Improvements to the Density-Functional Tight-Binding method: new, efficient parametrization schemes and prospects of a more precise self-consistency

After an introduction to the Density-Functional Tight-Binding (DFTB, a pairwise, LCAO-based approximation to Kohn Sham DFT) method, I deal with improving the treatment of the so-called repulsive energy. This pairwise, quasi-classical interaction energy of atoms covers the difference between calculated Kohn Sham energy and total DFTB energy. Parametrization of DFTB means the time-consuming task of optimizing repulsive potentials for every atomic type pair. To ease this task, I present an automaton that optimizes for different energetical targets, with a few example applications. I also propose the first steps of calculating repulsive potentials, instead of fitting them, and give the first preliminary results of this approach. Last, I propose several pieces of enhancement to the Self-Consistent-Charges (SCC) regime, the second-order extension of DFTB based on effective interactions between point-like atomic charge fluctuations. First, I derive a multipole extension of SCC, and second, I propose some semiempirical improvements to effective interaction profiles between atomic Mulliken charges.