  We present benchmark integrated and differential cross-sections for electron
collisions with H$_2$ using two different theoretical approaches, namely, the
R-matrix and molecular convergent close-coupling (MCCC). This is similar to
comparative studies conducted on electron-atom collisions for H, He and Mg.
Electron impact excitation to the $b \ ^3\Sigma_u^+$, $a \ ^3\Sigma_g^+$, $B \
^1\Sigma_u^+$, $c \ ^3\Pi_u$, $EF \ ^1\Sigma_g^+$, $C \ ^1\Pi_u$, $e \
^3\Sigma_u^+$, $h \ ^3\Sigma_g^+$, $B' \ ^1\Sigma_u^+$ and $d \ ^3\Pi_u$
excited electronic states are considered. Calculations are presented in both
the fixed nuclei and adiabatic nuclei approximations, where the latter is shown
only for the $b \ ^3\Sigma_u^+$ state. Good agreement is found for all
transitions presented. Where available, we compare with existing experimental
and recommended data.

Chemical Physics;Plasma Physics