Fast Semistochastic Heat-Bath Configuration Interaction

Abstract

In this thesis, I present my work on the fast semistochastic heatbath configuration interaction (Fast SHCI), which is an efficient algorithm for doing essentially exact electronic structure calculations within a finite basis. There are Hamiltonians for which the entire Hilbert space is enormous, but the important part of Hilbert space is of manageable size, say $10^{12}$. Quantum chemistry Hamiltonians, for reasonably small systems, have this property. For such Hamiltonians, selected configuration interaction plus perturbation theory (SCI+PT) methods can be useful. The most important part of the Hilbert space is treated variationally, and the resulting energy is improved by using perturbation theory. Fast SHCI is more than an order of magnitude faster than other SCI+PT algorithms, and also much faster than other essentially exact algorithms for many chemical systems. This thesis provides an in-depth description of the Fast SHCI algorithm and its implementation. I use SHCI to compute the electronic structure of several chemical systems and the homogeneous electron gas. Some of these calculations are more accurate than those achieved by other high-order quantum chemistry methods. Others treat systems larger than those that can be treated by other equally accurate methods. My implementation of SHCI uses a modular design, which not only makes the library highly extensible but also contributes several generic distributed computing building blocks to the open-source community. In this thesis, I also describe my design and implementation of these generic components. Finally, I also provide a brief discussion of the usability of general software engineering best practices for the development of medium-scale scientific software packages with lessons learned from designing, developing, and leading the development of our SHCI package. Medium-scale scientific software packages are common in scientific research where a small group of researchers works on the same code base. Due to the differences in the requirements, some best practices that are common in the industry need to be adjusted to be useful for these projects.