Introduction to Density Functional Theory
|
|
- Kory Mills
- 6 years ago
- Views:
Transcription
1 1 Introduction to Density Functional Theory 21 February 2011; V172 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
2 2
3 3
4 4 Ab initio Computational Based Design P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
5 5
6 6
7 7
8 8
9 9
10 10
11 11
12 12
13 13
14 14 Many Particle problem in Solids P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
15 15
16 16
17 17
18 18
19 19
20 Hartree Method for many particle Solids 20 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
21 Hartree Hamiltonian 21 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
22 SCF procedure 22 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
23 23
24 24
25 Introduction of Exchange (Spin) : Hartree Fock Method 25 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
26 26
27 Failure of HF Method 27 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
28 28 Exchange and Correlation P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
29 29
30 30
31 31
32 32
33 33
34 34
35 35
36 How to get an approximate XC functional? 36 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
37 37
38 What is functional? 38 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
39 39
40 Density Functional Theory (DFT) is a formally exact representation of the N electron Schrödinger Equation 40 Schrödinger view DFT view Formally equivalent electron interaction external potential Hard problem to solve (scales like N 5 ) Kohn-Sham particle (non-interacting) effective potential Easy problem to solve ( scales like N 3 or better) Hohenberg and Kohn proved this (1964) Nobel prize in Chemistry for Kohn in 1998 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
41 1998 Nobel Prize Laureates, Chemistry 41 "for his development of the density-functional theory" "for his development of computational methods in quantum chemistry" Advent of Quantitative Theory and Modeling P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
42 42
43 43
44 44 Exchange-Correlation Potential P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
45 45
46 46
47 47
48 48
49 49
50 50
51 51
52 52
53 53
54 54
55 55
56 56
57 Success and failure of standard DFT in solids 57 Standard LDA (GGA) gives good description of structural and electronic properties of most solids (lattice parameters within 1-2%, at least qualitatively correct bandstructure, metal-insulator, magnetism, ) Problems: localized (correlated) electrons late 3d transition metal oxides/halides metals instead of insulators (FeO, FeF 2, cuprates, ) nonmagnetic instead of anti-ferromagnetic (La 2 CuO 4, YBa 2 Cu 3 O 6 ) 4f, 5f electrons all f-states pinned at the Fermi energy, always metallic orbital moments much too small weakly correlated metals FeAl is ferromagnetic in theory, but nonmagnetic experimentally 3d-band position, exchange splitting, P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
58 58 Is LDA/GGA repairable? Ab initio methods GGA: usually improvement, but often too small. Hartree-Fock: completely neglects correlation, very poor in solids Exact exchange: imbalance between exact X and approximate (no) C Hybrid-Functionals: mix of HF + LDA; good for insulators, poor for metals GW: gaps in semiconductors, but ground state? expensive! Quantum Monte-Carlo: very expensive Not fully ab initio Self-interaction-correction: vanishes for Bloch states Orbital polarization: Hund s 2 nd rule by atomic Slater-parameter LDA+U: strong Coulomb repulsion via external Hubbard U parameter DMFT: extension of LDA+U for weakly correlated systems P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
59 59
60 60
61 61
62 62
63 Hybrid functionals (mixing of LDA with HF) 63 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
64 64
65 65
66 66
67 Lecture Summary 67 Density functional theory is an exact reformulation of many-body quantum mechanics in terms of the probability density rather than the wave function The ground-state energy can be obtained by minimization of the energy functional E[n]. All we know about the functional is that it exists, however, its form is unknown. Kohn-Sham reformulation in terms of single-particle orbitals helps in the development of approximations and is the form used in density functional calculations today. P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
68 68 Summary DFT has been the mainstay of electronic structure calculations more than 25 years. Because approximate functional provide a useful balance between accuracy and computational cost. This allowed much larger systems to be treated. DFT is a completely different way of approaching any interacting problem, by mapping it exactly to a much easier-to-solve non-interacting problem. Its methodology is applied into a large variety of systems as atoms,molecules, clusters and solids. Limitations of LDA/GGA were partly overcome by Hybrid functionals. P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT
69 69
70 70
Electronic band structure, sx-lda, Hybrid DFT, LDA+U and all that. Keith Refson STFC Rutherford Appleton Laboratory
Electronic band structure, sx-lda, Hybrid DFT, LDA+U and all that Keith Refson STFC Rutherford Appleton Laboratory LDA/GGA DFT is good but... Naive LDA/GGA calculation severely underestimates band-gaps.
