Electronic structure theory: Fundamentals to frontiers. 2. Density functional theory
|
|
|
- Winfred Allen
- 5 years ago
- Views:
Transcription
1 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 National Laboratory Berkeley CA 94720, USA
2 Outline 1. Basics 2. Limitations of standard functionals 3. Range-separated functionals
3 Branches of the family tree Wavefunction-based electronic structure theory: Minimize the energy by varying the wavefunction Tremendously complicated unknown function:! =!( r! 1, r! 2,..., r )! n Modeling the wavefunction yields model chemistries Density functional theory ( ) The unknown is very simple:! =! r! Hohenberg-Kohn theorem guarantees that: E = E! r! True functional is unknown and probably unknowable Modeling the functional gives DFT model chemistries. { ( )}
4 A brief overview of density functional theory First Hohenberg-Kohn theorem (1965): 1:1 mapping between ground state electron densities and Hamiltonians. Proof by contradiction: let H 1 and H 2 have the same ρ(r) E 1! 2 Use Ψ 2 as trial function in H 1 problem Use Ψ 1 as trial function in H 2 problem E { 1! } 2 =! ˆ 2 T + V ˆ! 2 + v 1 " E { 2! } 1 =! ˆ 1 T + Vˆ ee! 1 + v 2 " { } > E 1 E { 2! } 1 > E 2 # dr >! ˆ 1 T + V ˆ! 1 + # v 1 " dr # dr >! ˆ 2 T + Vˆ ee! 2 + # v 2 " dr Contradiction:! 2 ˆ T + ˆ V ee! 2 >! 1 ˆ T + ˆ V ee! 1! 1 ˆ T + ˆ V ee! 1 >! 2 ˆ T + ˆ V ee! 2
5 A brief overview of density functional theory First Hohenberg-Kohn theorem (1965): 1:1 mapping between ground state electron densities and Hamiltonians. Ground state energy E is determined directly from the Hamiltonian Hence E is given in terms of the density, ρ(r). A formal construction exists for the exact functional, E = E! r! Constrained search over all wavefunctions yielding ρ(r) (!!!) So, in practice the functional must be modeled. { ( )} Given a functional, and an external potential (nuclear field) ρ(r) is found by minimizing over allowed densities.
6 Construction of model density functionals To model kinetic, exchange, correlation functionals 1A) Find a model problem where the functional can be obtained H atom? Uniform electron gas? 1B) Assume a form for the functional and fix the parameters by Known exact conditions (e.g. get model problems right) Minimizing the errors on known data
7 2) Transfer the functional to problems of interest Test, test, test. If validation is encouraging enough, predict In one of your problems, you will extract the kinetic energy functional that solves the uniform electron gas problem. It is not much more difficult to extract the corresponding exchange functional. These are the main ingredients of the Thomas-Fermi model which is a Hohenberg-Kohn density functional.
8 Kohn-Sham density functional theory Largest (unknown) energy contribution is the kinetic energy. No satisfactory kinetic energy functional yet exists. Kohn-Sham framework (a beautiful sidestep): Use the kinetic energy of a non-interacting system with the same electron density (a Hartree-Fock type wavefunction). Leaves exchange and electron correlation (XC) to specify. Kohn-Sham computational cost: similar to Hartree-Fock. Still cheap enough to apply to large systems.
