  The equation of state of partially ionized hydrogen plasma is considered with
special focus on the contribution of $e-\rm H_2$ interaction. Within a cluster
virial expansion, the Beth-Uhlenbeck formula is applied to infer the
contribution of bound and scattering states to the temperature dependent second
virial coefficient. The scattering states are calculated using the phase
expansion method with the polarization interaction model that incorporates
experimental data for the $e-\rm H_2$ scattering cross section. We present
results for the scattering phase shifts, differential scattering cross
sections, the second virial coefficient due to $e-\rm H_2$ interaction. The
influence of this interaction on the composition of the partially ionized
hydrogen plasma is confined to the parameter range where both the $\rm H_2$ and
the free electron components are abundant.
