In this paper we present benchmark results for isoelectronic metal carbonyl complexes of the groups 11 and 12 of the periodic table. The focus is on the geometry, vibrational frequencies, bond dissociation energy and chemical bonding. The description of these complexes requires a good balance between electron correlation and relativistic effects. Our results demonstrate that the combination of the effective core potential and the MP2 method gives quantitative results for the first- and the second-row transition metal complexes and only qualitative agreement for the third-row complexes. In order to obtain quantitative results for the whole series the use of four-component or X2C methods is mandatory. The fourth-row transition metal carbonyl complexes from groups 11 and 12 have been studied for the first time. The metal-carbon bond strength pattern along the group is shown to be highly dependent on the correct description of the relativistic effects. Finally, the relativistic effects on the bonding are studied by means of electron density difference maps, the analysis of the bond critical points of the electron density and the mechanism for σ-donation and π-backdonation. Our analysis indicates that the fourth-row complexes exhibit a strong covalent character induced by relativistic effects ; We would like to thank Dr Georg Eickerling and Prof. Scherer's for providing a Mathematica script to analyze the topology of the density. Financial help has been furnished by the Polish Ministry of Science and Higher Education (project no. N N204 215634), the Spanish MICINN (project no. CTQ2011-23156/BQU and CTQ2011-23441/BQU) and by the FEDER fund (European Fund for Regional Development; grant UNGI08-4E-003). Financial support from the Generalitat de Catalunya (SGR637 and Xarxa de Referencia en Quimica Teorica i Computacional) is also acknowledged. E.M. acknowledges financial support from the EU under Marie Curie Career Integration grant (PCI09-GA-2011-294240) and the Beatriu de Pinos program from AGAUR for the postdoctoral grant (BP_B_00236). Most calculations reported in this paper have been performed in our (University of Szczecin) server SUN Fire X4400