*2.3. Construction of 2D Structures Based on Triol-Ligand Decorated Anderson-Evans POMs*

As mentioned above, when Cu2+ is used as a linker, its small coordination range represents a disadvantage for the formation of a 2D structure, and its synthetic environment with a low pH value is also not conducive to obtaining the triol ligand modified Anderson-Evans clusters in the δ/δ isomer. Considering these points, we selected Na4Mo8O26 as the Mo source, and used Na+ with a high solubility in a wide pH range in an aqueous solution and a large range of connection to obtain 2D structures based on triol-ligand modified Anderson-Evans clusters in δ/δ and χ/χ isomer. As expected, when the pH of the solution was 5, we obtained compound **8**, in which the triol ligand double-sided decorated Anderson-Evans polyanion was an δ/δ isomer. In this case, four Na<sup>+</sup> ions aggregated to form a {Na4(H2O)14} cluster, which linked the adjacent four polyanions through the terminal O atoms into a 2D planar network along the (011) direction (Figure 3a). When the pH of the solution was lowered to 3.5, the triol ligand modified Anderson-Evans polyanions in χ/χ isomer was obtained as in compound **9**. In this adduct, two Na+ ions form a dimer {Na2(H2O)4} and connect the adjacent four polyanions to form a 2D planar structure extending along the (100) direction (Figure 3b). It can be seen from the above two examples that the charges of the anions and cations have obvious matching characteristics. For the δ/δ isomer, because the charge of the polyanion was −4, four one-charged Na<sup>+</sup> ions combined to form a tetramer, thereby matching the charge with the anion. While for the χ/χ isomer, because the charge of polyanion was −2, two Na+ ions combined to form a dimer with two positive charges, and were neutralized with the anion in a 1:1 mode. In addition, compared with Cu2+, the tetramer and dimer of Na+ are larger and have wider connecting ranges, so that four polyanions can be uniformly arranged around them to form 2D planar structures, which can also be seen as the adjacent 1D chains connecting to each other to form 2D structures.

**Figure 3.** Ball-and-stick representations of compounds (**a**) **8** and (**b**) **9**, showing their 2D planar structures. Numbers in the diagram represent the distances of adjacent clusters in two dimensions. All H atoms except those attaching to tri-bridging O atoms in polyanions are omitted for clarity.

The size of the linking group and the bridging manner have an important effect on the distances between the order of the arranged anions. When the linking group was a Cu2+ ion, as in compounds **6** and **7**, the distances between two adjacent polyanions in the 1D chains were 14.090(2) Å and 13.312(2) Å, respectively (Figure S16). The slight difference between the two values is due to the steric hindrance caused by the triol ligand coordinated with linking Cu2+ (Figure 2). For inter-chains, and the distances between the two adjacent polyanions in compounds **6** and **7** are 11.128(2) Å and 8.872(2) Å, respectively (Figure S16). For compound **7**, the smaller distance between the adjacent polyanions is mainly due to the different orientations of the two polyanions in adjacent chains, which reduces the steric hindrance based on the rotation of one cluster, so that the distance between the two center heteroatoms decreases. When the linking group was a {Na4(H2O)14} tetramer, as in Compound **8**, the closest distances of the two adjacent polyanions in the 2D

structure were 16.218(2) Å and 9.175(2) Å, respectively (Figure 3). In compound **9**, when the linking group was a {Na2(H2O)4} dimer, the distances between the two adjacent polyanions were 13.204(2) Å and 10.202(2) Å, respectively. As shown in Figure 4, from the chemical environments of linkers in compounds **6–9**, we can see that when the bridging group is a single metal ion, the mode of bridging polyanions is simple, and the distance between polyanions mainly depends on the radius of the bridging metal ions. When the linker is a cluster formed by multiple metal ions, the bridging range becomes significantly larger, and it can interact with the polyanion through various modes, so that the polyanions have richer assembled structures.

**Figure 4.** Ball-and-stick representations of coordination environments of linkers for compounds (**a**) **6** and **7**, (**b**) **8**, and (**c**) **9**, showing their different sizes and bridging manners.

#### *2.4. Hirshfled Surface Analysis*

As demonstrated by the analysis above, the triol-ligand modified Anderson-Evans POMs can serve as building blocks for the construction of 1D or 2D assemblies based on different metal ions and their various combinations. In fact, with similar building blocks, 3D assemblies have also been prepared, through which ionic frameworks form and exhibit selective adsorption capacity to CO2 over N2, H2 and CH4 [39,40]. All these 1D to 3D assemblies are constructed based on a strong ionic bond or coordination bond and provide firm connections between each other, while in the absence of metal ions, there are still relatively weak contacts between building blocks, which also have an important influence on their packing styles. Herein, the Hirshfeld surface analysis was applied to illustrate the supramolecular interactions between triol-ligand modified Anderson-Evans polyanions. To exclude the effects of metal ions, only compounds **1**–**5** were analyzed in which an ammonium ion serves as the counter cation and cannot provide obvious directional interactions to the assembly behavior of building blocks such as that of metal ions. As the important supramolecular interactions, the hydrogen bonds in compounds **1**–**5** are summarized in Tables S1–S5 in the Supplementary Materials.

