Quantum chemical calculations of oxygen adsorption on potassium are presented. The surface was modeled by dusters of six atoms and the electronic structure evaluated in the Hartree-Fock and Hartree-Fock-Slater schemes. Adsorbed intermediates were identified by comparisons between calculated data and spectroscopic information, mainly from photoemission and vibrational spectroscopies. Low doses of oxygen at cryogenic temperatures lead to the formation of surface O- and higher doses to subsurface O-2(-) The O-2-species dissociate to bulk O- upon gentle annealing. Further annealing initiates the formation of a three-dimensional oxide. Lattice relaxation is critical to the understanding of atomic adsorption as well as molecular orientation.