A covalency-electrostatics crossover sets the threshold of eleven water molecules for HF dissociation

Abstract

Hydrofluoric acid (HF) is a prototypical weak acid whose onset size and microscopic electronic mechanism of dissociation in finite water clusters remain poorly unified. Here, we perform systematic structural searches and multi-level quantum-chemical calculations on HF(H₂O)_n (n = 1–12) clusters and, by combining energetic analysis with simulated infrared spectra, map out the microscopic evolution of spontaneous HF dissociation. Although metastable ion-pair isomers already emerge for n ≥ 4, the ion-pair configuration does not become the global minimum until n = 11. At this size, the H–F stretching band disappears completely from the simulated IR spectrum, while the characteristic vibrational features of the hydronium ion H₃O⁺ are strongly enhanced, allowing us to unambiguously identify n = 11 as the critical cluster size for a stable auto-dissociation of HF. Statistical analysis of 692 optimized structures further reveals a dual dependence of HF dissociation on both size and topology: a local water coordination number (WCN) ≥ 3 around HF is a necessary condition for triggering proton transfer, whereas an overall cluster size n ≥ 11 is required to thermodynamically stabilize the ion-pair state, underscoring the key role of cooperative hydrogen-bond networks in breaking the H–F bond. Our energy decomposition analysis based on sobEDAw further reveals that the pronounced stability of the undissociated HF is primarily governed by covalent orbital interactions. We identify 1.17 Å as a critical threshold, beyond which the dominant stabilization mechanism switches to ionic electrostatic interactions, thereby revealing an electronic mechanism: a covalency-electrostatics crossover that sets the threshold of eleven water molecules for HF dissociation. By jointly establishing the size threshold, structural motifs and electronic driving mechanism for the dissociation of a weak acid in finite water clusters, this work provides a new theoretical basis for a unified understanding of weak-acid solvation and proton-transfer mechanisms at the molecular level.