Spin gaps and spin flip energies in density functional theory
|
|
|
- Claud Garry Nash
- 6 years ago
- Views:
Transcription
1 Spin gaps and spin flip energies in density functional theory Klaus Capelle Universidade Federal do ABC Carsten Ullrich University of Missouri-Columbia G. Vignale University of Missouri-Columbia
2 Charge Gap GROUND-STATE ENERGY vs PARTICLE NUMBER IONIZATION ENERGY I(N) = E(N!1)! E(N) AFFINITY ENERGY A(N) = E(N)! E(N +1) = I(N +1) FUNDAMENTAL CHARGE GAP E g = I(N)! A(N) = E(N!1)! 2E(N)+ E(N +1) A discretized second derivative or stiffness
3 Difficulties in calculating charge gap by KOHN-SHAM EQUATION density functional theory #! " 2 r 2 +V(r)+V (r;n)+v (r;n) & % H xc (! " (r) = # " (N)! " (r) $ ' " =1,!, N ε 5 ε 4 ε 3 ε 2 ε 1 KOOPMAN S THEOREM I(N) =!! N (N) I(N +1) =!! N+1 (N +1) However, in practice, one uses EXACT E g =! N+1 (N +1)!! N (N) Derivative discontinuity correction E g,ks =! N+1 (N)!! N (N) = E g! " xc Error resides in the affinity energy
![Nonuniqueness and derivative discontinuities The basic Euler equation of DFT is!e[n]!n(r) = µ!f[n]!n(r) = µ!v(r)!t s [n]!n(r) = µ!v s (r) where E[n] = F[n]! +!](/docs-images/75/72923890/images/4-0.jpg "dr n(r)v(r) F[n] = Universal energy functional T s [n]! + E! [n] + E H!")
4 Nonuniqueness and derivative discontinuities The basic Euler equation of DFT is!e[n]!n(r) = µ!f[n]!n(r) = µ!v(r)!t s [n]!n(r) = µ!v s (r) where E[n] = F[n]! +! dr n(r)v(r) F[n] = Universal energy functional T s [n]! + E! [n] + E H! [n] xc Noninteracting kinetic energy Hartree energy Exchange-correlation energy The particle number N cannot uniquely determine the chemical potential µ. Therefore, the chemical potential must have discontinuous jumps as a function of particle number ant the functional derivative of F (T s ) is discontinuous.
5 Nonuniqueness and derivative discontinuity II Evolution of the spectrum of H ˆ µ = H ˆ! µ N ˆ Behavior of N vs µ!a(n) = µ + (N)!I(N) = µ! (N) E g = I! A = µ +! µ! =!E[n]!n(r) N+!N!!E[n]!n(r) N!!N
6 The effect of temperature e! E gap / kt A unique relation between N and µ is restored at finite temperature. However, because the finite-t curve approaches the T=0 curve exponentially fast, the transition from µ + (N-1) to µ + (N) takes place in an interval ΔN~ exp(-e gap /kt). Therefore the energy functional remains effectively discontinuous for kt<<e g.
7 Connection with Kohn-Sham theory E g,ks =!T s [n]!n(r) N+!N!!T s [n]!n(r) N!!N E g = E g,ks +! xc Difference between true gap and Kohn-Sham gap is connected to a discontinuity in the derivative of the exchange-correlation energy functional! xc =!E xc [n]!n(r) N+!N "!E xc [n]!n(r) N"!N Note: this connection is not required to define the xc correction in finite electronic systems however it appears naturally in periodic solids, where the total number of particles is infinite, and was first discovered in those systems (the so-called band-gap problem of DFT).
