Ab initio studies of solid phase diagrams with quantum chemical theories

Abstract

In this thesis, we first apply several existing methods, including full configuration interaction Monte Carlo (FCIQMC) and coupled cluster singles and doubles (CCSD), on the solid hydrogen phases under high pressures and find that CCSD predicts a static phase diagram that agrees well with the state-of-the-art diffusion Monte Carlo (DMC), especially on the most stable phases. Noticing that all existing studies on the solid hydrogen phases use structures which are optimized by density functional theory (DFT) using different exchange-correlation functionals, as a second step and to go beyond DFT, we develop and implement a program that calculates the MP2 forces using a plane wave basis set for the structural optimization of the solid hydrogen phases. The C2/c-24 model structures obtained via DFT-PBE are further relaxed using the MP2 forces and the resulting structures provide band gaps, calculated by the G0W0 method and with the electron-phonon interactions included perturbatively, that agree reasonably well with experiments. Furthermore, the H2 vibron frequencies versus pressure curve calculated based on the MP2 optimized structures agree almost perfectly with one of the experiments, providing valuable theoretical insights in dissolving a long-standing dispute among experiments over the pressure calibration curve at high pressures. Finally, to make existing methods more efficient and accurate, we combine the transcorrelation method (TC) and the coupled cluster methods, with an application on the three dimensional uniform electron gas (3D UEG) which is a model system for periodic solids. Traditionally, the TC method has been used to incorporate the short range cusp conditions in the wavefunction directly into the TC Hamiltonian, so that fewer basis functions are needed to achieve energies that are free from the basis-set incompleteness errors. We notice that the TC framework is very general and correlations in addition to the short range cusp conditions can also be included and potentially improve even the accuracy of approximate methods like coupled/distinguishable cluster doubles (CCD/DCD) in systems with strong correlations. Inspired by the pair-correlation functions in real space for the 3D UEG, we design a cor- relator that mimics their behaviours as a function of the electron density. In addition to that, a simple framework which aims to maximize the HF weight in the wavefunction is introduced to optimize the parameters in the correlator. As a result, the accuracy and efficiency of TC-CCD and TC-DCD are improved significantly compared to their canonical counterparts over a large range of electron densities, using FCIQMC and DMC results as benchmark data. We hope to generalize these methods to real periodic solid materials in the future.