Electronic structure methods | Density functional theory
Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density. DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry. DFT has been very popular for calculations in solid-state physics since the 1970s. However, DFT was not considered accurate enough for calculations in quantum chemistry until the 1990s, when the approximations used in the theory were greatly refined to better model the exchange and correlation interactions. Computational costs are relatively low when compared to traditional methods, such as exchange only Hartree–Fock theory and its descendants that include electron correlation. Since, DFT has become an important tool for methods of nuclear spectroscopy such as Mössbauer spectroscopy or perturbed angular correlation, in order to understand the origin of specific electric field gradients in crystals. Despite recent improvements, there are still difficulties in using density functional theory to properly describe: intermolecular interactions (of critical importance to understanding chemical reactions), especially van der Waals forces (dispersion); charge transfer excitations; transition states, global potential energy surfaces, dopant interactions and some strongly correlated systems; and in calculations of the band gap and ferromagnetism in semiconductors. The incomplete treatment of dispersion can adversely affect the accuracy of DFT (at least when used alone and uncorrected) in the treatment of systems which are dominated by dispersion (e.g. interacting noble gas atoms) or where dispersion competes significantly with other effects (e.g. in biomolecules). The development of new DFT methods designed to overcome this problem, by alterations to the functional or by the inclusion of additive terms, is a current research topic. Classical density functional theory uses a similar formalism to calculate properties of non-uniform classical fluids. Despite the current popularity of these alterations or of the inclusion of additional terms, they are reported to stray away from the search for the exact functional. Further, DFT potentials obtained with adjustable parameters are no longer true DFT potentials, given that they are not functional derivatives of the exchange correlation energy with respect to the charge density. Consequently, it is not clear if the second theorem of DFT holds in such conditions. (Wikipedia).
Time-Dependent Density Functional Theory
Associate Professor Neepa Maitra of Hunter College explains how she uses time-dependent density functional theory to examine the effects of magnetic fields on atoms, molecules and solids.
From playlist Density Functional Theory (DFT), Vasp, and Molecular Mechanics - Beginner's Lectures
Robert Seiringer: The local density approximation in density functional theory
We present a mathematically rigorous justification of the Local Density Approximation in density functional theory. We provide a quantitative estimate on the difference between the grand-canonical Levy-Lieb energy of a given density (the lowest possible energy of all quantum st
From playlist Mathematical Physics
Coordinate Scaling Constraints in Density and Density- Matrix Functional Theories
Mel Levy, Tulane University, USA
From playlist Distinguished Visitors Lecture Series
Andreas Savin - Beyond density functional approximations by lessons from density functional theory
Recorded 13 April 2022. Andreas Savin of Sorbonne Université presents "Getting beyond density functional approximations by using lessons from density functional theory" at IPAM's Model Reduction in Quantum Mechanics Workshop. Abstract: Joint work with Jacek Karwowski, Yvon Maday, Etienne P
From playlist 2022 Model Reduction in Quantum Mechanics Workshop
(PP 6.4) Density for a multivariate Gaussian - definition and intuition
The density of a (multivariate) non-degenerate Gaussian. Suggestions for how to remember the formula. Mathematical intuition for how to think about the formula.
From playlist Probability Theory
Physical Science 3.4b - Density
Density. The definition of density, the equation for density, and some numerical examples.
From playlist Physical Science Chapter 3 (Complete chapter)
Teach Astronomy - Density Parameter
http://www.teachastronomy.com/ Another fundamental quantity of the big bang model is the density parameter. It's defined as the ratio of the mean density of the universe to the density just needed to overcome the cosmic expansion. The density parameter is denoted by the Greek symbol capi
From playlist 22. The Big Bang, Inflation, and General Cosmology
Chp9Pr41: Probability Density Functions
A continuous random variable can be described using a function called the probability density function. This video shows us how to prove that a function is a probability density function. This is Chapter 9 Problem 41 from the MATH1231/1241 algebra notes. Presented by Dr Diana Combe from th
From playlist Mathematics 1B (Algebra)
Lecture 11-Jack Simons Electronic Structure Theory- Density functional theory
Density functional theory fundamentals, strengths and weaknesses. (1)Jack Simons Electronic Structure Theory- Session 1- Born-Oppenheimer approximation http://www.youtube.com/watch?v=Z5cq7JpsG8I (2)Jack Simons Electronic Structure Theory- Session 2- Hartree-Fock http://www.youtube.co
From playlist U of Utah: Jack Simons' Electronic Structure Theory course
Lec 7 | MIT 3.320 Atomistic Computer Modeling of Materials
Technical Aspects of Density Functional Theory View the complete course at: http://ocw.mit.edu/3-320S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 3.320 Atomistic Computer Modeling of Materials
Emmanuel Giner - Curing basis set convergence of WFT w/ DFT: overview of framework and some results
Recorded 03 May 2022. Emmanuel Giner of the Centre National de la Recherche Scientifique presents "Curing basis set convergence of WFT with DFT: overview of framework and some results" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Learn more online at: ht
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
Infinite-density versus large deviations theory for fat-tailed systems by Erez Aghion
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
Julien Toulouse - Basis-set correction based on density-functional theory - IPAM at UCLA
Recorded 02 May 2022. Julien Toulouse of Sorbonne University, LCT, presents "Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: We reexamine the
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
Alexandre Tkatchenko - Many-body perturbation theory and wavefunction methods: A Physics perspective
Recorded 08 March 2022. Alexandre Tkatchenko of the University of Luxembourg presents "Many-body perturbation theory and wavefunction methods: A Physics perspective" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Learn more online at: http://www.ipam.ucla.
From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022
Virginie Ehrlacher - Sparse approximation of the Lieb functional in DFT with moment constraints
Recorded 28 March 2023. Virginie Ehrlacher of the École Nationale des Ponts-et-Chaussées presents "Sparse approximation of the Lieb functional in DFT with moment constraints (joint work with Luca Nenna)" at IPAM's Increasing the Length, Time, and Accuracy of Materials Modeling Using Exasca
From playlist 2023 Increasing the Length, Time, and Accuracy of Materials Modeling Using Exascale Computing
Quantum Theory - the Born Interpretation: Oxford Mathematics 2nd Year Student Lecture
Here is the latest lecture in the series of undergraduate lectures that we are making available to give an insight in to life in Oxford Mathematics. This lecture from James Sparks is taken from his Second Year Quantum Theory course. So far in the course we've met the Schrodinger equation
From playlist Oxford Mathematics 2nd Year Student Lectures
Volker Bach - The Hartree-Fock Approximation and its Generalizations - IPAM at UCLA
Recorded 11 April 2022. Volker Bach of TU Braunschweig presents "The Hartree-Fock Approximation and its Generalizations" at IPAM's Model Reduction in Quantum Mechanics Workshop. Abstract: In the talk the Hartree-Fock (HF) approximation in quantum mechanics will be reviewed. The following p
From playlist 2022 Model Reduction in Quantum Mechanics Workshop
What is Density? | Gravitation | Physics | Don't Memorise
Understanding the concept of Density is very important in order to understand Physics. Watch this video to fully grasp the idea of density. To get access to the entire course based on Gravitation, enroll here: https://infinitylearn.com/microcourses?utm_source=youtube&utm_medium=Soical&u
From playlist Physics