Adiabatic connections in DFT
|
|
- Sophie Warren
- 5 years ago
- Views:
Transcription
1 Adiabatic connections in DFT Andreas Savin Torino, LCC2004, September 9, 2004
2 Multi reference DFT Kohn Sham: single reference Variable reference space capability to approach the exact result
3 Overview The problem Adiabatic connections in DFT Modified Hamiltonian Approximations An exact energy/particle ε x c
4 Overview The problem
5 Correlation energies in atomic series E c in the He (N 2) and Be series (N 4) E c Z He series: lim Z E c Z 0 Be series: lim Z E c Z 1
6 Difficulties with DFAs in atomic series DFA: density functional approximation DFAs transfer correlation from one system to another: do not describe both behaviors Perdew, McMullen, Zunger : LDA gives log Z
7 Difficulties with DFAs in atomic series DFAs transfer correlation from one system to another: do not describe both behaviors Solution (?) MBA describes near degeneracy, if present DFA describes the rest (He series type of behavior) MBA: many body approximation DFA: density functional approximation
8 An analogy Quantum Monte Carlo experience for Be,... 2 s 2 and 2 p 2 configurations Jastrow factor
9 A problem with exact Kohn Sham Identifying states (KS peculiar with quasi degeneracy) Be series C 2 at R e... Gritsenko, Baerends
10 A problem with exact Kohn Sham Identifying states (KS peculiar with quasi degeneracy) Kohn Sham ε 2 p ε 2 s in the Be series Ε p Ε s F. Colonna; also Kohn, Ullrich or Morrison Z
11 A problem with exact Kohn Sham Identifying states (KS peculiar with quasi degeneracy) States are easily identified in MBAs
12 Combining MBAs with DFAs Status of standard approximations MBAs too heavy when accurate. DFAs don t work for strongly correlated systems Objective Compromise with simple many body treatment (MBAs), density functional approximations (DFAs)
13 Combining MBAs with DFAs MBA DFA near degeneracy dynamic correlation
14 Overview The problem Adiabatic connections in DFT
15 Adiabatic connections in DFT = connections between the Kohn Sham and the physical system Kohn Sham system non interacting fermions physical ground state density Physical system electronic Schrödinger equation
16 Adiabatic connections in DFT Connection Hamiltonian changes along the path: MB effects progressively switched on
17 Adiabatic connections in DFT Connection Hamiltonian changes along the path: MB effects progressively switched on Connections Multiplicity of paths
18 Adiabatic connections in DFT DFT= Density Functional Theory Density functional corrects model energy to yield the physical one
19 Adiabatic connections in DFT Adiabatic DFT: ground state does not change along the path State following?
20 Adiabatic connections in DFT Adiabatic DFT: ground state does not change along the path
21 Choice of the intermediate system Mathematically Choice of the Hamiltonian Physically What is transferable? Short range (?) High lying states (?)
22 Adiabatic connections in DFT Moving from a pure DFA to a pure MBA, systematically series of approximations understanding what DFT does
23 Adiabatic connections in DFT: History Understand E xc Harris,Jones Langreth,Perdew Gunnarsson, Lundqvist Construct E xc Becke (hybrid functionals) Seidl (interpolation) Multiplicity of paths Yang
24 Acknowledgement F. Colonna (Paris) H. J. Flad (Leipzig) P. Gori Giorgi (Paris) T. Leininger (Toulouse) R. Pollet (Paris) H. Stoll (Stuttgart) J. Toulouse (Paris)
25 Acknowledgement János Ángyán (Nancy) Iann Gerber (Nancy) H. J. Jensen (Odensee) J. Pedersen (Odensee) C. Gutle (Paris) J. Rey (Paris)
26 Acknowledgement MOLPRO (modifications by J. Ángyán, F. Colonna, I. Gerber, Th. Leininger, H. Stoll, J. Toulouse, H. J. Werner) CASDI (D. Maynau) Service programs (F. Colonna) Mathematica DALTON (J. Pedersen, H. J. Jensen)
27 Overview The problem Adiabatic connections in DFT Modified Hamiltonian
28 Modified Hamiltonian Ground state energy expression Traditional way E min T V ne V ee
29 Modified Hamiltonian Ground state energy expression Traditional way E min T V ne V ee Kohn Sham E min T V ne 0 n
30 Modified Hamiltonian Ground state energy expression Traditional way E min T V ne V ee Kohn Sham E min T V ne 0 n Kohn Sham extensions E min T V ne W W n
31 Modified Hamiltonian Ground state energy expression Traditional way E min T V ne V ee Kohn Sham E min T V ne 0 n Kohn Sham extensions E min T V ne W W n W i j w r i, r j 0, or V ee special cases
32 Modified Hamiltonian Ground state energy expression E min T V ne W W n
33 Parametric dependence of W E min T V ne W W n W: dependence on parameter Μ Infinity of choices of w W W Μ i j w r, r ; Μ Limiting cases Limit Μ W W n Kohn Sham 0 0 n physical V ee 0
