  We present results from high-resolution three-dimensional simulations of
turbulent interstellar gas that self-consistently follow its coupled thermal,
chemical and dynamical evolution, with a particular focus on the formation and
destruction of H2 and CO. We quantify the formation timescales for H2 and CO in
physical conditions corresponding to those found in nearby giant molecular
clouds, and show that both species form rapidly, with chemical timescales that
are comparable to the dynamical timescale of the gas.
  We also investigate the spatial distributions of H2 and CO, and how they
relate to the underlying gas distribution. We show that H2 is a good tracer of
the gas distribution, but that the relationship between CO abundance and gas
density is more complex. The CO abundance is not well-correlated with either
the gas number density n or the visual extinction A_V: both have a large
influence on the CO abundance, but the inhomogeneous nature of the density
field produced by the turbulence means that n and A_V are only poorly
correlated. There is a large scatter in A_V, and hence CO abundance, for gas
with any particular density, and similarly a large scatter in density and CO
abundance for gas with any particular visual extinction. This will have
important consequences for the interpretation of the CO emission observed from
real molecular clouds.
  Finally, we also examine the temperature structure of the simulated gas. We
show that the molecular gas is not isothermal. Most of it has a temperature in
the range of 10--20 K, but there is also a significant fraction of warmer gas,
located in low-extinction regions where photoelectric heating remains
effective.
