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

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.