In this series of three papers we present results from a combined experimental and theoretical, particle-based study to quantitatively describe capacitively coupled radio-frequency discharges in oxygen. The particle-in-cell Monte Carlo model on which the theoretical description is based is described in this paper. It treats space charge fields and transport processes on an equal footing with the most important plasma–chemical reactions. For given external voltage and pressure, the model determines the electric potential within the discharge and the distribution functions for electrons, negatively charged atomic oxygen and positively charged molecular oxygen. Previously used scattering and reaction cross section data are critically assessed and in some cases modified. To validate our model, we compare the densities in the bulk of the discharge with experimental data and find good agreement, indicating that essential aspects of an oxygen discharge are captured.