A combination of Artificial Bee Colony algorithm, eXtended Tight Binding and Density functional theory methods were performed to study the activation process of carbon dioxide (CO2) over copper (Cu4 cluster) based catalytic systems. The findings revealed that the activation of the C-O bond resulted from the electron transfer to σ*, π* - MO of CO2. The more the electrons are transferred to CO2, the more the C-O bond is activated and elongated. The suitability of several metal oxide supports (Fe2O3, Al2O3, MgO, ZnO) is estimated using calculated electronic parameters (global electrophilicity index, vertical ionization potential and vertical electron affinity). Aside from demonstrating the appropriateness of Al2O3 and ZnO, a thorough examination of MgO revealed that, due to the formation of stable carbonate products, this oxide is not really appropriate as a support for copper-based catalysts in CO2 conversion. Our studies have also shown that the electron enrichment of copper atoms plays a key role in the activation of C-O bonds. Alkali metal doping (Li, K, Cs) significantly improves the catalytic efficiency of the Cu4 cluster. Based on the results of electron transfer to the CO2 molecule, the effect of doping alkali metal atoms may be organized in the following order: Cs > K > Li. A new core/shell catalytic system with potassium atoms in the core and copper atoms in the shell has been proposed and has proven to be a promising, efficient catalytic system in the CO2 adsorption and activation.