M8L6 clusters (M = Cu(I), Ag(I); L = dichalcogeno ligand) are known for their ability to encapsulate various kinds of saturated atomic anions. Calculations on the models [M-8(E2PH2)(6)](2+) (M = Cu(I), Ag(I); E = S, Se) and the ionic or neutral [M-8(X)(E2PH2)(6)](q) (X = H, F, Cl, Br, O, S, Se, N, P, C) indicate that the cubic M8L6 cage adapts its shape for maximizing the host-guest bonding interaction. The interplay between size, covalent and ionic bonding favors either a cubic, tetracapped tetrahedral, or bicapped octahedral structure of the metal framework. Whereas the large third- and fourth-row main group anions maintain the cubic shape, a distortion toward a tetracapped tetrahedral arrangement of the metals occurs in the case of hydride, fluoride, and oxide. The distortion is strong in the case of hydride, weak in the case of fluoride, and intermediate in the case of oxide. Density functional theory (DFT) calculations predict a bicapped octahedral architecture in the case of nitride and carbide. These computational results are supported by X-ray structures, including those of new fluorine- and oxygen-containing compounds. It is suggested that other oxygen-containing as well as so far unknown nitride-containing clusters should be feasible. For the first time, the dynamical behavior of the encapsulated hydride has been investigated by metadynamics simulations. Our results clearly demonstrate that the interconversion mechanism between two identical tetracapped tetrahedral configurations occurs through a succession of M-H bonds breaking and forming which present very low activation energies and which involve a rather large number of intermediate structures. This mechanism is full in accordance with Ag-109 and H-1 state NMR measurements.