A self-contained ground-state approach for the correction of self-interaction error in approximate density-functional theory - MOYNIHAN, GLENN (Trinity College Dublin. School of Physics. Discipline of Physics, 2018)
Density functional theory (DFT), in its approximate Kohn-Sham formalism, is a highly-acclaimed computational tool that affords the practical and expeditious calculation of ground-state properties of molecules and solids, often with a very reasonable accuracy. It finds routine application in the fields of chemistry, physics, materials science, and biochemistry, where it now contributes in both a descriptive and predictive capacity. It is not, in practice, without systematic errors such as those defined by self-interaction and static correlation. These errors undermine the accurate description of particular systems that are beyond the scope of the approximate exchange-correlation functionals, particularly for those comprising so-called strongly-correlated electrons. The effective treatment of these errors is laid down in a number of formative works now adopted within the canon of Kohn-Sham DFT. Many of the most popular and affordable correction schemes entail the calculation of external parameters to diagnose and treat these pervasive errors on a per-electron basis, such as the DFT+Hubbard U method. A possibility that has not yet been explored, however, is the automation of these correction schemes for the provision of greater efficiency, versatility and comparability between DFT calculations. An automated procedure would enable the correction process to be self-contained, thereby circumventing the need for human input, and establish a standardised approach between the various softwares and electronic systems. Of particular interest is the application in high-throughput materials design, and the comparability of DFT+U total-energies for the calculation of thermodynamical quantities. In this dissertation, we present a comprehensive account of our work in pursuit of this goal. We motivate and describe an efficient self-contained approach for correcting the many-body self-interaction error in strongly-correlated systems from ground-statequantities within the DFT+U framework. Moreover, we implement this procedure in a linear-scaling code, which extends its applicability to large-scale systems. Specifically, we develop a highly accurate variational linear-response approach for calculating the Hubbard U and Hund's J parameters, for which a unique criterion for their self-consistency is identified. Our results demonstrate that this scheme is accurate and versatile, and facilitates the correction of many-body self-interaction error for various systems. Moreover, we propose the novel construction of a generalised DFT+U functional that resolves Koopmans' condition exactly in a one-electron system when supplied with the appropriate self-consistent U value. Our research provides insight into important questions about the practice and consequences of calculating corrective parameters for approximate DFT self-consistently, and opens up several new avenues for future developments.
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Keywords: Condensed matter theory; Density-functional theory; Strong correlation; DFT+U; Self-interaction error; Koopmans' theorem