Orbital dependent correlation potentials in ab initio density functional theory
|
|
- Poppy Carpenter
- 6 years ago
- Views:
Transcription
1 Orbital dependent correlation potentials in ab initio density functional theory noniterative - one step - calculations Ireneusz Grabowski Institute of Physics Nicolaus Copernicus University Toruń, Poland OEP Workshop, Berlin March 2005
2 Collaborators: So Hirata Stanislav Ivanov Victor Lotrich Igor Schweigert Rod Bartlett Quantum Theory Project University of Florida, Gainesville, FL
3 Two independent theories of the electronic structure of atoms, molecules and solids. WFT Expensive, but provides results which are quaranteed to converge to the solution of the Schrödinger equation as electron correlation and basis set is extended. MBPT(2) < CCD < CCSD < CCSD(T) < CCSDTQ < FCI DFT Its one particle structure make it possible to treat much larger systems than WFT. Almost all unknown informations are contained in an exchange correlation functional Exc and its associated potential Vxc. In standard formulation parameter dependent
4 Whereas WFT is a constructive theory that provides a prescription for obtaining increasingly more accurate solutions of Schrödinger equation, DFT provides the existence of Exc, but does not provide the energy functional (or even theoretical prescription), nor systematic converging series of approximations to it. Standard LDA, GGA, or hybrid functionals works well in some cases but usually results are unpredictable and it is difficult (or impossible) to improve the functional approximation systematically.
5 Method which could define a rigorious exchangecorrelation functional, potential and orbitals in context of the Kohn-Sham theory: The exploiting in DFT orbital-dependent functionals and potentials OEP method. Ab initio density functional theory From coupled-cluster theory and many-body perturbation theory we derived the local exchangecorrelation potential of DFT in an orbital dependent form. Parameter free It guarantees to converge to the right answer in the correlation and basis set limit, just as does ab initio WFT. Specyfying initially to second-order terms Optimized Effective Potential Method with correlation included - OEP-MBPT(2)-KS, OEP-MBPT(2)-f,...
6 Two different ways to obtain OEP methods with correlation included Functional derivative path Density condition path taking functional derivative General theoretical with respect to density of framework based on the orbital dependent energy density condition in Kohn functional (from ab initio Sham theory involving WFT) to get exchangecorrelation potential in KS many body perturbation coupled cluster method, theory. theory, and technically MBPT(2) level diagramatic manipulation. Problems with extending to higher orders
7 Basic formalism functional derivative path The spin densities ρ σ (r) and KS orbitals {φ pσ (r)} are obtained by a self consistently solving the KS equation: The local exchange-correlation potential is formally defined as the functional derivative of the exchange-correlation energy
8 In the Optimized Effective Potential (OEP) method, the E xc OEP [{φ pσ }] is an explicit functional of spinorbitals, and the spinorbitals are the solutions of the KS equation with a local effective OEP potential, which is determined by the condition that its orbitals be ones that minimize the energy functional: The resulting integral OEP equation have to be solved for the V XC in each KS(OEP) iteration,
9 Formally we can represent V xc as Where X sσ -1 is the inverse of the static KS linear response function of a system of noninteracting particles In the LCAO-OEP procedure, the potential and response function and it inverse are represented in the AO basis.
10 E xc =E x +E c E x - HF exchange energy functional in terms of KS orbitals V x orbital dependent exchage-only OEP potential
11 Orbital dependent OEP DFT correlation functional Energy expression for the second order RS Perturbation Theory OEP-MBPT(2)-KS method I. Grabowski, S. Hirata, S. Ivanov, R. J. Bartlett Ab-initio density functional theory: OEP- MBPT(2) a new orbital-dependent correlation functional.,j. Chem. Phys. 116, 4415 (2002
12
13 Density condition in KS theory & Coupled Cluster theory The KS density by construction is an exact density, then any corrections to the converged KS density introduced by changes in φ i (r) have to vanish. ρ(r)= ρ KS (r)+δρ(r) and δρ(r)=0 The total density from Coupled Cluster (CC) density matrix