9 Modern Kohn-Sham density functionals Local density approximation (LDA): 1960 s, 1970 s Functional depends only on the density at each point, ρ(r) LDA overbinds as much as Hartree-Fock (mean field) underbinds! Generalized gradient approximations (GGA s): 1988 Functional depends on density ρ(r) and its gradients at each r Greatly improved results! 4-6 kcal/mol error for BLYP, PBE etc. Exact exchange mixing (adiabatic connection): 1992 Mix some Hartree-Fock exchange with GGA s (Becke) Best yet! 2-3 kcal/mol error for B3LYP
10 Classes of Kohn-Sham density functionals Local spin density approx 1966 E XC = { ( )} " dr! XC # r Example: SVWN G3/99 test set Generalized gradient approx 1985 E XC = " dr! XC #( r),$# r Example: BLYP { ( )} Hybrid density functionals 1993 Wave function exchange Example: B3LYP 223 atomization energies Mean abs errors (kcal/mol)
11 Multiple choice questions. In Kohn-Sham DFT, which energy contribution is not strictly a functional of the electron density? (a) electron-nuclear attraction (b) exchange-correlation (c) kinetic energy Which of the following properties is obeyed by B3LYP? (a) variationality (b) exact for the uniform electron gas (c) exact for 1-electron systems (d) size-consistency
12 Outline 1. Basics 2. Limitations of standard functionals 3. Range-separated functionals
13 Challenges for density functionals Accuracy: lack of systematic improvability confronts (1) Limitations of the exchange functional Self-interaction (2) Limitations of the correlation functional London forces Strong correlations
14 B3LYP dissociation of H 2 + (0.65Å to 3Å) 0 relative energy (kcal/mol) HF B3LYP 0.65Å 3Å
15 B3LYP dissociation of H 2 + (3Å to 13Å) 0 relative energy (kcal/mol) HF B3LYP 3Å 13Å
16 Alkali halide dissociation curves B3LYP products have fractional charges -- due to electronegativity difference
17 Charge transfer states in time-dependent DFT! CT ( r) " IP ZnBC + EA BC # 1 / R " 2.7eV BLYP/6-31G* CT states are too low & lack Coulomb attraction!
18 Importance of long-range exact exchange Ground state potential energy surfaces Diatomic cation dissociation problem (H 2+, Ar 2+, etc) Barrier height problems: generally too low Electrons tend to be too delocalized Charge-transfer excited states D-A Coulomb attraction is missing! Magnitude of CT states is greatly underestimated Contaminates the TDDFT spectrum of large molecules
19 Reducing self-interaction: Range-separation long-range exchange via erf(ωr) erf(ωr): long-range. Do exactly. erfc(ωr): short-range. Do GGA. 1 r 12 = erfc(! r 12 ) r 12 + erf (! r 12 ) r 12 Key contributions: Savin (1996): concept Gill et al (1996): solved short-range LSDA exchange Hirao et al (2001): long-range corrected (LC) functional Handy, Gerber & Angyan, Scuseria, Perdew, Yang, One can view this as justified within a generalized Kohn-Sham framework, or via adiabatic connection.
20 Dispersive effects: e.g. supramolecular interactions fullerene-porphyrin dimer binding is 31 kcal/mol GGA s give little or no binding energy Y. Jung, MHG, Phys. Chem. Chem. Phys. 8, 2831 (2006)
21 Recovering Van der Waals interactions: Empirical dispersion (-D) corrections Additional non-local correlation energy contribution: E disp =! atoms ij C 6 " f damp R ij i< j R ij 6 ( ) C 6 ij = C i j 6 C 6 f damp = " # 1+ a(r ij / R r )!12 C 6 i are atomic C 6 factors; f damps at short-range Greatly improves dispersion-dominated interactions: R. Ahlrichs, R. Penco, G. Scoles, Chem. Phys. 19, 119 (1977) Q. Wu and W.T. Yang, J. Chem. Phys. 116, 515 (2002) S. Grimme, J. Comput. Chem. 25, 1463 (2004); 27, 1787 (2006) Not actually a density functional, but... Computationally free Physically reasonable (but double counting problem)!1 $ %
22 Recovering Van der Waals interactions: Double hybrid functionals (assigned paper) Gorling-Levy perturbation theory motivates mixing 2nd order perturbation theory (for correlation) with semilocal correlation functionals... Physically, PT2 includes non-local long-range correlation that is missing in semilocal functionals... But, there is again a double counting problem...
23 Strongly correlated molecules Cope rearrangement Oxygen-evolving complex: Mn4O4
24 No easy answers for strong correlations... Either requires a tremendously powerful correlation functional, or,... lies beyond generalized Kohn-Sham theory. For instance using a multi-configuration reference wave-function... While this is an important challenge, it is one that is not yet satisfactorily answered today...
