This paper assesses the roles of the presence of warm H2, and the increased formation rate due to the ion-neutral drift. We performed ideal MHD simulations that include the heating and cooling of the multiphase ISM, and where we treat dynamically the formation of H2. In a post-processing step we compute the abundances of species at chemical equilibrium. We show that CH+ is efficiently formed at the edge of clumps, in regions where the H2 fraction is low, but nevertheless higher than its equilibrium value, and where the gas temperature is high. We show that warm and out of equilibrium H2 increases the integrated column densities of CH+ by one order of magnitude, up to values still 3-10 times lower than those observed in the diffuse ISM. We balance the Lorentz force with the ion-neutral drag to estimate the ion-drift velocities (vd). We find that the vd distribution peaks around 0.04 km s-1, and that high vd are too rare to have a significant statistical impact on the abundances of CH+. Compared to previous works, our multiphase simulations reduce the spread in vd, and our self-consistent treatment of the ionisation leads to much reduced vd. Nevertheless, our resolution study shows that this velocity distribution is not converged: the ion-neutral drift has a higher impact on CH+ at higher resolution. On the other hand, our ideal MHD simulations do not include ambipolar diffusion, which would yield lower drift velocities. Within these limitations, we conclude that warm H2 is a key ingredient in the efficient formation of CH+ and that the ambipolar diffusion has very little influence on the abundance of CH+, mainly due to the small drift velocities obtained. However, we point out that small-scale processes and other non-thermal processes not included in our MHD simulation may be of crucial importance, and higher resolution studies with better controlled dissipation processes are needed.
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