Developing methods to accelerate convergence to the thermodynamic limit for periodic coupled cluster theory
Creators: name: Mihm, Tina N.
Publisher: name: University of Iowa
Year: 2024
Subjects: coupled cluster theory
Material science
Methods Development
solids
public abstract
Computational Chemistry
Electronic Structure

description: A central goal of electronic-structure methods in material science is to solve themany-electron Schrodinger Equation. Despite the apparent simplicity of this equation, it is notoriously hard to solve exactly.Different groups of methods have been developed to treat this equation with varying degrees of accuracy and cost. One such group of methods that are known for providing high accuracy is wavefunction-based theories. The work presented in this thesis uses one of these wavefunction-based theories called coupled cluster theory, which is known for treating the correlation effects systematically by including higher-order excitations in a step-wise fashion. These excitations are designed to correct the Hartree-Fock method and add in the correlation energy that is otherwise absent. While coupled cluster theory has already been shown to be able to reach chemical accuracy molecules, it is still under active development for solids with the aim of achieve the same level of accuracy. Currently, one of the main roadblocks for using coupled cluster theory on solids is the treatment of the errors known as finite size effects, which come from modeling solids with a finite simulation cell. As these are relatively large errors, they often slow the convergence of the energy to the thermodynamic limit—the limit at an infinite particle system size. My work over the past few years has focused on studying these finite size effects and their convergence in coupled cluster theory as well as developing methods to help treat them and speed up convergence to the thermodynamic limit.
description: A popular way to treat finite size effects is by using twist averaging. Twist averaging uses an average over a set of offsets to the orbitals known as “twist angles” to break the orbital degeneracy and reduce finite size effects. However, each twist angle requires its own calculation, which causes the cost of running twist averaging to scale with the number of twist angles. Here, I present three new twist angle selection methods we developed that help reduce finite size effects while reducing the cost of obtaining twist averaged energies on solids down to a single coupled cluster calculation. All three methods work by using a chosen property of the energy to select the twist angle that reproduces the twist averaged energies and, therefore, has the smallest amount of finite size effects present. For each method, a different property of the energy was used to select the twist angle. For our connectivity twist averaging method (cTA), developed for use in our uniform electron gas (UEG) model system, the momentum transfer between orbitals was used to select our twist angle. For our energy-matching twist averaging (emTA) we used the energies from a cheaper method to select the special twist angle. Finally, our structure-factor-based twist averaging (sfTA) method, developed for use with real solids, used the property of the energy known as the transition structure factor to select our special twist angle. The advantage of these methods is that I can now get twist-averaged energies for larger systems where previously I was limited due to the cost.
description: We used this advantage that our new methods offers to explore the convergence rate of finite size effects in solids as the energy converges to the thermodynamic limit. Specifically, we used cTA with our UEG model system to help determine how the correlation energy converges to the thermodynamic limit. In the literature, there has been a lot of debate around the convergence of the correlation energy. The most commonly used rate was N-1. However, more recent studies have suggested that the energy actually converges at a N-1/3 rate. Here, I performed two studies on these power-laws to help try to resolve this issue. In the first study, we show that the N-1/3 is only an apparent power-law that occurs at smaller system sizes. In the second study, we show that there is an exchange-like component that is present in the correlation energy as it converges to the thermodynamic limit that needs to be accounted for to recover the exact correlation energy at high density. With these two studies, I help to not only resolve a debate in the literature but shed new light on an on-going area of research. Through improving our understanding of how the energy converges, these studies will have a major impact on applying wavefunction quantum chemistry to the solid state.