We examine methods for solving the electronic structure problem with the primary objective being to provide a better mathematical understanding of these theories. First, we discuss electronic excitations and the dissociation limit within Kohn-Sham Density Functional Theory (KS-DFT). The second part deals with tensor methods; in particular, we consider matrix product states, aka tensor-trains, which lie at the heart of the Quantum Chemistry - Density Matrix Renormalization Group (QC-DMRG) method.     «

We examine methods for solving the electronic structure problem with the primary objective being to provide a better mathematical understanding of these theories. First, we discuss electronic excitations and the dissociation limit within Kohn-Sham Density Functional Theory (KS-DFT). The second part deals with tensor methods; in particular, we consider matrix product states, aka tensor-trains, which lie at the heart of the Quantum Chemistry - Density Matrix Renormalization Group (QC-DMRG) method...     »