8 The band gap problem
9 Spin Gaps In analogy with ionization and affinity energies we define the spin-down flip and the spin-up flip energies E! = E(N, S!1)! E(N, S) E + = E(N, S +1)! E(N, S) analogous to ionization analogous to negative affinity Note: in contrast to charge gaps, in which both N and S were changed, here only S is changed. SPIN-STIFFNESS GAP E s = E! + E + = E(N, S +1)! 2E(N, S)+ E(N, S!1) Discretized spin stiffness
10 Kohn-Sham spin gaps SPIN-FLIP GAPS E! KS =! L"!! H#! Lowest unoccupied orbital Highest occupied orbital SPIN-CONSERVING GAPS E sc! g,ks =! L! "! H! E sc! g,ks =! L! "! H! E + KS =! L! "! H# SPIN-STIFFNESS GAP E S,KS = (! L! "! H# ) + (! L# "! H! ) CORRECTION TO KOHN-SHAM SPIN GAPS E ± = E ± ± KS +! xc = E ± KS +!E w=0 xc [n!, n " ]!n! (r) n " =n " (0) #!E xc w [n!, n " ]!n " (r) n " =n " (w)
11 Kohn-Sham spin gaps - continued E sc! g,ks + E sc" g,ks = E # + KS + E KS SPIN-POLARIZED INSULATOR FERROMAGNETIC SEMIMETAL E! KS =! L"!! H# E sc! g,ks =! L! "! H! E sc! g,ks =! L! "! H! E + KS =! L! "! H#
12 Example: The Li atom 2p 2s 1s! L! = 2p!! H! = 2s!L! = 2s!!! H! =1s! E! KS =! 2s"!! 2s# E + KS =! 2 p! "! 1s#
13 The Li atom - continued Simple LSDA calculations give rise to serious qualitative errors. Even precise KS eigenvalues do not predict the exact spin flip energies and stiffness. Exchange-only calculations overestimate the size of the gap corrections. The xc correction to the up-flip energy and the spin stiffness turns out to be negative.
14 Time-dependent approach Consider the response of a stationary system to a small spin-dependent periodic potential V ± (r,ω)e -iωt, which can flip the spin up (+) or down (-) by coupling to the spin-flip density operators ˆn! ( r) = " + # (r)" $ (r) ˆn + ( r) =! + " (r)! # (r) The induced spin-flip density is!n ± ( r," ) =! # ± (r, r',")v ± ( r'," ) dr' = # KS eff! ± (r,r',")v ± ( r'," ) dr' where χ KS (r,r,ω) is the Kohn-Sham response function and V ± eff (r) = V ± (r)+! f xc,±± (r, r',!)"n ± (r',!)dr' Where f xc, ±± is the exchange-correlation kernel.
15 A simple approximation for Δ xc Following the method of Petersilka et al. (single-pole approximation), we find + = # dr # dr'! L" (r)! H$ (r) f xc ++ (r,r', E + KS )! L" (r)! H$ (r')! xc " = $ dr $ dr'! L# (r)! H% (r) f xc "" (r,r', E " KS )! L# (r)! H% (r')! xc In adiabatic local density approximation (LSDA) f ++ xc (r,r',!) =!(r! r') = f!! xc (r,r',!) In exact exchange approximation (XX) f ++ xc (r, r',!) = = f!! xc (r,r',!)
16 Numerical results The TDDFT excitation energies are not much improved compared to the KS orbital energy differences. The xc correction to the spin stiffness is reasonably close to the exact value, and has the correct sign.
Dept 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
Density 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
A FRESH LOOK AT THE BAND-GAP PROBLEM IN DENSITY FUNCTIONAL THEORY
A FRESH LOOK AT THE BAND-GAP PROBLEM IN DENSITY FUNCTIONAL THEORY JOHN P. PERDEW PHYSICS & CHEMISTRY, TEMPLE UNIVERSITY PHILADELPHIA, PENNSYLVANIA, USA SUPPORTED BY THE U.S. DEPARTMENT OF ENERGY, EFRC
Self-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,
Time-dependent density functional theory
Time-dependent density functional theory E.K.U. Gross Max-Planck Institute for Microstructure Physics OUTLINE LECTURE I Phenomena to be described by TDDFT Some generalities on functional theories LECTURE
Time-Dependent Density-Functional Theory
Summer School on First Principles Calculations for Condensed Matter and Nanoscience August 21 September 3, 2005 Santa Barbara, California Time-Dependent Density-Functional Theory X. Gonze, Université Catholique
Short Course on Density Functional Theory and Applications VIII. Time-dependent DFT
Short Course on Density Functional Theory and Applications VIII. Time-dependent DFT Samuel B. Trickey Sept. 2008 Quantum Theory Project Dept. of Physics and Dept. of Chemistry trickey@qtp.ufl.edu Time-dependent
DENSITY 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
Many 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
Solutions to selected problems from Giuliani, Vignale : Quantum Theory of the Electron Liquid
Solutions to selected problems from Giuliani, Vignale : Quantum Theory of the Electron Liquid These problems have been solved as a part of the Independent study class with prof. Neepa Maitra. Compiled
Advanced TDDFT PDF Created with deskpdf PDF Writer - Trial ::
Advanced TDDFT TDDFT Humanity has advanced, when it has advanced, not because it has been sober, responsible, and cautious, but because it has been playful, rebellious, and immature Tom Robbins US novelist
