Highly accurate methods such as coupled cluster (CC) techniques can be used for periodic systems within the framework of the method of increments. Its extension to a low-dimensional conducting system is considered. To demonstrate the presented approach, a clean Mg(0001) surface is selected, where the CC treatment with single and double excitations and perturbative triples is used for calculation of the surface energy. A further example concerns the adsorption energy of Xe on the metal surface. The obtained results can be used to verify the performance of the approximate methods. Along with the computational speed-up at the high level of accuracy, application of the method of increments provides for a possibility to analyze the influence of individual correlation energy increments on the studied property.