From weak to functional: network cooperativity effects in cyclic neutral (HF)_m(NH₃)_n hydrogen bonded clusters

Individual hydrogen bond (HB) energies and cooperativity contributions were characterized across 66 HBs in twelve cyclic neutral (HF)_m(NH₃)_n clusters (m + n = 3-7) using a molecular tailoring approach (MTA)-based fragmentation method at the MP2/aug-cc-pVTZ level. In addition, we derive an explicit algebraic connection relating these MTA-derived HB descriptors to the conventional many-body expansion (MBE). The four HB types observed in the (HF)_m(NH₃)_n clusters follow an unambiguous energetic hierarchy: F-H⋯N (mean 22.7 ± 4.1 kcal mol^-1) > F-H⋯F (12.1 ± 3.3 kcal mol^-1) > N-H⋯F ≈ N-H⋯N (both 4.7 kcal mol^-1). Network cooperativity accounts for 27.5% of F-H⋯N strength but reaches 68% for N-H⋯F HBs, revealing a striking inversion between absolute strength and cooperative enhancement. Twelve of 66 HBs (18.2%) exhibit the cooperativity-amplified bond (CAB) effect: dimer energies below 4.0 kcal mol^-1 yet MTA in-cluster energies exceeding 6.0 kcal mol^-1, consistent with network polarization from adjacent F-H⋯N anchors. HF fraction correlates strongly with both average MTA HB energy (R² = 0.85) and average cooperativity per HB (R² = 0.79), consistent with HF content as a compositional determinant of cooperative efficiency within the topology examined here. QTAIM-derived topological parameters provide complementary support for the energetic results from MTA. Notably, the electron density at the bond critical point (ρ_BCP) correlates strongly with MTA HB energy (R² = 0.97) across all 66 HBs. These results provide a quantitative, topology-resolved framework for HB cooperativity in F/N systems, with prospective relevance to atmospheric aerosol nucleation, astrochemistry, crystal engineering, ion-transport materials, benchmarking of force fields and ML potentials, and proton-transfer reactivity in interstellar HF/NH₃ ices for prebiotic chemistry.