We computationally evaluated the standard hydrogen electrode (SHE) potential in aqueous phase and the Gibbs energy of a proton from the experimental pK(a) values of alcohol molecules. From the golden standard CCSD(T)/aug-cc-pVTZ level calculation, we estimated the SHE potential as 4.48 V, which is very close to the IUPAC-recommended experimental value of 4.44 V. As applications to the Gaussian-3 (G3) methods, which also reproduce the golden standard level calculations, we computed various pK(a) values and redox potentials for a vitamin series. For vitamin C, we support the experimental result of +0.35 V and predict the pKa value of d-ascorbic acid to be 3.7-3.9. Using a model molecule for nicotinamide adenine dinucleotide (NAD), we reproduced the redox potential and determined the order of the proton/electron addition, based on both the proton affinity and redox potential.