More informationModified Becke-Johnson (mbj) exchange potential
Modified Becke-Johnson (mbj) exchange potential Hideyuki Jippo Fujitsu Laboratories LTD. 2015.12.21-22 OpenMX developer s meeting @ Kobe Overview: mbj potential The semilocal exchange potential adding
More informationIntroduction to Density Functional Theory with Applications to Graphene Branislav K. Nikolić
Introduction to Density Functional Theory with Applications to Graphene Branislav K. Nikolić Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, U.S.A. http://wiki.physics.udel.edu/phys824
More informationCollege of Chemistry, Peking University, Beijing, China. Fritz-Haber-Institut der MPG, Berlin, Germany
KITP Program Excitations in Condensed Matter Localized and Itinerant States in a Unified Picture beyond Density Functional Theory Hong Jiang 1, Patrick Rinke 2 and Matthias Scheffler 2 1 College of Chemistry,
More informationDensity Functional Theory (DFT)
Density Functional Theory (DFT) An Introduction by A.I. Al-Sharif Irbid, Aug, 2 nd, 2009 Density Functional Theory Revolutionized our approach to the electronic structure of atoms, molecules and solid
More informationDENSITY FUNCTIONAL THEORY FOR NON-THEORISTS JOHN P. PERDEW DEPARTMENTS OF PHYSICS AND CHEMISTRY TEMPLE UNIVERSITY
DENSITY FUNCTIONAL THEORY FOR NON-THEORISTS JOHN P. PERDEW DEPARTMENTS OF PHYSICS AND CHEMISTRY TEMPLE UNIVERSITY A TUTORIAL FOR PHYSICAL SCIENTISTS WHO MAY OR MAY NOT HATE EQUATIONS AND PROOFS REFERENCES
More informationDensity Functional Theory. Martin Lüders Daresbury Laboratory
Density Functional Theory Martin Lüders Daresbury Laboratory Ab initio Calculations Hamiltonian: (without external fields, non-relativistic) impossible to solve exactly!! Electrons Nuclei Electron-Nuclei
More informationPrinciples of Quantum Mechanics
Principles of Quantum Mechanics - indistinguishability of particles: bosons & fermions bosons: total wavefunction is symmetric upon interchange of particle coordinates (space,spin) fermions: total wavefuncftion
More information1 Density functional theory (DFT)
1 Density functional theory (DFT) 1.1 Introduction Density functional theory is an alternative to ab initio methods for solving the nonrelativistic, time-independent Schrödinger equation H Φ = E Φ. The
More informationThe Gutzwiller Density Functional Theory
The Gutzwiller Density Functional Theory Jörg Bünemann, BTU Cottbus I) Introduction 1. Model for an H 2 -molecule 2. Transition metals and their compounds II) Gutzwiller variational theory 1. Gutzwiller
More informationIntroduction to density-functional theory. Emmanuel Fromager
Institut de Chimie, Strasbourg, France Page 1 Emmanuel Fromager Institut de Chimie de Strasbourg - Laboratoire de Chimie Quantique - Université de Strasbourg /CNRS M2 lecture, Strasbourg, France. Institut
More informationThe LDA+U method: a primer and implementation within SIESTA
The LDA+U method: a primer and implementation within SIESTA Daniel Sánchez-Portal Thanks to Javier Junquera, Sampsa Riikonen and Eduardo Anglada Source of the failure of LDA to describe Mott insulators
More informationMagnetism in transition metal oxides by post-dft methods
Magnetism in transition metal oxides by post-dft methods Cesare Franchini Faculty of Physics & Center for Computational Materials Science University of Vienna, Austria Workshop on Magnetism in Complex
More informationComputational Nanoscience: Do It Yourself!
