On the origin of the relative stability of Wells-Dawson isomers: a DFT study of α-, β-, γ-, α*-, β*-, and γ*-[(PO4)2W18O54](6-) anions

Abstract

Density functional theory calculations have been carried out to investigate α-, β-, γ-, α*-, β*-, and γ*-[(PO(4))(2)W(18)O(54)](6-) Wells-Dawson isomers, which exhibited stability in the order of α > β > γ > γ* > β* > α*, reproduced the experimental observations (α > β > γ), and confirmed the hypothesis of Contant and Thouvenot (γ* > β* > α*). Energy decomposition analysis reveals that both the spatial arrangement of the host W(18)O(54) cage (eclipsed or staggered) and its structural distortion induced by the encapsulated guest anions are two dominant factors in control of the stability order, while the influences of host-guest interaction and distortion of the guest anions are very small. A building block decomposition approach is designed and provides an effective means to clarify the detailed relationship between the local distortion and energy. By using this method, it is found that the eclipsed belt, and in particular the staggered belt, significantly distort the two caps inside the Wells-Dawson structure. Notably, there is a direct relationship between the overall stability and distortion in the belts, which is proven to be partly originating from the dominance in the quantity of the belt building blocks over that of the caps (12:6). Besides, half-unit {XW(9)} decomposition confirms that [(XO(4))(2)W(18)O(54)](n-) (X = Si, Ge, Al, and Ga) are thermodynamically instable because of the notable electrostatic repulsion between two {XW(9)} units induced by the highly charged guest anions.