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Francesco Sottile
and
Lucia Reining
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.
Read more
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.
Read more
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.
Register for this course and see more details by visiting:
OpenCourser.com/course/w1xmeh/density
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What's inside
Syllabus
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.
Read more
Syllabus
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.
Read more
From density to the Kohn-Sham world
This second week introduces the Kohn-Sham world, a weird and very efficient world in which independent particles are governed by equations that give the exact density. At least, in principle, for the potential felt by the independent particle is unknown, as well as pathological. Again, a brief historical point of view ends the module.
Approximations and strategies
This third week tackles some more practical aspects of DFT. In particular the strategies for approximating the unknown exchange-correlation potential. Two other important points are the concept of band-gap and the practical scheme to solve the KS equations, via a self-consistent approach.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Intends for students and researchers with knowledge of basic quantum mechanics
Provides a thorough introduction to Density Functional Theory, making it suitable for beginners
Emphasizes the features and reasons that lead DFT to become the dominant method for simulating quantum mechanical systems
Covers fundamentals of DFT as well as its advanced concepts
Taught by Francesco Sottile and Lucia Reining, recognized researchers in the field of quantum mechanics
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Reviews summary
Density functional theory: principles and applications
**Learners say** this course provides a well-prepared introduction to density functional theory (DFT). It covers the basics of DFT, including its history, development, and applications. The course is taught by experts in the field and includes a mix of lectures, readings, and exercises. While the course focuses on the theoretical aspects of DFT, students also gain an understanding of how DFT is used in real-world applications. Overall, this course is a solid choice for students who want to learn more about DFT.
Provides historical context and the development of DFT.
"This course was just fantastic. DFT is not trivial and it has taken decades of experience of the instructors to distil their knowledge into this introduction. Every instructor was superb and the way they communicated it appeared as if I was listening to them in person."
"I enjoyed learning this course. I was exposed to the rigorous mathematics that makes up DFT, the current practical applications and limitations that DFT faces, with a dash of the historical storyline that has brought DFT this far."
"Even though I have taken courses in Atomic Physics and Quantum Mechanics including QFT, much of the material was new to me and very interesting."
Provides practical applications of DFT.
"An excellent course to learn DFT, how it emerged and how to apply DFT in real world situations."
"DFT has become the dominant method for simulating quantum mechanical systems. It was an honor to learn DFT fundamentals from this prestigious institute via Coursera."
"Great course. I will recommend it to anyone who wants to learn with rigor the basics of DFT, Kohn-Sham method and its applicability."
Suitable for beginners with little to no prior knowledge of DFT.
"It is a very well-prepared course. From getting the interest of students through History and Scientists of DFT to making them solve complex differential equations, this course provides it all. It is a very suitable course for a beginner in DFT."
"It's worth everyone's time; period! It gives a very informative introduction to DFT."
"Truly insightful course, though still in the introductory part the course provides the best example for the beginner"
Engaging instructors who explain concepts clearly.
"Great course explains very well, understand everything they say"
"An interesting and understanding lecture thanks to subtitles, movies, exercises and references."
"The teachers are fantastic. They explain things in depth with simple words."
Focuses on theoretical concepts over practical applications.
"This class focused a little bit more on theory rather than execution of DFT simulations than I would have liked."
"Well. It is an introductory course to DFT theory without any actual practice on real DFT codes."
"This Density Functional Theory course provides a thorough theoretical foundation, shedding light on the intricacies of electronic structure."
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in Density Functional Theory with these
activities:
Review Introduction to Quantum Mechanics 3rd Edition by Griffiths
Show steps
This book provides a solid foundation in quantum mechanics and will refresh your knowledge before taking this course.
View
Introduction to Quantum Mechanics
on Amazon
Show steps
-
Read chapters 1-3 to refresh the basics of quantum mechanics.
-
Complete the practice problems at the end of each chapter.
Solve exercises on the Hohenberg-Kohn theorems
Show steps
Solving exercises on the Hohenberg-Kohn theorems will help you understand the fundamental concepts of DFT.
Show steps
-
Find a resource with exercises on the Hohenberg-Kohn theorems.
-
Solve several exercises to test your understanding.
-
Review your solutions and identify areas where you need further clarification.
