**2. Experimental section**

#### **2.1 Materials**

K7[α-PW11O39]11H2O (Contant, 1987) and Cs7[γ-PW10O36]19H2O (Domaille, 1990; Knoth, 1981) were prepared as described in the literature. The number of solvated water molecules was determined by thermogravimetric/differential thermal analyses. Acetonitrile-soluble, tetra-*n*-butylammonium salts of [α-PW12O40]3- and [α-PW11O39]7- were prepared by the addition of excess tetra-*n*-butylammonium bromide to the aqueous solutions of Na3[α-PW12O40]16H2O (Rosenheim & Jaenicke, 1917) and K7[α-PW11O39]11H2O. All the reagents and solvents were obtained and used as received from commercial sources. Al(NO3)39H2O (Aldrich, 99.997% purity) was used in the synthesis. The X-ray crystal structure of

OH)2]4H2O (TBA = tetra-*n*-butylammonium) (Kikukawa et al., 2008), a monomeric, *mono*aluminum-substituted α-Keggin polyoxometalate K6H3[ZnW11O40Al]9.5H2O (Yang et al., 1997), and a dimeric aluminum complex having *mono*- and *di*-aluminum sites sandwiched by *tri*-lacunary α-Keggin polyoxometalate K6Na[(A-PW9O34)2{W(OH)(OH2)}{Al(OH)(OH2)}

{Al(μ-OH)(OH2)2}2]19H2O (Kato et al., 2010); these structures are shown in Fig. 2.

Fig. 1. Some examples of lacunary phosphotungstates. The polyhedral representations of *mono*-lacunary α-Keggin [α-PW11O39]7- (left), *di*-lacunary γ-Keggin [γ-PW10O36]7- (center), and *tri*-lacunary α-Keggin [A-α-PW9O34]9- (right) phosphotungstates. The WO6 and internal PO4 groups are represented by the white octahedra and red tetrahedron, respectively.

In this study, we successfully obtained a monomeric, α-Keggin *mono*-aluminum-substituted polyoxotungstate in the form of crystals (suitable for X-ray structure analysis) of [(*n*-C4H9)4N]4[α-PW11{Al(OH2)}O39] that were fully characterized by X-ray crystallography; elemental analysis; thermogravimetric/differential thermal analysis; Fourier transform infrared spectroscopy; and solution 31P, 27Al, and 183W nuclear magnetic resonance spectroscopies. Although the X-ray crystallography of [α-PW11{Al(OH2)}O39]4- showed that the *mono*-aluminum-substituted site was not identified because of the high symmetry in the compound, the bonding mode (bond lengths and bond angles) were significantly influenced by the insertion of aluminum ions into the *mono*-vacant sites. In addition, density-functionaltheory (DFT) calculations showed a unique coordination sphere around the *mono*aluminum-substituted site in [α-PW11{Al(OH2)}O39]4-; this was consistent with the X-ray crystal structure and spectroscopic results. In this paper, we report the complete details of the synthesis, molecular structure, and characterization of [(*n*-C4H9)4N]4[α-PW11

K7[α-PW11O39]11H2O (Contant, 1987) and Cs7[γ-PW10O36]19H2O (Domaille, 1990; Knoth, 1981) were prepared as described in the literature. The number of solvated water molecules was determined by thermogravimetric/differential thermal analyses. Acetonitrile-soluble, tetra-*n*-butylammonium salts of [α-PW12O40]3- and [α-PW11O39]7- were prepared by the addition of excess tetra-*n*-butylammonium bromide to the aqueous solutions of Na3[α-PW12O40]16H2O (Rosenheim & Jaenicke, 1917) and K7[α-PW11O39]11H2O. All the reagents and solvents were obtained and used as received from commercial sources. Al(NO3)39H2O (Aldrich, 99.997% purity) was used in the synthesis. The X-ray crystal structure of

{Al(OH2)}O39].

**2.1 Materials** 

**2. Experimental section** 

[(CH3)2NH2]4[α-PW11ReVO40] (Kato et al., 2010) was resolved by SHELXS-97 (direct methods) and re-refined by SHELXL-97 (Sheldrick, 2008). The crystal data are as follows: C8H32N3O4PReW11: *M* = 3063.87, *trigonal*, space group *R-3m*, *a* = 16.53(2) Å, *c* = 25.21(4) Å, *V* = 5963(12) Å3, *Z* = 6, *D*c = 5.119 g/cm3, *R1* = 0.0559 (*I* > 2(*I*)) and *wR2* = 0.1513 (for all data). The four dimethylammonium ions could not be identified due to the disorder (Nomiya et al., 2001, 2002; Weakley & Finke, 1990; Lin et al., 1993). CCDC number 851154.
