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Density Functional Theory
  • Level Expert
  • Duration 25 hours
  • Course by École Polytechnique
  • Offered by

About

The aim of this course is to give a thorough introduction to Density Functional Theory (DFT). DFT is today the most widely used method to study interacting electrons, and its applicability ranges from atoms to solid systems, from nuclei to quantum fluids. In this course, we introduce the most important concepts underlying DFT, its foundation, and basic ideas. We will in particular stress the features and reasons that lead DFT to become the dominant method for simulating quantum mechanical systems. The course is intended for students and researchers with knowledge of basic quantum mechanics. No experience in simulation or solid-state physics is required. We try to give a concise mathematical background when particular concepts are needed.

Modules

Introduction

    • 1 Videos
    • 2 Readings
Show info about module content

1 Videos

  • Introduction

2 Readings

  • Reading and References
  • on Notations

1.1 The Many-Body Problem

    • 1 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • The many-body wavefunction: a big beast

1 Videos

  • The many-body problem

1 Readings

  • Recent literature on the many-body problem

1.2 What do we want? Observables!

    • 1 Videos
    • 1 Assignment
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1 Assignment

  • Functional strategy

1 Videos

  • First objective: observables

1.3 Which observables ?

    • 2 Videos
    • 1 Assignment
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1 Assignment

  • Which strategy ?

2 Videos

  • Examples of observables
  • Observables in terms of compact quantities

1.4 What is a functional ?

    • 2 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Exercises on Derivatives

2 Videos

  • Introduction to functionals and functionals of the density
  • Functional derivatives

1 Readings

  • Lecture Notes :: Functional derivatives

1.5 The Hohenberg-Kohn Theorem

    • 3 Videos
    • 2 Readings
    • 1 Assignment
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1 Assignment

  • around Hohenberg-Kohn

3 Videos

  • Define the system: the external potential
  • Demonstration of the Hohenberg-Kohn theorem
  • HK theorem: some important aspects

2 Readings

  • A simple matrix (degenerate eigenvalue)
  • Extra references

1.6 A bit of History :: Hilleth Thomas and the density functional

    • 3 Videos
    • 1 Readings
    • 2 Assignment
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2 Assignment

  • Thomas-Fermi density functional
  • Beyond Thomas-Fermi

3 Videos

  • The Thomas(-Fermi) approach
  • Thomas-Fermi as density functional
  • Beyond Thomas-Fermi

1 Readings

  • Lecture Notes :: Thomas-Fermi approximation

2.1 What we have learnt so far

    • 1 Videos
    • 1 Readings
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1 Videos

  • Functional of the density :: a summary

1 Readings

  • on the functional of the density

2.2 Auxiliary systems

    • 2 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • Simple auxiliary system

2 Videos

  • Auxiliary system 2.3 part1
  • Auxiliary systems 2.3 part2

1 Readings

  • References :: auxiliary systems

2.3 The Kohn-Sham equations

    • 3 Videos
    • 2 Readings
    • 1 PeerReview
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1 Peer Review

  • Kohn-Sham equations :: derivation and total energy

3 Videos

  • The exchange-correlation term
  • The Kohn-Sham equations
  • Thoughts on the Kohn-Sham equations

2 Readings

  • Lecture Notes for functional of the density
  • Lecture notes for Kohn-Sham derivation

2.4 The Kohn-Sham potential

    • 2 Videos
    • 1 Assignment
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1 Assignment

  • the exchange-correlation potential

2 Videos

  • The shape of the Kohn-Sham potential
  • How real is the Kohn-Sham world ?

2.5 A bit of History: from Hartree to Kohn-Sham

    • 2 Videos
    • 1 Readings
    • 2 Assignment
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2 Assignment

  • the Koopmans' theorem
  • Hartree's other interests

2 Videos

  • The Hartree equations
  • From Thomas and Hartree to Walter Kohn

1 Readings

  • The Hartree equations

3.1 What about approximations

    • 2 Videos
    • 2 Readings
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2 Videos

  • 3.1 The universal functional
  • 3.2 Strategies for approximations

2 Readings

  • more about the Universal Functional
  • Extra references

3.2 Local Density approximation (LDA) and GGA

    • 2 Videos
    • 1 Readings
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2 Videos

  • The local density approximation (LDA)
  • Exact constraints and GGA

1 Readings

  • Coupling constant integration and PBE

3.3 More complex functionals

    • 2 Videos
    • 1 Readings
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2 Videos

  • Meta-GGAs
  • Hybrids functionals

1 Readings

  • Lecture Notes for explicit and implicit functionals

3.4 Band-gap of solids

    • 2 Videos
    • 3 Readings
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2 Videos

  • What is a band gap ?
  • Band gap? What about hybrids?

3 Readings

  • Extra References
  • Lecture Notes for locality and non-locality
  • Lecture Notes for the derivative discontinuity

3.5 Solving the Kohn-Sham equations

    • 1 Videos
    • 1 Readings
    • 1 Assignment
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1 Assignment

  • the SCF scheme

1 Videos

  • Solving the KS equation

1 Readings

  • Solving KS equations (and another bit of history)

Final Summary

    • 2 Videos
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2 Videos

  • Summary of the Mooc
  • Extra

Auto Summary

Explore the foundations of Density Functional Theory (DFT) in this expert-level course designed for students and researchers with basic quantum mechanics knowledge. Delve into the key concepts, mathematical background, and reasons behind DFT's dominance in simulating quantum mechanical systems. This comprehensive 1500-minute course, offered by Coursera, is perfect for those interested in science and engineering. Subscription options include Starter and Professional tiers. No prior experience in simulation or solid-state physics is required.

Francesco Sottile
Instructors

Francesco Sottile

Lucia Reining
Instructors

Lucia Reining