I will present the work of my PhD thesis, in which quantum impurity problems are tackled with the use of natural orbitals, a representation rooted in the framework of quantum chemistry. From the inherent simplicity of these problems under this representation, a new algorithm is developed to generate an optimized few-body wavefunction, which surpasses usual ground state computations. In the first place, the algorithm is used to compute the screening cloud in large one-dimensional chains and in a 2D square lattice coupled to a localized atom. Then, a statistical study on large systems is performed, in which the the fate of the correlation cloud spreading into the disordered electronic bath is investigated.