# Before choosing course

Density functional theory (DFT) is a method for calculating materials properties, which has become very popular in the last years. DFT now forms the basis of a rapidly growing research field, and also in industry it is starting to find applications. With this method, it is possible to calculate materials properties from “first principles”, which means that the only input into the theoretical method is the atomic number. In this course, we will go through the basics of DFT and how computer programs based on this theory are built up. In hands-on sessions, you will write your own simple DFT code for the helium atom in Matlab, and also calculate and analyze materials properties yourself using an open-access professional DFT program package.

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## Content and learning outcomes

### Course contents^{}

Repetition of basic quantum mechanics and solid state physics (operators, Schrödinger equation, expectation values, atomic orbitals, solving the Schrödinger equation in spherical coordinates, variational calculus, Bloch’s theorem, Bravais lattice, reciprocal space, band structure, k-points). DFT model for the helium atom. Solving this model numerically (in Matlab) using finite differences. Calculation and analysis of simpler materials properties using a DFT program package. Assessment of the quality of the calculations. The concepts self-consistency and convergence in DFT calculations. Limitations of DFT calculations.

### Intended learning outcomes^{}

When you have finished this course, you will be able to perform DFT calculations of certain simpler materials properties (e.g., density, bulk modulus, band gaps). You will also be able to analyze the results of your calculations, and understand the limitations of DFT calculations. In order to do that, you will have to integrate your computer skills (Matlab, Linux) with your knowledge of quantum mechanics, atomic physics, numerical methods and solid state physics.

### Course Disposition

Lectures 8 h (i.e. 4 lectures 2 h each)

Computer exercises 40 h (i.e. 10 computer exercises 4 h each)

## Literature and preparations

### Specific prerequisites^{}

IF1621 Kvantmekanik I, or similar like:

- Quantum mechanics or quantum physics, introductory level.
- Solid state physics or semiconductor physics, introductory level
- Numerical methods, introductory level

### Recommended prerequisites

You will need basic knowledge of numerical methods, quantum mechanics, atomic physics, and solid state physics / semiconductor physics. We will use Matlab and Linux. Some knowledge of this software is therefore useful. We will provide tutorial sessions on both Matlab and Linux for those not familiar with this software.

### Equipment

We will provide access to all necessary software (Matlab, DFT code, Linux environment)

### Literature

- Richard M. Martin “Electronic Structure, Basic Theory and Practical Methods” Cambridge University Press, 2004.
- J.M. Thijssen, “Computational Physics”, Cambridge University Press, 2007

A general text book in solid state physics is also very useful, e.g., Ashcroft and Mermin, “Solid State Physics”.

A general text book in quantum mechanics is also very useful, e.g., P. W. Atkins “Molecular Quantum Mechanics”.

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

### Grading scale^{}

A, B, C, D, E, FX, F

### Examination^{}

- LABA - Laboratory work, 2,0 hp, betygsskala: P, F
- TENA - Examination, 4,0 hp, betygsskala: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Completing all the home assignments and computer exercises. Written exam at the end of the course.

### Other requirements for final grade^{}

Grade E: All HA and CE have been completed and handed in on time.

In order to get a higher grade (A-D) you will need to do the written exam.

The grade Fx is given if the requirements for grade E have not been fulfilled.

### Opportunity to complete the requirements via supplementary examination

*No information inserted*

### Opportunity to raise an approved grade via renewed examination

*No information inserted*

### Examiner

### Ethical approach^{}

- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web MH2425### Offered by

### Main field of study^{}

Materials Science, Materials Science and Engineering

### Education cycle^{}

Second cycle

### Add-on studies

*No information inserted*

### Contact

Associate Professor Anna Delin, annadel@kth.se

### Supplementary information

The course is replaced by MH2426