In this study, we present results from path integral molecular dynamics simulations that describe the characteristics of the quantum spatial delocalizations of protons participating in OH bonds in (MeOH)2H+ and in (MeOH)3H+. The characterization was carried out by examining the overall structures of the corresponding isomorphic polymers. To introduce full flexibility in the force treatment, we have adopted a neural network fitting procedure based on second-order Møller-Plesset perturbation theory predictions. For the dimer case, we found that the spatial extent of the shared connective proton can be portrayed in terms of a prolate-like structure with typical dimensions of ∼0.1 Å. On the other hand, the dangling polymers lie confined within a thin spherical layer, spread over length scales of the order of ∼0.25 Å. In contrast, connective protons in (MeOH)3H+ exhibit larger delocalizations along the O-H bond and more localized ones along perpendicular directions, compared to their dangling counterparts. We also examined the characteristics of the relative propensities of H and D isotopes to be localized in dangling and connective positions. Physical interpretations of the different thermodynamic trends are provided in terms of the local geometrical characteristics and of the strengths of the corresponding intermolecular connectivities.
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