Atomic chemisorption of hydrogen and oxygen on Cu(100) has been studied using up to 25 copper atoms as a model of the surface. The computational procedure used involves a reduction of the metal atoms to one-electron systems and extensive configuration-interaction calculations of the adsorbate and the cluster-adsorbate bonds. The calculations support the fourfold hollow site as the preferred chemisorption site for oxygen, with a barrier-to-surface migration of 25 kcal/mol. The calculated chemisorption energies for both hydrogen and oxygen, 51 and 90 kcal/mol, respectively, are in good agreement with experimental estimates (56 kcal/mol for hydrogen and 97 kcal/mol for oxygen). The effects of reducing the metal atoms to one-electron systems have been investigated through comparisons with all-electron calculations for ${\mathrm{Cu}}_5$H and ${\mathrm{Cu}}_5$O at the self-consistent-field level and by comparisons to previous calculations on ${\mathrm{Cu}}_5$Cl and ${\mathrm{Cu}}_9$Cl in which the 3d electrons were treated explicitly.