OVERVIEW 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
Key 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
Independent electrons in an effective potential
ABC of DFT Adiabatic approximation Independent electrons in an effective potential Hartree Fock Density Functional Theory MBPT - GW Density Functional Theory in a nutshell Every observable quantity of
v(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
Density 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
Band 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
Adiabatic connection for near degenerate excited states
PHYSICAL REVIEW A 69, 052510 (2004) Adiabatic connection for near degenerate excited states Fan Zhang Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey
Advanced Solid State Theory SS Roser Valentí and Harald Jeschke Institut für Theoretische Physik, Goethe-Universität Frankfurt
Advanced Solid State Theory SS 2010 Roser Valentí and Harald Jeschke Institut für Theoretische Physik, Goethe-Universität Frankfurt i 0. Literatur R. M. Martin, Electronic Structure: Basic Theory and
Time-dependent density functional theory : direct computation of excitation energies
CECAM Tutorial Electronic excitations and spectroscopies : Theory and Codes Lyon 007 Time-dependent density functional theory : direct computation of excitation energies X. Gonze Université Catholique
Advanced TDDFT I: Memory and Initial-State Dependence
Advanced TDDFT I: Memory and Initial-State Dependence when the adiabatic approximation commits a crime Where were you at the time the photon was annihilated? I..um I just can t remember! V xc( r,t ) n(r,t)
Quantum Continuum Mechanics for Many-Body Systems
Workshop on High Performance and Parallel Computing Methods and Algorithms for Materials Defects, 9-13 February 2015 Quantum Continuum Mechanics for Many-Body Systems J. Tao 1,2, X. Gao 1,3, G. Vignale
Advanced TDDFT II. Double Excitations in TDDFT
Advanced TDDFT II. Double Excitations in TDDFT f xc Neepa T. Maitra Hunter College and the Graduate Center of the City University of New York First, quick recall of how we get excitations in TDDFT: Linear
Modified 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
Australian Journal of Basic and Applied Sciences
AENSI Journals Australian Journal of Basic and Applied Sciences ISSN:1991-8178 Journal home page: www.ajbasweb.com Theoretical Study for the Effect of Hydroxyl Radical on the Electronic Properties of Cyclobutadiene
3: Density Functional Theory
The Nuts and Bolts of First-Principles Simulation 3: Density Functional Theory CASTEP Developers Group with support from the ESF ψ k Network Density functional theory Mike Gillan, University College London
Ensemble-generalization approach:
Ensemble-generalization approach: addressing some long-standing problems in DFT Eli Kraisler Max Planck Institute of Microstructure Physics, Halle (Saale), Germany DFT2016 summer school, Los Angeles, August
GW Many-Body Theory for Electronic Structure. Rex Godby
GW Many-Body Theory for Electronic Structure Rex Godby Outline Lecture 1 (Monday) Introduction to MBPT The GW approximation (non-sc and SC) Implementation of GW Spectral properties Lecture 2 (Tuesday)
Preface 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
Multi-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
Quantum 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
Teoría 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
1 Back to the ground-state: electron gas
1 Back to the ground-state: electron gas Manfred Lein and Eberhard K. U. Gross 1.1 Introduction In this chapter, we explore how concepts of time-dependent density functional theory can be useful in the
Exchange-Correlation Functional
Exchange-Correlation Functional Aiichiro Nakano Collaboratory for Advanced Computing & Simulations Depts. of Computer Science, Physics & Astronomy, Chemical Engineering & Materials Science, and Biological
Lecture 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
Introduction to Density Functional Theory
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 3 4 Ab initio Computational
Time-dependent density functional theory
Annual Review of Physical Chemistry 2004 1056-8700/97/0610-00 Time-dependent density functional theory M. A. L. Marques and E.K. U. Gross Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee
1 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
Solid 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.