Follow tutorials on Kohn-Sham equations
Show steps
Following tutorials on Kohn-Sham equations will provide you with deeper insights into the practical aspects of DFT.
Show steps
-
Identify reputable online resources or video tutorials on Kohn-Sham equations.
-
Watch or read the tutorials carefully.
-
Take notes and highlight key concepts.
Three other activities
Expand to see all activities and additional details
Show all six activities
Write a summary of the course material
Show steps
Writing a summary of the course material will help you consolidate your understanding and improve retention.
Show steps
-
Review your notes and the course materials.
-
Identify the key concepts and main points.
-
Write a concise summary that covers the essential points.
Attend a workshop on Density Functional Theory
Show steps
Attending a workshop on DFT will provide you with hands-on experience and the opportunity to interact with experts in the field.
Show steps
-
Research and identify relevant workshops.
-
Register for a workshop that aligns with your interests and schedule.
-
Actively participate in the workshop sessions.
Contribute to an open-source DFT project
Show steps
Contributing to an open-source DFT project will provide you with practical experience and the opportunity to collaborate with others in the field.
Show steps
-
Identify an open-source DFT project that aligns with your interests and skillset.
-
Review the project's documentation and contribute code or documentation.
-
Engage with the project's community and provide feedback.
Review Introduction to Quantum Mechanics 3rd Edition by Griffiths
Show steps
This book provides a solid foundation in quantum mechanics and will refresh your knowledge before taking this course.
View
Introduction to Quantum Mechanics
on Amazon
Show steps
Show steps
Show steps
- Read chapters 1-3 to refresh the basics of quantum mechanics.
- Complete the practice problems at the end of each chapter.
Solve exercises on the Hohenberg-Kohn theorems
Show steps
Solving exercises on the Hohenberg-Kohn theorems will help you understand the fundamental concepts of DFT.
Show steps
Show steps
Show steps
- Find a resource with exercises on the Hohenberg-Kohn theorems.
- Solve several exercises to test your understanding.
- Review your solutions and identify areas where you need further clarification.
Follow tutorials on Kohn-Sham equations
Show steps
Following tutorials on Kohn-Sham equations will provide you with deeper insights into the practical aspects of DFT.
Show steps
Show steps
Show steps
- Identify reputable online resources or video tutorials on Kohn-Sham equations.
- Watch or read the tutorials carefully.
- Take notes and highlight key concepts.
Three other activities
Expand to see all activities and additional details
Show all six activities
Write a summary of the course material
Show steps
Writing a summary of the course material will help you consolidate your understanding and improve retention.
Show steps
Show steps
Show steps
- Review your notes and the course materials.
- Identify the key concepts and main points.
- Write a concise summary that covers the essential points.
Attend a workshop on Density Functional Theory
Show steps
Attending a workshop on DFT will provide you with hands-on experience and the opportunity to interact with experts in the field.
Show steps
Show steps
Show steps
- Research and identify relevant workshops.
- Register for a workshop that aligns with your interests and schedule.
- Actively participate in the workshop sessions.
Contribute to an open-source DFT project
Show steps
Contributing to an open-source DFT project will provide you with practical experience and the opportunity to collaborate with others in the field.
Show steps
Show steps
Show steps
- Identify an open-source DFT project that aligns with your interests and skillset.
- Review the project's documentation and contribute code or documentation.
- Engage with the project's community and provide feedback.
Career center
Learners who complete Density Functional Theory will develop knowledge and skills
that may be useful to these careers:
Computational Materials Scientist
Computational Materials Scientist
Computational Materials Scientists research new materials and their properties using computer modeling. They use Density Functional Theory (DFT) to simulate the behavior of atoms and molecules, and to predict the properties of new materials. This course will provide you with a strong foundation in the theory and practice of DFT, which will be essential for success in this field.
Materials Scientist
Materials Scientist
Materials Scientists research and develop new materials, and study the properties of existing materials. They use a variety of techniques, including DFT, to understand the structure and properties of materials. This course will provide you with a strong foundation in the theory and practice of DFT, which will be essential for success in this field.
Theoretical Chemist
Theoretical Chemist
Theoretical Chemists use computer modeling to study the behavior of atoms and molecules. They use DFT to simulate the behavior of atoms and molecules, and to predict the properties of new materials. This course will provide you with a strong foundation in the theory and practice of DFT, which will be essential for success in this field.