34 A choice for the e e interaction w r, r ; Μ w erf Μ r r r r Limits: w Μ 0 0 w Μ w Μ 1 r r w erf Μ r r Μ Μ 1 Μ r
35 A choice for the e e interaction w r, r ; Μ w erf Μ r r r r Remaining effects ("1 r r w") via W n Better with DFA?
36 Short range/long range separation Long history... Uniform electron gas (e.g., Nozières, Pines) Hanke, Kohn (unpublished) + H. Stoll (correlation) + H. J. Flad
37 Choosing W w erf Μ r r r r connects KS with physical system easy to implement uniform electron gas molecular integrals (GTOs) systematic improvement
38 Overview The problem Adiabatic connections in DFT Modified Hamiltonian Approximations
39 Approximations? E min T V ne W W n Exact: accurate, but very heavy, calculations possible. W n : approximations needed MBA: can be accurate, for certain W, without considerable effort
40 MBA: expansion of Errors due to expansion in terms of, as a function of Μ, for Be E s2s 1s2s2p 1s2s2p3s 1s2s3p3s3p Μ Errors increase with Μ (no error for Μ=0)
41 DFAs W n W n must be approximated Same type of approximations as in Kohn Sham
42 Splitting W n E min T V ne W W n Coulomb (classical) 1 2 n r n r 1 r r w Exchange correlation W Exc n
43 Splitting W n Coulomb (classical) Exchange correlation W Exc n Exchange W Ex n Correlation W Ec n
44 Splitting W n : Relative contributions No systematic approximations for n in Kohn Sham Μ 0 W n 0 as Μ E. n W n : accurate results (Be) U n W n E c n E x n 5 10 Μ
45 Errors due to Μ LDA (Be) Exchange energy, E W x n Correlation energy, E W c n E x LDA Μ E c LDA Μ Errors decrease with Μ
46 Why is Μ LDA good at large Μ? E W x a local functional (exact result, no double counting, no self interaction) E W x n Μ 2 Π 8 n 2 r d 3 r Μ 4 3 Π 48 n n 2 Τ... 8 n (closed shell)
47 Why is Μ LDA good at large Μ? E W x a local functional (exact result, no double counting, no self interaction) E W x n Μ 2 Π 8 n 2 r d 3 r Μ 4 3 Π 48 n n 2 Τ... 8 n E W c depends on the on top pair density, P 2 r, r (well approximated by LDA, Perdew, et al.) E W c n Μ 2 Π 2 P 2 r, r n r 2 2 d 3 r Μ 3 2 Π 3 P 2 r, r d 3 r
48 W Ec n Μ 2 Π 2 P 2 r, r 1 2 n r 2 d 3 r +... E W c n, Μ 2 Π 2 P 2 r, r 1 2 n r 2 d 3 r (CI,.., LDA, very accurate) Ec He Μ
49 E x : expansion in Μ, validity of Μ LDA 0 He -0.2 Ex Μ Μ LDA accurate
50 E x : expansion in Μ, validity of Μ LDA 0 Be Ex Μ Μ LDA accurate
51 E c : expansion in Μ, validity of Μ LDA 0 He Ec Μ Μ LDA accurate
52 E c : expansion in Μ, validity of Μ LDA 0 Be Ec Μ Μ LDA accurate
53 River in Stølsheimen
54 Error in E xc n, Be E xc LDA GEA PBE Μ
55 Total energy, in Μ LDA: E(Μ)
56 E(Μ): different expansions Etot s2s 1s2s2p 1s2s2p3s 1s2s2p3s3p Μ
57 E(Μ): different expansions Μ LDA Μ PBE Etot Etot s2s 1s2s2p 1s2s2p3s 1s2s2p3s3p s2s 1s2s2p 1s2s2p3s 1s2s2p3s3p Μ Μ
58 Overview The problem Adiabatic connections in DFT Modified Hamiltonian Approximations An exact energy/particle ε x c
59 An exact energy/particle ε x c No unique definition Local Μ
60 ε c with global Μ=0.2 Be ε c Μ r
61 ε c with global Μ=0.2 and Μ dependent on n r and n r Be ε c Μ r
62 Summary
63 Summary W Μ : Kohn Sham physical system w erf Μ r r Μ Μ 1 Μ r
64 Summary W Μ : Kohn Sham physical system Effect: MBA and a better transferable DF Etot 1s2s2p Μ Large error in n compromise Large error in expansion
65 Summary W Μ : Kohn Sham physical system Effect: MBA and a better transferable DF ε: a tool for locally checking DFAs ε c Μ r
66 E(R), scaled: Μ LDA van der Waals dimers János Ángyán, Iann Gerber
Long-range/short-range energy decomposition in density functional theory
p. 1/2 Long-range/short-range energy decomposition in density functional theory Julien Toulouse François Colonna, Andreas Savin Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, Paris
More informationJULIEN TOULOUSE, PAOLA GORI-GIORGI, ANDREAS SAVIN
Scaling Relations, Virial Theorem, and Energy Densities for Long-Range and Short-Range Density Functionals JULIEN TOULOUSE, PAOLA GORI-GIORGI, ANDREAS SAVIN Laboratoire de Chimie Théorique, CNRS et Université
More informationCombining density-functional theory and many-body methods
Combining density-functional theory and many-body methods Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France Vrije Universiteit Amsterdam, Netherlands November 2017 Outline 2/23 1
More informationThéorie de la fonctionnnelle de la densité avec séparation de portée pour les forces de van der Waals
Théorie de la fonctionnnelle de la densité avec séparation de portée pour les forces de van der Waals Julien Toulouse 1 Iann Gerber 2, Georg Jansen 3, Andreas Savin 1, János Ángyán 4 1 Laboratoire de Chimie
More informationDensity-functional theory at noninteger electron numbers
