The two-step SET + HAT procedure, that was satisfactorily applied by us to the calculation of the autoprotolysis of water and other protic liquids, is used in the present work for the calculation of the structural proton transfer rates from the ions formed by autoprotolysis in pure water. The calculated real time value (τ) for the proton transfer reaction initiated by hydronium cation (τH+ = 1.29 ps) is in good agreement with the experimental values (1.0–2.5 ps). We were also able to determine the real time value for the proton transfer reaction initiated by hydroxide anion (τOH– = 3.47 ps). Interestingly, the resulting relative diffusion rate, DH+/DOH– = τOH–/τH+ = 3.47/1.29 = 2.69, is in good agreement with the experimental diffusion-rate values, located in the range 1.8 ± 1.0. On the other hand, our computations reinforce Parrinello's standpoint that the (H2O)HO─(H2O)3 apical complex is pivotal in the transfer reaction initiated by hydroxide, due to its shorter O–····H-O distance, computed to be 1.566 Å, and significant kinetic instability. All these results support the workability of the SET + HAT mechanism along with TD-DFT methodology (SET + HAT//TD-DFT) to predict real time kinetics of proton transfer reactions involving water or similar protic liquids. Our results reveal that use of the term “hypercoordinated” for the hydroxide water complexes is misleading, since electrostatic interactions are predominant in these systems.