The three-HOMO-site rule: a frontier-orbital descriptor for low-barrier multi-proton synchronous hopping

Proton exchange membrane fuel cells suffer from severe proton conductivity loss under low-humidity conditions, largely owing to an incomplete understanding of multi-proton synchronous hopping (MPSH). Using Nafion side chains as prototypes, α,ω-alkanedisulfonic acid monohydrates were studied by density functional theory, HOMO analysis, and multi-method charge analysis. A clear correlation emerges between the frontier-orbital distribution and proton-transfer barriers: low-barrier MPSH systems consistently exhibit simultaneous HOMO sites on the proton donor, proton acceptor, and proton-carrier water molecule, whereas the loss of any site substantially raises the barrier. This work summarizes this as the "Three-HOMO-Site Rule": by Hirshfeld orbital composition analysis, both the proton donor and proton acceptor groups must make a significant non-zero contribution to the HOMO; a contribution of either group approaching zero signals an elevated barrier. For the proton-carrier site, whether the HOMO isosurface remains continuous across the three sites serves as the key criterion. Dynamic charge analysis of the O-H⋯O/N bridge further reveals that rule-satisfying systems undergo cooperative electronic polarization. In contrast, high-barrier systems show a completely frozen charge response, a dichotomy consistently identified by three density-based charge methods (Hirshfeld, CM5, ADCH). The rule is validated in alkyl homologues, geometrically constrained systems, Nafion side-chain fragments, as well as phosphonate-water bridges and sulfonate-ammonia systems, confirming its transferability among sulfonate-water/ammonia and phosphonate-water motifs. This work provides an electronic descriptor based on the topological features of frontier orbitals for rapid pre-screening of proton-transfer motifs, shifting from computationally intensive post-factum interpretation toward efficient a priori identification of favorable proton-conducting structures.