practice it is not always easy to ascertain whether the carbonyl or nitrile group in question is engaged in such interactions. Herein, we use 4-cyanoindole and cyclopentanone as models to show that, when a fundamental C[double bond, length as m-dash]O or C[triple bond, length as m-dash]N stretching mode is involved in Fermi resonance, the underlying vibrational coupling constant (W) is a convenient reporter of the hydrogen-bonding status of the corresponding carbonyl or nitrile group. Specifically, we find that for both groups a W value of 7.7 cm^-1 or greater is indicative of their involvement in hydrogen-bonding interactions. Furthermore, we find that, as observed in similar studies, the Fermi resonance coupling leads to quantum beats in the two-dimensional infrared spectra of 4-cyanoindole in isopropanol, with a period of about 1.9 ps.