Computational Materials Physics

quick start
2 Topics
practical info
about you
setting the stage
11 Topics
the creation of materials from thought
the ab initio way  
solids as quantum systems
so what’s the problem?
advantages
theory versus computation
hardware
software
let’s play (w1)
exit (w1)
webinar (w1)
density functional theory 
24 Topics
a DFT teaser
functions and functionals
the Schrödinger equation
the Born-Oppenheimer approximation
(post-)Hartree-Fock method(s)
the external potential
the electron density
let’s play (w2)
for project only (w2)
exit (w2)
webinar (w2)
first Hohenberg-Kohn theorem
second Hohenberg-Kohn theorem
Kohn-Sham equations
XC-functional
correlation
Hartree-Fock versus DFT
numerical solution methods
for later use
(optional) basis sets in more depth
(optional) back to the teaser
let’s play (w3)
exit (w3)
webinar (w3)
crystallography
8 Topics
CIF files and how to find them
what’s in a cif ?
more useful tools
(optional) more on crystallography
let’s play (w4)
for project only (w4)
exit (w4)
webinar (w4)
geometry optimization
18 Topics
hands-on task
step 1: volume optimization
bulk modulus and pressure
step 2: cell shape
upload your answer (geom 1)
exit (w5)
webinar (w5)
introduction to forces
classical forces
quantum forces
symmetry and forces
step 3: position optimization
full optimization
phase diagrams
upload your answer (geom 2)
let’s play (w5-6)
exit (w6)
webinar (w6)
electronic structure
8 Topics
reciprocal space
plane waves and the reciprocal lattice
quantum numbers
plotting wave functions and densities
quantum numbers for a crystal
let’s play (w7)
exit (w7)
webinar (w7)
chemical bonding
8 Topics
chemical bonding in textbooks
cohesive energy problem
chemical bonding from DFT
an old puzzle
let’s play (w8)
exit (w8)
only for project (w8)
webinar (w8)
elasticity
9 Topics
elastic constants: definition
computing elastic constants
applications of elastic constants
a hard example ;-)
a database of elastic constants
let’s play (w9)
only for project (w9)
exit (w9)
webinar (w9)
supercells and surfaces
3 Topics
concept and uses
surface properties
exit (w10-part 1)
precision and accuracy
6 Topics
P&A lecture
P&A tasks
let’s play (w10)
for project only (w10)
exit (w10-part 2)
webinar (w10)
magnetism
4 Topics
spin magnetism
orbital magnetism
long-range magnetic order
exit (magnetism)
phonons and temperature
4 Topics
the basics of phonons
the Phonopy code : a guided example
phonons by QE + visualizer
soft modes and phase transitions
band gaps
2 Topics
which gap?
gap predictions
let’s play!
17 Topics
setting the stage – prepare your environment
setting the stage – HPC info (Flanders only)
setting the stage – help section
density functional theory 1 – a basic calculation
density functional theory 2 – basis set size and k-mesh
density functional theory 2 – convergence testing
crystallography – crystal viewers
crystallography – from cif to DFT input
geometry optimization – geometry: towards the ground state
geometry optimization – geometry: E(V) and EOS
electronic structure – band structure and DOS
chemical bonding – charge density difference plots
elasticity – elasticity
supercells and surfaces – creating supercells
supercells and surfaces – work function
magnetism
a frozen phonon calculation
project
8 Topics
w2 – project 2024-2025
w2 – assessment choice / sign up for project
w4 – project milestone 1
w8 – project milestone 2
w9 – online writing in latex
w12 – submit your project
w12 – gallery of project results (2024)
w12 – self-assessment and team introspection
FAQ
1 Topic
FAQ
Previous Topic
Next Topic

XC-functional

Computational Materials Physics density functional theory  XC-functional

One cannot talk about DFT without touching the issue of the exchange-correlation functional. In this video, you will learn what a XC-functional is, how the simplest ones are constructed, and how the hierarchy among XC-functionals looks like.

Download printable slides

Now read this Perspective from Science (2002) (you have to go through a free registration first to download the original pdf — an alternative is this link to an image of the pdf) about the search for the “divine” exchange-correlation functional. Part of the text deals with the Jacob’s ladder analogy (optional: a 6-minute oral explanation of this analogy by John Perdew). Now use the forum to explain in your own words what Jacob’s ladder is in the context of DFT :

Home › Forums › XC-functional

Viewing 15 topics - 31 through 45 (of 65 total)
1 2 3 4 5
Viewing 15 topics - 31 through 45 (of 65 total)
1 2 3 4 5
  • You must be logged in to create new topics.

optional: digging deeper
The XC-functional is one of those topics one can understand at various levels, from conceptual to (very) technical. The latter is not better than the former, it depends in the first place on what you need this knowledge for. For those of you who want to dig deeper into the topic of exchange-correlation functionals, now or later, a set of optional material is collected here:

  • Two Youtube-lectures by C.J. Cramer, about LDA and GGA at a more technical level then discussed above (underneath).
  • The 1996 paper from Physical Review Letters by Perdew, Burke and Ernzerhof with the promising title Generalized Gradient Approximation Made Simple, where the PBE functional has been proposed.
  • A comprehensive discussion of the 400 XC-functionals that are available in the libxc-library (open access review paper in SoftwareX, 2018, by Lehtola, Steigemann, Oliveira and Marques)
  • Nearly 4 hours of pedagogical lectures by John Perdew, covering LDA, GGA, meta-GGA up to the SCAN functional (underneath). The second video in this series deals with the Jacob’s ladder analogy that is discussed also in the paper at the top of this page. (all of these are part of part of a CECAM school on Teaching the Theory in DFT).

The two videos by J.C. Cramer:

compChem.05.05 Density Functional Theory: Local Density Approximation    

compChem.05.06 Density Functional Theory: Generalized Gradient Approximation

 

The four videos by John Perdew :

local density approximation

generalized Gradient Approximation

meta GGA

the SCAN functional

expected time: 35m
report time spent (page code AW03D)

Previous Topic
Back to Lesson
Next Topic
Scroll to Top