About this Course

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Advanced Level
Approx. 25 hours to complete
English
Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Advanced Level
Approx. 25 hours to complete
English

Offered by

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École Polytechnique

Syllabus - What you will learn from this course

Week
1

Week 1

9 hours to complete

From the Many-Body problem to Density Functional Theory

9 hours to complete
13 videos (Total 99 min), 7 readings, 7 quizzes
13 videos
The many-body problem6m
First objective: observables8m
Examples of observables4m
Observables in terms of compact quantities7m
Introduction to functionals and functionals of the density7m
Functional derivatives11m
Define the system: the external potential8m
Demonstration of the Hohenberg-Kohn theorem9m
HK theorem: some important aspects9m
The Thomas(-Fermi) approach8m
Thomas-Fermi as density functional6m
Beyond Thomas-Fermi6m
7 readings
Reading and References15m
on Notations3m
Recent literature on the many-body problem15m
Lecture Notes :: Functional derivatives1h 30m
A simple matrix (degenerate eigenvalue)10m
Extra references10m
Lecture Notes :: Thomas-Fermi approximation1h
7 practice exercises
The many-body wavefunction: a big beast30m
Functional strategy5m
Which strategy ?5m
Exercises on Derivatives1h
around Hohenberg-Kohn10m
Thomas-Fermi density functional1h
Beyond Thomas-Fermi1h
Week
2

Week 2

10 hours to complete

From density to the Kohn-Sham world

10 hours to complete
10 videos (Total 90 min), 5 readings, 5 quizzes
10 videos
Auxiliary system 2.3 part19m
Auxiliary systems 2.3 part25m
The exchange-correlation term6m
The Kohn-Sham equations9m
Thoughts on the Kohn-Sham equations10m
The shape of the Kohn-Sham potential6m
How real is the Kohn-Sham world ?4m
The Hartree equations9m
From Thomas and Hartree to Walter Kohn13m
5 readings
on the functional of the density10m
References :: auxiliary systems1h
Lecture Notes for functional of the density10m
Lecture notes for Kohn-Sham derivation1h 10m
The Hartree equations1h
4 practice exercises
Simple auxiliary system45m
the exchange-correlation potential30m
the Koopmans' theorem30m
Hartree's other interests30m
Week
3

Week 3

7 hours to complete

Approximations and strategies

7 hours to complete
11 videos (Total 99 min), 8 readings, 1 quiz
11 videos
3.2 Strategies for approximations5m
The local density approximation (LDA)7m
Exact constraints and GGA9m
Meta-GGAs9m
Hybrids functionals11m
What is a band gap ?11m
Band gap? What about hybrids?7m
Solving the KS equation9m
Summary of the Mooc10m
Extra12m
8 readings
more about the Universal Functional1h
Extra references30m
Coupling constant integration and PBE1h
Lecture Notes for explicit and implicit functionals10m
Extra References10m
Lecture Notes for locality and non-locality20m
Lecture Notes for the derivative discontinuity30m
Solving KS equations (and another bit of history)1h
1 practice exercise
the SCF scheme30m

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