Preamble

Density Functional Theory (DFT) is one of the most powerful theoretical frameworks for studying the electronic structure of atoms, molecules, and solids. It is widely used in condensed matter physics, quantum chemistry, and materials science to predict structural, electronic, magnetic, and optical properties of materials.

Course Curriculum

This course bridges the gap between rigorous quantum mechanical theory and state-of-the-art computational materials science, moving from fundamental equations to real-world software applications.

Part I: Theoretical Foundations of DFT

Starting from the quantum many-body problem, we detail the exact mathematical proofs behind the Hohenberg–Kohn theorems and the derivation of the effective single-particle Kohn–Sham equations. With the exact theory established, you will systematically unpack the approximations required for real-world materials. This includes navigating the hierarchy of exchange-correlation functionals (from LDA to hybrids), constructing exact basis sets and pseudopotentials (such as PAW methods), and treating magnetic ordering via Spin-Polarised DFT. Finally, we address the self-interaction error in strongly correlated \(d\) and \(f\) electron systems using the DFT+U (Hubbard) method.

Part II: Numerical Implementations & Practical DFT

Theoretical knowledge is only half the battle. The second half of the course opens the black box of industry-standard DFT codes like VASP and Quantum ESPRESSO. You will learn how to translate continuous mathematics into robust iterative algorithms by mastering Self-Consistent Field (SCF) Convergence—including how to diagnose charge sloshing in metals and apply advanced density mixing schemes (Pulay/DIIS, Broyden). We also cover rigorous Brillouin Zone Integration, detailing \(k\)-point sampling and the specific smearing methods (Methfessel-Paxton, tetrahedron) required to stabilise metallic Fermi surfaces.

By the end of this course, you will possess the practical expertise to run, troubleshoot, and analyze high-accuracy simulations for contemporary materials science research.

Meet your instructor

Prerequisites

Participants should be familiar with:

• Basic Quantum Mechanics
• Thermodynamics and Statistical Mechanics
• Solid State Physics
• Elementary linear algebra and differential equations

Course Objectives

By the end of this course, participants will:

• Understand the theoretical foundations of Density Functional Theory
• Learn the derivation and significance of the Hohenberg–Kohn theorems
• Understand the Kohn–Sham formalism and its practical implementation
• Become familiar with common exchange–correlation functionals
• Learn how to perform and analyze DFT calculations
• Explore advanced extensions such as DFT+U and time-dependent DFT

Target Audience

This course is designed for:

• Graduate students in Physics, Chemistry, and Materials Science
• Researchers entering the field of computational materials science
• Students interested in electronic structure theory