  We explore the origin of fast molecular outflows that have been observed in
Active Galactic Nuclei (AGN). Previous numerical studies have shown that it is
difficult to create such an outflow by accelerating existing molecular clouds
in the host galaxy, as the clouds will be destroyed before they can reach the
high velocities that are observed. In this work, we consider an alternative
scenario where molecules form in-situ within the AGN outflow. We present a
series of hydro-chemical simulations of an isotropic AGN wind interacting with
a uniform medium. We follow the time-dependent chemistry of 157 species,
including 20 molecules, to determine whether molecules can form rapidly enough
to produce the observed molecular outflows. We find H$_2$ outflow rates up to
140 M$_\odot$ yr$^{-1}$, which is sensitive to density, AGN luminosity, and
metallicity. We compute emission and absorption lines of CO, OH and warm (a few
hundred K) H$_2$ from the simulations in post-processing. The CO-derived
outflow rates and OH absorption strengths at solar metallicity agree with
observations, although the maximum line of sight velocities from the model CO
spectra are a factor $\approx$2 lower than is observed. We derive a CO (1-0) to
H$_2$ conversion factor of $\alpha_{\rm{CO} (1-0)}$ = 0.13 M$_\odot$ (K km
s$^{-1}$ pc$^2$)$^{-1}$, 6 times lower than is commonly assumed in observations
of such systems. We find strong emission from the mid-infrared lines of H$_2$.
The mass of H$_2$ traced by this infrared emission is within a few per cent of
the total H$_2$ mass. This H$_2$ emission may be observable by JWST.
