DFT Study of α-Keggin-type Iso-polyoxotungstate Anions [HnW12O40](8–n)– (n =1–4): Can [H4W12O40]4– Exist?

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(31) We refer that [HnW12O40](8−n)− ’s have the same occupation pattern when their geometries can

be superposed with each other by proper rotational operations.

(32) We performed various calculations to confirm the results where there were apparently

different total energies for cases with the same occupation pattern for protonation. For example,

we tried to refine the structure of H1[H3W12O40]4−−18, starting from a geometry with the similar

O−H bond directions to those of H1[H3W12O40]4−−6. The results obtained were, however, not

significantly different from those shown in the Table S1 and Figure S2.

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geometrical optimization of H1[Hn−1W12O40](8−n)− and [HnW12O40](8−n)− were performed by the

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geometries; that is, the NTChem optimization lost the Keggin-type structure as mentioned in

the text, while the Gaussian16 optimization kept the structure. As long as concerning to these

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results, we believe that the resulting geometries of the NTChem optimization are more reliable

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and the Gaussian16 optimization from the resulting geometry obtained by NTChem gives

almost the same results as those of NTChem. Thus, Table 1 shows the values by NTChem for

H1[H0W12O40]7− ’s and those by Gaussian16 for the other species.

(34) We never have calculated all possible occupation patterns except for H1[H3W12O40]4− and

[H4W12O40]4−. However, we believe that this suggestion is reasonable, because it has been

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[HnW12O40](8−n)− (n=2−3). Regarding the transfer from H1[H0W12O40](8−n)− to [H1W12O40](8−n)−,

it may compete with the deformation reaction of Keggin-type POT framework of

H1[H0W12O40](8−n)−.

(35) We also searched MEPs for the transfer from the Oc or Oe sites to the lower Oi sites, but the

geometries of images on the obtained MEP did not correspond to the direct transfer to the lower

Oi. They rather indicated a concerted transfer reaction from the Oc or Oe site to an upper Oi site

and from the upper Oi to the lower Oi site. Furthermore, the IRC search did not correctly

connect the TSs obtained for these pathways by the STQN method to the reactant

H1[Hn−1W12O40](8−n)− ’s and the products [HnW12O40](8−n)− ’s used in the MEP search.

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Table of Contents

For further understanding the speciation of Keggin-type iso-polyoxotungstate anions, we

investigated the relative stabilities and the proton transfer reactions between H1[Hn−W12O40](8−n)−

and [HnW12O40](8−n)− (n=1−4) by using the first-principles calculations (the nudged elastic band

method, the synchronous transit-guided quasi-Newton method, the intrinsic reaction coordinate

method, and frequency analysis calculations). The DFT calculations showed us the details of the

proton transfer on the iso-polyoxotungstate anions, and indicated that [H4W12O40]4− can exist.

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