
After completion of this course the student is able to; 
Contributes to intended learning outcome; 
 Understand the need for approximation methods in quantum mechanics
 Name the most important differences between and advantages/disadvantages of wavefunctionbased, densitybased, and Green’s functionbased electronic structure methods
 Derive the HohenbergKohn theorem of density functional theory and understand the origin of the KohnSham equations
 Understand the difference between ground state and excited state electronic properties
 Interpret energy level diagrams/band structures and get a grasp on how reliable different types of approximations are in predicting them
 Use the HellmannFeynman theorem to calculate forces
 Write basic code for various practical aspects of electronic structure calculations based on density functional theory and Quantum Monte Carlo








The structure of molecules and cluster, the color of solids and of living beings such as plants, the device physics of semiconductors for applications from solar cells to sensing and quantum information, the stability of chemical compounds, the temperaturedependence of structural, optoelectronic, and thermodynamic properties of materials, in short, almost all relevant properties of matter, rely on quantum mechanics. Under the assumption that relativistic effects can be neglected or approximated by a simple spinorbit coupling Hamiltonian (see Griffith Chapter 7.3.2), they can all be derived by solving the (timedependent) Schrödinger equation of the system of interest. This could be the end of the story, if for all practical purposes, solving this Schrödinger equation was not impossible.
The course “Electronic Structure Theory” is centered around the main methods that allow for an approximate but accurate solution of this problem. We will cover the most important methods based on the quantum mechanics wavefunctions (e.g. Quantum Monte Carlo), the electronic density (Density Functional Theory), and Green’s functions (e.g. the GW approach). The lectures will provide an introduction into the methods, their fundamental properties, practical approximations, and main advantages and disadvantages. In the tutorials and two handson assignments you will solve practical problems both analytically and numerically, helping you to bridge the gap between theory and practical applications.
Topics:
 Recap of the manybody problem of quantum mechanics, HartreeFock
 Basics of DFT
 Interpretation of DFT eigenvalues (generalized KohnSham, quasiparticle equations)
 Green's functionbased MBPT
 Quantum Monte Carlo, wavefunctionbased methods
 Nuclear dynamics, potential energy surfaces, molecular dynamics



Assignment(s) and oral exam
Assessment description
The course will be assessed through two handson assignments (A1 and A2) and an oral exam (O). Handson assignments are assessed based on two short written reports that have to be handed in with the assignments. The final grade will be calculated as (A1 + A2 + O)/3.



 Assumed previous knowledgeRequired: Quantum mechanics TN Module 6, Quantum Mechanics II Mandatory: math courses BTN Recommended, but not necessary: Theoretical Solid State Physics, Advanced Quantum Mechanics, Computational Physics 
  Required materialsRecommended materialsInstructional modesAssignment
 Lectorial
 Lecture
 Tutorial

 TestsElectronic Structure Theory


 