Computational Materials Physics

This module presents an introduction to modern theoretical methods for calculating material properties using computers. We will focus on theoretical methods that allow for microscopic descriptions of physical and chemical properties of real materials, namely compounds that are already used in devices such as solar cells. These methods include in particular density functional theory and "ab-initio" molecular dynamics. The fundamental physical aspects of these methods will be explained and discussed, and their advantages and disadvantages will be demonstrated with well-known examples. A direct understanding of the prospects and challenges of these methods will be enables in this way. The physical contents include topics such as:

• Many-body problem
• Hartree-Fock method
• Correlation problem
• Density functional theory: Fundamentals & applications
• Adiabatic approximation
• Theoretical calculations of phonons
• Theoretical calculations of infrared and Raman spectra
• Molecular dynamics: Fundamentals & applications
• Time-dependent density functional theory and many-body perturbation theory

After successful completion of the module the students are able to:

1. Understand and explain the fundamental physical aspects of modern computational materials physics methods, such as density functional theory and molecular dynamics.
2. To illustrate the prospects, challenges and limitations of the discussed methods as well as explaining their connections.
3. To independently apply the discussed methods to simple material systems and interpret the results.

No preconditions in addition to the requirements for the Master’s program in Physics.

The module includes a lecture and exercises.

The lecture will explain methods and calculation schemes in a thematically structured manner with a particular focus on their fundamentals and most important findings and implications. To demonstrate the prospects, challenges and limitations of these methods, literature examples of theoretical and experimental results will be illustrated in computer presentations. Students will be encouraged to participate in scientific discussions both during the lectures as well as after them, in order to strengthen their analytical skills.

The exercises focus, next to detailed discussions for deepening the understanding of the theoretical contents and methods, especially on obtaining the practical skillset to perform computer-based calculations on simple material systems. To this end, the students will also learn the required tools to employ the theoretical methods and analyze the results on the computer. Together with intensive scientific discussions regarding their findings, this will allow students to independently perform such calculations.

online lecture, online notes, online forum, supporting website, exercises and examples, example programs, reference data

Richard M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press

The achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using presentations independently prepared by the students. The exam of 30 minutes consists of the presentation and a subsequent discussion.

For example an assignment in the exam might be:

• Implement an equation-of-state to optimize lattice constants
• Use various DFT functionals to compute electronic material properties and discuss the findings
• Study the convergence behavior of phonon calculations in DFT
• Implement an algorithm to compute correlation functions from MD calculations
• Compute and discuss the radial distribution functional from MD calculations

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.

There will be a bonus (one intermediate stepping of "0,3" to the better grade) on passed module exams (4,3 is not upgraded to 4,0). The bonus is applicable to the exam period directly following the lecture period (not to the exam repetition) and subject to the condition that the student passes the mid-term of successful participation at the exercises, which means: taking part in at least at 10 exercises, reach at least 50 % of the exercise points, and the presentation of at least one solution in the exercises.