TDDFT in Chemistry and Biochemistry III
TDDFT in Chemistry and Biochemistry III Dmitrij Rappoport Department of Chemistry and Chemical Biology Harvard University TDDFT Winter School Benasque, January 2010 Dmitrij Rappoport (Harvard U.) TDDFT
Computational 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
The 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
All 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
A bird s-eye view of density-functional theory
A bird s-eye view of density-functional theory Klaus Capelle arxiv:cond-mat/0211443 v2 20 Feb 2003 Contents Departamento de Química e Física Molecular Instituto de Química de São Carlos Universidade de
Linear-response excitations. Silvana Botti
from finite to extended systems 1 LSI, CNRS-CEA-École Polytechnique, Palaiseau, France 2 LPMCN, CNRS-Université Lyon 1, France 3 European Theoretical Spectroscopy Facility September 3, 2008 Benasque, TDDFT
Received 27 February 2000; revised 6 June 2000; accepted 7 June 2000
Excitation Energies from Time-Dependent Density Functional Theory Using Exact and Approximate Potentials M. PETERSILKA, 1 E. K. U. GROSS, 1 KIERON BURKE 2 1 Institut für Theoretische Physik, Universität
Advanced TDDFT II. II. Frequency-Dependent Kernels: Double Excitations. f xc
Advanced TDDFT II II. Frequency-Dependent Kernels: Double Excitations f xc Neepa T. Maitra Hunter College and the Graduate Center of the City University of New York Plan -- Double-Excitations in TDDFT
3/23/2010 More basics of DFT Kieron Burke and friends UC Irvine Physics and Chemistry References for ground-state DFT ABC of DFT, by KB and Rudy Magyar, http://dft.uci.edu A Primer in Density Functional
Exact exchange (spin current) density-functional methods for magnetic properties, spin-orbit effects, and excited states
Exact exchange (spin current) density-functional methods for magnetic properties, spin-orbit effects, and excited states DFT with orbital-dependent functionals A. Görling Universität Erlangen-Nürnberg
Exchange 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,
Time-dependent density functional theory
Time-dependent density functional theory E.K.U. Gross Max-Planck Institute of Microstructure Physics Halle (Saale) OUTLINE Phenomena to be described by TDDFT Basic theorems of TDDFT Approximate xc functionals:
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.
Electron 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
Excitation energies from time-dependent density-functional theory beyond the adiabatic approximation
JOURNAL OF CHEMICAL PHYSICS VOLUME 11, NUMBER 1 1 JULY 004 Excitation energies from time-dependent density-functional theory beyond the adiabatic approximation C. A. Ullrich a) Department of Physics, University
f xc Advanced TDDFT PDF Created with deskpdf PDF Writer - Trial :: II. Frequency-Dependent Kernels: Double Excitations
Advanced TDDFT II. Frequency-Dependent Kernels: Double Excitations f xc Neepa T. Maitra Hunter College and the Graduate Center of the City University of New York First, quick recall of how we get excitations
Density-functional-theory response-property calculations with accurate exchange-correlation potentials
PHYSICAL REVIEW A VOLUME 57, NUMBER 4 APRIL 1998 Density-functional-theory response-property calculations with accurate exchange-correlation potentials S. J. A. van Gisbergen, 1 F. Kootstra, 2 P. R. T.
