Many-body cooperativity in water clusters revealed by information decomposition and finite-size scaling analysis with...

A systematic many-body expansion (MBE) analysis is presented for 1169 (H2O)4-23 cluster structures at the B3LYP-D3(BJ)/def2-TZVP level, with full enumeration of all monomer, dimer, and trimer subsystems. The per-molecule interaction energy converges toward the large-cluster limit following finite-size scaling governed by the evolution of surface-to-interior molecular coordination. While the individual 2B and 3B fractional contributions require second-order c/n2 corrections, the total energy converges to a simpler functional form concealing a nontrivial redistribution between pairwise and cooperative interactions. Machine-learning information decomposition reveals a hierarchical descriptor structure: pairwise interactions require explicit hydrogen orientational information beyond O⋯O distances, whereas 3B cooperativity is predominantly encoded within the pairwise interaction landscape itself, with orientational refinement contributing only marginally. Further analysis indicates that the remaining variance arises primarily from hydrogen-bond directionality: classifying chain trimers according to their directed donor-relay topology nearly perfectly separates cooperative from anti-cooperative configurations, increasing the out-of-fold R2 from 0.808 to 0.917. Machine learning models constructed from these local descriptors reproduce the finite-size scaling relations and extrapolated large-cluster asymptotes (R2 ≥ 0.985). Cross-method validation against coupled-cluster single double triple-level many-body potentials and explicit delta corrections indicates that the scaling forms and the descriptor hierarchy are transferable across methods, while the quantitative MBE ratios remain method-dependent. These results demonstrate that the energetic evolution of water clusters is governed primarily by transferable local interaction patterns, suggesting a route toward size-transferable interaction models based on limited structural descriptors and low-order energy decompositions.