Concerted proton transfer in homogeneous and heterogeneous cyclic hydrogen-bonded clusters of H₂O, HF, and HCl

This work examines various homogeneous and heterogeneous clusters of hydrogen-bonded (HF)_x(H₂O)_y(HCl)_z complexes, where x + y + z = 3 or 4. For each unique cyclic structure associated with the xyz permutations, the geometries of the reactant, product, and transition state (TS) for concerted proton transfer (CPT) were fully optimized using second-order Møller-Plesset perturbation theory (MP2) with a mixed basis set consisting of cc-pVTZ for H atoms and aug-cc-pVTZ for O, Cl, and F atoms (denoted haTZ). Harmonic vibrational frequencies were also computed at the same level of theory to verify the nature of the stationary points. Intrinsic reaction coordinate (IRC) calculations confirm that all transition states reported herein connect the two minima associated with the CPT process, and these reaction profiles provide a means to assess the associated barrier width. Single-point energies were computed on the optimized structures using an explicitly correlated coupled cluster method with an analogous quadruple-ζ basis set (CCSD(T)-F12/haQZ-F12) to determine the dissociation energy (D_e) of each trimer and tetramer minimum, as well as the barrier height (ΔE^‡) and energy difference between the reactants and products (ΔE) associated with the CPT process in each cluster. The energetics calculated utilizing this methodology were compared to CCSD(T) benchmark data for the homogeneous clusters (Y. Xue, T. M. Sexton, J. Yang and G. S. Tschumper, Phys. Chem. Chem. Phys., 2024, 26, 12483-12494, DOI: https://doi.org/10.1039/D4CP00422A), and deviations never exceeded 0.1 kcal mol^-1. For the heterogeneous trimer systems, (H₂O)₂(HCl)₁ had the smallest ΔE^‡ at only 11.9 kcal mol^-1, just below the corresponding D_e of 13.8 kcal mol^-1. Among the heterogeneous tetramers, six systems were identified with an even smaller ΔE^‡ (7.9 to 11.8 kcal mol^-1) and a larger D_e (19.8 to 30.8 kcal mol^-1). Among those, (HF)₃(H₂O)₁ has one of the narrowest barrier widths of any tetramer system, based upon MP2/haTZ IRC profiles.