In this context, the present work extends our investigation to boron pnictides with heavier elements (As, Sb, and Bi). As in previous works , the studies are based on quantum mechanics calculations of the ground-state energy structures and derived properties in the framework of the density functional theory (DFT) . It is shown that BX phases (X = As, Sb, Bi) with qtz topology are cohesive and stable both mechanically (elastic constants and their combinations) and dynamically (phonon band structures). It should be noted, however, that there is a small dynamical instability of qtz BX in the case of the heaviest pnictogen, bismuth. The respective equations of state (EOS) have been determined for all phases, and the transition pressures from zb-BX to the corresponding high-pressure qtz structures have been estimated. The electronic band structures show a reduction of the band gaps in the proposed qtz phases compared to zb-BX, with metallization observed in the case of qtz BBi. Finally, the thermodynamic properties (heat capacity and entropy) of the new phases have been calculated and compared with the available experimental data.