Towards more scalable selected configuration interaction methods

146 pagesSelected configuration interaction plus perturbation theory (SCI+PT) methods are an importantclass of electronic structure theory methods. By taking advantage of the fact that typically only a tiny fraction of the Hilbert space contributes significantly to the ground and low-lying excited states in \textit{ab initio} quantum chemistry calculations, these methods can provide high-precision solutions for both single- and multi-reference systems for which exact diagonalization, or full configuration interaction (FCI), becomes prohibitively expensive. In this dissertation, I present my work on increasing the scalability of SCI+PT methods to larger system sizes. I focus on a particular version of such methods, the semistochastic heat-bath configuration interaction (SHCI) method developed in our research group, and address two aspects that limit the method's scalability. First, I show how orbital optimization can be used to produce more compact variational wavefunctions in order to reduce the memory usage of SCI calculations. Here, the orbital optimization problem is framed as the simultaneous optimization in two subspaces: configuration interaction coefficients and orbital rotation parameters. Starting from natural orbitals, I present three classes of optimization methods based on how they treat coupling between these subspaces, namely uncoupled, fully coupled, and quasi-fully coupled methods. I show that taking the coupling into account is crucial for fast convergence and recommend two quasi-fully coupled methods: accelerated diagonal Newton, and Broyden–Fletcher–Goldfarb–Shanno with block matrix inversion. Second, I show how density-based basis-set corrections can be used to accelerate the slowconvergence of SHCI energies with respect to basis size, a problem plaguing all accurate wave function theory methods operating in finite basis sets. These correction methods map the divergent Coulomb interaction in a finite basis set to a non-divergent effective interaction in the infinite basis limit and use density functionals from range-separated density functional theory to recover the dominant part of the short-range correlation effects missing from finite basis wave functions. Two schemes are used in this study, differing in the functional used. They provide basis-set corrections that can be added \textit{a posteriori} to SHCI energies. Finally, I perform benchmark studies on two suites of realistic systems: 1) the Gaussian-2 set of55 first- and second-row molecules, and 2) seven transition metal atoms and their corresponding ions and monoxide molecules. The methodological improvements discussed in this dissertation help produce highly accurate results for these benchmark systems