John von Neumann Institute for Computing (NIC) Computational Nanoscience: Do It Yourself! edited by Johannes Grotendorst Stefan Blugel Dominik Marx Winter School, 14-22 February 2006 Forschungszentrum
More informationCHEM6085: Density Functional Theory
Lecture 5 CHEM6085: Density Functional Theory Orbital-free (or pure ) DFT C.-K. Skylaris 1 Consists of three terms The electronic Hamiltonian operator Electronic kinetic energy operator Electron-Electron
More informationIntroduction to Density Functional Theory
Introduction to Density Functional Theory S. Sharma Institut für Physik Karl-Franzens-Universität Graz, Austria 19th October 2005 Synopsis Motivation 1 Motivation : where can one use DFT 2 : 1 Elementary
More informationKevin Driver 1 Shuai Zhang 1 Burkhard Militzer 1 R. E. Cohen 2.
Quantum Monte Carlo Simulations of a Single Iron Impurity in MgO Kevin Driver 1 Shuai Zhang 1 Burkhard Militzer 1 R. E. Cohen 2 1 Department of Earth & Planetary Science University of California, Berkeley
More informationAn introduction to the dynamical mean-field theory. L. V. Pourovskii
An introduction to the dynamical mean-field theory L. V. Pourovskii Nordita school on Photon-Matter interaction, Stockholm, 06.10.2016 OUTLINE The standard density-functional-theory (DFT) framework An
More informationThe electronic structure of materials 2 - DFT
Quantum mechanics 2 - Lecture 9 December 19, 2012 1 Density functional theory (DFT) 2 Literature Contents 1 Density functional theory (DFT) 2 Literature Historical background The beginnings: L. de Broglie
More informationDFT calculations of NMR indirect spin spin coupling constants
DFT calculations of NMR indirect spin spin coupling constants Dalton program system Program capabilities Density functional theory Kohn Sham theory LDA, GGA and hybrid theories Indirect NMR spin spin coupling
More informationMulti-Scale Modeling from First Principles
m mm Multi-Scale Modeling from First Principles μm nm m mm μm nm space space Predictive modeling and simulations must address all time and Continuum Equations, densityfunctional space scales Rate Equations
More informationDFT: Exchange-Correlation
DFT: Local functionals, exact exchange and other post-dft methods Stewart Clark University of Outline Introduction What is exchange and correlation? Quick tour of XC functionals (Semi-)local: LDA, PBE,
More informationModule 6 1. Density functional theory
Module 6 1. Density functional theory Updated May 12, 2016 B A DDFT C K A bird s-eye view of density-functional theory Authors: Klaus Capelle G http://arxiv.org/abs/cond-mat/0211443 R https://trac.cc.jyu.fi/projects/toolbox/wiki/dft
More informationDFT: Exchange-Correlation
DFT: Exchange-Correlation Local functionals, exact exchange and other post-dft methods Paul Tulip Centre for Materials Physics Department of Physics University of Durham Outline Introduction What is exchange
More informationQuantum Mechanical Simulations
Quantum Mechanical Simulations Prof. Yan Wang Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332, U.S.A. yan.wang@me.gatech.edu Topics Quantum Monte Carlo Hartree-Fock
More informationFirst principle calculations of plutonium and plutonium compounds: part 1
First principle calculations of plutonium and plutonium compounds: part 1 A. B. Shick Institute of Physics ASCR, Prague, CZ Outline: u Lecture 1: Methods of Correlated band theory DFT and DFT+U u Lecture
More informationBand calculations: Theory and Applications
Band calculations: Theory and Applications Lecture 2: Different approximations for the exchange-correlation correlation functional in DFT Local density approximation () Generalized gradient approximation
More informationCHEM6085: Density Functional Theory Lecture 10
CHEM6085: Density Functional Theory Lecture 10 1) Spin-polarised calculations 2) Geometry optimisation C.-K. Skylaris 1 Unpaired electrons So far we have developed Kohn-Sham DFT for the case of paired
More informationTeoría del Funcional de la Densidad (Density Functional Theory)
Teoría del Funcional de la Densidad (Density Functional Theory) Motivation: limitations of the standard approach based on the wave function. The electronic density n(r) as the key variable: Functionals
More informationDensity Functional Theory for Electrons in Materials
Density Functional Theory for Electrons in Materials Richard M. Martin Department of Physics and Materials Research Laboratory University of Illinois at Urbana-Champaign 1 Density Functional Theory for
More informationOVERVIEW OF QUANTUM CHEMISTRY METHODS
