Benchmark Calculations of Electron Impact Electronic Excitation of the Hydrogen Molecule

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 $b ^3Sigma_u^+$, $a ^3Sigma_g^+$, $B ^1Sigma_u^+$, $c ^3Pi_u$, $EF ^1Sigma_g^+$, $C ^1Pi_u$, $e ^3Sigma_u^+$, $h ^3Sigma_g^+$, $B ^1Sigma_u^+$ and $d ^3Pi_u$ 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 $b ^3Sigma_u^+$ state. Good agreement is found for all transitions presented. Where available, we compare with existing experimental and recommended data.