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)
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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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webinar (w3)
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
8 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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chemical bonding
8 Topics
chemical bonding in textbooks
cohesive energy problem
chemical bonding from DFT
an old puzzle
let’s play (w8)
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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
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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 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
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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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