OVERVIEW OF QUANTUM CHEMISTRY METHODS Outline I Generalities Correlation, basis sets Spin II Wavefunction methods Hartree-Fock Configuration interaction Coupled cluster Perturbative methods III Density
More informationElectron Correlation
Electron Correlation Levels of QM Theory HΨ=EΨ Born-Oppenheimer approximation Nuclear equation: H n Ψ n =E n Ψ n Electronic equation: H e Ψ e =E e Ψ e Single determinant SCF Semi-empirical methods Correlation
More informationExchange Correlation Functional Investigation of RT-TDDFT on a Sodium Chloride. Dimer. Philip Straughn
Exchange Correlation Functional Investigation of RT-TDDFT on a Sodium Chloride Dimer Philip Straughn Abstract Charge transfer between Na and Cl ions is an important problem in physical chemistry. However,
More informationDept of Mechanical Engineering MIT Nanoengineering group
1 Dept of Mechanical Engineering MIT Nanoengineering group » To calculate all the properties of a molecule or crystalline system knowing its atomic information: Atomic species Their coordinates The Symmetry
More informationDensity Functional Theory - II part
Density Functional Theory - II part antonino.polimeno@unipd.it Overview From theory to practice Implementation Functionals Local functionals Gradient Others From theory to practice From now on, if not
More informationExchange-Correlation Functional
Exchange-Correlation Functional Aiichiro Nakano Collaboratory for Advanced Computing & Simulations Depts. of Computer Science, Physics & Astronomy, Chemical Engineering & Materials Science, and Biological
More informationSession 1. Introduction to Computational Chemistry. Computational (chemistry education) and/or (Computational chemistry) education
Session 1 Introduction to Computational Chemistry 1 Introduction to Computational Chemistry Computational (chemistry education) and/or (Computational chemistry) education First one: Use computational tools
More informationLecture 8: Introduction to Density Functional Theory
Lecture 8: Introduction to Density Functional Theory Marie Curie Tutorial Series: Modeling Biomolecules December 6-11, 2004 Mark Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Science
More informationIntroduction to DFT and Density Functionals. by Michel Côté Université de Montréal Département de physique
Introduction to DFT and Density Functionals by Michel Côté Université de Montréal Département de physique Eamples Carbazole molecule Inside of diamant Réf: Jean-François Brière http://www.phys.umontreal.ca/~michel_
More informationOslo node. Highly accurate calculations benchmarking and extrapolations
Oslo node Highly accurate calculations benchmarking and extrapolations Torgeir Ruden, with A. Halkier, P. Jørgensen, J. Olsen, W. Klopper, J. Gauss, P. Taylor Explicitly correlated methods Pål Dahle, collaboration
More informationComputational Methods. Chem 561
Computational Methods Chem 561 Lecture Outline 1. Ab initio methods a) HF SCF b) Post-HF methods 2. Density Functional Theory 3. Semiempirical methods 4. Molecular Mechanics Computational Chemistry " Computational
More informationMany electrons: Density functional theory Part II. Bedřich Velický VI.
Many electrons: Density functional theory Part II. Bedřich Velický velicky@karlov.mff.cuni.cz VI. NEVF 514 Surface Physics Winter Term 013-014 Troja 1 st November 013 This class is the second devoted to
More informationarxiv: v1 [cond-mat.str-el] 18 Jul 2007
arxiv:0707.2704v1 [cond-mat.str-el] 18 Jul 2007 Determination of the Mott insulating transition by the multi-reference density functional theory 1. Introduction K. Kusakabe Graduate School of Engineering
More informationComputational Chemistry I
Computational Chemistry I Text book Cramer: Essentials of Quantum Chemistry, Wiley (2 ed.) Chapter 3. Post Hartree-Fock methods (Cramer: chapter 7) There are many ways to improve the HF method. Most of
More informationElectronic correlation and Hubbard approaches
Electronic correlation and Hubbard approaches Matteo Cococcioni Department of Chemical Engineering and Materials Science University of Minnesota Notable failures of LDA/GGA: transition-metal oxides Introduction
More informationHartree-Fock Theory Variational Principle (Rayleigh-Ritz method)
Hartree-Fock Theory Variational Principle (Rayleigh-Ritz method) (note) (note) Schrodinger equation: Example: find an approximate solution for AHV Trial wave function: (note) b opt Mean-Field Approximation
More informationPseudopotentials: design, testing, typical errors
Pseudopotentials: design, testing, typical errors Kevin F. Garrity Part 1 National Institute of Standards and Technology (NIST) Uncertainty Quantification in Materials Modeling 2015 Parameter free calculations.
