We investigate the interaction between methane and a [Li](0) center on MgO(100) using ab initio cluster methodology. We focus on the catalytic activation of the C-H bond, an essential reaction step in the oxidative coupling of methane (OCM), In the first part of the study we use a simple embedded cluster model that allows us to compare different levels of theory and to study the influence of electron correlation on the calculated energy profile for the H abstraction reaction. Hartree-Fock (HF) calculations are compared to results obtained from post-HF (Moller-Plesset perturbation theory) and gradient-corrected density functional theory (DFT) computational schemes. We show that the use of the density functional exchange potential without self-interaction corrections leads to sin inadequate potential energy surface for the hydrogen abstraction reaction at the [Li](0) center. The second part of the study is devoted to Substrate relaxation effects, employing a much larger cluster model The geometry of the lattice around the [Li](0) cener is optimized for key stages along the reaction path. Comparison with previous studies shows the importance of including extensive relaxation if accurate geometries about the surface defect sites are to be calculated.