Generalized Pairing Wave Functions and Nodal Properties for Electronic Structure Quantum Monte Carlo

The quantum Monte Carlo (QMC) is one of the most promising many-body electronic structure approaches. It employs stochastic techniques for solving the stationary Schr\" odinger equation and for evaluation of expectation values. The key advantage of QMC is its capability to use the explicitly correlated wave functions, which allow the study of many-body effects beyond the reach of mean-field methods. The most important limit on QMC accuracy is the fixed-node approximation, which comes from necessity to circumvent the fermion sign problem. The size of resulting fixed-node errors depends on the quality of the nodes (the subset of position space where the wave function vanishes) of a used wave function. In this dissertation, we analyze the nodal properties of the existing fermionic wave functions and offer new types of variational wave functions with improved nodal structure.