Spin contamination error in the total energy of the Au-2/MgO system was estimated using the density functional theory/plane-wave scheme and approximate spin projection methods. This is the first investigation in which the errors in chemical phenomena on a periodic surface are estimated. The spin contamination error of the system was 0.06 eV. This value is smaller than that of the dissociation of Au-2 in the gas phase (0.10 eV). This is because of the destabilization of the singlet spin state due to the weakening of the Au-Au interaction caused by the Au-MgO interaction. (C) 2018 Elsevier B.V. All rights reserved.