More informationSolid State Theory: Band Structure Methods
Solid State Theory: Band Structure Methods Lilia Boeri Wed., 11:15-12:45 HS P3 (PH02112) http://itp.tugraz.at/lv/boeri/ele/ Plan of the Lecture: DFT1+2: Hohenberg-Kohn Theorem and Kohn and Sham equations.
More informationJoint ICTP-IAEA Workshop on Fusion Plasma Modelling using Atomic and Molecular Data January 2012
2327-3 Joint ICTP-IAEA Workshop on Fusion Plasma Modelling using Atomic and Molecular Data 23-27 January 2012 Qunatum Methods for Plasma-Facing Materials Alain ALLOUCHE Univ.de Provence, Lab.de la Phys.
More informationMetal-insulator transitions
Metal-insulator transitions What can we learn from electronic structure calculations? Mike Towler mdt26@phy.cam.ac.uk www.tcm.phy.cam.ac.uk/ mdt26 Theory of Condensed Matter Group Cavendish Laboratory
More informationMODULE 2: QUANTUM MECHANICS. Principles and Theory
MODULE 2: QUANTUM MECHANICS Principles and Theory You are here http://www.lbl.gov/cs/html/exascale4energy/nuclear.html 2 Short Review of Quantum Mechanics Why do we need quantum mechanics? Bonding and
More informationAdvanced Quantum Chemistry III: Part 3. Haruyuki Nakano. Kyushu University
Advanced Quantum Chemistry III: Part 3 Haruyuki Nakano Kyushu University 2013 Winter Term 1. Hartree-Fock theory Density Functional Theory 2. Hohenberg-Kohn theorem 3. Kohn-Sham method 4. Exchange-correlation
More informationSelf-Consistent Implementation of Self-Interaction Corrected DFT and of the Exact Exchange Functionals in Plane-Wave DFT
Self-Consistent Implementation of Self-Interaction Corrected DFT and of the Exact Exchange Functionals in Plane-Wave DFT Kiril Tsemekhman (a), Eric Bylaska (b), Hannes Jonsson (a,c) (a) Department of Chemistry,
More informationAdditional background material on the Nobel Prize in Chemistry 1998
Additional background material on the Nobel Prize in Chemistry 1998 The Royal Swedish Academy of Sciences has decided to award the 1998 Nobel Prize in Chemistry with one half to Professor WALTER KOHN,
More informationHyperfine interactions Mössbauer, PAC and NMR Spectroscopy: Quadrupole splittings, Isomer shifts, Hyperfine fields (NMR shifts)
Hyperfine interactions Mössbauer, PAC and NMR Spectroscopy: Quadrupole splittings, Isomer shifts, Hyperfine fields (NMR shifts) Peter Blaha Institute of Materials Chemistry TU Wien Definition of Hyperfine
More informationThe Basics of Theoretical and Computational Chemistry
Bernd M. Rode, Thomas S. Hofer, and Michael D. Kugler The Basics of Theoretical and Computational Chemistry BICENTENNIA BICENTBNN I AL. WILEY-VCH Verlag GmbH & Co. KGaA V Contents Preface IX 1 Introduction
More informationPreface Introduction to the electron liquid
Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2
More informationElectronic structure of correlated electron systems. Lecture 2
Electronic structure of correlated electron systems Lecture 2 Band Structure approach vs atomic Band structure Delocalized Bloch states Fill up states with electrons starting from the lowest energy No
More informationAb Initio modelling of structural and electronic. Matt Probert University of York
Ab Initio modelling of structural and electronic properties of semiconductors Matt Probert University of York http://www-users.york.ac.uk/~mijp1 Overview of Talk What is Ab Initio? What can we model? How
More informationKey concepts in Density Functional Theory (I) Silvana Botti
From the many body problem to the Kohn-Sham scheme European Theoretical Spectroscopy Facility (ETSF) CNRS - Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France Temporary Address: Centre
More informationAndré Schleife Department of Materials Science and Engineering
André Schleife Department of Materials Science and Engineering Yesterday you (should have) learned this: http://upload.wikimedia.org/wikipedia/commons/e/ea/ Simple_Harmonic_Motion_Orbit.gif 1. deterministic
More informationMulti-reference Density Functional Theory. COLUMBUS Workshop Argonne National Laboratory 15 August 2005
