The Application of Density Functional Theory in Materials Science

The Application of Density Functional 

Theory in Materials Science

Outline

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Atomistic Modelling Group at MUL

●

Density Functional Theory

●

Numerical Details

●

HPC Cluster at the MU Leoben

●

Applications

Atomistic Modelling @ MUL

●

Since November 2005

●

Head: Prof. Claudia Ambrosch-Draxl

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Researchers

Atomistic Modelling

●

Since November 2005

●

Head: Prof. Claudia Ambrosch-Draxl

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Researchers

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1 Full Professor, 1 University Assistant

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10 PostDocs

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5 PhD's

●

1 Sysadmin

Competences

●

Theoretical Solid State Physics

●

Density Functional Theory

●

Molecular Dynamics

●

Computer Code Development

Competences

 

Y

Ba

Cu

O

electron­phonon coupling

●

Theoretical Solid State Physics

●

Density Functional Theory

●

Molecular Dynamics

●

Computer Code Develeopment

●

Materials Physics

Competences

●

Theoretical Solid State Physics

●

Density Functional Theory

●

Molecular Dynamics

●

Computer Code Develeopment

●

Materials Physics

●

Superconductors

Competences

●

Theoretical Solid State Physics

●

Density Functional Theory

●

Molecular Dynamics

●

Computer Code Develeopment

●

Materials Physics

●

Superconductors

●

Organic Semiconductors

Competences

●

Theoretical Solid State Physics

●

Density Functional Theory

●

Molecular Dynamics

●

Computer Code Develeopment

●

Materials Physics

●

Superconductors

●

Organic Semiconductors

●

Carbon Nanotubes

Electronic Structure Problem

Coulomb­Force

Quantum Mechanics

+

type of bonding

crystal

structure

elastic constants 

lattice

vibrations

band

structure

=

Many Electron Problem

Zp

+

e

­

Many­electron Schrödinger equation 

Electron Density as a Loophole

Electron Density in a (10,0) single­walled Carbon Nano­Tube 



Electron density n(r) is the basic variable



Density Functional Theory (DFT) provides rigorous framework



All microscopic and macroscopic properties depend on n(r) 

Hohenberg-Kohn Theorem

●

The total energy of a system of interacting electrons is a 

functional of the density.

●

The energy takes its minimum at the ground state density. 

Suggestion of Kohn and Sham:

external potential due to atomic nuclei

universal functional of the electron density

exchange­correlation energy

Kohn-Sham Equations

●

Replace the system of interacting electrons by a fictitious system of 

non­interacting electrons with the same density 

the only 

Kohn-Sham Equations

Replace the system of interacting electrons by a fictitious system of 

the only 

approximation!

Self­

consistency

Density Functional Theory

(DFT)

electrons

DFT

Nobelprize 1998

Walter Kohn

atomic nuclei

Walter Kohn

 Rev. Mod. Phys. 

71, 1253 (1999)

What Can Be Calculated?

•

Structural Properties

Lattice Parameters

Elastic Constants

Atomic Forces, Equilibrium Geometry

Surface Relaxations

Defect Structures

•

Lattice Dynamics

Vibrational Frequencies

Phonon DOS, Vibrational Entropy

•

Electron Density

Charge Rearrangements

Electric Field Gradients

•

Electronic Structure

Band Structure

Density of States

•

Spectroscopy

Photoemission 

Electron Energy Loss 

Optical Absorption

Dielectric Function

Core Level Spectroscopies

Raman Scattering

Compton Scattering

Positron Annihilation

Numerical Approach

Kohn­Sham equation

(differential eigenvalue equation)

Kohn­Sham equation

Matrix Eigenvalue Equation

Hamilton matrix

Linear expansion in 

known basis functions

Overlap matrix

HPC @ MU Leoben

●

IBM­Power 5+ System 

➢

74 Computing Nodes

➢

300 Computer Cores

➢

about 1000 GByte RAM

➢

9 TByte Storage

➢

> 1 TeraFLOP

➢

600 000 Euro

HPC @ MU Leoben

HPC @ MU Leoben

Job Management

•

_{IBM LoadLeveller}

•

_{About 20 users}

•

_{Typically 4 – 16 cores / job}

Organic Semiconductors

Organic Solar Cell (Linz  Institute for Solar Cells) Samsung ultra­thin 0.05mm 4­inch OLED  display (480×272 resolution, 100,000:1  contrast , 200cd/m2₎ Sample of a 10x10 cm2 white OLED              (from HC Starck CleviosTM  PH510 PEDOT layer)

The work is part of the National Research Network

„Interface controlled and functionalized organic films“

Organic

-Conjugated Molecules

Pentacene (C

₂₂

H

₁₄

)

Para­Sexiphenyl (C

₃₆

H

₂₆

)

2.6 nm

OFET

Organic 

Field Effect

Transistor

OLED

Angle-Resolved Photoemission

h

h



_

(21eV)

(21eV)

_e

_­

6P(20­3)

6P(20­3)

h

h



_

(35eV)

(35eV)

e

­

k

k

_xx

Reconstruction of Molecular Orbitals

h

h



_

(35eV)

(35eV)

e

­

k

k

_xx

H

O

MO

H

O

MO

LUM

O

LUM

O

ex

p

ex

p

D

FT

FT

„Industry Project“ within the MPPE centre

●

Motivation for steel industry partners:

Development of TWIP steels which combine high strength with high formability

A

B

C

A

B

B

A

B

C

A

Stacking Faults in Steel

Stacking Faults in Steel