# On the Nature of Self-Consistency in Density Functional Theory

## TL;DR

This paper provides a comprehensive overview of self-consistency challenges in density functional theory, introduces a new preconditioning method, and discusses its implementation in the CASTEP software to improve convergence efficiency.

## Contribution

It introduces a novel, computationally efficient preconditioning strategy for achieving self-consistency in density functional theory calculations.

## Key findings

- Identifies inefficiencies in current self-consistent field methods.
- Proposes a new preconditioning approach that enhances convergence.
- Demonstrates implementation in CASTEP software with improved performance.

## Abstract

A thesis providing a pedagogical introduction to the problem of achieving self-consistency in density functional theory. Contained is an introduction to the framework of Kohn-Sham density functional theory, leading then to the considerations required to solve the equations of Kohn-Sham density functional theory. Specifically, a focus is placed on where current self-consistent field methodology is inefficient and/or fails to converge to a solution. As such, this review spans sub-disciplines such as numerical analysis of linear and non-linear systems, linear response theory, and general electronic structure theory. Toward the end of the thesis, certain contemporary methods for achieving self-consistency from literature are outlined, and a novel, computationally efficient preconditioning strategy is proposed. This work is implemented in the CASTEP software.