Course Summary
This course provides an introduction to density functional theory, a quantum mechanics-based method for predicting and understanding the electronic structure of atoms, molecules, and solids. Students will learn the fundamental concepts and mathematical tools necessary to apply density functional theory to real-world problems.Key Learning Points
- Learn the basics of density functional theory and its application to electronic structure calculations
- Develop an understanding of the mathematical foundations of density functional theory
- Apply density functional theory to real-world problems in chemistry, physics, and materials science
Related Topics for further study
Learning Outcomes
- Understand the fundamental concepts of density functional theory
- Apply density functional theory to solve real-world problems in chemistry, physics, and materials science
- Develop a foundation for further study in quantum mechanics and electronic structure calculations
Prerequisites or good to have knowledge before taking this course
- A basic understanding of quantum mechanics and chemistry
- Familiarity with mathematical modeling and programming
Course Difficulty Level
IntermediateCourse Format
- Self-paced
- Online
- Video Lectures
- Assignments
- Quizzes
Similar Courses
- Introduction to Quantum Mechanics
- Solid State Chemistry
- Introduction to Materials Science
Related Education Paths
Notable People in This Field
- Walter Kohn
- John P. Perdew
Related Books
Description
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.
Knowledge
- 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
Outline
- 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
Summary of User Reviews
Learn about Density Functional Theory with this highly-rated course on Coursera. Many users found the course to be informative and easy to follow, making it a great resource for anyone interested in the subject.Key Aspect Users Liked About This Course
The course provides a comprehensive overview of Density Functional Theory, covering both theory and practical applications.Pros from User Reviews
- The course content is well-organized and easy to follow.
- The instructors are knowledgeable and provide clear explanations.
- The course includes helpful exercises and quizzes to reinforce learning.
- The course is accessible to learners with varying levels of background knowledge in the subject.
- The course provides a deep understanding of Density Functional Theory and its applications.
Cons from User Reviews
- Some users found the pace of the course to be too slow.
- The course requires a significant time commitment.
- Some users felt that the course could benefit from more hands-on exercises.
- The course may be too technical for beginners.
- The course may not be suitable for those looking for a quick introduction to Density Functional Theory.
Francesco Sottile
4.9 Raiting
From Atoms to Materials: Predictive Theory and Simulations
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Learn how materials look and work at atomic scales. Explore this five-unit course and discover a unified framework for understanding the essential physics that govern materials at atomic scales....
Density Functional Theory
- 4.9
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The aim of this course is to give a thorough introduction to Density Functional Theory (DFT). The course is intended for students and researchers with knowledge of basic quantum mechanics....
