Origin of the Hadži ABC structure: An ab initio study

Medium and strong hydrogen bonds are well known to give rise to broad features in the vibrational spectrum often spanning several hundred wavenumbers. In some cases, these features can span over 1000 cm⁻¹ and even contain multiple broad peaks. One class of strongly hydrogen-bonded dimers that includes many different phosphinic, phosphoric, sulfinic, and selenic acid homodimers exhibits a three-peaked structure over 1500 cm⁻¹ broad. This unusual feature is often referred to as the Hadži ABC structure. The origin of this feature has been debated since its discovery in the 1950s. Only a couple of theoretical studies have attempted to interpret the origin of this feature; however, no previous study has been able to reproduce this feature from first principles. Here, we present the first ab initio calculation of the Hadži ABC structure. Using a reduced dimensionality calculation that includes four vibrational modes, we are able to reproduce the three-peak structure and much of the broadness of the feature. Our results indicate that Fermi resonances of the in-plane bend, out-of-plane bend, and combination of these bends play significant roles in explaining this feature. Much of the broadness of the feature and the ability of the OH stretch mode to couple with many overtone bending modes are captured by including an adiabatically separated dimer stretch mode in the model. This mode modulates the distance between the monomer units and accordingly the strength of the hydrogen-bonds causing the OH stretch frequency to shift from 2000 to 3000 cm⁻¹. Using this model, we were also able to reproduce the vibrational spectrum of the deuterated isotopologue which consists of a single 500 cm⁻¹ broad feature. Whereas previous empirical studies have asserted that Fermi resonances contribute very little to this feature, our study indicates that while not appearing as a separate peak, a Fermi resonance of the in-plane bend contributes substantially to the feature