Self-reaction is an important sink for the hydroperoxy radical (HO2) in the atmosphere. It has been suggested (Denis, P. A.; Ornellas, F. R. J. Phys. Chem. A, 2009, 113 (2), 499-506) that the minor product hydrogen tetroxide (HO4H) may act as a reservoir of HO2. Here, we compute the thermochemistry of HO2 self-reactions to determine if either HO4H or the cyclic hydrogen-bound dimer (HO2)2 can act as reservoirs. We computed electronic energies using coupled-cluster calculations in the complete basis set limit, CCSD(T)/CBS//CCSD(T)/cc-pVTZ. Our model chemistry includes corrections for vibrational anharmonicity in the zero-point energy and vibrational partition functions, core-valence correlation, scalar relativistic effects, diagonal Born-Oppenheimer, spin-orbit splitting, and higher-order corrections. We compute the Gibbs energy of dimerization to be (-20.1 ± 1.6) kJ/mol at 298.15 K (2σ uncertainty), and (-32.3 ± 1.5) kJ/mol at 220 K. For atmospherically relevant [HO2] = 10(8) molecules per cm(3), our thermochemistry indicates that dimerization will be negligible, and thus H2O4 species are atmospherically unimportant. Under conditions used in laboratory experiments ([HO2] > 10(12) molecules per cm(3), 220 K), H2O4 formation may be significant. We compute two absorption spectra that could be used for laboratory detection of HO4H: the OH stretch overtone (near-IR) and electronic (UV) spectra.