**4. Natural Atomic Charge and Bond Order Characterizations**

Among the many descriptors provided by NBO analysis, the natural atomic charges {*Q*A} and interatomic bond orders {*b*AB} are most intimately associated with traditional empirical concepts of chemical bonding theory. Long-held perceptions of *dichotomy* between intra- vs. intermolecular forces (viz., "covalency" for chemical bond formation (*b*AB = 1, 2, 3,...) vs. "electrostatics" for H-bond formation (*b*H···<sup>O</sup> ≈ 0.1–0.2)) have long impeded true progress in the supramolecular domain. Demonstrations of how quantal *Q*A, *b*AB descriptors extend seamlessly across the supposed divide can therefore serve to refute the obsolete dipole–dipole conceptions of H-bonding (and other so-called "noncovalent" interactions) that still pervade freshman-level pedagogy and classical force-field methodology. In the present section, we wish to test the usefulness of NBO/NRT-based *Q*A, *b*AB descriptors when applied to the large data base of windowpane water clusters as described above.

### *4.1. General Features of Donor–Acceptor Interactions in Water Clusters*

In every H-bond of every water cluster, NBO analysis reveals the characteristic *n*O→σ\*OH donor–acceptor ("charge transfer") interaction that transfers a slight electronic charge (*Q*CT) from the oxygen lone pair (*n*O) of the Lewis base (LB) site into the valence antibond (σ\*OH) of the proximal Lewis acid (LA) site. Figure 5 depicts the *n*O-σ\*OH interaction for one of the H-bonds of W4c, showing the strongly overlapping forms of pre-orthogonal PNBOs deep inside van der Waals contact. The insets show details of the interaction that are routinely provided in NBO output, including (in kcal/mol; upper right) the second-order perturbative estimate of *n*O-σ\*OH donor–acceptor attraction (Δ*E*CT(2)), the corresponding steric opposition of *n*O-σOH donor–donor repulsion (Δ*E*steric), and the net binding energy (Δ*E*net). The known high transferability of NBOs [61] then assures that the individual *n*O, σ\*OH orbitals are quite similar to those in water monomer and dimer as well as other windowpane clusters. However, one can also recognize the slight misalignments of ring strain

that lower PNBO overlaps throughout the windowpane series and lead to the nuances in charge distribution, structure, and bond strength discussed below.

**Figure 5.** Pre-orthogonal (PNBO) depiction of *n*O→σ\*OH orbital interaction in one H-bond of W4c, with energetic (kcal/mol) and charge transfer (*e*) details as insets (see text).

Alternatively, the effects of *n*O(4)→σ\*O(1)H(2) interaction can be quantified by *deleting* this single specific matrix element from the DFT calculation (with standard \$DEL keylist options [62]) and recalculating the energy and reoptimized geometry as though it were absent in nature. As shown in Figure 6, this single deletion "breaks" the O(4)···H(2)−O(1) hydrogen bond (and initial *S*<sup>4</sup> symmetry) to give an open-chain structure with *R*O(1)···O(4) separation increased by ~0.5 Å to near-van der Waals contact distance. The monomers at each chain terminus also reorient to near coplanarity (contrary to the ~120◦ dihedral twisting of the two remaining monomers), thereby allowing partial re-gain of *n*(σ) O(4)→σ\*O(1)H(2) attraction with the weaker *in*-plane *n*(σ) O(4) lone pair of O(4). By such \$DEL deletion searches, one verifies that the specific *n*O(4)→σ\*O(1)H(2) interaction is the unique "smoking gun" that is both *necessary and sufficient* for characteristic H-bonding between O(1) and O(4) monomers.

**Figure 6.** \$DEL (partially)-reoptimized structure of original W4c cluster (Figure 1), showing effects of deleting the single *n*O(4)→σ\*O(1)H(2) interaction of Figure 5 (at the point where the maximum number of optimization steps was completed).

All such NBO-based energetic and \$DEL deletion descriptors can be obtained for other windowpane clusters of Figures 2 and 3. In the following, we focus instead on subtleties of the charge distributions and H-bond strengths that relate to the interesting cooperative effects of the highly ordered proton patterns ("water wires") formed by the H-bond networks.