Multi-reference Density Functional Theory COLUMBUS Workshop Argonne National Laboratory 15 August 2005 Capt Eric V. Beck Air Force Institute of Technology Department of Engineering Physics 2950 Hobson
More informationLecture 6. Fermion Pairing. WS2010/11: Introduction to Nuclear and Particle Physics
Lecture 6 Fermion Pairing WS2010/11: Introduction to Nuclear and Particle Physics Experimental indications for Cooper-Pairing Solid state physics: Pairing of electrons near the Fermi surface with antiparallel
More informationTable of Contents. Table of Contents Spin-orbit splitting of semiconductor band structures
Table of Contents Table of Contents Spin-orbit splitting of semiconductor band structures Relavistic effects in Kohn-Sham DFT Silicon band splitting with ATK-DFT LSDA initial guess for the ground state
More informationDensity functional theory
Density functional theory Seminar Ib - 1. letnik, II. stopnja Author: Matic Pečovnik Mentor: Doc. Dr. Tomaž Rejec Faculty of Mathematics and Physics, University in Ljubljana Abstract Many-body problems
More informationGEM4 Summer School OpenCourseWare
GEM4 Summer School OpenCourseWare http://gem4.educommons.net/ http://www.gem4.org/ Lecture: Molecular Mechanics by Ju Li. Given August 9, 2006 during the GEM4 session at MIT in Cambridge, MA. Please use
More informationFrustrated Magnetic Materials from an ab initio prespective Roser Valentí Institute of Theoretical Physics University of Frankfurt Germany
Frustrated Magnetic Materials from an ab initio prespective Roser Valentí Institute of Theoretical Physics University of Frankfurt Germany Highly Frustrated Magnetism Tutorial, July 9 th 2018, UC Davis
More informationImproved Electronic Structure and Optical Properties of sp-hybridized Semiconductors Using LDA+U SIC
286 Brazilian Journal of Physics, vol. 36, no. 2A, June, 2006 Improved Electronic Structure and Optical Properties of sp-hybridized Semiconductors Using LDA+U SIC Clas Persson and Susanne Mirbt Department
More informationMolecular Mechanics: The Ab Initio Foundation
Molecular Mechanics: The Ab Initio Foundation Ju Li GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7 18, 2006, MIT, Cambridge, MA, USA 2 Outline Why are electrons quantum? Born-Oppenheimer
More informationFYS-6306 QUANTUM THEORY OF MOLECULES AND NANOSTRUCTURES
i FYS-6306 QUANTUM THEORY OF MOLECULES AND NANOSTRUCTURES Credit units: 6 ECTS Lectures: 48 h Tapio Rantala, prof. Tue 10 12 SC203 SG219 8 10 SG312 FirstName.LastName@tut.fi http://www.tut.fi/~trantala/opetus/
More informationAll electron optimized effective potential method for solids
All electron optimized effective potential method for solids Institut für Theoretische Physik Freie Universität Berlin, Germany and Fritz Haber Institute of the Max Planck Society, Berlin, Germany. 22
More informationCLIMBING THE LADDER OF DENSITY FUNCTIONAL APPROXIMATIONS JOHN P. PERDEW DEPARTMENT OF PHYSICS TEMPLE UNIVERSITY PHILADELPHIA, PA 19122
CLIMBING THE LADDER OF DENSITY FUNCTIONAL APPROXIMATIONS JOHN P. PERDEW DEPARTMENT OF PHYSICS TEMPLE UNIVERSITY PHILADELPHIA, PA 191 THANKS TO MANY COLLABORATORS, INCLUDING SY VOSKO DAVID LANGRETH ALEX
More informationInstitut Néel Institut Laue Langevin. Introduction to electronic structure calculations
Institut Néel Institut Laue Langevin Introduction to electronic structure calculations 1 Institut Néel - 25 rue des Martyrs - Grenoble - France 2 Institut Laue Langevin - 71 avenue des Martyrs - Grenoble
More informationStudy of Ozone in Tribhuvan University, Kathmandu, Nepal. Prof. S. Gurung Central Department of Physics, Tribhuvan University, Kathmandu, Nepal
Study of Ozone in Tribhuvan University, Kathmandu, Nepal Prof. S. Gurung Central Department of Physics, Tribhuvan University, Kathmandu, Nepal 1 Country of the Mt Everest 2 View of the Mt Everest 3 4 5
More informationSpring College on Computational Nanoscience May Variational Principles, the Hellmann-Feynman Theorem, Density Functional Theor
2145-25 Spring College on Computational Nanoscience 17-28 May 2010 Variational Principles, the Hellmann-Feynman Theorem, Density Functional Theor Stefano BARONI SISSA & CNR-IOM DEMOCRITOS Simulation Center
