Relative Energies of α and β Isomers of Keggin Dodecatungstogallate

The relative energies of β Keggin heteropolytungstates,
Xn+W12O40(8-n)-, decrease as Xn+ is varied within period 3, from
P5+ to Si4+ to Al3+. With heating of α-H5Ga3+W12O40 at 200 °C in
water, an equilibrated mixture of α (Td; one 183W NMR signal)
and β (C3v; three signals; 1:2:1 ratio) isomers is obtained. From
ΔGexp = −RT ln Kβ→α, in which (from 71Ga NMR spectra) Kβ→α
(= [α]/[β]) = 5.0, β-GaW12O405- is 0.65 kcal mol-1 higher in
energy than α-GaW12O405-. This finding is evaluated by analysis
of the X-ray crystal structure α-K2Na3[GaW12O40]·9.3H2O [trigonal,
space group P3221, a = 18.9201(13) Å, b = 18.9201(13) Å, c =
12.5108(12) Å, Z = 3, T = 100(2)K], comparison of the Shannon
and Prewitt radii and Pauling electronegativities of Al3+ and Ga3+,
and insight from density functional theory calculations, which
predicted Eβ − Eα = 0.32 kcal mol-1.