Density Functional Theory
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Density Functional Theory at Coursera Overview
Duration | 25 hours |
Start from | Start Now |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Advanced |
Official Website | Explore Free Course  |
Credential | Certificate |
Density Functional Theory at Coursera Highlights
- 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 Bachelor in physics/chemistry. Knowledge of quantum mechanics.
- Approx. 25 hours to complete
- English Subtitles: English
Density Functional Theory at Coursera Course details
- 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.
Density Functional Theory at Coursera Curriculum
From the Many-Body problem to Density Functional Theory
Introduction
The many-body problem
First objective: observables
Examples of observables
Observables in terms of compact quantities
Introduction to functionals and functionals of the density
Functional derivatives
Define the system: the external potential
Demonstration of the Hohenberg-Kohn theorem
HK theorem: some important aspects
The Thomas(-Fermi) approach
Thomas-Fermi as density functional
Beyond Thomas-Fermi
Reading and References
on Notations
Recent literature on the many-body problem
Lecture Notes :: Functional derivatives
A simple matrix (degenerate eigenvalue)
Extra references
Lecture Notes :: Thomas-Fermi approximation
The many-body wavefunction: a big beast
Functional strategy
Which strategy ?
Exercises on Derivatives
around Hohenberg-Kohn
Thomas-Fermi density functional
Beyond Thomas-Fermi
From density to the Kohn-Sham world
Functional of the density :: a summary
Auxiliary system 2.3 part1
Auxiliary systems 2.3 part2
The exchange-correlation term
The Kohn-Sham equations
Thoughts on the Kohn-Sham equations
The shape of the Kohn-Sham potential
How real is the Kohn-Sham world ?
The Hartree equations
From Thomas and Hartree to Walter Kohn
on the functional of the density
References :: auxiliary systems
Lecture Notes for functional of the density
Lecture notes for Kohn-Sham derivation
The Hartree equations
Simple auxiliary system
the exchange-correlation potential
the Koopmans' theorem
Hartree's other interests
Approximations and strategies
3.1 The universal functional
3.2 Strategies for approximations
The local density approximation (LDA)
Exact constraints and GGA
Meta-GGAs
Hybrids functionals
What is a band gap ?
Band gap? What about hybrids?
Solving the KS equation
Summary of the Mooc
Extra
more about the Universal Functional
Extra references
Coupling constant integration and PBE
Lecture Notes for explicit and implicit functionals
Extra References
Lecture Notes for locality and non-locality
Lecture Notes for the derivative discontinuity
Solving KS equations (and another bit of history)
the SCF scheme
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