Fast and accurate electronic structure methods : large systems and applications to boron-carbon heterofullerenes

The interactions among electrons and nuclei, which are the constituents of matter, are governed by the fundamental laws of quantum mechanics. Methods that use these laws in order to determine the properties of matter are called ab-initio approaches. However, due to the enormous complexity of the equations, a straightforward solution is in general not possible, even when evaluated numerically on a computer. Consequently one has to use approximate methods. Kohn-Sham Density Functional Theory (KS-DFT) is one of the most famous approaches due to its good balance between accuracy and speed. Nevertheless the usage of this method is limited to systems containing some hundred atoms due to the cubic scaling with respect to the size of the system. Fortunately this problem can be overcome by the introduction of so-called linear scaling methods, which extend the range for which DFT calculations can be performed. Even though the basic ideas of these methods have been developed already quite a while ago, their implementation is still very challenging.
The first part of this Thesis shows in the beginning the theoretical background of DFT and linear scaling methods and describes then in detail the various steps that had to be taken in order to develop a fully functional code that can perform ab-initio calculations with a time requirement scaling only linearly with respect to the size of the system. The benchmarks done with the code demonstrate its ability to give very accurate results, its appealing speed and its excellent parallelization.
The second part of the Thesis uses an existing DFT code in order to investigate the energy landscape of boron-carbon heterofullerenes. It turned out that there exist many configurations which are much lower in energy than those known so far. Furthermore they exhibit a completely new structural motif. Whereas up to now it has been believed that the boron atoms should be isolated and distributed over the entire surface of the cluster, this new structural motif consists of configurations where the boron atoms are aggregated at one location to form a patch.