The reaction thermodynamics of the 1,2-dimethoxi-ethane (DME) in a highly oxidizing environment has been studied by first principles methods to predict the spontaneous degradation processes of this model solvent molecule commonly used in electrolytes for Li-O₂ rechargeable batteries. The potential energy surfaces of the reactivity of DME towards the O₂^- superoxide radical anion in oxygen-poor or oxygen rich environments have been calculated by quantum chemistry techniques. A large set of density functional theory (DFT) methods has been used and compared to post-Hartree-Fock predictions to evaluate their predictive relative performances and select the best for the calculation of the full reactivity. Solvation effects have been considered by employing self-consistent reaction field in a continuum solvation model. The onset reaction of the degradation of the DME model molecule is the H-extraction by the O₂^- superoxide anion to form an ether radical with an unpaired electron on a carbon atom. The subsequent reactivity of this radical molecule differs depending on the availability of molecular oxygen molecules. In oxygen rich environment this radical species follow multistep paths to give formaldehyde and alkyl carbonates whereas in oxygen poor environment the final products are alkyl oxalates or alkyl formates.