RPA, TDDFT AND RELATED RESPONSE FUNCTIONS : APPLICATION TO CORRELATION ENERGIES
|
|
|
- Ellen Harvey
- 5 years ago
- Views:
Transcription
1 RPA, TDDFT AND RELATED RESPONSE FUNCTIONS : APPLICATION TO CORRELATION ENERGIES John Dobson, Qld Micro & Nano Tech. Centre, Griffith University, Qld, Australia FAST collaboration: Janos Angyan, Sebastien Lebegue,, Tim Gould, Andreas Savin, Julien Toulouse, Ian Snook : also Judith Harl, Georg Kresse for graphite Funding: Australian Dept of SIIR, French EGIDE Angel Rubio, Pablo Garcia-Gonzalez. Jeil Jung Why is E c still important? (vdw+). How does TDDFT relate to E c? (ACFDT) Ec RPA as E (ACFDT ) with f xc =0. Why ΔE RPA is often good enough. E c (RPA) results for cohesion of layered vdw xtals What are the fxc effects beyond RPA in ACFDT? Various f xc s and their effect of vdw C 6 coefficients Proposed long-ranged density dependence of f xc in vdw dimers
2 How can TDDFT help to predict groundstate energies? Pair distribution / xc hole n xc E xc ground (Adiabatic connection) f xc dyn. dens-dens response χ (fluct-diss theorem) n xc
3 Electronic response functions in TDDFT (exact but looks like mean-field theory) r' Density-density response function χ λ r Bare Resp to ext field (one-body physics) Bare Response to int field RPA,TDH χ λ = χ 0 + χ 0 U λ = χ λ Eff. Internal field (beyond-rpa MB physics)
4 Generalized response function χ AB Ext "Force" "Displacement" χ BA (ω=iu) I = MB grdstate
5 T=0K Fluctuation-dissipation theorem II Hermitian Fluct-Diss Thm
6 EXACT ADIABATIC CONNECTION-FDT APPROACH FOR CORRELATION ENERGY (INCL VDW) Zero-tempFluct-dissipation thm ACF-FDT (exact) Insert expr. for χ KS from {φ i } E x = E HF ({φ i }) Our E xc contains EXACT DFT EXCHANGE Can show χ RPA gives asy -C 6 R -6 result for vdw betw small systs.
7 GROUNDSTATE CORRELATION ENERGIES AND TDDFT What has TDDFT got to do with groundstate energies? ACF/FDT = ( - ) χ λ χ 0 χ 0 (λw+f xc λ ) χ λ = + TDDFT (Gross-Kohn) Why are groundstate energies still interesting? (vdw, soft solids)
8 Diagrams and RPA Bare coulomb χ λ χ 0 χ 0 U λ χ λ TDLDA Screening equ. = + RPA Screening equ. = χ λ χ 0 χ 0 λw χ λ + = = Sum of rings -
9 CORRELATION ENERGY VIA RPA-LIKE SCHEMES Want electronic groundstate energies of large soft matter systems, with "seamless" treatment of all forces incl. vdw, at any separation RPA is a response-based energy scheme: gets covalent, electrostatic bonds and does not rely on non-overlap condition = Infinite Sum of rings RPA gets vdw qualitatively right (contains the zero-point energy of plasmons coupled by the long-ranged Coulomb interaction between subsystems) RPA not quantitatively correct for vdw, except in special geometries (for jellium slabs, f-sum rule fixes distant vdw, and RPA exact). E.g. C 6 vdw,rpa too small for Li-Li (atomic polarizability too small) Therefore need MODIFIED RPA SCHEMES (TDDFT response)
10 ORIGIN OF VDW (DISPERSION) FORCE R d A correlation effect, highly nonlocal so LDA & GGA FAIL Get from 2nd order perturbation theory (for small systems) Or via theory of response (polarisability, coupled plasmons) Weak but ubiquitous - additional to covalent, ionic bonds
11 Distant vdw interaction from coupled -plasmon ZPE / RPA (Dobson Wed pm) L << D a λ D W >>D L>>D D Insulators, 3D metals: ΣC 6 R -6 gives qualitatively OK results, but ΣC 6 R -6 can be very wrong for anisotropic conductors where electrons can move large distances leading to large poorly screened polarizations
12 2D BLOCH BANDSTRUCTURE OF GRAPHENE E(k) k y k y k x k y K 2 (0,4π/(3a)) Bandstructure near Dirac K-points in Brillioun Zone is crucial for density response at low frequency and wavenumber: see next slide. K 1 (2π/( 3a), 2π/(3a)) Γ (0, 0) M k x K 2 K 2 K 1 1 st Brillouin Zone (k space)
