  We report the first full-dimensional potential energy surface (PES) and
quantum mechanical close-coupling calculations for scattering of SiO due to
H$_2$. The full-dimensional interaction potential surface was computed using
the explicitly correlated coupled-cluster (CCSD(T)-F12b) method and fitted
using an invariant polynomial approach. Pure rotational quenching cross
sections from initial states $v_1=0$, $j_1$=1-5 of SiO in collision with H$_2$
are calculated for collision energies between 1.0 and 5000 cm$^{-1}$.
State-to-state rotational rate coefficients are calculated at temperatures
between 5 and 1000 K. The rotational rate coefficients of SiO with para-H$_2$
are compared with previous approximate results which were obtained using SiO-He
PESs or scaled from SiO-He rate coefficients. Rovibrational state-to-state and
total quenching cross sections and rate coefficients for initially excited
SiO($v_1=1, j_1$=0 and 1) in collisions with para-H$_2$($v_2=0,j_2=0$) and
ortho-H$_2$($v_2=0,j_2=1$) were also obtained. The application of the current
collisional rate coefficients to astrophysics is briefly discussed.
