  Several nitrogen-bearing molecules, such as methyl cyanide (or acetonitrile,
CH$_3$CN) and methyl isocyanide (CH$_3$NC) of interest here, have been observed
in various astrophysical environments. The accurate modeling of their abundance
requires the calculation of rate coefficients for their collisional excitation
with species such as He atoms or H$_2$ molecules at low temperatures. In this
work we compute new three-dimensional potential energy surfaces for the
CH$_3$NC-He and CH$_3$CN-He van der Waals complexes by means of the explicitly
correlated coupled cluster approach with single, double and perturbative triple
excitation CCSD(T)/F12a in conjunction with the aug-cc-pVTZ basis set. We find
a global minimum with $D_e= 55.10$ and 58.61 cm$^{-1}$ for CH$_3$CN-He and
CH$_3$NC-He, respectively, while the dissociation energy $D_0$ of the complexes
are 18.64 and 18.65 cm$^{-1}$, respectively. Low energy scattering calculations
of pure rotational (de-)excitation of CH$_3$CN and CH$_3$NC by collision with
He atoms are carried out with the close-coupling method and the collisional
cross sections of $ortho-$ and $para-$CH$_3$NC and CH$_3$CN are computed for
kinetic energies up to 100 cm$^{-1}$. While the PESs for both complexes are
qualitatively similar, that of CH$_3$NC-He is more anisotropic, leading to
different propensity rules for rotational excitation. For CH$_3$NC-He, we find
that |$\Delta j$| = 1 transitions are dominant at low kinetic energy and a
propensity rule that favors odd $\Delta j$ transitions is observed, whereas for
CH$_3$CN the dominant cross sections are associated to transitions with
|$\Delta j$| = 2. We expect that the findings of this study will be beneficial
for astrophysical investigations as well as laboratory experiments.
