**2.6 Computational details**

604 Advances in Crystallization Processes

Chemical shifts were reported as negative for resonance upfields of Na2WO4 (δ 0). Potentiometric titration was carried out with 0.4 mol/L tetra-*n*-butylammonium hydroxide as a titrant under argon atmosphere (Weiner et al., 1996). The compound [(*n*-C4H9)4N]4[α-PW11{Al(OH2)}O39] (0.018 mmol) was dissolved in acetonitrile (30 mL) at 25 °C and the solution was stirred for approximately 5 min. The titration data were obtained with a pH meter (Mettler Toledo). Data points were obtained in milivolt. A solution of tetra-*n*butylammonium hydroxide (9.0 mmol/L) was syringed into the suspension in 0.25-

Cs7[γ-PW10O36]19H2O (2.00 g; 0.538 mmol) was dissolved in water (600 mL) at 40 °C, and solid Al(NO3)39H2O (0.250 g, 0.666 mmol) was added to the colorless clear solution. After stirring for 1 h at 40 ºC, a solid [(*n*-C4H9)4N]4Br (12.14 g; 37.7 mmol) was added to the solution, followed by stirring at 25 °C for 3 days. The white precipitate was collected on a glass frit (G4) and washed with water (ca. 1 L). At this stage, a crude product was obtained in a 1.662 g yield. The crude product (1.662 g) was dissolved in acetonitrile (10 mL), followed by filtering through a folded filter paper (Whatman #5). After the product was left standing for a week at 25 °C, colorless platelet crystals were formed. The obtained crystals weighted 0.752 g (the yield calculated considering that [mol of [(*n*-C4H9)4N]4[α-PW11{Al(OH2)}O39]/[mol of Cs7[γ-PW10O36]19H2O] 100 was 36.9%). The elemental analysis results were as follows: C, 20.73; H, 4.00; N, 1.58; P, 0.84; Al, 0.77; W, 54.6; Cs, <0.1%. The calculated values for [(*n*-C4H9)4N]4[α-PW11{Al(OH2)}O39] = C64H146AlN4O40PW11: C, 20.82; H, 3.99; N, 1.52; P, 0.84; Al, 0.73; W, 54.77; Cs, 0%. A weight loss of 2.16% was observed in the product during overnight drying at room temperature under 10-3–10-4 Torr before the analysis, thereby suggesting the presence of two weakly solvated or adsorbed acetonitrile molecules (2.18%). TG/DTA under atmospheric conditions showed a weight loss of 31.0% with an exothermic peak at 337 °C was observed in the temperature range from 25 to 500 °C; our calculations indicated the presence of four [(C4H9)4N]+ ions, two acetonitrile molecules, and a water molecule (calcd. 28.4%). The results were as follows: IR soectroscopy results (KBr disk): 1078s, 964s, 887s, 818s, 749m, 702w, 518w cm–1; 31P NMR (25C, acetonitrile-*d*3): δ -12.5; 27Al NMR (25 C, acetonitrile-*d*3): δ 16.1; 183W NMR (25 C, acetonitrile-*d*3): -56.2 (2W), -93.1 (2W), -108.6 (2W), -115.8 (2W), -118.5 (1W), -153.9 (2W).

A colorless platelet crystal of [(*n*-C4H9)4N]4[α-PW11{Al(OH2)}O39] (0.16 0.16 0.01 mm3) was mounted on a MicroMount. All measurements were made on a Rigaku VariMax with a Saturn diffractometer using multi-layer mirror monochromated Mo Kα radiation (λ= 0.71075 Å) at 93 K. Data were collected and processed using CrystalClear for Windows, and structural analysis was performed using the CrystalStructure for Windows. The structure was solved by SHELXS-97 (direct methods) and refined by SHELXL-97 (Sheldrick, 2008). Since one aluminum atom was disordering over twelve tungsten sites in [α-PW11{Al(OH2)}O39]4-, the occupancies for the aluminum and tungsten sites were fixed at 1/12 and 11/12 throughtout the refinement. Four tetra-*n*-butylammonium ions could not be modelled with disordered atoms. Accordingly, the residual electron density was removed

equivalent intervals.

**2.4 X-Ray crystallography** 

using the SQUEEZE routine in PLATON (Spek, 2009).

**2.3 Synthesis of [(***n***-C4H9)4N]4[α-PW11{Al(OH2)}O39]** 

The optimal geometry of [α-PW11{Al(OH2)}O39]4- was computed by means of a DFT method. First, we optimized the crystal geometries and followed this up with single-point calculations with larger basis sets. All calculations were performed by a spin-restricted B3LYP on Gaussian09 program package (Frisch et al., 2009). The basis sets used for the geometry optimization were LANL2DZ for W atoms, 6-31+G\* for P atoms and 6-31G\* for H, O, and Al atoms. LANL2DZ and 6-31+G\* were used for W and other atoms, respectively, for the single-point calculations. The geometry optimizations were started using the X-ray structure of [-PW12O40]3- as an initial geometry, and they were performed under the gas phase condition. The optimized geometries were confirmed to be true minima by frequency analyses. All atomic charges used in this text were obtained from Mulliken population analysis.
