With an increasing complexity of nanoscopic systems and the modeling thereof, new theoretical tools are needed for a reliable calculation of complex systems with strong electronic correlations. To this end, we propose a new approach based on the recently introduced dynamical vertex approximation. We demonstrate its reliability already on the one-particle vertex (i.e., dynamical mean field theory) level by comparison with the exact solution. Modeling a quantum point contact with 110 atoms, we show that the contact becomes insulating already before entering the tunneling regime due to a local Mott-Hubbard transition occurring on the atoms which form the point contact.