More informationFrom Materials to Models and Back. Dieter Vollhardt
From Materials to Models and Back Dieter Vollhardt 28 th Edgar Lüscher Seminar, Klosters; February 8, 2017 From Materials to Models and Back - The Need for Models in Condensed Matter Physics - Outline:
More informationWalter Kohn was awarded with the Nobel Prize in Chemistry in 1998 for his development of the density functional theory.
Walter Kohn was awarded with the Nobel Prize in Chemistry in 1998 for his development of the density functional theory. Walter Kohn receiving his Nobel Prize from His Majesty the King at the Stockholm
More informationTowards ab initio device Design via Quasiparticle self-consistent GW theory
Towards ab initio device Design via Quasiparticle self-consistent GW theory Mark van Schilfgaarde and Takao Kotani Arizona State University Limitations to the local density approximation, the GW approximation
More informationCorrelatd electrons: the case of high T c cuprates
Correlatd electrons: the case of high T c cuprates Introduction: Hubbard U - Mott transition, The cuprates: Band structure and phase diagram NMR as a local magnetic probe Magnetic susceptibilities NMR
More informationThe Schrödinger equation for many-electron systems
The Schrödinger equation for many-electron systems Ĥ!( x,, x ) = E!( x,, x ) 1 N 1 1 Z 1 Ĥ = " $ # " $ + $ 2 r 2 A j j A, j RAj i, j < i a linear differential equation in 4N variables (atomic units) (3
More informationExchange Mechanisms. Erik Koch Institute for Advanced Simulation, Forschungszentrum Jülich. lecture notes:
Exchange Mechanisms Erik Koch Institute for Advanced Simulation, Forschungszentrum Jülich lecture notes: www.cond-mat.de/events/correl Magnetism is Quantum Mechanical QUANTUM MECHANICS THE KEY TO UNDERSTANDING
More informationThe Overhauser Instability
The Overhauser Instability Zoltán Radnai and Richard Needs TCM Group ESDG Talk 14th February 2007 Typeset by FoilTEX Introduction Hartree-Fock theory and Homogeneous Electron Gas Noncollinear spins and
More informationDensity Functional Theory
Chemistry 380.37 Fall 2015 Dr. Jean M. Standard October 28, 2015 Density Functional Theory What is a Functional? A functional is a general mathematical quantity that represents a rule to convert a function
More informationOrbital dependent correlation potentials in ab initio density functional theory
Orbital dependent correlation potentials in ab initio density functional theory noniterative - one step - calculations Ireneusz Grabowski Institute of Physics Nicolaus Copernicus University Toruń, Poland
More informationMagnetic state and electronic structure of the and phases of metallic Pu and its compounds
Magnetic state and electronic structure of the and phases of metallic Pu and its compounds A. O. Shorikov, 1 A. V. Lukoyanov, 1,2 M. A. Korotin, 1 and V. I. Anisimov 1 1 Institute of Metal Physics, Russian
More informationIntroduction to Computational Quantum Chemistry: Theory
Introduction to Computational Quantum Chemistry: Theory Dr Andrew Gilbert Rm 118, Craig Building, RSC 3108 Course Lectures 2007 Introduction Hartree Fock Theory Configuration Interaction Lectures 1 Introduction
More informationOne-Electron Hamiltonians
One-Electron Hamiltonians Hartree-Fock and Density Func7onal Theory Christopher J. Cramer @ChemProfCramer 2017 MSSC, July 10, 2017 REVIEW A One-Slide Summary of Quantum Mechanics Fundamental Postulate:
More informationMott insulators. Mott-Hubbard type vs charge-transfer type
Mott insulators Mott-Hubbard type vs charge-transfer type Cluster-model description Chemical trend Band theory Self-energy correction Electron-phonon interaction Mott insulators Mott-Hubbard type vs charge-transfer
More informationElectronic structure of correlated electron systems. G.A.Sawatzky UBC Lecture
Electronic structure of correlated electron systems G.A.Sawatzky UBC Lecture 6 011 Influence of polarizability on the crystal structure Ionic compounds are often cubic to maximize the Madelung energy i.e.
