We have computed line emission cooling rates for the main cooling species in models of interstellar molecular clouds .
The models are based on numerical simulations of super–sonic magneto–hydrodynamic ( MHD ) turbulence .
Non-LTE radiative transfer calculations have been performed to properly account for the complex density and velocity structures in the MHD simulations .

Three models are used .
Two of the models are based on MHD simulations with different magnetic field strength ( one model is super–Alfvénic , while the other has equipartition of magnetic and kinetic energy ) .
The third model includes the computation of self-gravity ( in the super–Alfvénic regime of turbulence ) .
The density and velocity fields in the simulations are determined self–consistently by the dynamics of super–sonic turbulence .
The models are intended to represent molecular clouds with linear size L \approx 6 pc and mean density \langle n \rangle \approx 300 cm ^ { -3 } , with the density exceeding 10 ^ { 4 } cm ^ { -3 } in the densest cores .

We present ^ { 12 } CO , ^ { 13 } CO , C ^ { 18 } O , O _ { 2 } , O I , C I and H _ { 2 } O cooling rates in isothermal clouds with kinetic temperatures 10–80 K. Analytical approximations are derived for the cooling rates .

The inhomogeneity of the models reduces photon trapping and enhances the cooling in the densest parts of the clouds .
Compared with earlier models the cooling rates are less affected by optical depth effects .
The main effects come , however , from the density variation since cooling efficiency increases with density .
This is very important for the cooling of the clouds as a whole since most cooling is provided by gas with density above the average .