Quantum Chemist
Quantum Chemist
Quantum Chemists use quantum mechanics to study the behavior of atoms and molecules. They use DFT to simulate the behavior of atoms and molecules, and to predict the properties of new materials. This course will provide you with a strong foundation in the theory and practice of DFT, which will be essential for success in this field.
Computational Physicist
Computational Physicist
Computational Physicists use computer modeling to study the behavior of matter. They use DFT to simulate the behavior of atoms and molecules, and to predict the properties of new materials. This course will provide you with a strong foundation in the theory and practice of DFT, which will be essential for success in this field.
Data Scientist
Data Scientist
Data Scientists use data to solve problems and make predictions. They use a variety of techniques, including DFT, to analyze data and build models. This course will provide you with a strong foundation in the theory and practice of DFT, which will be useful for success in this field. Additionally, this course will help you build a foundation in data analysis and modeling, which are essential skills for Data Scientists.
Research Scientist
Research Scientist
Research Scientists conduct research in a variety of fields, including physics, chemistry, and materials science. They use a variety of techniques, including DFT, to simulate the behavior of atoms and molecules, and to predict the properties of new materials. This course will provide you with a strong foundation in the theory and practice of DFT, which will be essential for success in this field.
Process Engineer
Process Engineer
Process Engineers design and develop processes for manufacturing products. They use a variety of techniques, including DFT, to simulate the behavior of atoms and molecules, and to predict the properties of new materials. This course may be useful for success in this field.
Software Engineer
Software Engineer
Software Engineers design and develop software applications. They use a variety of programming languages and techniques to create software that meets the needs of users. This course may be useful for success in this field.
Business Analyst
Business Analyst
Business Analysts analyze business processes and data to identify opportunities for improvement. They use a variety of techniques, including DFT, to analyze data and build models. This course may be useful for success in this field.
Financial Analyst
Financial Analyst
Financial Analysts analyze financial data to make investment recommendations. They use a variety of techniques, including DFT, to analyze data and build models. This course may be useful for success in this field.
Marketing Manager
Marketing Manager
Marketing Managers develop and implement marketing campaigns to promote products and services. They use a variety of techniques, including DFT, to analyze data and build models. This course may be useful for success in this field.
Sales Manager
Sales Manager
Sales Managers lead and motivate sales teams to achieve sales goals. They use a variety of techniques, including DFT, to analyze data and build models. This course may be useful for success in this field.
Human Resources Manager
Human Resources Manager
Human Resources Managers recruit, hire, and train employees. They use a variety of techniques, including DFT, to analyze data and build models. This course may be useful for success in this field.
Operations Manager
Operations Manager
Operations Managers oversee the day-to-day operations of a business. They use a variety of techniques, including DFT, to analyze data and build models. This course may be useful for success in this field.
For more career information including salaries, visit:
OpenCourser.com/course/w1xmeh/density
Reading list
We've selected eight books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Density Functional Theory.
Save
Another classic text, providing a very rigorous and in-depth overview of solid state physics.
Provides a comprehensive overview of quantum mechanics.
Provides a comprehensive overview of quantum theory.
The book provides a more mathematical introduction to quantum mechanics.
A classic textbook in solid state physics. Good for getting a solid theoretical understanding of the field.
Provides a good overview of many body quantum theory.
Provides an accessible introduction to quantum mechanics.
Provides an accessible introduction to the topic of excited states in quantum chemistry.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/w1xmeh/density
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Effort
3 weeks of study, 9-10 hours/week
Level
Advanced
Via
Coursera
Institution
École Polytechnique
Instructors
Francesco Sottile
Lucia Reining
Language
English
Transcripts
Español
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Deutsch
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Good to know
Intends for students and researchers with knowledge of basic quantum mechanics
Provides a thorough introduction to Density Functional Theory, making it suitable for beginners
Emphasizes the features and reasons that lead DFT to become the dominant method for simulating quantum mechanical systems
Covers fundamentals of DFT as well as its advanced concepts
Taught by Francesco Sottile and Lucia Reining, recognized researchers in the field of quantum mechanics
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