UCLA

Electronic structure theory has become a powerful predictive tool in chemistry. Results from calculations provide insights into understanding a variety of material properties, as well as chemical and biological processes. A central challenge in the field is to develop methods with better efficiency, such that simulations can be carried out on larger scale and realistic systems. Different strategies are employed to address this problem, including the development of composite methods, incorporation of novel numerical schemes, as well as search for better effective Hamiltonians. In this dissertation, we present three projects that we carried out in the quest for highly efficient electronic structure theory methods.

In Chapter 2, we give an introduction to our stochastic quantum chemsitry (sQC) framework. Central to the framework is a numerical technique called stochastic resolution of identity (sRI). It allows us to replace the expensive sum of states by an average over much fewer stochastic samples. In this way the computational cost of calculations is drastically reduced. We then discuss two methods under the sQC framework, where we separately combined sRI with density functional theory (DFT) and the GW method. The resulting stochastic DFT and stochastic GW methods produce results that are in good agreement with traditional deterministic implementations, but at a much lower computational cost.

Chapter 3 presents the stochastic embedding DFT method, which is an extention of the stochastic DFT method. It is designed to selectively reduce the stochasic error of results for a specific subsystem. We applied it to study a p-nitroaniline molecule in water, and indeed it managed to reduce the stochastic error of calculated forces on the p-nitroaniline molecule by 10-fold, without increasing the computational time required in the simulation.

Chapter 4 presents the stochastic GW/RSH method, aiming at finding an optimal DFT starting point for stochastic GW calculations. We applied the method to study a few solids, and results were in good agreement with those obtained from self-consistent GW calculations.

We will also introduce another project, where we developed a novel formulation of the projector augmented wave (PAW) method. The PAW method improves the efficiency of the calculations by eliminating explicit treatment of core electrons. However, traditional implementations of PAW destroys the orthogonality of wavefunctions. In our orthogonal PAW (OPAW) method, we set to restore this orthogonality. Chapter 5 provides a short introduction to pseudopotentials and PAW, and Chapter 6 gives a detailed account of OPAW. We applied OPAW in a DFT code and succesfully reproduced results from existing non-orthogonal PAW calculations from the ABINIT package.