4.9
stars
145 ratings

Francesco Sottile +1 more instructor

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Density Functional Theory

École Polytechnique

About this Course

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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.

Flexible deadlines

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Shareable Certificate

Earn a Certificate upon completion

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Coursera Labs

Includes hands on learning projects.

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Advanced Level

Bachelor in physics/chemistry. Knowledge of quantum mechanics.

Approx. 25 hours to complete

English

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What you will learn

Foundation (mathematical and historical) of DFT, approximation strategies.
Quality and accuracy of different approximations, practical procedure to solve the equations.
Ready to be operative and use DFT for your own research

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Coursera Labs

Includes hands on learning projects.

Learn more about Coursera Labs

Advanced Level

Bachelor in physics/chemistry. Knowledge of quantum mechanics.

Approx. 25 hours to complete

English

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

Instructors

Instructor rating

4.88/5 (84 Ratings)

Francesco Sottile

Researcher

Laboratoire des Solides Irradies (LSI), Ecole Polytechnique

11,077 Learners

1 Course

Lucia Reining

Directrice de Recherche au CNRS

Theoretical Spectroscopy Group

11,077 Learners

1 Course

Offered by

École Polytechnique

École polytechnique combines research, teaching and innovation at the highest scientific and technological level worldwide to meet the challenges of the 21st century. At the forefront of French engineering schools for more than 200 years, its education promotes a culture of multidisciplinary scientific excellence, open in a strong humanist tradition.\n

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Syllabus - What you will learn from this course

Content Rating97%(1,115 ratings)

Week1

Week 1

9 hours to complete

From the Many-Body problem to Density Functional Theory

This week will introduce the Density Functional Theory concepts. The week starts from an introduction to the many-body problem, and how things could be reformulated using the electron density. We will focus on observables, in particular those most directly related to the density. Finally we will discuss the Hohenberg-Kohn theorems. A little historical detour is taken at the end, where we will follow the footprints of the first steps to introduce a functional of the density in quantum problems.

9 hours to complete

13 videos (Total 99 min), 7 readings, 7 quizzes

13 videos

Introduction2mThe many-body problem6mFirst objective: observables8mExamples of observables4mObservables in terms of compact quantities7mIntroduction to functionals and functionals of the density7mFunctional derivatives11mDefine the system: the external potential8mDemonstration of the Hohenberg-Kohn theorem9mHK theorem: some important aspects9mThe Thomas(-Fermi) approach8mThomas-Fermi as density functional6mBeyond Thomas-Fermi6m

7 readings

Reading and References15mon Notations3mRecent literature on the many-body problem15mLecture Notes :: Functional derivatives1h 30mA simple matrix (degenerate eigenvalue)10mExtra references10mLecture Notes :: Thomas-Fermi approximation1h

7 practice exercises

The many-body wavefunction: a big beast30mFunctional strategy5mWhich strategy ?5mExercises on Derivatives1haround Hohenberg-Kohn10mThomas-Fermi density functional1hBeyond Thomas-Fermi1h

Week2

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

Functional of the density :: a summary14mAuxiliary system 2.3 part19mAuxiliary systems 2.3 part25mThe exchange-correlation term6mThe Kohn-Sham equations9mThoughts on the Kohn-Sham equations10mThe shape of the Kohn-Sham potential6mHow real is the Kohn-Sham world ?4mThe Hartree equations9mFrom Thomas and Hartree to Walter Kohn13m

5 readings

on the functional of the density10mReferences :: auxiliary systems1hLecture Notes for functional of the density10mLecture notes for Kohn-Sham derivation1h 10mThe Hartree equations1h

4 practice exercises

Simple auxiliary system45mthe exchange-correlation potential30mthe Koopmans' theorem30mHartree's other interests30m

Week3

Week 3

7 hours to complete

Approximations and strategies

7 hours to complete

11 videos (Total 99 min), 8 readings, 1 quiz

11 videos

3.1 The universal functional4m3.2 Strategies for approximations5mThe local density approximation (LDA)7mExact constraints and GGA9mMeta-GGAs9mHybrids functionals11mWhat is a band gap ?11mBand gap? What about hybrids?7mSolving the KS equation9mSummary of the Mooc10mExtra12m

8 readings

more about the Universal Functional1hExtra references30mCoupling constant integration and PBE1hLecture Notes for explicit and implicit functionals10mExtra References10mLecture Notes for locality and non-locality20mLecture Notes for the derivative discontinuity30mSolving KS equations (and another bit of history)1h

1 practice exercise

the SCF scheme30m

Reviews

4.9

50 reviews

5 stars
87.67%
4 stars
11.64%
3 stars
0.68%

TOP REVIEWS FROM DENSITY FUNCTIONAL THEORY

by AAMar 27, 2023

Although I am a materials engineering student, I found the course very valuable and gained a good understanding of the discussed theory

by NCFeb 27, 2021

Thank you to the instructors for explaining it so well and making it so interesting. i learned a lot.

by SWMar 17, 2022

I like the way this course explains the DFT. It would be better if we can have some practice on small project, even trivial, such as using VASP or GPAW, if possible.

by DPJun 18, 2022

more application base examples should be thaught this course was more theoritical and after completing my course I still dont know how to implement on my work

View all reviews

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Density Functional Theory

Density Functional Theory

About this Course

What you will learn