25 Outline 1. Basics 2. Limitations of standard functionals 3. Range-separated functionals
26 Functional ingredients... and parameters... B97 XC density functional: 12 linear parameters (M=4) E B97 =! LSDA dr " # M ( j =0 c j # $ % ( ) f s # 2 s! = "#! / #! 4 /3 Long-range exact exchange: 1 non-linear parameter (ω) E X LR! HF =! 1 2 % ij dr 1 " # i r 1 ( )# j r 1 & ' j erf ( $r ( ) dr 12 ) 2 " # i ( r 2 )# j r 2 r 12 ( ) Short-range exact exchange: 1 linear parameter (cx) E X SR! HF =! c X 2 % ij dr 1 " # i r 1 ( )# j r 1 erfc ( $r ( ) dr 12 ) 2 " # i ( r 2 )# j r 2 r 12 ( )
27 2 types of non-local correlation corrections Empirical atom-atom dispersion (-D): 1 parameter (a) E disp =! atoms ij C 6 " f damp R ij i< j R ij 6 ( ) C 6 ij = C i j 6 C 6 f damp = " # 1+ a(r ij / R r )!12 Similar to R. Ahlrichs, W.T. Yang, S. Grimme... Computational cost is zero, but not a density functional!1 $ % Or: Double hybrid perturbation theory: 2 parameters E PT 2 = c OS E (2) OS + c SS E SS (2) Includes effect of unoccupied orbitals Significantly more computational expense
28 4 long-range corrected B97 functionals (Jeng-Da Chai) ωb97: 100% long-range exact exchange (13 parameters)! E B97 LR" XC = E HF SR" X + E B97 B97 X + E C ωb97x: adds some short-range exact exchange (14)! B97 E X LR" XC = E HF SR" X + c X E HF SR" X + E B97 B97 X + E C ωb97x-d: adds empirical dispersion (15)! B97 X " E D LR" XC = E HF SR" X + c X E HF SR" X + E B97 X + E B97 disp C + E C ωb97x-2: adds non-local second order correlation (16)! B97 X E "2 LR" XC = E HF SR" X + c X E HF SR" X + E B97 X + E B97 PT 2 C + E C
29 Why must these functionals be trained? All parameters should be determined self-consistently... subject to constraints that preserve the LDA limit hence cannot adopt existing B97 values For ωb97 and ωb97x: GGA parameters: short-range exchange; semi-local correlation Range separator: compromise across problems of interest For ωb97x-d: Additionally minimize the correlation double-counting error
30 Training set: 412 data points (Jeng-Da Chai) Bond-breaking energies: G3/99 dataset (296) Curtiss, Raghavachari, Redfern, Pople, JCP 112, 7374 (2000) Barrier heights for simple chemical reactions (76) Zhao, Truhlar et al, JPC A 108, 2715 (2005), 109, 2012 (2006) Non-covalent interactions (22) Jurecka, Sponer, Cerny, Hobza, PCCP 8, 1985 (2006) Absolute atomic energies (18) Chakravorty, Gwaltney, Davidson, Parpia, Fischer, PR A 47, 3649 (1993)
31 Comparison of optimizable functionals: All trained identically (Jeng-Da Chai) HCTH*: 12 parameter GGA (like ωb97 with ω=0) B97*: 13 parameter hybrid (like ωb97x with ω=0) ωb97: 13 parameter range-separated. ω opt =0.4 ωb97x: 14 parameter range-separated hybrid ω opt =0.3, c X =0.16 ωb97x-d: 15 parameter, with dispersion ω opt = 0.2, c X = 0.22 All are exact for the uniform electron gas (constraints)... What is the value of range separation? And dispersion?
32 223 G3/99 atomization energies (Jeng-Da Chai) Training set data range-separated family hybrid GGA
33 38 non-hydrogen transfer barriers (Jeng-Da Chai) Training set data range-separated family hybrid GGA
34 22 intermolecular interactions (Jeng-Da Chai) Training set data range-separated family hybrid GGA
35 Test performance for energies (Jeng-Da Chai) Test set data
36 Alanine tetrapeptide conformational energies Compare against basis set limit MP2 27 conformations Calculations by Daniel Lambrecht
37 Conclusions and open issues For molecular problems, particularly where selfinteraction is significant, range-separated functionals are a significant improvement over hybrids ωb97, ωb97x, and ωb97x-d are widely useful though significant weaknesses remain... and further testing & comparison is desirable (e.g. vs M06) Challenges include strong correlation (unresolved) can self-interaction can be further reduced? increased exact exchange degrades performance for metals *
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
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
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,
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
Combining 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
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
Density 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
Module 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
Methods for van der Waals Interactions
Methods for van der Waals Interactions Alexandre Tkatchenko Theory Department, Fritz Haber Institut der MPG Berlin, Germany tkatchen@fhi berlin.mpg.de Haber Institute FHI DFT and Beyond Workshop, Jul.
Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory
Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory Title Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections Permalink https://escholarship.org/uc/item/8559x299
Electronic structure theory: Fundamentals to frontiers. 1. Hartree-Fock theory
Electronic structure theory: Fundamentals to frontiers. 1. Hartree-Fock theory MARTIN HEAD-GORDON, Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National
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
Density 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
Advanced 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
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
Combining 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
Advanced Electronic Structure Theory Density functional theory. Dr Fred Manby
Advanced Electronic Structure Theory Density functional theory Dr Fred Manby fred.manby@bris.ac.uk http://www.chm.bris.ac.uk/pt/manby/ 6 Strengths of DFT DFT is one of many theories used by (computational)
Applications: Molecular crystals Graphite MgO(001)/CO MIL-53(Al) 2
Bartolomeo Civalleri Voice: Loredana Valenzano B3LYP augmented with an empirical dispersion term (B3LYP-D*) as applied to solids Università di Torino Dipartimento di Chimica IFM & NIS Torino - MSSC2009-10/09/09
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
Extending 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
Role 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
XYZ 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
Intermediate 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
Molecular 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
Computational 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
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
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,...)
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
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
GEM4 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
DFT: 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,
Session 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
Introduction 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
Accurate van der Waals interactions from ground state electron density
Accurate van der Waals interactions from ground state electron density Alexandre Tkatchenko Theory Department, Fritz Haber Institut der MPG Berlin, Germany tkatchen@fhi berlin.mpg.de Haber Institute EXCITCM09,
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
Non-covalent force fields computed ab initio
Non-covalent force fields computed ab initio Supermolecule calculations Symmetry-adapted perturbation theory (SAPT) Supermolecule calculations Requirements: E = E AB E A E B. Include electron correlation,
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
Range-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
Study 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
5/27/2012. Role of van der Waals Interactions in Physics, Chemistry, and Biology
Role of van der Waals Interactions in Physics, Chemistry, and Biology 1 Role of van der Waals Interactions in Physics, Chemistry, and Biology Karin Jacobs: Take van der Waals forces into account in theory,
Intermolecular Forces in Density Functional Theory
Intermolecular Forces in Density Functional Theory Problems of DFT Peter Pulay at WATOC2005: There are 3 problems with DFT 1. Accuracy does not converge 2. Spin states of open shell systems often incorrect
Self-consistent implementation of meta-gga exchange-correlation functionals within the ONETEP linear-scaling DFT code
Self-consistent implementation of meta-gga exchange-correlation functionals within the ONETEP linear-scaling DFT code James C. Womack, Chris-Kriton Skylaris Chemistry, Faculty of Natural & Environmental
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.
Pseudopotentials for hybrid density functionals and SCAN
Pseudopotentials for hybrid density functionals and SCAN Jing Yang, Liang Z. Tan, Julian Gebhardt, and Andrew M. Rappe Department of Chemistry University of Pennsylvania Why do we need pseudopotentials?
