  Accurate intermolecular potential-energy surfaces (IPESs) for the ground and
first excited states of the Sr-H$_2$ and Yb-H$_2$ complexes were calculated.
After an extensive methodological study, the CCSD(T) method with the
Douglas-Kroll-Hess Hamiltonian and correlation-consistent basis sets of
triple-$\zeta$ quality extended with 2 sets of diffuse functions and a set of
midbond functions were chosen. The obtained ground-state IPESs are similar in
both complexes, being relatively isotropic with two minima and two transition
states (equivalent by symmetry). The global minima correspond to the collinear
geometries with $R=$ 5.45 and 5.10~{\AA} and energies of $-$27.7 and
$-$31.7~cm$^{-1}$ for the Sr-H$_2$ and Yb-H$_2$ systems, respectively. The
calculated surfaces for the Sr($^3P$)-H$_2$ and Yb($^3P$)-H$_2$ states are
deeper and more anisotropic and they exhibit similar patterns within both
complexes. The deepest surfaces, where the singly occupied \textit{p}-orbital
of the metal atom is perpendicular to the intermolecular axis, are
characterised by the global minima of ca. $-$2053 and $-$2260~cm$^{-1}$ in the
T-shape geometries at $R=$ 2.41 and 2.29~{\AA} for Sr-H$_2$ and Yb-H$_2$,
respectively. Additional calculations for the complexes of Sr and Yb with the
He atom revealed a similar, strong dependence of the interaction energy on the
orientation of the \textit{p}-orbital in the the Sr($^3P$)-He and Yb($^3P$)-He
states.