14 We can represent CC density using antisymmetrized diagrams
15
16 Equivalence with the OEP-MBPT(2) correlation potential derived from functional derivative path.
17 17
18 For defining our perturbation at the second order level, we have several different choices for the partitioning of the Hamiltonian. OEP MBPT(2) KS H 0 = OEP MBPT(2) f H 0 = + ε p{ p p} OEP MBPT(2) sc p p f pp + { p p} H 0 = f pp{ p p} + fij{ i j} + fab{ a b} p i j a b
19 19 Results We are NOT doing CC calculations or more complicated MBPT(2)! We are doing KS DFT OEP iterations with correctly defined exchange correlation potentials (orbital dependent) In each KS DFT iteration, using one and twoelectron integrals we calculate V XC, Going back with V XC to the KS equation we obtain new set of orbitals and then we can repeat our procedure until self consistency is achieved.
20 Correlation potential of helium 0,04 Correlation potential / a.u. 0,02 0, ,02-0,04-0,06-0,08-0,10 R / a.u. Exact (Umrigar & Gonze) Vosko-Wilk-Nusair correlation potential Lee-Yang-Parr correlation potential KLICS correlation potential OEP-MBPT(2)-KS OEP-MBPT(2)-f
21 21
22 22
23 Correlation potential of neon (Roos-ATZPU basis set) Correlation potential / a.u. 0,32 VWN 0,27 LYP exact correlation potential 0,22 OEP-MBPT(2)SD and D 0,17 OEP-MBPT(2)-SD-f 0,12 0,07 0,02-0, radial charge density -0,08-0,13 R / a.u.
24 0 Exchange-correlation potential of neon (Roos-ATZPU) one step calculations Potential / a.u exchange-correlation OEP-MBPt(2)-f and OEP-MBPT(2) `exchange-only' OEP SVWN BLYP OEP-MBPT(2)-f-1shot-HF -9 R / a.u.
25
26 Correlation potentials of Be atom 0,10 0, Correlation potential / a.u. -0,10-0,20-0,30 OEP-MBPT(2)-f vc exact OEP-MBPT(2)-KS - (non converged) LYP -0,40 VWN -0,50 R / a.u.
27
28 Energy surface of He2 (17s10p2d) 0,002 0,001 E-E / ev -0,001-0, MBPT(2) CCSDT -0,003 OEP-MBPT(2) PBE -0,004 r / au
29 Ne 2 dimer potential energy - AUG-CC-PVTZ basis set 300 Energy[cm -1 ] MP2 CCSD CCSD(T) OEP_MBPT(2)-fsc 5 5,5 6 6,5 7 7, r [a.u]
30 Approximated one step calculations Using exchange-only OEP orbitals we can generate correlation potentials using one step procedure by simply inserting orbitals into an orbital-dependent expression for the correlation potential. We can even do the same one step procedure using HF orbitals, and then generate correlation and exchange correlation potential, without doing any OEP & KS self interaction procedure.
31 Correlation potential of helium 1 step calculations 0,04 0,02 Correlation potential / a.u. 0, ,02-0,04-0,06-0,08-0,10 R / a.u. Exact (Umrigar & Gonze) Vosko-Wilk-Nusair correlation potential Lee-Yang-Parr correlation potential KLICS correlation potential OEP-MBPT(2)SD-f OEP-MBPT(2)-f-SD-1 shot OEP-MBPT(2)-SD-f-1shot-HF
32 Correlation potential of neon 1 step calculations Correlation potential / a.u. 0,32 LYP 0,27 exact correlation potential 0,22 OEP-MBPT(2)-f-SD and D OEP-MBPT(2) -f-sd 1 shot 0,17 OEP-MBPT(2)-f-SD-1 shot HF 0,12 0,07 0,02-0, VWN -0,08-0,13 R / a.u.
33 Correlation potential of magnesium (Roos-ATZPU basis set) 1 step calculations VWN Correlation potential / a.u. 0,13 0,08 0,03-0,02-0,07 LYP OEP-MBPT(2)SD-f OEP-MBPT(2)-f-1 shot OEP-MBPT(2)-f-1 shot - HF 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5-0,12-0,17 r / a.u.
