In this report, a first-principles investigation of the Fe3O4 (001) surface using Density Functional Theory (DFT) with Hubbard U and inter-site V corrections (DFT + U + V) is presented. By considering the DFT and DFT + U approaches, a semi-metallic nature is observed, while by applying the DFT + U + V method, a pronounced gap is created at the Fermi level, in agreement with the insulating nature of the surface. Furthermore, Cu2+ adsorption simulations were performed, revealing that the incorporation of both U and V parameters is crucial for accurately modeling the adsorption processes, which are essential for catalysis and environmental applications. These findings highlight the importance of considering both on-site and inter-site electron interactions to achieve a comprehensive understanding of the surface chemistry of transition metal oxides, with an impact on applications of the Fe3O4 (001) surface chemistry.