More informationnanohub.org learning module: Prelab lecture on bonding and band structure in Si
nanohub.org learning module: Prelab lecture on bonding and band structure in Si Ravi Vedula, Janam Javerhi, Alejandro Strachan Center for Predictive Materials Modeling and Simulation, School of Materials
More information?What are the physics questions?
?What are the physics questions? charge transfer: --how much charge moves? -- how far? --into what orbitals? --causing what lattice relaxations? order parameter transfer: --penetration depth --domain walls
More informationDensity Functional Theory
Density Functional Theory March 26, 2009 ? DENSITY FUNCTIONAL THEORY is a method to successfully describe the behavior of atomic and molecular systems and is used for instance for: structural prediction
More informationDensity Functional Theory Studies for Transition Metals: Small (Fe,Co)-clusters in fcc Ag, and the Spin Density Wave in bcc Chromium.
Density Functional Theory Studies for Transition Metals: Small (Fe,Co)-clusters in fcc Ag, and the Spin Density Wave in bcc Chromium. Promotor: Prof. Dr. S. Cottenier Proefschrift ingediend tot het behalen
More informationSame idea for polyatomics, keep track of identical atom e.g. NH 3 consider only valence electrons F(2s,2p) H(1s)
XIII 63 Polyatomic bonding -09 -mod, Notes (13) Engel 16-17 Balance: nuclear repulsion, positive e-n attraction, neg. united atom AO ε i applies to all bonding, just more nuclei repulsion biggest at low
More informationCHEM3023: Spins, Atoms and Molecules
CHEM3023: Spins, Atoms and Molecules Lecture 5 The Hartree-Fock method C.-K. Skylaris Learning outcomes Be able to use the variational principle in quantum calculations Be able to construct Fock operators
More informationLocal moment approach to the multi - orbital single impurity Anderson and Hubbard models
Local moment approach to the multi - orbital single impurity Anderson and Hubbard models Anna Kauch Institute of Theoretical Physics Warsaw University PIPT/Les Houches Summer School on Quantum Magnetism
More informationv(r i r j ) = h(r i )+ 1 N
Chapter 1 Hartree-Fock Theory 1.1 Formalism For N electrons in an external potential V ext (r), the many-electron Hamiltonian can be written as follows: N H = [ p i i=1 m +V ext(r i )]+ 1 N N v(r i r j
More informationKohn Sham density functional theory [1 3] is. Role of the Exchange Correlation Energy: Nature s Glue STEFAN KURTH, JOHN P. PERDEW.
Role of the Exchange Correlation Energy: Nature s Glue STEFAN KURTH, JOHN P. PERDEW Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118 Received 11 March 1999;
More informationProgress & challenges with Luttinger-Ward approaches for going beyond DFT
Progress & challenges with Luttinger-Ward approaches for going beyond DFT Sohrab Ismail-Beigi Yale University Dept. of Applied Physics and Physics & CRISP (NSF MRSEC) Ismail-Beigi, Phys. Rev. B (2010)
More informationBasics of density-functional theory and fast guide to actual calculations Matthias Scheffler
Basics of density-functional theory and fast guide to actual calculations Matthias Scheffler http://www.fhi-berlin.mpg.de/th/th.html I. From the many-particle problem to the Kohn-Sham functional II. From
More information