34 Summary Starting from a general theoretical framework based on the density condition in Kohn-Sham theory and coupled cluster theory, we have defined a rigorious exchange-correlation functionals, potentials and orbitals. We have performed an ab initio correlated dft calculations employing the OEP-MBPT(2) exchange and correlation potentials. We show the interconnections between the CC & MBPT approach and DFT. The calculations are fully self-consistent. (Except approximated one step calculations)
35 The OEP-MBPT(2) correlation potentials and the exact correlation potentials are in the excellent agreement with each other, while the standard approximate DFT correlation potentials have a qualitatively wrong behavior. The total energies, and highest occupied orbital energies calculated by OEP-MBPT(2) method are very accurate (CCSD(T) accuracy). With OEP-MBPT(2) method we can treat with almost CCSD(T) accuracy week interactions systems. Our ab initio dft correlation potentials will be instrumental in developing accurate and systematically improvable exchangecorrelation functionals and potentials. The non expensive one step procedure which do not need self consistent process can be very useful in obtaining approximate correlation potentials
36 36 Some negative aspects E xc and V xc are orbital dependent Strong basis set dependency of the LCAO-OEP results Slow convergence in some cases Numerical cost scales as N it n occ2 n 3 virt Exchange and correlation potentials are very complicated they reflects the shell structure, changes in number of particles
37 Ab initio dft (OEP) papers S. Hirata,, S. Ivanov, I. Grabowski, R.J. Bartlett, K. Burke and J. Talman Is an OEP potential determined uniquely? J. Chem. Phys. 115,1635,(2001) I. Grabowski, S. Hirata, S. Ivanov, R. J. Bartlett Ab initio density functional theory: OEP MBPT(2) a new orbital dependent correlation functional., J. Chem. Phys. 116, 4415 (2002) S. Hirata, S. Ivanov, I. Grabowski, R. J. Bartlett Time dependent density functional theory employing optimized effective potentials, J. Chem. Phys. 116, 6468, (2002) S. Ivanov, S. Hirata, I. Grabowski, R. J. Bartlett Connections between Second Order Gorling Levy and Many Body perturbation Approaches in Density Functional Theory. J. Chem. Phys. 118, 461 (2003) R. J. Bartlett, I. Grabowski, S. Hirata, S. Ivanov, The Exchange Correlation Potential in ab initio Density Functional Theory. J. Chem. Phys. 122, (2005) V. Lotrich, I.Grabowski, R.J. Bartlett Intermolecular potential energy surfaces of weakly bound dimers computed from ab initio dft: the right answer for the right reason. Chem. Phys. Lett. xxx, (2004) I. Grabowski, V. Lotrich Acurate orbital dependent correlation and exchangecorrelation potentials from noniterative ab initio dft calculations. Mol. Phys. xxx (2005) S. Hirata, S. Ivanov, R. J. Bartlett, I. Grabowski Exact Exchange time dependent density functional theory for frequency dependent polarizabilities., Phys. Rev. A 71, 1, (2005)
38 38
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
More informationDFT calculations of NMR indirect spin spin coupling constants
DFT calculations of NMR indirect spin spin coupling constants Dalton program system Program capabilities Density functional theory Kohn Sham theory LDA, GGA and hybrid theories Indirect NMR spin spin coupling
More 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 informationUNEDF- PACK FOREST. RODNEY J. BARTLETT Quantum Theory Project, Departments of Chemistry and Physics University of Florida, Gainesville, Florida USA
UNEDF- PACK FOREST Ab-initio dft: The seamless connection with wave-function theory June 25, 2008 RODNEY J. BARTLETT Quantum Theory Project, Departments of Chemistry and Physics University of Florida,
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 informationElectron Correlation - Methods beyond Hartree-Fock
Electron Correlation - Methods beyond Hartree-Fock how to approach chemical accuracy Alexander A. Auer Max-Planck-Institute for Chemical Energy Conversion, Mülheim September 4, 2014 MMER Summerschool 2014
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 informationOslo node. Highly accurate calculations benchmarking and extrapolations
Oslo node Highly accurate calculations benchmarking and extrapolations Torgeir Ruden, with A. Halkier, P. Jørgensen, J. Olsen, W. Klopper, J. Gauss, P. Taylor Explicitly correlated methods Pål Dahle, collaboration
More informationElectron Correlation
Electron Correlation Levels of QM Theory HΨ=EΨ Born-Oppenheimer approximation Nuclear equation: H n Ψ n =E n Ψ n Electronic equation: H e Ψ e =E e Ψ e Single determinant SCF Semi-empirical methods Correlation
More informationTDDFT 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
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 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 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 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 informationIntroduction to Computational Quantum Chemistry: Theory
