*Article* **High-Density "Windowpane" Coordination Patterns of Water Clusters and Their NBO/NRT Characterization**

**Frank Weinhold**

Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, Madison, WI 53706, USA; weinhold@chem.wisc.edu

**Abstract:** Cluster mixture models for liquid water at higher pressures suggest the need for water clusters of higher coordination and density than those commonly based on tetrahedral H-bonding motifs. We show here how proton-ordered water clusters of increased coordination and density can assemble from a starting cyclic tetramer or twisted bicyclic (Möbius-like) heptamer to form extended *Aufbau* sequences of stable two-, three-, and four-coordinate "windowpane" motifs. Such windowpane clusters exhibit sharply reduced (~90◦) bond angles that differ appreciably from the tetrahedral angles of idealized crystalline ice Ih. Computed free energy and natural resonance theory (NRT) bond orders provide quantitative descriptors for the relative stabilities of clusters and strengths of individual coordinative linkages. The unity and consistency of NRT description is demonstrated to extend from familiar supra-integer bonds of the molecular regime to the near-zero bond orders of the weakest linkages in the present H-bond clusters. Our results serve to confirm that H-bonding exemplifies resonance–covalent (fractional) bonding in the sub-integer range and to further discount the dichotomous conceptions of "electrostatics" for intermolecular bonding vs. "covalency" for intramolecular bonding that still pervade much of freshman-level pedagogy and force-field methodology.

**Keywords:** supramolecular chemistry; hydrogen bonding; water clusters; natural bond orbitals; natural resonance theory; natural bond orders; Grotthuss proton ordering; water wires; glassy water; quantum cluster equilibrium