Hirshfeld surfaces mapped with the *d*norm of compounds **1**–**5** were firstly investigated, in which *d*norm was the normalized sum of *d*<sup>i</sup> and *d*e, and is defined as follows [41]:

$$d\_{\rm norm} = (d\_{\rm i} - r\_{\rm I}^{\rm vdw}) / r\_{\rm I}^{\rm vdw} + (d\_{\rm e} - r\_{\rm E}^{\rm vdw}) / r\_{\rm E}^{\rm vdw}$$

*d*<sup>i</sup> is the distance from Hirshfeld surface to the nearest atom I internal to the surface, *d*<sup>e</sup> is the distance from Hirshfeld surface to the nearest atom E external to the surface, *r*<sup>I</sup> vdw is the van der Waals radius of the nearest atom I closest to and inside the Hirshfeld surface, and *r*<sup>E</sup> vdw is the van der Waals radius of the nearest atom E closest to and outside the Hirshfeld surface. As shown in Figure 5, when a methyl-containing triol ligand was used in compounds **1** and **2**, the main interaction sites (marked with red cones) were concentrated at the lateral edge of the disk-shaped cluster, where the terminal O atoms can serve as hydrogen bonding acceptors, while for compounds with hydroxyl or protonated amino groups such as compounds **3**–**5**, their ability to serve as hydrogen bonding donors resulted in a relatively uniform distribution of strong contact sites surrounding the cluster.

**Figure 5.** Hirshfeld analysis results for compounds (**a**) **1**, (**b**) **2**, (**c**) **3**, (**d**) **4**, and (**e**) **5**, respectively. For each column, from left to right, the four images are as follows: Hirshfeld surface mapped with *d*norm in a transparent mode, colored 2D fingerprint plot showing contacts between H (internal to the surface) and H and O (external to the surface), colored 2D fingerprint plot showing contacts between O (internal to the surface) and H and O (external to the surface), and percentage distribution of various short contacts (the detailed percentages of contacts are labeled with the corresponding colors).

Hirshfeld surface images provide qualitative descriptions of the supramolecular interactions of clusters, and 2D fingerprint plots in the range of 0.6–2.6 Å for *d*<sup>i</sup> and *d*<sup>e</sup> were further applied to analyze the detailed contacts in quantitative accuracy (Figure 5). All five compounds have some common characteristics, such as for interactions of H atoms

internal to the surface with H or O atoms external to the surface with generally small *d*<sup>i</sup> values (0.6–2.0 Å) and large *d*<sup>e</sup> values (1.0–2.4 Å), while O atoms internal to the surface with H or O atoms external to the surface have an opposite trend with large *d*<sup>i</sup> values (1.0–2.6 Å) and small *d*<sup>e</sup> values (0.6–2.4 Å). These features indicate that the triol-ligand modified clusters are preferred as hydrogen bonding acceptors than donors, which is also in accordance with the traits of O-rich surfaces. It should be noted that the modification sites of the triol ligand also have an obvious influence on the intermolecular interactions. For example, compounds **1** and **2** have the same triol ligand on the cluster and different positions to the δ/δ and χ,/χ isomers, respectively. In compound **1**, trio ligands were located at the center position of the cluster, which enlarged the distances of methene and methyl H to other species and results in relatively large *d*<sup>i</sup> and *d*<sup>e</sup> values (both more than 1.0 Å) in 2D fingerprint plot. As a comparison, in compound **2**, triol ligands were located at the edge of the disk-like cluster, which enhanced their abilities as hydrogen-bonding donors and generated relatively stronger contacts between H atoms internal to the surface with H and O atoms external to the surface. In addition, the χ,/χ isomer in compound **2** also provides two extra protonated μ3-O atoms as hydrogen bonding donors compared with compound **1**, which are important components of short contacts. On the contrary, the positions of triol ligands have little influence on the hydrogen-bonding-acceptor ability of the cluster, and the 2D fingerprint plots showing contacts between O (internal to the surface) and H and O (external to the surface) of compounds **1** and **2** are very similar. Lastly, the discoid distributions of various contacts indicate that all five triol-ligand modified clusters are mainly used as hydrogen-bonding acceptors with the percentages of O—H contacts ranging from 50.1% to 65.6%.
