| 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 wavefunction-based, density-based, and Green’s function-based electronic structure methods
- Derive the Hohenberg-Kohn theorem of density functional theory and understand the origin of the Kohn-Sham 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 Hellmann-Feynman theorem to calculate forces
- Write basic code for various practical aspects of electronic structure calculations based on density functional theory and Quantum Monte Carlo
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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 temperature-dependence 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 spin-orbit coupling Hamiltonian (see Griffith Chapter 7.3.2), they can all be derived by solving the (time-dependent) 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 hands-on 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 many-body problem of quantum mechanics, Hartree-Fock
- Basics of DFT
- Interpretation of DFT eigenvalues (generalized Kohn-Sham, quasiparticle equations)
- Green's function-based MBPT
- Quantum Monte Carlo, wavefunction-based methods
- Nuclear dynamics, potential energy surfaces, molecular dynamics
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Assignment(s) and oral exam
Assessment description
The course will be assessed through two hands-on assignments (A1 and A2) and an oral exam (O). Hands-on 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.
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