In this thesis, we focused on the alternative methodologies that are based on the reconstruction of density matrices. While in DFT several benchmarks can be found in the literature, for the rest of alternative methodologies there were not any comprehensive benchmarks where the quality of the approximated reduce density matrices (RDMs) were analyzed. Thus, in this thesis, we have performed an exhaustive benchmark for the approximations available in the literature that reconstruct the 2- and 3-order RDMs.
RDMs provide access to physical magnitudes as the intracule probability density (IPD). Actually, the radial IPD can be measured experimentally from X-Ray scattering; hence we focused on a deep understanding of this magnitude and, to that end, we analyzed the evolution of the radial IPD in isolated atoms and in the bond formation process. Finally, since RDMs also provide means to evaluate the bond order, we characterized the so-called harpoon mechanism.
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