13 C B N E(k x,k y ) E(k x,k y ) E(k x,k y ) k y k x k y k x k y k x Bandstructure of metal (e.g. e - doped BN plane) Bandstructure of single graphene plane (semimetal) Bandstructure of single BN plane (semiconductor) α=χ 0 q -2 diverges if u 0 α=χ 0 q -2 diverges if BOTH q,u 0 α=χ 0 q -2 not divergent
14 Lattice and bandstructure of graphite E(k x,k y ) k y k x Bandstructure of single graphene plane (semimetal) From J. C. Charlier, X. Gonze and J.-P. Michenaud, PRA 43, 4579 (1991)
15 DETAILS OF VASP RPA CALCULATION OF GRAPHITE LAYER BINDING ENERGY Previous full RPA calculations for crystals: Si, Na, boron nitride.. Miyake, Aryasetiawan, et al: Marini, Rubio et al Graphite, Sebastien Lebegue et al unpublished 2009 AB graphite geometry with in-plane lattice parameter fixed at exptal value 2.46 A. Computations done for various values of layer stacking parameter D. Plane wave cut-offs: 800 ev for the correlation part and 700 ev for the Hartree Fock part. k-points used: Up to for correlation part, for HF part This fine k subdivision was needed to sample reasonably finely the regions round the Dirac points K, K in the 2D graphene Brillouin zone, where the gapless feature of the graphene electronic bandstructure occurs. leading to small pockets of electrons and holes and unusual singularities in response functions at long wavelength and low frequency
16 LAYER BINDING ENERGY GURVE OF AB GRAPHITE: Lebegue et al, unpub 2010
17 LAYER BINDING PROPERTIES OF GRAPHITE IN MONTE CARLO (VMC, DMC) Spanu, Sorella & Galli, Phys. Rev. Lett. 103, (2009) In view of importance of the D -3 term arising from long-wavelength charge fluctuations in the graphene plane, it is quite likely that these calculations have too small a repeat cell (2 2) in the graphene plane. i.e. not converged. Indeed Spanu et al could fit their results to D -4, i.e. the result for INSULATING layers.
18 LAYER BINDING PROPERTIES OF GRAPHITE Lebegue et al unpublished 2009 LDA (Present) vdw-df DMC ACFDT -RPA (present) Expts Equilibrium interplanar c 3.6 a 3.59 b m distance D 0 C33 (Gpa) c, na, 27 b? e 36.5 ef 38.7 g 37 h Binding energy (mev /atom) c 45.5 a 50 b 56 m i 35 j 52 k (All suspect and involve assumptions of additive vdw forces)
19 LAYER BINDING PROPERTIES OF GRAPHITE: % ERROR COMPARED WITH MEAN EXPERIMENTAL DATA LDA (Present) vdw-df DMC ACFDT -RPA (present) Equilibrium interplanar -1% +11%, +7%, +7% +3% -0.3% distance D0 C 33 (Gpa) -22% -66%, na, -29%? -3% Binding energy (-44%) (-44%), (+6%), (+16%) (+30%) (11%) (mev / atom)
20 Energy opt f xc : little effect on jellium slab binding cw RPA LDA L = 3a B L RPA NLEnOpt D D D J. Jeil, P. Garcia-Gonzalez+JFD+, PRB 70, (2004)
21 RPA in Ne2 binding curve J. Toulouse et al,
22 Severe failure of RPA in Be2 binding curve: related to SIC and/or degeneracy effects? J. Toulouse et al,
23 FUTURE DIRECTIONS GRAPHITIC ENERGETICS VIA RPA The present graphite calculation was a tour de force, made possible because VASP is efficient and a large number of k points were able to be used. More complicated geometries intercalates, nanotubes, etc etc would be very difficult within RPA (even within VASP) if many need k points are needed. A possible solution involves the use of much coarser k grids, but with analytic calculation of the response contributions from the sensitive regions near the Dirac K points. The failure of the short-ranged correlation hole in RPA should be addressed, although experience with jellium layer problems suggests its effect on the energy differences of interest here is probably quite small. One way to improve this is the range-separated approach in which the short -ranged correlations are treated separately. One can hopefully also try higher theories (eg RPAx vs present d-rpa).