TDDFT Explorations in Phase-Space. Neepa T. Maitra Hunter College and the Graduate Center of the City University of New York
TDDFT Explorations in Phase-Space Neepa T. Maitra Hunter College and the Graduate Center of the City University of New York TDDFT in Phase-Space Outline Why phase-space DFT? Some motivating examples and
Density functionals from deep learning
Density functionals from deep learning Jeffrey M. McMahon Department of Physics & Astronomy March 15, 2016 Jeffrey M. McMahon (WSU) March 15, 2016 1 / 18 Kohn Sham Density-functional Theory (KS-DFT) The
CLIMBING 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
Excitation energies of dissociating H 2 : A problematic case for the adiabatic approximation of time-dependent density functional theory
JOURNAL OF CHEMICAL PHYSICS VOLUME 113, NUMBER 19 15 NOVEMBER 2000 Eitation energies of dissociating H 2 : A problematic case for the adiabatic approximation of time-dependent density functional theory
Key concepts in Density Functional Theory
From the many body problem to the Kohn-Sham scheme ILM (LPMCN) CNRS, Université Lyon 1 - France European Theoretical Spectroscopy Facility (ETSF) December 12, 2012 Lyon Outline 1 The many-body problem
The potential of Potential Functional Theory
The potential of Potential Functional Theory IPAM DFT School 2016 Attila Cangi August, 22 2016 Max Planck Institute of Microstructure Physics, Germany P. Elliott, AC, S. Pittalis, E.K.U. Gross, K. Burke,
The 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
Many electron effects in semiconductor quantum dots
Bull. Mater. Sci., Vol. 26, No. 1, January 2003, pp. 63 67. Indian Academy of Sciences. Many electron effects in semiconductor quantum dots K PANDEY*, MANOJ K HABOLA, V ANJAN and VIJAY A SINGH Physics
Orbital Density Dependent Functionals
Orbital Density Dependent Functionals S. Kluepfel1, P. Kluepfel1, Hildur Guðmundsdóttir1 and Hannes Jónsson1,2 1. Univ. of Iceland; 2. Aalto University Outline: Problems with GGA approximation (PBE, RPBE,...)
Generalized generalized gradient approximation: An improved density-functional theory for accurate orbital eigenvalues
PHYSICAL REVIEW B VOLUME 55, NUMBER 24 15 JUNE 1997-II Generalized generalized gradient approximation: An improved density-functional theory for accurate orbital eigenvalues Xinlei Hua, Xiaojie Chen, and
Excitation energies from density functional perturbation theory
Excitation energies from density functional perturbation theory Claudia Filippi Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 C. J. Umrigar Cornell Theory Center
One-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:
Key concepts in Density Functional Theory (II)
Kohn-Sham scheme and band structures European Theoretical Spectroscopy Facility (ETSF) CNRS - Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France Present Address: LPMCN Université
Notes on Density Functional Theory
Notes on Density Functional Theory Rocco Martinazzo E-mail: rocco.martinazzo@unimi.it Contents 1 Introduction 1 Density Functional Theory 7 3 The Kohn-Sham approach 11 1 Introduction We consider here a
TDCDFT: Linear-response regime
Lecture TDCDFT: Linear-response regime Carsten A. Ullrich University of Missouri Benasque, January 01 Overview Lecture I: Basic formalism of TDCDFT Lecture II: Applications of TDCDFT in linear response
Multi-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
DFT in practice : Part II. Ersen Mete
pseudopotentials Department of Physics Balıkesir University, Balıkesir - Turkey August 13, 2009 - NanoDFT 09, İzmir Institute of Technology, İzmir Outline Pseudopotentials Basic Ideas Norm-conserving pseudopotentials
Hartree-Fock-Roothan Self-Consistent Field Method
Hartree-Fock-Roothan Self-Consistent Field Method 1. Helium Here is a summary of the derivation of the Hartree-Fock equations presented in class. First consider the ground state of He and start with with
A self-interaction free non-local correlation functional derived from exact criteria
A self-interaction free non-local correlation functional derived from exact criteria Tobias Schmidt and Stephan Kümmel Theoretical Physics IV University of Bayreuth Germany - International Workshop DFT
Time-dependent density functional theory
Time-dependent density functional theory E.K.U. Gross Max-Planck Institute of Microstructure Physics Halle (Saale) OUTLINE Phenomena to be described by TDDFT: Matter in weak and strong laser fields Basic
Excitons in time-dependent density-functional theory
Excitons in time-dependent density-functional theory Carsten A. Ullrich and Zeng-hui Yang Abstract This article gives an overview of the description of the optical and dielectric properties of bulk insulators
Basics 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
Yingwei Wang Computational Quantum Chemistry 1 Hartree energy 2. 2 Many-body system 2. 3 Born-Oppenheimer approximation 2
Purdue University CHM 67300 Computational Quantum Chemistry REVIEW Yingwei Wang October 10, 2013 Review: Prof Slipchenko s class, Fall 2013 Contents 1 Hartree energy 2 2 Many-body system 2 3 Born-Oppenheimer
Many electrons: Density functional theory
Many electrons: Density functional theory Bedřich Velický V. NEVF 54 Surface Physics Winter Term 0-0 Troja, 8 th November 0 This class is devoted to the many-electron aspects of the solid state (computational
Walter 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
Introduction 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
Current density functional theory for optical spectra Boeij, P.L. de; Kootstra, F.; Berger, Johannes; Leeuwen, R. van; Snijders, J.G.