Density-functional theory at noninteger electron numbers Tim Gould 1, Julien Toulouse 2 1 Griffith University, Brisbane, Australia 2 Université Pierre & Marie Curie and CRS, Paris, France July 215 Introduction
More informationDFT basée sur le théorème de fluctuation-dissipation avec séparation de portée pour les interactions de van der Waals
DFT basée sur le théorème de fluctuation-dissipation avec séparation de portée pour les interactions de van der Waals Julien Toulouse 1 Iann Gerber 2, Georg Jansen 3, Andreas Savin 1, János Ángyán 4 1
More informationRange-separated density-functional theory with long-range random phase approximation
Range-separated density-functional theory with long-range random phase approximation Julien Toulouse 1 Wuming Zhu 1, Andreas Savin 1, János Ángyán2 1 Laboratoire de Chimie Théorique, UPMC Univ Paris 6
More informationCombining density-functional theory and many-body methods
Combining density-functional theory and many-body methods Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France Albuquerque New Mexico, USA June 2016 Outline 2/23 1 A brief overview of
More informationModel Hamiltonians in Density Functional Theory
Centre de Recherches Mathématiques CRM Proceedings and Lecture Notes Volume 41, 2006 Model Hamiltonians in Density Functional Theory Paola Gori-Giorgi, Julien Toulouse, and Andreas Savin Abstract. The
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 informationarxiv:cond-mat/ v1 13 Nov 2006
Kohn-Sham calculations combined with an average pair-density functional theory Paola Gori-Giorgi and Andreas Savin Laboratoire de Chimie Théorique, CNRS UMR7616, Université Pierre et Marie Curie, 4 Place
More informationExchange correlation potentials and local energies per particle along nonlinear adiabatic connections
Molecular Physics, Vol. 13, No. 2, 2 October 25, 2725 2734 Ehange correlation potentials and local energies per particle along nonlinear adiabatic connections JULIEN TOULOUSE, FRANC OIS COLONNA and ANDREAS
More informationvan der Waals forces in density functional theory: Perturbational long-range electron-interaction corrections
van der Waals forces in density functional theory: Perturbational long-range electron-interaction corrections János G. Ángyán and Iann C. Gerber Laboratoire de Cristallographie et de Modélisation des Matériaux
More informationElectronic structure theory: Fundamentals to frontiers. 2. Density functional theory
Electronic structure theory: Fundamentals to frontiers. 2. Density functional theory MARTIN HEAD-GORDON, Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley
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 informationAdiabatic-connection fluctuation-dissipation density-functional theory based on range separation
Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation Julien Toulouse 1 I. Gerber 2, G. Jansen 3, A. Savin 1, W. Zhu 1, J. Ángyán 4 1 Laboratoire de Chimie Théorique,
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 informationExtending Kohn-Sham density-functional theory
Extending Kohn-Sham density-functional theory Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France Email: julien.toulouse@upmc.fr Web page: www.lct.jussieu.fr/pagesperso/toulouse/ January
More informationThe calculation of the universal density functional by Lieb maximization
The calculation of the universal density functional by Lieb maximization Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry,
More informationAssessment of range-separated time-dependent density-functional theory for calculating C 6 dispersion coefficients
1/10 Assessment of range-separated time-dependent density-functional theory for calculating C 6 dispersion coefficients Julien Toulouse 1,2, Elisa Rebolini 1, Tim Gould 3, John F. Dobson 3, Prasenjit Seal
More informationIn electronic structure calculations using density
Short-Range Exchange-Correlation Energy of a Uniform Electron Gas with Modified Electron Electron Interaction JULIEN TOULOUSE, ANDREAS SAVIN, HEINZ-JÜRGEN FLAD 2 Laboratoire de Chimie Théorique, CNRS et
More informationImporting ab-initio theory into DFT: Some applications of the Lieb variation principle
Importing ab-initio theory into DFT: Some applications of the Lieb variation principle Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department
More informationShort-range exchange and correlation energy density functionals: Beyond the local-density approximation
THE JOURNAL OF CHEMICAL PHYSICS 122, 014110 2005 Short-range exchange and correlation energy density functionals: Beyond the local-density approximation Julien Toulouse, François Colonna, and Andreas Savin
