Benchmark-quality W4 (and related) thermochemical data were obtained for the fluorine and chlorine oxides and some related hydrides, all of which are of interest for computational modeling of atmospheric processes. Our best available estimates for total atomization energies at 0 K are the following: HO2 165.97 +/- 0.14, H2O2 252.08 +/- 0.14, HOF 149.24 +/- 0.14, FO 51.17 +/- 0.10, F20 89.43 +/- 0.14, FO2 130.15 +/- 0.16, F2O2 146.00 +/- 0.16, ClO 63.40 +/- 0.10, HOCl 156.73 +/-0.14, Cl2O 96.93 +/- 0.16, OClO 122.33 +/- 0.16, ClOO 121.88 +/- 0.32, Cl2O2 142.9 +/- 0.3, ClO3 159.9 +/- 0.4, HClO2 192.0 +/- 0.4, HClO3 258.1 +/- 0.3, and HClO4 313.4 +/- 1 kcal/mol. For several of these species, the total atomization energy contains unusually large components from correlation effects beyond CCSD(T). The geometry of FOOF is significantly affected by connected quadruple excitations. A large variety of DFT exchange-correlation functionals have been evaluated for these systems and observations on their performance are offered. Our best available estimates for Delta H-f(o),0 are the following: HO2 3.65 +/- 0.14, H2O2 - 30.82 +/- 0.14, HOF - 20.15 +/-0.14, FO 26.28 +/- 0.11, F2O 6.48 +/- 0.14, FO, 6.30 +/- 0.16, F2O2 8.90 +/- 0.18, ClO 24.19 +/- 0.10, HOCl - 17.51 +/- 0.14, Cl2O 19.24 +/- 0.16, OClO 24.26 +/- 0.16, ClOO 24.69 +/- 0.16, Cl2O2 32.3 +/- 0.3, ClO3 45.7 +/- 0.4, HClO2 6.2 +/- 0.4, HClO3 -0-9 +/- 0.3, and HClO4 2.9 +/- 1.0 kcal/mol. (The corresponding values at 298.15 K are 2.96 +/-0.14, -32.24 +/- 0.14, -20.84 +/- 0.14, 26.43 +/- 0.11, 5.94 +/- 0.14, 5.87 +/- 0.16, 7.84 +/- 0.18, 24.18 +/- 0.10, -18.20 +/- 0.14, 18.82 +/- 0.16, 23.67 +/- 0.16, 24.30 +/- 0.16, 31.5 +/- 0.3, 44.3 +/- 0.4, 5.0 +/- 0.4, -2.6 +/- 0.3, and -0.1 +/- 1.0 kcal/mol, respectively.)