Introduction to Computational Quantum Chemistry: Theory Dr Andrew Gilbert Rm 118, Craig Building, RSC 3108 Course Lectures 2007 Introduction Hartree Fock Theory Configuration Interaction Lectures 1 Introduction
More informationAb 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
More informationComputational Chemistry I
Computational Chemistry I Text book Cramer: Essentials of Quantum Chemistry, Wiley (2 ed.) Chapter 3. Post Hartree-Fock methods (Cramer: chapter 7) There are many ways to improve the HF method. Most of
More 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 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. 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 informationDensity-functional theory in quantum chemistry. Trygve Helgaker. From Quarks to the Nuclear Many-Body Problem
1 Density-functional theory in quantum chemistry Trygve Helgaker Centre for Theoretical and Computational Chemistry, University of Oslo, Norway From Quarks to the Nuclear Many-Body Problem A conference
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 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 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 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 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 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 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 informationIntroduction to Computational Chemistry
Introduction to Computational Chemistry Vesa Hänninen Laboratory of Physical Chemistry Chemicum 4th floor vesa.hanninen@helsinki.fi September 10, 2013 Lecture 3. Electron correlation methods September
More informationA new generation of density-functional methods based on the adiabatic-connection fluctuation-dissipation theorem
A new generation of density-functional methods based on the adiabatic-connection fluctuation-dissipation theorem Andreas Görling, Patrick Bleiziffer, Daniel Schmidtel, and Andreas Heßelmann Lehrstuhl für
More informationWalter Kohn was awarded with the Nobel Prize in Chemistry in 1998 for his development of the density functional theory.
Walter Kohn was awarded with the Nobel Prize in Chemistry in 1998 for his development of the density functional theory. Walter Kohn receiving his Nobel Prize from His Majesty the King at the Stockholm
More 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 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 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 informationMethods for Treating Electron Correlation CHEM 430
Methods for Treating Electron Correlation CHEM 430 Electron Correlation Energy in the Hartree-Fock approximation, each electron sees the average density of all of the other electrons two electrons cannot
More informationPseudopotentials 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?
More informationIntroduction to Computational Chemistry: Theory
Introduction to Computational Chemistry: Theory Dr Andrew Gilbert Rm 118, Craig Building, RSC andrew.gilbert@anu.edu.au 3023 Course Lectures Introduction Hartree Fock Theory Basis Sets Lecture 1 1 Introduction
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 informationBand calculations: Theory and Applications
Band calculations: Theory and Applications Lecture 2: Different approximations for the exchange-correlation correlation functional in DFT Local density approximation () Generalized gradient approximation
More 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 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 informationAdvanced 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)
More informationIntroduction 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
More informationAb-initio Electronic Structure Calculations β and γ KNO 3 Energetic Materials
ISSN 0974-9373 Vol. 15 No.3 (2011) Journal of International Academy of Physical Sciences pp. 337-344 Ab-initio Electronic Structure Calculations of α, β and γ KNO 3 Energetic Materials Pradeep Jain and
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 informationRecent advances in development of single-point orbital-free kinetic energy functionals
PacifiChem 2010 p. 1/29 Recent advances in development of single-point orbital-free kinetic energy functionals Valentin V. Karasiev vkarasev@qtp.ufl.edu Quantum Theory Project, Departments of Physics and
More informationDensity Functional Theory
Chemistry 380.37 Fall 2015 Dr. Jean M. Standard October 28, 2015 Density Functional Theory What is a Functional? A functional is a general mathematical quantity that represents a rule to convert a function
More informationNWChem: Hartree-Fock, Density Functional Theory, Time-Dependent Density Functional Theory
NWChem: Hartree-Fock, Density Functional Theory, Time-Depent Density Functional Theory Hartree-Fock! Functionality! Input! Wavefunctions! Initial MO vectors! Direct and semidirect algorithms! Convergence,
