Density Functional Theory

Go to Course: https://www.coursera.org/learn/density-functional-theory

Introduction

### Course Review: Density Functional Theory on Coursera #### Overview The "Density Functional Theory" course on Coursera stands as a significant resource for students and professionals alike who are keen on delving into the intricacies of quantum mechanics and computational physics. Density Functional Theory (DFT) is, without a doubt, one of the most pivotal methods for studying the behavior of interacting electrons, applicable across a broad spectrum of systems—from atoms and solid-state materials to nuclei and quantum fluids. This course aims to provide participants with a comprehensive introduction to DFT, covering its foundational concepts, key theoretical developments, and practical applications. #### Course Structure and Content The course is structured into three comprehensive weeks, each focusing on different foundational aspects of DFT. 1. **From the Many-Body Problem to Density Functional Theory** This initial week sets the stage by addressing the complexities of the many-body problem. Learners will explore how to reformulate the challenge using electron density rather than wavefunctions. Key observables related to density will be examined, culminating in a discussion of the Hohenberg-Kohn theorems, pivotal results that form the backbone of DFT. The addition of a historical perspective enriches the learning experience by linking theoretical concepts back to their origins in quantum mechanics. 2. **From Density to the Kohn-Sham World** Building upon the concepts introduced in the first week, the second week dives into the Kohn-Sham equations, highlighting the concept of treating electrons as independent particles governed by a potential that produces the same electron density as the interacting system. This week effectively bridges theoretical foundations to practical applications, elucidating how DFT forms a useful tool within computational physics. Historical insights also help illustrate the development of these critical concepts. 3. **Approximations and Strategies** This final week tackles the pragmatic aspects of DFT. It emphasizes the strategies for approximating the exchange-correlation potential—a significant hurdle in DFT applications. This section also covers the band-gap problem and outlines the self-consistent approach to solving Kohn-Sham equations, providing participants with practical insights necessary for implementing DFT in their own work. #### Recommendations I highly recommend the "Density Functional Theory" course, whether you are a student of physics, chemistry, or materials science, or a professional working in related industries. The course offers: - **In-Depth Knowledge**: With a robust grounding in both theory and application, participants can expect to exit the course with a profound understanding of DFT and its relevance. - **Expert Instruction**: The instructors are not only knowledgeable but also experienced in the field, providing valuable insights that are often hard to find in textbooks. - **Accessibility**: The course is designed to cater to various backgrounds, making it an excellent choice for both newcomers and those seeking to refresh their comprehension of DFT. - **Interdisciplinary Insights**: The course is not narrowly focused; it indeed traverses multiple disciplines within physics and chemistry, enhancing its applicability. In conclusion, if you're looking to enhance your understanding of quantum mechanics and computational methods through the lens of Density Functional Theory, enrolling in this Coursera course is a commendable step. The blend of theoretical concepts, historical context, and practical solutions in DFT will undoubtedly equip you with the necessary tools to explore and analyze complex quantum systems effectively.

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.

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.

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.