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
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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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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
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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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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)
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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
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only for project (w8)
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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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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
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for project only (w10)
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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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first Hohenberg-Kohn theorem

Computational Materials Physics density functional theory  first Hohenberg-Kohn theorem

The two Hohenberg-Kohn theorems are the cornerstone of DFT. Let us examine the first theorem:

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Go to the Density Functional Theory entry in Wikipedia or another encyclopedia of your choice, and read what is written there about the first Hohenberg-Kohn theorem. Probably you will see many similarities with the video you just watched, but perhaps there is a different emphasis or a different point of view as well. Find out for yourself what are the similarities and differences between these two explanations. Feel free to report your thoughts on the forum (not mandatory, but you need to report yourself before you can see the other forum contributions).

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The mathematical proof of this fundamental theorem is surprisingly short and elegant. As an optional item, you can look at the proof here:

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