This study employs DFT (density functional theory) to investigate the formation of hydrazine like (N-N) cross-linked structures between DNA base pair diradicals that are likely to result from the interaction of high linear energy transfer (LET) radiation such as ion-beam radiation with DNA. In our calculations, we generated the guanine (G), cytosine (C), adenine (A) and thymine (T) radicals by removing one hydrogen atom from an N-H bond involved in the normal base pairing. The radical species formed are those that naturally result from one electron oxidation of the bases followed by deprotonation. N-N cross-links between G and C or A and T diradicals were studied using the BHandHLYP, B3LYP, M06 and M06-2X density functionals and 6-31G* basis set. From a comparison to several test cases performed with the G3B3 method which gives thermodynamically reliable values, we found that calculations employing the BHandHLYP/6-31G* method predict the best estimates of bonding energies for hydrazine like structures. Our study shows that the N-N cross-link formed between guanine radical and a neutral cytosine is endothermic in nature but can form metastable structures. However, the reactions between two DNA base radicals (diradical) to form several N-N cross-linked structures are found to be highly exothermic in nature. The N-N cross-links formed between various G-C, G-G, and C-C diradicals have binding energies in the range ca. −54 to −68 kcal/mol, −41 to −47 kcal/mol and −67 to −75 kcal/mol, respectively, while A-T, A-A and T-T have binding energies −80 kcal/mol, −60 kcal/mol and −98 kcal/mol, respectively. In all purine-pyrimidine N-N cross-linked structures, the highest occupied molecular orbital (HOMO) is found to be localized on the purine moiety and LUMO on the pyrimidine moiety.