*4.2. Natural Atomic Charge Distributions*

In principle, the simple water dimer (W2) might be seen as the fundamental conceptual building block for studies of electronic charge distribution and stability in clusters of higher complexity. However, Figure 7 exhibits the detailed comparisons of H atom (italic) and O atom (plain text) natural charges in W2 vs. cubane-like 0,8,0W8 to show the surprising *contrasts* between these species. In the two panels of Figure 7, the O(1) and O(16) monomers of the cubane cluster (right) are, respectively, the direct analogs of O(4) and O(2) monomers in the dimer (left), yet the net charges on the monomers of the dimer are directly *opposite* those in the cluster. Similar contrasts between charge distributions of the supposed "building block" dimer and those of higher coordination complexes are found throughout the clusters of Figures 2 and 3.

**Figure 7.** Natural atomic charges for H (italics; white) and O (plain text; white) atoms of water dimer (**left**) and cubane-like 0,8,0W8 cluster (**right**), with corresponding net charges (yellow) of formal Lewis acid (*e*-acceptor) and Lewis base (*e*-donor) water molecules in each species, showing the *reversal* of apparent charge flow in the two cases. (Parenthesized per-monomer energy and free energy for W2 also allow direct stability comparisons with clusters of Figures 2–4).

How can the conflicting charge patterns of Figure 7 be rationalized? At the termini of each H-bond are two water monomers that can be identified as the LB (formal *e*-pair "donor") and LA (formal σ\*OH "acceptor" vacancy). In the simple water dimer, the *n*O→ σ\*OH donor–acceptor interaction necessarily results in net charge transfer (ca. 0.017*e*) from LB to LA (Figure 7, left), resulting in the LBδ+···LAδ<sup>−</sup> charge pattern. However, in more complex water clusters, the surroundings of any chosen H-bond may be seen as a network of "water wires" that allow charge to redistribute as necessary to optimize overall cluster stability. Specifically, the multiple network connections allow electronic charge to be redistributed to achieve near *neutrality* at *q*- or *d*-coordinated sites, whose equal numbers of donor and acceptor interactions can be tuned to avoid capacitive build-up. However, at *t*-coordinated sites, which necessarily have an imbalance of donor (*t*d, LB) vs. acceptor (*t*a, LA) connections, it becomes advantageous to confer excess *anionic* charge on *t*<sup>d</sup> sites (increasing LB strength) and *cationic* charge on *t*a sites (increasing LA strength), thus leading to the commonly observed LB<sup>δ</sup>−···LAδ<sup>+</sup> charge pattern.

To illustrate these propensities of cluster charge distribution, Figure 8 displays selected *Q*<sup>O</sup> (plain text) and *Q*<sup>H</sup> (italic) atomic charges of the 8,0,8W16 cluster for two *q*-type sites (centered at O(1), O(13)) and one *d*-type site (at O(46)), showing the significantly reduced net monomer charges compared to those of the water dimer. More complete listings of monomer charge values and coordination type at each O atom for all clusters of this study are included in SI, as illustrated for the 8,0,8W16 cluster in Table 1. The subtle variations in molecular charge indicate the extreme "feedback" sensitivity to every detail of the surrounding H-bond network, showing that overall network topology has taken precedence over characteristics of the water dimer (single H-bond) "building block" of which the network is composed.

**Figure 8.** Similar to Figure 7, for representative quadruply (*q*-type) coordinated O(1)H(2)H(3) and O(13)H(14)H(15) molecules of the cubane-like core, and doubly (*d*-type) coordinated O(46)H(47)H(48) molecule on a bridged wing of the 8,0,8W16 cluster.

**Table 1.** Total natural charge *Q*<sup>i</sup> and *q/t/d* coordination type for each water monomer (centered on O(*i*)) of the 4,4,6W16 cluster. (Similar tables are found in SI for each q,t,dWn cluster of the present work).

