Electronic Structure Theories for Periodic Systems

Abstract

Electronic structure theory for periodic system is a crucially important branch of quantum chemistry and condensed matter physics. For many solid-state phenomena, for instance, high temperature superconductivity, the effect of the strong correlation between electrons is profound and cannot be accurately described by means of a mean-field theory like density functional theory (DFT). The inherent single-reference nature of DFT together with the absence of a systematic approach to approximate the exchange-correlation functional result in its poor performances in predicting several solid-state properties, such as cohesive energy, heat of formation, and band gap. Quantum chemical treatment beyond DFT for strongly correlated solids is often impractical due to their poor scaling with the system size. Alternatively, quantum embedding theories is a powerful ansatz to overcome the computational cost challenge. This is achieved by fragmentating the system into smaller pieces and only treating the chemically relevant fragments using an expensive yet accurate method. In this thesis, I discuss our effort in combining density matrix embedding theory (DMET) with wave function theories to treat electron correlation in solids. We introduce an algorithm to perform DMET on periodic system where the unit cell can be seen as a chemically relevant fragment. Mostly importantly, we demonstrate how multireference methods such as complete active space self-consistent field and n-electron valence state perturbation theory can be extended to solid-state systems within the DMET framework. I hope that our exploration of multireference wave function theories discussed in this dissertation can inspire further developments of electronic structure theories and numerical algorithms for periodic solids.