Authors: Ayoub Aouina
Source: SPIRE - Sciences Po Institutional REpository (preprint, 2022-02-01)
Field: Materials Science — Materials Chemistry

A novel shortcut for computational materials design Density functional theory (DFT) tells us that any property of an interacting system is a functional of the ground-state electronic density. The Kohn-Sham scheme has made DFT a practical computational tool to study the electronic structure of materials. The main quantity that needs to be approximated is the exchange correlation (xc) potential. In the local density approximation (LDA), the real system is treated locally as a homogeneous electrons gas (HEG) with a density equal to the local density of the real system. The xc potential is then imported locally from the HEG, which serves as a model. It has been obtained, once for all, by accurate quantum Monte Carlo calculations (QMC) of the HEG at various densities. These calculations contributed immensely to the success of DFT being one of the most widely used method for modelling solids and molecules.Inspired by the LDA and the use of the HEG, in this thesis we generalise the idea of using models to simulate real systems. Our approach, called "Connector Theory" (COT), is an in principle exact prescription of how to use data from models to calculate quantities in materials. The power of this approach is twofold: first, starting from an in principle exact theory provides a guideline to build systematic and improvable approximations. Second, since models are usually simpler systems, one can also afford high level calculations with great precision for new model quantities. The benefit is enormous since these calculations are done once and for all and serve as building blocks to approximate real quantities.After introducing the general scheme of COT, we used it to build non-local functionals of the density for the xc potential, starting from a linear expansion. We showed that the LDA can be derived as a particular case of the COT approximation. In order to test the COT strategy, we applied it to reproduce a non-local functional of the xc potential based on the weighted density approximation. The results were very promising: on the one hand, we could obtain the LDA within the COT scheme by making the Coulomb interaction short range. On the other hand, we constructed a non-local description of the functional that goes beyond the LDA and the linear expansion. To examine the COT approximation of the xc potential, we implemented it in the self-consistent Kohn-Sham loop and computed the electronic densities of silicon, a semiconductor, and sodium chloride, an insulator. When compared to benchmark QMC results, the densities produced from this COT xc potential were very accurate. This was due to the ability of COT functional to capture a significant amount of the non-local information of the system.Independently of the COT, we have examined the inverse question of obtaining the xc potential from the accurate QMC density. The main aim was to analyse the features of the exact xc potential and to compare them with the COT and other DFT approximations. We addressed various technical issues related to the algorithm of the inversion, which was applied for the first time in solids, including the influence of the basis set and the statistical error of QMC. The inverted xc potential enabled us to determine the exact xc energies, Kohn-Sham band gaps and band structures of Si and NaCl, and to benchmark corresponding COT approximations. This also provided the motivation to build and test a new COT functional optimised for the xc energy.Finally, we demonstrated that COT is not limited to DFT by using it to estimate the density without diagonalising an independent-particle Hamiltonian. We have also explained how to use COT to approximate non-local objects such as the density matrix; in this example, we showed that a non-homogenous model can boost COT approximations. These more complex models could be calculated using nowadays computer capacities, and the results could be interpolated and parametrised using available machine learning techniques. Computer science Machine Learning in Materials Science ; Graphene and Nanomaterials Applications ; Graphene research and applications