Computational Materials Science II

Syllabus

Introduction to DFT

Schrödinger equation for polyelectronic systems and methods for its solution. Exchange and correlation potential. Calculation of molecules energy and reactions enthalpy.

Crystalline solids

Density and bulk modulus calculation using Bloch theorem. Energy bands.

Extension of theory to semi-periodic structures

The concept of surface tension. Influence of adsorbed molecules on surface properties. Adsorption enthalpy.

Magnetic materials

The role of spin in the magnetic properties of materials, such as iron, as well as in the cohesion of nonmagnetic molecules, such as H₂. The concept of density of states and its calculation. Oscillations of simple molecules.

Experimental techniques

Basic principles of experiments for the depiction of the electronic structure, such as STM (Scanning Tunneling Microscope) and their simulation. Electronic band structure calculations in metals, insulators, and semiconductors.

Reaction speeds

TST (Transition State Theory) and nudged elastic band method for the calculation of the speed of a chemical reaction. Application to diffusion constants calculation.

Learning Outcomes

By the end of the course, students are expected to:

1. Become familiar with the modern theory of electronic structure, and more specifically with DFT (Density Functional Theory), by employing large software packages.
2. Know the basic principles of solving quantum mechanical problems in materials science as well as how to perform computational experiments in order to study properties of standard materials.
3. Develop scientific computing and software related technical skills.
4. Acquire hands-on experience in first principles calculations for solving challenging problems in materials science.

The course according to the European Qualifications Framework for Lifelong Learning belongs to level 6 as an advanced first cycle course and to level 7 as a second cycle course.

Recommended Bibliography

• Frank Jensen, Introduction to Computational Chemistry, Wiley-VCH, 2nd edition 2006.
• Efthimios Kaxiras, Atomic and Electronic Structure of Solids, Cambridge University Press, 2003.
• Richard M. Martin, Electronic Structure: Basic Theory and Practical Methods, Cambridge University Press, 2004.
• Jos M. Thijssen, Computational Physics, Cambridge University Press, 1999