Computational Materials Physics

quick start
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practical info
about you
setting the stage
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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)
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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)
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crystallography
8 Topics
CIF files and how to find them
what’s in a cif ?
more useful tools
(optional) more on crystallography
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for project only (w4)
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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)
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electronic structure
9 Topics
reciprocal space
plane waves and the reciprocal lattice
quantum numbers
plotting wave functions and densities
quantum numbers for a crystal
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only for project (w7)
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chemical bonding
7 Topics
chemical bonding in textbooks
cohesive energy problem
chemical bonding from DFT
an old puzzle
let’s play (w8)
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webinar (w8)
elasticity
9 Topics
elastic constants: definition
computing elastic constants
applications of elastic constants
a hard example ;-)
a database of elastic constants
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only for project (w9)
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supercells and surfaces
3 Topics
concept and uses
surface properties
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precision and accuracy
6 Topics
P&A lecture
P&A tasks
let’s play (w10)
for project only (w10)
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webinar (w10)
magnetism
4 Topics
spin magnetism
orbital magnetism
long-range magnetic order
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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 2022-2023
w2 – assessment choice / sign up for project
w4 – project milestone 1
w7 – project milestone 2
w9 – online writing in latex
w11 – submit your project
w12 – gallery of project results (2022)
w12 – self-assessment and team introspection
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Kohn-Sham equations

Computational Materials Physics density functional theory  Kohn-Sham equations

Practical DFT is nearly always done within the framework established by Kohn and Sham in 1965. We’ll have a look at their method:

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DFT is a method to describe a many-body system: a system of more than two mutually interacting particles. Atoms, molecules and solids are many body systems based on the electromagnetic interaction. The solar system is a many body system based on gravitational interaction. Describe in words how you would use DFT and the Kohn-Sham method to study the many body system of gravitationally interacting planets and the Sun.

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Optional: If you want to dig deeper (now or later), you may study this pedagogical lecture by Kieron Burke on the Kohn-Sham equations (part of the CECAM school on Teaching the Theory in DFT):
 

expected time: 20m
report time spent (page code AW03C)

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