More informationMultideterminant density-functional theory for static correlation. Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France
Multideterminant density-functional theory for static correlation Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France Basel, Switzerland September 2015 Kohn-Sham DFT and static correlation
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 in the solid state
Density functional theory in the solid state Ari P Seitsonen IMPMC, CNRS & Universités 6 et 7 Paris, IPGP Department of Applied Physics, Helsinki University of Technology Physikalisch-Chemisches Institut
More informationSystem-adapted correlation energy density functionals from effective pair interactions
Philosophical Magazine, Vol. 86, Nos. 17 18, 11 21 June 26, 2643 2659 System-adapted correlation energy density functionals from effective pair interactions P. GORI-GIORGI* and A. SAVIN Laboratoire de
More informationIntermediate DFT. Kieron Burke and Lucas Wagner. Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA
Intermediate DFT Kieron Burke and Lucas Wagner Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA October 10-19th, 2012 Kieron (UC Irvine) Intermediate DFT Lausanne12
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 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 informationXYZ of ground-state DFT
XYZ of ground-state DFT Kieron Burke and Lucas Wagner Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA January 5-9th, 2014 Kieron (UC Irvine) XYZ of ground-state
More informationAdiabatic connection from accurate wave-function calculations
JOURNAL OF CHEMICAL PHYSICS VOLUME 112, NUMBER 12 22 MARCH 2000 Adiabatic connection from accurate wave-function calculations Derek Frydel and William M. Terilla Department of Chemistry, Rutgers University,
More informationShort Course on Density Functional Theory and Applications VII. Hybrid, Range-Separated, and One-shot Functionals
Short Course on Density Functional Theory and Applications VII. Hybrid, Range-Separated, and One-shot Functionals Samuel B. Trickey Sept. 2008 Quantum Theory Project Dept. of Physics and Dept. of Chemistry
More informationarxiv:physics/ v1 [physics.chem-ph] 10 Oct 2004
Long-range/short-range separation of the electron-electron interaction in density functional theory arxiv:physics/4162v1 [physics.chem-ph] 1 Oct 24 Julien Toulouse, François Colonna, and Andreas Savin
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 informationAb-initio studies of the adiabatic connection in density-functional theory
Ab-initio studies of the adiabatic connection in density-functional theory Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry,
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 information3: 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
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 informationAdiabatic 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
More informationRange-separated hybrids
Range-separated hybrids A. Savin MSSC2009 (Torino) Hybrids Wave function (Y) + density functional (n) hybrid E pluribus unum ("Out of many one") : Seal of the USA Overview Components (Y, n) Hybrids (Y
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 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 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 informationElectronic 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 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 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 informationIntroduction 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
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 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 informationRandom-phase approximation and beyond for materials: concepts, practice, and future perspectives. Xinguo Ren
Random-phase approximation and beyond for materials: concepts, practice, and future perspectives Xinguo Ren University of Science and Technology of China, Hefei USTC-FHI workshop on frontiers of Advanced
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 informationAn Approximate DFT Method: The Density-Functional Tight-Binding (DFTB) Method
Fakultät für Mathematik und Naturwissenschaften - Lehrstuhl für Physikalische Chemie I / Theoretische Chemie An Approximate DFT Method: The Density-Functional Tight-Binding (DFTB) Method Jan-Ole Joswig
More informationAnswers Quantum Chemistry NWI-MOL406 G. C. Groenenboom and G. A. de Wijs, HG00.307, 8:30-11:30, 21 jan 2014
Answers Quantum Chemistry NWI-MOL406 G. C. Groenenboom and G. A. de Wijs, HG00.307, 8:30-11:30, 21 jan 2014 Question 1: Basis sets Consider the split valence SV3-21G one electron basis set for formaldehyde