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 informationBasics 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
More informationIntroduction to Density Functional Theory
Introduction to Density Functional Theory S. Sharma Institut für Physik Karl-Franzens-Universität Graz, Austria 19th October 2005 Synopsis Motivation 1 Motivation : where can one use DFT 2 : 1 Elementary
More 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 informationCoupled-cluster and perturbation methods for macromolecules
Coupled-cluster and perturbation methods for macromolecules So Hirata Quantum Theory Project and MacroCenter Departments of Chemistry & Physics, University of Florida Contents Accurate electronic structure
More informationABC 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
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 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 informationABC 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 July 31, 2014 Kieron (UC Irvine) ABC of ground-state DFT HoW
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 informationDensity functional theory in magnetic fields
Density functional theory in magnetic fields U. E. Ekström, T. Helgaker, S. Kvaal, E. Sagvolden, E. Tellgren, A. M. Teale Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry,
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 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.
More informationWhat correlation eœects are covered by density functional theory?
MOLECULAR PHYSICS, 2000, VOL. 98, NO. 20, 1639 ± 1658 What correlation eœects are covered by density functional theory? YUAN HE, JU È RGEN GRA È FENSTEIN, ELFI KRAKA and DIETER CREMER* Department of Theoretical
More informationGeneralized 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
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 informationA 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
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 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 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 informationMany electrons: Density functional theory Part II. Bedřich Velický VI.
Many electrons: Density functional theory Part II. Bedřich Velický velicky@karlov.mff.cuni.cz VI. NEVF 514 Surface Physics Winter Term 013-014 Troja 1 st November 013 This class is the second devoted to
More informationSession 1. Introduction to Computational Chemistry. Computational (chemistry education) and/or (Computational chemistry) education
Session 1 Introduction to Computational Chemistry 1 Introduction to Computational Chemistry Computational (chemistry education) and/or (Computational chemistry) education First one: Use computational tools
More 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 informationMolecular Magnetism. Magnetic Resonance Parameters. Trygve Helgaker
Molecular Magnetism Magnetic Resonance Parameters Trygve Helgaker Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry, University of Oslo, Norway Laboratoire de Chimie Théorique,
More informationTHE PERFORMANCE OF DENSITY FUNCTIONALS WITH RESPECT TO THE CORRELATION CONSISTENT BASIS SETS. Xuelin Wang, B.S., M.S
THE PERFORMANCE OF DENSITY FUNCTIONALS WITH RESPECT TO THE CORRELATION CONSISTENT BASIS SETS Xuelin Wang, B.S., M.S Dissertation Prepared for the Degree of DOCTOR OF PHILOSOPHY UNIVERSITY OF NORTH TEXAS
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 informationOther methods to consider electron correlation: Coupled-Cluster and Perturbation Theory
Other methods to consider electron correlation: Coupled-Cluster and Perturbation Theory Péter G. Szalay Eötvös Loránd University Institute of Chemistry H-1518 Budapest, P.O.Box 32, Hungary szalay@chem.elte.hu
More informationOrbital functionals derived from variational functionals of the Green function
Orbital functionals derived from variational functionals of the Green function Nils Erik Dahlen Robert van Leeuwen Rijksuniversiteit Groningen Ulf von Barth Lund University Outline 1. Deriving orbital
More informationExcitation 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
More informationQuantum Chemical and Dynamical Tools for Solving Photochemical Problems
2.165430 3.413060 3.889592 9 H 3.413060 2.165430 1.099610 2.165430 3.413060 10 H 3.889592 3.413060 2.165430 1.099610 2.165430 11 H 3.413060 3.889592 3.413060 2.165430 1.099610 12 H 2.165430 3.413060 3.889592
More informationMolecular Magnetic Properties
Molecular Magnetic Properties Trygve Helgaker Hylleraas Centre, Department of Chemistry, University of Oslo, Norway and Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo,
More informationCOUPLED-CLUSTER CALCULATIONS OF GROUND AND EXCITED STATES OF NUCLEI
COUPLED-CLUSTER CALCULATIONS OF GROUND AND EXCITED STATES OF NUCLEI Marta Włoch, a Jeffrey R. Gour, a and Piotr Piecuch a,b a Department of Chemistry,Michigan State University, East Lansing, MI 48824 b
More informationThe Nuclear Many Body Problem Lecture 4. Coupled Cluster theory and its application to medium sized nuclei.
