We report a quantum chemical characterization of the non-natural (synthetic) H-bonded base pair formed by 6-amino-5-nitro-2(1H)-pyridone (Z) and 2-amino-imidazo [1,2-a]-1,3,5-triazin-4(8H)-one (P). The Z:P base pair, orthogonal to the classical G:C base pair, has been introduced in DNA molecules for expanding the genetic code. Our results indicate that the Z:P base pair closely mimics the G:C base pair both in terms of structure and stability. To clarify the role of the NO2 group on the C5 position of the Z base, we compared the stability of the Z:P base pair with that of base pairs having different functional group on the C5 position of Z. Our results indicate that the electron donating/withdrawing properties of the group in the C5 position has a clear impact on the stability of the Z:P base pair, with the strong electron withdrawing nitro group achieving the largest stabilizing effect on the H-bonding interaction, and the strong electron donating NH2 group destabilizing the Z:P pair by almost 4 kcal/mol. Finally, our gas phase and in water calculations confirm that the Z-nitro group reinforce the stacking interaction with its adjacent purine or pyrimidine ring.