The one-electron oxidation potentials [EoxNHE(H2Q)], pKa (pKa1 and pKa2) values, and bond dissociation energies (BDE1 and BDE2) of 118 important p- and o-dihydroquinones in DMSO were systematically predicted for the first time by using DFT method and the PCM cluster continuum model. The calculated results agree well with the available experimental determinations. The study shows that all the five thermodynamic parameters correlate well with the Hammett substituent parameters σp (for p-H2Q, EoxNHE(H2Q·+/H2Q) = 1.66Σσp + 0.54, pKa1 = −5.69Σσp + 16.54, pKa2 = −5.19Σσp + 23.91, BDE1 = 3.43Σσp + 82.29, BDE2 = 4.64Σσp + 67.70 and for o-H2Q, EoxNHE(H2Q·+/H2Q) = 1.85Σσp + 0.46, pKa1 = −5.53Σσp + 13.28, pKa2 = −5.24Σσp + 26.70, BDE1 = 3.54Σσp + 82.08, BDE2 = 3.82Σσp + 75.93), which hints that we can get these thermodynamic parameters as long as the structure of the hydroquinones were known. The comparisons of the calculated five thermodynamic parameters between p-hydroquinones and o-hydroquinones and the number of the phenyl ring effects on these thermodynamic parameters were also studied. At last, intramolecular hydrogen bond energies in hydroquinones at neutral, radical cation, radical, anion different state were systematically calculated and analyzed. Combined with the papers published in our group before, we will have a systematic thermodynamic picture of the transfer details between different kinds of quinones and corresponding hydroquinones, which strongly promote the fast development of the understanding and applications of quinones