Approximations and Effectiveness of QMC and Other Electronic Structure Methods in Molecules and Solids

Accompanying the development of methodologies and computer technology, firstprinciple electronic structure calculations are gaining a stronger foothold as well as wider applicability in predicting material properties. We examined and compared fundamental approximations made in different electronic structure methods like Hartree-Fock (HF), Density Functional Theory (DFT) and quantum Monte Carlo (QMC). Some of their boundaries and effectiveness are analyzed through both simple systems as well as real world materials.;Thorium monoxide's energy and electric properties were studied using HF and subsequently QMC. Thorium dioxide crystal (thoria)'s various electric properties in normal phase were studied using DFT and energetics of phase transition were studied using both DFT and QMC. This is the first attempt of QMC calculations on actinide materials known to the author. Calculations on manganese oxides are not only benchmarks but also serving the purpose of illustrating QMC method's variational property for checking and potentially optimizing DFT exchange-correlation functional parameters.;Last but not least, nodal shapes, topologies and fixed-node errors were analyzed for simple atomic and molecular systems, as fixed-node biases are the most important yet elusive errors for QMC. Mathematical quantity "nodal domain average" was proposed to aid the analysis of fixed-node error.