More informationDensity Func,onal Theory (Chapter 6, Jensen)
Chem 580: DFT Density Func,onal Theory (Chapter 6, Jensen) Hohenberg- Kohn Theorem (Phys. Rev., 136,B864 (1964)): For molecules with a non degenerate ground state, the ground state molecular energy and
More informationExchange-Correla.on Func.onals for Chemical
Exchange-Correla.on Func.onals for Chemical Applica.ons from the Strong Coupling Limit of DFT Stefan Vuckovic Theore.cal Chemistry, VU University Amsterdam Density fixed Adiaba.c Connec.on of DFT electron
More information3/23/2010 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
More informationElectronic Structure Calculations and Density Functional Theory
Electronic Structure Calculations and Density Functional Theory Rodolphe Vuilleumier Pôle de chimie théorique Département de chimie de l ENS CNRS Ecole normale supérieure UPMC Formation ModPhyChem Lyon,
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 informationOrbital currents in the Colle-Salvetti correlation energy functional and the degeneracy problem. Abstract
Orbital currents in the Colle-Salvetti correlation energy functional and the degeneracy problem S. Pittalis 1, S. Kurth 1, S. Sharma 1,2 and E.K.U. Gross 1 1 Institut für Theoretische Physik, Freie Universität
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 informationRESEARCH ARTICLE. Excited states from range-separated density-functional perturbation theory
To appear in Molecular Physics Vol. 00, No. 00, Month 200x, 1 15 RESEARCH ARTICLE Excited states from range-separated density-functional perturbation theory Elisa Rebolini 1,2,4, Julien Toulouse 1,2, Andrew
More informationOne-electron Hamiltonians: HF & DFT
MSSC06 Ab initio Modelling in Solid State Chemistry Torino, 4 9/09/06 One-electron Hamiltonians: HF & DFT Bartolomeo Civalleri Department of Chemistry IS Centre of xcellence University of Torino bartolomeo.civalleri@unito.it
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 informationCurriculum Vitae PAOLA GORI-GIORGI 7/1/2011
Curriculum Vitae PAOLA GORI-GIORGI 7/1/2011 Personal details Title(s), first name, surname: Dr. Paola Gori-Giorgi Male/female: female Date and place of birth: 30/04/71 Rome (Italy) Nationality: Italian
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 informationA multiconfigurational hybrid density-functional theory
THE JOURNAL OF CHEMICAL PHYSICS 137, 044104 (01) A multiconfigurational hybrid density-functional theory Kamal Sharkas, 1,,a) Andreas Savin, 1 Hans Jørgen Aa. Jensen, 3 and Julien Toulouse 1,b) 1 Laboratoire
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 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 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 informationDispersion energies from the random-phase approximation with range separation
1/34 Dispersion energies from the random-phase approximation with range separation Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France Web page: www.lct.jussieu.fr/pagesperso/toulouse/
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 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 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 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 informationarxiv: v1 [physics.chem-ph] 24 Jan 2019
Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density Anthony Ferté, Emmanuel Giner, and Julien Toulouse Laboratoire de Chimie
More informationElectrochemistry project, Chemistry Department, November Ab-initio Molecular Dynamics Simulation
Electrochemistry project, Chemistry Department, November 2006 Ab-initio Molecular Dynamics Simulation Outline Introduction Ab-initio concepts Total energy concepts Adsorption energy calculation Project
More informationShort Course on Density Functional Theory and Applications III. Implementations
Short Course on Density Functional Theory and Applications III. Implementations Samuel B. Trickey Sept. 2008 Quantum Theory Project Dept. of Physics and Dept. of Chemistry trickey@qtp.ufl.edu KS E xc and
More informationAN INTRODUCTION TO QUANTUM CHEMISTRY. Mark S. Gordon Iowa State University
AN INTRODUCTION TO QUANTUM CHEMISTRY Mark S. Gordon Iowa State University 1 OUTLINE Theoretical Background in Quantum Chemistry Overview of GAMESS Program Applications 2 QUANTUM CHEMISTRY In principle,
More informationQMC dissociation energy of the water dimer: Time step errors and backflow calculations
QMC dissociation energy of the water dimer: Time step errors and backflow calculations Idoia G. de Gurtubay and Richard J. Needs TCM group. Cavendish Laboratory University of Cambridge Idoia G. de Gurtubay.
