Geometry optimizations demonstrate that the proton (H-9) transfers spontaneously on oxidation by electron detachment from HOMO just for the single H-bond (N-(HN)-N-...) coupling mode complexes, NA and NB, and the intrinsic mechanism of this proton transfer is presented. The absence of the imaginary frequencies for the DFT (UB3LYP/6-311+G*) structures shows that these complexes present indeed the local minima on the energy surface. Significant bond length changes for those in bonding or antibonding regions on oxidation are found with the HOMO analyses for all of these five complexes, and water ligation does not significantly affect the complex geometries. The frequency analyses indicate that a distinct red-shift occurs for the N-(HN)-N-... stretching vibration of the single H-bond coupling mode complexes on oxidation and a slight blue-shift occurs for the C-(HN)-N-... stretching vibration of the double H-bond coupling mode complexes on oxidation. The difference of the N-(HO)-O-... and O-(HN)-N-... H-bonds is compared. Both the oxidation and the water ligation increase the Es, leading to the strengthening of the combination of two moieties of each isomer. The coupling mode gives more contribution to Es as compared to the orientation, and the oxidation effect is significantly larger than the water ligation effect on the complex structures.