University of Groningen Current density functional theory for optical spectra Boeij, P.L. de; Kootstra, F.; Berger, Johannes; Leeuwen, R. van; Snijders, J.G. Published in: The Journal of Chemical Physics
Introduction to density-functional theory
Introduction to density-functional theory Julien Toulouse Laboratoire de Chimie Théorique Université Pierre et Marie Curie et CNRS, 75005 Paris, France julien.toulouse@upmc.fr June 21, 2017 http://www.lct.jussieu.fr/pagesperso/toulouse/enseignement/introduction_dft.pdf
Several Theorems in Time-Dependent Density Functional Theory
Several Theorems in Time-Dependent Density Functional Theory Paul Hessler,* Jang Park, and Kieron Burke Department of Chemistry, Rutgers University, 315 Penn Street, Camden, New Jersey 08102 (Received
The 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
Key concepts in Density Functional Theory (II) Silvana Botti
Kohn-Sham scheme, band structure and optical spectra European Theoretical Spectroscopy Facility (ETSF) CNRS - Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France Temporary Address:
arxiv:cond-mat/ v1 [cond-mat.mes-hall] 21 Jun 1998
![arxiv:cond-mat/ v1 [cond-mat.mes-hall] 21 Jun 1998](/thumbs/91/107291164.jpg "arxiv:cond-mat/ v1 [cond-mat.mes-hall] 21 Jun 1998")
arxiv:cond-mat/986252v1 [cond-mat.mes-hall] 21 Jun 1998 Collective intersubband transitions in quantum wells: a comparative density-functional study C. A. Ullrich and G. Vignale Department of Physics,
Institut 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
Electronic 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
Density 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
Time-dependent density functional theory
Time-dependent density functional theory E.K.U. Gross Max-Planck Institute for Microstructure Physics OUTLINE LECTURE I Phenomena to be described by TDDFT LECTURE II Review of ground-state DFT LECTURE
Many-Body Perturbation Theory. Lucia Reining, Fabien Bruneval
, Fabien Bruneval Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France European Theoretical Spectroscopy Facility (ETSF) Belfast, 27.6.2007 Outline 1 Reminder 2 Perturbation Theory
arxiv:cond-mat/ v1 [cond-mat.mtrl-sci] 10 May 2006
![arxiv:cond-mat/ v1 [cond-mat.mtrl-sci] 10 May 2006](/thumbs/75/72264699.jpg "arxiv:cond-mat/ v1 [cond-mat.mtrl-sci] 10 May 2006")
Optical excitations in organic molecules, clusters and defects studied by first-principles Green s function methods arxiv:cond-mat/65248v [cond-mat.mtrl-sci] May 26 Murilo L. Tiago (a) and James R. Chelikowsky
Lecture 4: Hartree-Fock Theory
Lecture 4: Hartree-Fock Theory One determinant to rule them all, One determinant to find them, One determinant to bring them all and in the darkness bind them Second quantization rehearsal The formalism
DFT 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
Ab initio Electronic Structure
Ab initio Electronic Structure M. Alouani IPCMS, UMR 7504, Université Louis Pasteur, Strasbourg France http://www-ipcms.u-strasbg.fr In coll. with: B. Arnaud, O. Bengone, Y. Dappe, and S. Lebègue 1965
Generator coordinate method in time-dependent density-functional theory: Memory made simple
THE JOURNAL OF CHEMICAL PHYSICS 127, 124101 2007 Generator coordinate method in time-dependent density-functional theory: Memory made simple E. Orestes Departamento de Química e Física Molecular, Instituto
Second-order Kohn-Sham perturbation theory: Correlation potential for atoms in a cavity
THE JOURNAL OF CHEMICAL PHYSICS 123, 224102 2005 Second-order Kohn-Sham perturbation theory: Correlation potential for atoms in a cavity Hong Jiang and Eberhard Engel a Center for Scientific Computing,
Optical properties of nanostructures from time-dependent density functional theory
Optical properties of nanostructures from time-dependent density functional theory Alberto Castro Departamento de Física Teórica, Universidad de Valladolid, E-47011 Valladolid (Spain) and Donostia International