On the shape of the simulated infrared spectral density of strongly hydrogen-bonded systems: Mapping and identification of Hadži ABC structure in phosphonic acid dimers in gas phase

Herein, we explore the origin of three-peaked structure, referred to as the Hadži ABC structure, illustrated within the absorption bands in infrared (IR) spectra of strongly H-bonded systems. The exploration is particularly elucidated for two phosphinic acid dimers (R₂POOH) in gas phase, namely bis-(iodomethyl)-phosphinic acid dimer (i.e., R = CH₂I) at 465 K and dibutyl-phosphinic acid dimer (i.e., R = C₄H₉O) at 425 K. A direct theoretical illustration of this spectral signature, related predominantly to very strongly hydrogen bonded complexes, is proposed. The spectral density, ${\upsilon }_S\left(O-H\right)$,is determined by the aid of an approach describing the high-frequency O − H stretching modes by harmonic potentials. The intermolecular potential modes (O…O) are assumed to be of anharmonic nature. The approach is founded on the strong anharmonic coupling approximation, which prescribes a linear dependency of the O − H frequency on the O…O stretching coordinate as rationalized by the fundamental model of Maréchal and Witkowski. Both direct relaxation of the O − H vibrational mode and its homolog, indirect one, affecting the O…O stretching mode are taken into consideration. The model also considers Davydov coupling, which describes the mutual interaction that takes place in the centrosymmetric dimer between the two existent hydrogen bonds as well as Fermi resonances, which occur between the bending modes arising in- and out-of-plane of the dimer and the fundamental O − H stretching mode. Interestingly, we illustrate how the (A, B, and C) triplet detected in the IR absorption band of phosphonic acids can be generated and discuss how the ABC structure can be numerically simulated. The approach provides a direct explanation of the emergence of this unusual feature and mainly reveals that the A peak is due to the Davydov coupling mechanism, whereas the BC diad is found to be generated by Fermi resonances. This was elucidated in a distinctly different approach, rationalized by Sheppard and Claydon, affirming that the provenance of the BC diad is exclusively due to Fermi resonances mechanism. Altogether, our results highlight the congregated effects of both Fermi resonance mechanism and Davydov coupling for the formation of the ABC structure. The model paves the way for a deeper understanding of the ABC structure, characteristic of very toxic strongly hydrogen-bonded dimers. This is of capital importance as it allows one to develop a solid understanding of nerve agents, such as phosphonic acids, from theory alone, so as to avoid difficult and dangerous experiments since they are extremely toxic.