Elucidating the indirect relaxation mechanism’s impress on the IR spectral profiles of H-bonded complexes: A benchmark for quantum and quantum-classical methods

Zakia Hassan Alhashem and Najeh Rekik

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: In the quest to thoroughly elucidate the quantum impress of various mechanisms that could affect the IR spectra of damped hydrogen-bonded systems, we have examined which of the previous models that integrate the indirect relaxations of the intermonomer mode into the medium, regarded as a thermal bath, can successfully account for the spectral characteristics that may activate this mechanism on the IR spectral density. We elucidate the results derived from the classical-quantum theory proposed by Robertson and Yarwood, alongside the quantum theory based on the adiabatic approximation suggested by Boulil et al. Additionally, we consider the theory of indirect relaxation as presented by Blaise et al., which extends beyond the adiabatic approximation. Through numerical calculations, we have identified significant differences between the classical-quantum approaches and the quantum theories. The findings indicate that indirect damping results in a broadening of the lineshape in the quantum-classical approach, while it causes a smoothing effect on the IR spectral densities in the quantum approaches. The increasing of the indirect relaxation parameter within quantum–classical approach results in a broadening effect, which is primarily attributed to the decay exponential term. The different transitions |m〉|0〉→|n〉|1〉 that occur between the ground state |0〉 and its associated first excited state|1〉, along with the transitions happening between the slow-frequency stretch mode states, specifically|m〉 and|n〉, undergo broadening. As a result, the sub-bands become progressively broadened in relation to the transition|0〉|0〉→|0〉|1〉. According to the adiabatic approximation proposed by Boulil et al., as the indirect relaxation parameter is increased, one may notice a smoothing effect and a change in the intensity of the sub-bands as one approach the low and high frequency tails of the IR profiles. Beyond the adiabatic approximation proposed by Blaise et al., the sub-bands’ shapes experience a smoothing change in a consistent manner across the entire spectra. The result of the comparative illustration between the three approaches suggests that the quantum treatment proposed by Blaise et al. appears to be the appropriate approach. This method facilitates the analysis of scenarios that extend beyond the adiabatic approximation, which was not feasible in previous methods.

Keywords: Hydrogen bond; Indirect relaxations; IR spectral density; Adiabatic approximation; Strong anharmonic coupling; Dyson time ordering; Bosons normal ordering; Quantum thermal bath (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926008441

DOI: 10.1016/j.chaos.2026.118703

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