DFT from an „exciting“ perspective

Pasquale PavoneHumboldt-Universität zu Berlin

http://exciting-code.org

Outline

Electronic many-body problem

What is DFT

DFT in exciting

HoW exciting! 2016

Born-Oppenheimer Surfaces

The many-body electronic problem

Electronic kinetic energy

‘’External’’ energy

Electron-electroninteraction energy

What is Density-Functional Theory

One parameter-free theory for

Which properties can be obtained?

Strictly speaking, everything related to density andtotal energy

– Bonding properties

– Geometries:Lattice parameters, atomic positions, bond lengths & angles, surface

relaxations, …

– Stable phases / phase diagrams

– Vibrational frequencies & eigenvectors

– Elastic constants

As a starting point for methods going beyond

– Band structures

– Excitation spectra

Essence of density-functional theory

Every observable quantity of a quantum

system can be calculated from the

ground-state density of the system alone!

Mathematical foundation by Hohenberg &Kohn, 1964

The ground-state density of interacting

particles can be calculated from the

ground-state density of an auxiliary

system of non-interacting particles

Practical approach by Kohn & Sham, 1965

Nobel prize to Walter Kohn

1998 for chemistry (!)

Nobel lecture …

The many-body wavefunction of a system of 1000

electrons cannot be stored in the whole universe

(and any calculation would be utterly wrong …) Van Vleck catastrophy (1936)

W. Kohn, Rev. Mod. Phys. 11, 1253 (1999)

A simpler example: The Neon atom

10 electrons

30 coordinates

10 entries for each coordinate

1 byte per entry

5 x 109 bytes per DVD

10g per DVD

10

1030 entries

1030 bytes

2 x 1020 DVDs

2 x 1015 t DVDs

16 GB per smartphone

7 x 109 people on earth

~ 1020 smartphones

1.5 x 1010 smart./person

Hohenberg-Kohn …

Consequence: Every quantum mechanical observable isfully determined by the ground-state density

DFT for Excited States?

DFT in

Solution of Kohn-Sham (KS) equations:

Expansion in basis functions

Size of the basis set controlled by parameter

(Andris!)

(rgkmax)

DFT in

Secular equations (matrix equations)

Brilloiun zone integration:

Regular grid of points in reciprocal space (ngridk)

<input><title> Title </title>

<structure …> … </structure>

<groundstatengridk=´´8 8 8´´rgkmax=´´7.0´´…>

…</groundstate>…

</input>

input.xml

Total-Energy Convergence: Diamond

KS Electronic Band Structure: fcc Ag

Visualization of KS Orbitals: fcc Si

CF + BN Monolayer

Visualization of KS Orbitals

Download

http://exciting-code.org

exciting carbon

August 12, 2016

HoW exciting! 2016

Tutorials

Tutorials

Tutorials

Tutorials

... and let‘s listen now to Andris!

The Last Slide: We are so Excited!