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 of ca. -54 to -68, -41 to -47, and -67 to -75 kcal/mol, respectively, whereas A-T, A-A, and T-T have binding energies of -80, -60, 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 the lowest unoccupied molecular orbital (LUMO) is on the pyrimidine moiety.