The dynamics of molecular clouds is characterized by supersonic random moti
ons in the presence of a magnetic held. We study this situation using numer
ical solutions of the three-dimensional compressible magnetohydrodynamic (M
HD) equations in a regime of highly supersonic random motions. The non-LTE
radiative transfer calculations are performed through the complex density a
nd velocity fields obtained as solutions of the MHD equations, and more tha
n 5 x 10(5) spectra of (CO)-C-12, (CO)-C-13, and CS are obtained. In this w
ay we build synthetic molecular clouds of 5 and 20 pc diameter, evolved for
about one dynamical time from their initial cofiguration. We use a numeric
al flow without gravity or external forcing. The flow is super-Alfvenic.
Synthetic data consist of sets of 90 x 90 synthetic spectra with 60 velocit
y channels, in five molecular transitions: J=1-->0 and J=2-->1 for (CO)-C-1
2 and (CO)-C-13 and J=1-->0 for CS. Although we do not consider the effects
of stellar radiation, gravity, or mechanical energy input from discrete so
urces, our models do contain the basic physics of magneto fluid dynamics an
d non-LTE radiation transfer and are therefore more realistic than previous
calculations. As a result, these synthetic maps and spectra bear a remarka
ble resemblance to the corresponding observations of real clouds.