# MH2425 Simulation and Modelling on the Atomic Scale6.0 credits

## Simulering och modellering på atomär skala

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.

Second cycle
• #### Main field of study

Materials Science
Materials Science and Engineering

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

## Information for research students about course offerings

Contact course responsible

## 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.

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.

## Disposition

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

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

## Eligibility

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.

## 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”.

## Required equipment

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

## Examination

• LABA - Laboratory work, 2.0, grading scale: P, F
• TENA - Examination, 4.0, grading scale: A, B, C, D, E, FX, F

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

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.

## Offered by

ITM/Materials Science and Engineering