Studying the effect of phonon coherence and inflow on hydrogen bond formation in the $[({\mathrm{H}}_2\mathrm{O}{)}_2{]}^m$ cluster

Abstract

We propose a simplified open-quantum-system model for hydrogen-bond formation in water clusters, where each subsystem is mapped to a $\hat{I}»$-type three-level system coupled to two effective phonon modes: a micro-vibration mode ($\hat{I}{\text{c◯}}_{\mathrm{hyd}}$) representing the O--H stretching vibration, and a macro-displacement mode ($\hat{I}{\text{c◯}}_{\mathrm{dist}}$) representing the intermolecular donor-acceptor motion. The $[({\mathrm{H}}_2\mathrm{O}{)}_2{]}^m$ cluster is studied for $m=2$ to $6$ in the incoherent case (independent phonon modes) and the coherent case (shared phonon modes). We find that phonon coherence significantly alters the dynamics. In the dissipative case, coherence induces a redistribution of steady-state populations: intermediate hydrogen-bond counts are enhanced while edge counts are suppressed -- a ``squeezing'' effect explained by the interplay of subradiant states and dark states. For $m\ge 3$, true dark states emerge, rooted in the permutation symmetry of the system. Inflow of $\hat{I}{\text{c◯}}_{\mathrm{dist}}$ phonons promotes hydrogen bond formation, while inflow of $\hat{I}{\text{c◯}}_{\mathrm{hyd}}$ phonons inhibits it. Our results reveal a nontrivial role of quantum coherence and dark states in hydrogen-bond dynamics, providing a foundation for extending the framework to more complex systems.

10 pages, 5 figures, 3 tables; Supplementary Information: 12 pages, 6 figures, 6 animations

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