Abstract We present 3D ‘zoom-in’ simulations of the formation of two molecular clouds out of the galactic interstellar medium. We model the clouds – identified from the SILCC simulations – with a resolution of up to 0.06 pc using adaptive mesh refinement in combination with a chemical network to follow heating, cooling and the formation of H2 and CO including (self-) shielding. The two clouds are assembled within a few million years with mass growth rates of up to ∼10−2 M⊙ yr−1 and final masses of ∼50 000 M⊙. A spatial resolution of ≲0.1 pc is required for convergence with respect to the mass, velocity dispersion and chemical abundances of the clouds, although these properties also depend on the cloud definition such as based on density thresholds, H2 or CO mass fraction. To avoid grid artefacts, the progressive increase of resolution has to occur within the free-fall time of the densest structures (1–1.5 Myr) and ≳200 time-steps should be spent on each refinement level before the resolution is progressively increased further. This avoids the formation of spurious, large-scale, rotating clumps from unresolved turbulent flows. While CO is a good tracer for the evolution of dense gas with number densities n ≥ 300 cm−3, H2 is also found for n ≲ 30 cm−3 due to turbulent mixing and becomes dominant at column densities around 30–50 M⊙ pc−2. The CO-to-H2 ratio steadily increases within the first 2 Myr, whereas XCO ≃ 1–4 × 1020 cm−2 (K km s−1)−1 is approximately constant since the CO(1−0) line quickly becomes optically thick.