Systematic theoretical studies of the [XMYH]_n, inorganic rings and clusters (M = Al, Ga, In; Y = N, P, As; X = H, F, Cl, Br, I; n = 1-6) have been carried out using hybrid Hartree-Fock density functional theory. A consistent set of the structural and thermodynamic properties has been obtained. The stability of the MY bond decreases in the order Al > Ga ≥ In; N ≫ P > As. Terminal groups X have a minor influence on the subsequent elimination enthalpies of the clusters. In the case of X = H, hydrogen elimination makes formation of the [HMYH]₆ oligomers from MH ₃ and YH₃ thermodynamically favorable; while in the case of halide substituents, formation of [XMYH]₆ is thermodynamically unfavorable, except for the system with the strongest MY bond (AIN). Substitution of the acidic hydrogen by X is favorable energetically for all [HMYH]₆ clusters, but is complicated by the processes of cluster destruction to form the [X₂MYH₂]₂ dimers. The high stability of the [HMNH]₆ clusters makes them attractive single-source precursors for the production of 13-15 composites.