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
DFT: 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
Dispersion Interactions from the Exchange-Hole Dipole Moment
Dispersion Interactions from the Exchange-Hole Dipole Moment Erin R. Johnson and Alberto Otero-de-la-Roza Chemistry and Chemical Biology, University of California, Merced E. R. Johnson (UC Merced) Dispersion
MO Calculation for a Diatomic Molecule. /4 0 ) i=1 j>i (1/r ij )
MO Calculation for a Diatomic Molecule Introduction The properties of any molecular system can in principle be found by looking at the solutions to the corresponding time independent Schrodinger equation
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
Basics of DFT. Kieron Burke and Lucas Wagner. Departments of Physics and of Chemistry, University of California, Irvine, CA 92697, USA
Basics of 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) Basics of DFT Lausanne12 1
Adiabatic-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,
DFT 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
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
Importing 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
The 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,
The 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
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
One-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
Short 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
ABC of ground-state DFT
ABC 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) ABC of ground-state
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
QUANTUM 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
CHEM6085: 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
Introduction to Computational Chemistry Computational (chemistry education) and/or. (Computational chemistry) education
Introduction to Computational Chemistry Computational (chemistry education) and/or (Computational chemistry) education First one: Use computational tools to help increase student understanding of material
Random-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
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
Adiabatic connections in DFT
Adiabatic connections in DFT Andreas Savin Torino, LCC2004, September 9, 2004 Multi reference DFT Kohn Sham: single reference Variable reference space capability to approach the exact result Overview The
CHEM6085: 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
Computational Chemistry. An Introduction to Molecular Dynamic Simulations
Computational Chemistry An Introduction to Molecular Dynamic Simulations Computational chemistry simulates chemical structures and reactions numerically, based in full or in part on the fundamental laws
Spring College on Computational Nanoscience
2145-29 Spring College on Computational Nanoscience 17-28 May 2010 At the Fifth Rung of Jacob's Ladder: A Discussion of Exact Exchange plus Local- and Nonlocal-density Approximations to the Correlation
Orbital 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
Self-consistent implementation of meta-gga exchange-correlation functionals within the ONETEP linear-scaling DFT code
Self-consistent implementation of meta-gga exchange-correlation functionals within the linear-scaling DFT code, August 2016 James C. Womack,1 Narbe Mardirossian,2 Martin Head-Gordon,2,3 Chris-Kriton Skylaris1
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:
THE JOURNAL OF CHEMICAL PHYSICS 127,
THE JOUNAL OF CHEMICAL PHYSICS 127, 214103 2007 Avoiding singularity problems associated with meta-gga generalized gradient approximation exchange and correlation functionals containing the kinetic energy
Density functional theory (DFT) has revolutionized the role
Doubly hybrid density functional for accurate descriptions of nonbond interactions, thermochemistry, and thermochemical kinetics Ying Zhang a, Xin Xu a,1, and William A. Goddard III b,1 a Department of
Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations
1554 J. Phys. Chem. A 2007, 111, 1554-1561 Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations Gang Zhang and Charles B. Musgrave* Department of Chemical Engineering, Stanford UniVersity,
Assessment of Density Functional Methods for Exciton. Binding Energies and Related Optoelectronic Properties
Assessment of Density Functional Methods for Exciton Binding Energies and Related Optoelectronic Properties Jui-Che Lee, Jeng-Da Chai* and Shiang-Tai Lin* Department of Chemical Engineering, National Taiwan
Q-Chem 4.0: Expanding the Frontiers. Jing Kong Q-Chem Inc. Pittsburgh, PA
Q-Chem 4.0: Expanding the Frontiers Jing Kong Q-Chem Inc. Pittsburgh, PA Q-Chem: Profile Q-Chem is a high performance quantum chemistry program; Contributed by best quantum chemists from 40 universities
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
Additional 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,
Adiabatic 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,
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
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
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
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
Density 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
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
An 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
Dispersion Correcting Atom Centered Potentials (DCACP) and Many-Body Dispersion (MBD) contributions to interatomic vdw forces
Dispersion Correcting Atom Centered Potentials (DCACP) and Many-Body Dispersion (MBD) contributions to interatomic vdw forces O. Anatole von Lilienfeld Current: Argonne Leadership Computing Facility From
Ab initio calculations for potential energy surfaces. D. Talbi GRAAL- Montpellier
Ab initio calculations for potential energy surfaces D. Talbi GRAAL- Montpellier A theoretical study of a reaction is a two step process I-Electronic calculations : techniques of quantum chemistry potential
High-level Quantum Chemistry Methods and Benchmark Datasets for Molecules
High-level Quantum Chemistry Methods and Benchmark Datasets for Molecules Markus Schneider Fritz Haber Institute of the MPS, Berlin, Germany École Polytechnique Fédérale de Lausanne, Switzerland دانشگاه
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.
Ab-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,
Electronic 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,
The 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
DFT augmented with an empirical dispersion term as applied to solids Bartolomeo Civalleri
MSSC2011 - Ab initio Modelling in Solid State Chemistry Torino, 05/09/2011 1 DFT augmented with an empirical dispersion term as applied to solids Bartolomeo Civalleri Theoretical Chemistry Group Department
Short 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
Introduction 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
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,