**Description:**

In this PhD course, density function theory (DFT) and it’s tight-binding approximation are introduced as practical tools for atomistic simulations of atomic, molecular, and nanoscale electronic systems. The theoretical basis of DFT is explained and various versions of the method are discussed. The local density approximation is taken as a detailed example. Throughout the course, lectures will alternate between theory and computer exercises written in Fortran or Matlab. We will implement the method for atoms and atomic ions as an exercise and compute several quantities of experimental interest.

In the second half of the course, the atomic DFT states are used to obtain a tight-binding parameterization for molecules containing C and N atoms. This parameterization will be applied to compute the band structure of graphene. We will then investigate N-doped graphene and implement geometric relaxation of the defects. Finally, recursive methods of obtaining density of states and related quantities are introduced. The ten days of the course will cover these subjects:

1. 14/1: Electronic theory: Tight binding (TB), DFT and DFTB

2. 15/1: Atoms. Periodic table. Radial Schrödinger equation.

3. 16/1: Gauss basis. H0 problem

4. 17/1: Implementation of DFT. Mixing

5. 18/1: Atomic properties. Electron affinity and ionization potential.

6. 21/1: TB matrix elements

7. 22/1: DFTB parametrization. Example: CN molecule.

8. 23/1: Example: Graphene and N-doped graphene.

9. 24/1 (only until 12.00) Results: Recursive LDOS and DOS.

10. 25/1: Electric and optical properties.

Organizer:

Thomas G. Pedersen, Aalborg University, email: tgp@physics.aau.dk

Lecturers:

Thomas G. Pedersen, Aalborg University

ECTS:

2.5

Time:

January 14, 15, 16, 17, 18, 21, 22, 23, 24 and 25, 2013

(each day from 9.00 – 12.00 and 13.00 to 15.30)

Place:

Aalborg University

Skjernvej 4**Zip code: **9220

**Aalborg**

City:

City:

**50**

Number of seats:

Number of seats:

**Deadline:**

January 10, 2013

**Important information concerning PhD courses **

We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.

- Teacher: Thomas Garm Pedersen