On excited states for defects in solids using coupled cluster theories

Abstract

The study of the electronic structure for solid state systems is central for understanding novel physical phenomena of interacting systems and for unlocking future material properties. The road to the qualitative and quantitative understanding of these condensed matter systems is however not without its challenges. Interacting electrons imply a steep combinatorial scaling of the solution space, thus requiring the need of exponentially increasing computational resources for the exact resolution of the behavior of interacting electrons. In this context, Density Functional Theory (DFT) remains the most successful practical method offering a delicate balance between computational resources and accuracy of the results for systems up to several thousands of atoms. The achievements of DFT notwithstanding, it fails to deliver consistently accurate outcomes for some physical properties in simple systems. Truncated coupled cluster theory seeks to offer systematically accurate ground-state energies at a moderate computational cost for weakly correlated systems composed of some tens of atoms.Defects in solids present an attractive breeding ground for testing electronic structure theories due to their resemblance to a molecule embedded in an effective crystal field. Additionally, properties of extended systems are highly influenced by both the type and concentration of defects embedded within them. This dependence of bulk material properties on the defect electronic structure is also given by the dynamics and spectrum of the electronic excited state manifold of the defects. Therefore, a robust and accurate methodology to perform both ground-state and excited-state calculations of the electrons in solid-state defects is of paramount importance for both practical applications and theoretical development.In this thesis, we implement, develop and apply coupled cluster based methodologies to calculate the ground state and excited states of defects embedded in solids. These excited states are based on the Equation Of Motion Coupled Cluster (EOM-CC) corpus of theories. Our implementation of EOM-CC theory is applied to study F-centers in alkaline earth oxides employing a periodic supercell approach with plane wave basis set and the Projector Augmented Wave (PAW) theory.The second part of this thesis deals with a different challenge, namely the basis set problem. All wavefunctions inherit from the Coulomb interaction sharp features at coalescence points, these features are called cusps. In order to resolve these cusps, one needs to devote effort both in treating many body correlation and refining the basis set employed in the many body correlation. In this domain, we present a basis set correction scheme for the coupled cluster singles and doubles (CCSD) method. We test this approach on the Uniform Electron Gas (UEG) and on a series of molecular systems where we show the effectiveness of the scheme.