The Nuclear Many Body Problem Lecture 4 Coupled Cluster theory and its application to medium sized nuclei. Extending the Ab Initio program beyond the lightest nuclei. Need a theory which scales softly
More informationHECToR CSE technical meeting, Oxford Parallel Algorithms for the Materials Modelling code CRYSTAL
HECToR CSE technical meeting, Oxford 2009 Parallel Algorithms for the Materials Modelling code CRYSTAL Dr Stanko Tomi Computational Science & Engineering Department, STFC Daresbury Laboratory, UK Acknowledgements
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 informationTreating atomic anions with density functional theory
Accuracy of Electron Affinities of Atoms in Approximate Density Functional Theory Donghyung Lee,* Filipp Furche, and Kieron Burke Department of Chemistry, University of California, Irvine, California 92697
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 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 informationHigh-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
More information7/29/2014. Electronic Structure. Electrons in Momentum Space. Electron Density Matrices FKF FKF. Ulrich Wedig
Electron Density Matrices Density matrices Γ, an alternative to the wavefunction Ψ, for the description of a quantum system Electronic Structure The N-particle density matrix Electrons in Momentum Space
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 informationOrbital 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,...)
More informationNWChem: Coupled Cluster Method (Tensor Contraction Engine)
NWChem: Coupled Cluster Method (ensor Contraction Engine) What we want to solve H Ψ = E Ψ Many Particle Systems Molecular/Atomic Physics, Quantum Chemistry (electronic Schrödinger equations) Solid State
More informationIntroduction to Electronic Structure Theory
CSC/PRACE Spring School in Computational Chemistry 2017 Introduction to Electronic Structure Theory Mikael Johansson http://www.iki.fi/~mpjohans Objective: To get familiarised with the, subjectively chosen,
More informationΨ = Σ m C i,m φ 1...φ m...φ N + φ 1...φ i...φ N.
Chapter 19 Corrections to the mean-field model are needed to describe the instantaneous Coulombic interactions among the electrons. This is achieved by including more than one Slater determinant in the
More informationJoint ICTP-IAEA Workshop on Fusion Plasma Modelling using Atomic and Molecular Data January 2012
2327-3 Joint ICTP-IAEA Workshop on Fusion Plasma Modelling using Atomic and Molecular Data 23-27 January 2012 Qunatum Methods for Plasma-Facing Materials Alain ALLOUCHE Univ.de Provence, Lab.de la Phys.
More informationAb initio methods: The e-e cusp and DFT
Ab initio methods: The e-e cusp and DFT Alston J. Misquitta Centre for Condensed Matter and Materials Physics Queen Mary, University of London March 20, 2012 Density-Functional Theory I Hohenberg & Kohn
More informationPractical Advice for Quantum Chemistry Computations. C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology
Practical Advice for Quantum Chemistry Computations C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology Choice of Basis Set STO-3G is too small 6-31G* or 6-31G** 6 probably
More informationElectronic structure calculations: fundamentals George C. Schatz Northwestern University
Electronic structure calculations: fundamentals George C. Schatz Northwestern University Electronic Structure (often called Quantum Chemistry) calculations use quantum mechanics to determine the wavefunctions
More informationComparison 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,
More information