WHILE carbon fullerenes are studied theoretically, we tend to predict if there may be some pure nitrogen molecules which possibly consist of the same geometric structures as carbon fullerenes. Experimentally Vogler et al. have obtained the intermediate absorbed at 380 nm which was assigned to N_6 molecules in 1980. Some reports of ab initio calculations have appeared concerning theoretical aspects of nitrogen cage-like structures. Bliznyuk et al.calculated the geometrical structure of N_(20) molecules with I_h symmetry at HF level, showing that N_(20) has a metastable dodecahedral geometry, with 209.34 kJ of nitrogen atoms more than that of 10N_2. The N_(20) molecule might be a very effective high energy density material