More informationBasic Concepts and First Principles Computations for Surface Science: Applications in Chemical Energy Conversion and Storage.
International Summer School on Basic Concepts and First Principles Computations for Surface Science: Applications in Chemical Energy Conversion and Storage Norderney, Germany, July 21 26, 2013 Let s start
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 information1 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
More informationFONCTIONNELLES DE DENSITÉ AVEC SÉPARATION DE PORTÉE: AU CIEL DFT SANS ÉCHELLE DE JACOB
FONCTIONNELLES DE DENSITÉ AVEC SÉPARATION DE PORTÉE: AU CIEL DFT SANS ÉCHELLE DE JACOB, Iann Gerber, Paola Gori-Giorgi, Julien Toulouse, Andreas Savin Équipe de Modélisation Quantique et Cristallographique
More informationIntroduction to DFTB. Marcus Elstner. July 28, 2006
Introduction to DFTB Marcus Elstner July 28, 2006 I. Non-selfconsistent solution of the KS equations DFT can treat up to 100 atoms in routine applications, sometimes even more and about several ps in MD
More informationExact high-density limit of correlation potential for two-electron density
JOURAL OF CHEMICAL PHYSICS VOLUME 0, UMBER JUE 999 Exact high-density limit of correlation potential for two-electron density Stanislav Ivanov a) Department of Chemistry and Quantum Theory Group, Tulane
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 informationAlgorithms and Computational Aspects of DFT Calculations
Algorithms and Computational Aspects of DFT Calculations Part I Juan Meza and Chao Yang High Performance Computing Research Lawrence Berkeley National Laboratory IMA Tutorial Mathematical and Computational
More informationDensity matrix functional theory vis-á-vis density functional theory
Density matrix functional theory vis-á-vis density functional theory 16.4.007 Ryan Requist Oleg Pankratov 1 Introduction Recently, there has been renewed interest in density matrix functional theory (DMFT)
More informationMany 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
More informationQUANTUM CHEMISTRY FOR TRANSITION METALS
QUANTUM CHEMISTRY FOR TRANSITION METALS Outline I Introduction II Correlation Static correlation effects MC methods DFT III Relativity Generalities From 4 to 1 components Effective core potential Outline
More informationOptimization of quantum Monte Carlo wave functions by energy minimization
Optimization of quantum Monte Carlo wave functions by energy minimization Julien Toulouse, Roland Assaraf, Cyrus J. Umrigar Laboratoire de Chimie Théorique, Université Pierre et Marie Curie and CNRS, Paris,
More informationIndependent 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
More informationRole of van der Waals Interactions in Physics, Chemistry, and Biology
Role of van der Waals Interactions in Physics, Chemistry, and Biology How can we describe vdw forces in materials accurately? Failure of DFT Approximations for (Long-Range) Van der Waals Interactions 1
More informationDegeneracy and size consistency in electronic density functional theory
Degeneracy and size consistency in electronic density functional theory Paola Gori-Giorgi and Andreas Savin Laboratoire de Chimie Théorique, CNRS UMR7616 and Université Pierre et Marie Curie, 4 Place Jussieu,
More informationDensity Functional Theory: from theory to Applications
Density Functional Theory: from theory to Applications Uni Mainz November 29, 2010 The self interaction error and its correction Perdew-Zunger SIC Average-density approximation Weighted density approximation
More informationThe adiabatic connection
The adiabatic connection Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, Norway Dipartimento di Scienze
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 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 information