Context. The results of an observational search for gas phase urea, (NH 2 ) 2 CO toward the Sgr B2-LMH region, have been reported recently. In spite of strong presumptions, whether it is urea or another species (for example an isomer) seems to remain a pending question. Aims. In this note, we consider the energetic aspect of this would-be detection by addressing the relative stabilities of the 22 isomers that can possibly be formed with the CH 4 N 2 O set of atoms. By extension, we also consider the 22 sulphur analogues of CH 4 N 2 S chemical formula. Methods. The question was first addressed by means of quantum density functional theory (DFT) simulations. The hybrid B3LYP functional was used throughout. The geometries of the 44 molecules part of this survey were fully optimized and verified to be real minima by vibrational analysis. The lowest isomers found this way were then reconsidered in higher level post Hartree-Fock MP2 and coupled cluster CCSD and CCSD(T) calculations to derive more accurate energy differences and dipole moments, whose knowledge is crucial for interpreting micro-and millimetre-wave spectra. Results. We found that urea and thio-urea are the most stable compounds in their respective families. The closest isomers on the energy scale are the iminol tautomeric forms, HN=COH-NH 2 and HN=CSH-NH 2 , whose rotational constants and dipole moments have also been determined. Conclusions. That urea is the lowest energy isomer possibly formed is a strong argument making the detection of this species more than probable. After formamide and acetamide, this result confirms the greatest stability of the -[NH-C=O]-linkage, underlining the interest of the minimum energy criterion as a tool for the primary search of target molecules. Additionally, thio-urea should the analogue to search for.