  Quantum calculations are reported for the stereodynamic control of the H +
D$_{2}\longleftrightarrow$ D + HD chemical reaction in the energy range of 1-50
K. Stereodynamic control is achieved by a formalism similar to that reported by
Perreault et al. [Nature Chem. 10, 561 (2018)] in recent experimental works in
which the alignment of the molecular bond axis relative to the incident
relative velocity is controlled by selective preparations of the molecule in a
specific or superposition of magnetic projection quantum numbers of the initial
molecular rotational level. The approach presented here generalizes the
experimental scheme of Perreault et al. and offers additional degree of control
through various experimental preparation of the molecular alignment angle.
Illustrative results presented for the H + D$_{2}$ and D + HD reactions show
significant control with the possibility of turning the reaction completely on
or off with appropriate stereodynamic preparation of the molecular state.
Various scenarios for maximizing and minimizing the reaction outcomes are
identified with selective preparation of molecular rotational states.