24 ADVANTAGES OF RPA ENERGY FORMULA No local assumption, treats long-ranged correlations in a reasonable way Following has been proved (JFD book chapter 1994, reproduced in cond-mat/ : Combined dimer correlation energy in RPA yields the generalised Casimir-Polder formula for the vdw interaction of the monomers, in the well-separated limit: RPA RPA RPA is less computationally intensive than higher-order quantum chemical methods, for large systems. RPA correlation energy is compatible with exact exchange, and indeed RPA yields exact exchange if interacting χ is replaced by bare χ 0
25 SOME WEAKNESSES OF RPA ENERGY (ACFDT with f xc = 0) RPA does not exclude incorrect orbital self-interaction in the dynamical response This can be a big problem where one wants to describe correlations between s electrons eg He2, Be2. But SIC is not a major problem (e.g.) for spatially extended 2π orbitals that are important in graphitic cohesion. RPA gives a poor account of the short ranged part of the correlation hole. It therefore often grossly overestimates the absolute correlation energy. E.g. Homogeneous electron gas, r s = 10,: e c = -22 mh/e. e crpa = -30 mh/e As pointed out by John Perdew et al, the RPA error in E c often largely cancels out in forming isoelectronic energy differences e.g. change in correlation energy when one moves two nanostructures apart, as in binding energy curve calculations. See example next slide. This sr corr hole problem can also be addressed by (e.g.) RPA+f xcr or range separation methods. But application to layer binding of graphitics in ACFDT is not complete (Seb Lebegue has preliminary results). RPA as usually implemented may strongly depend on input orbitals (need SC RPA?)
26 Interacting(λ) and KS (λ=0) dens response Operator for dens at r : Fully interacting M-B eigenstate Fully interacting M-B energy Fermi factor Kohn-Sham orbital Kohn-Sham eigenvalue
27 W 12 perturbation theory and vdw: Bare inter-system Coulomb e 2 /r Gen. nonoverlapping finite systems nonlocal dens-dens resp of isolated system 2 (incl W 11 to all orders) H.C. Longuet-Higgins, Disc. Faraday Soc. 40, 7 (1965). E. Zaremba and W. Kohn, P.R.B (1976). W 12 ZK formula, Generalised Casimir Polder formula W 12
28 MPx, ZK, SA perturbation theory W 11 W 11 MP W 12 W 12 MPx includes all e-e interactions w, not just w 12. MP2 vdw only includes bare responses OK for many small weakly polarizable systems eg Ar-Ar, not v. good for (e.g.) Be-Be, wrong for extended metals. MPx OK for overlapped systems, ( seamless ) but can require higher and higher order as systems become larger Response includes internal interaction W 11 to all orders ZK W 12 W 12 ZK Not valid for overlapped systems cannot deal with indistinguishability, exchange: symmetry adapted pert. th. is better See Jeziorski Mon: also Fri session.
29 ACF/FDT STARTING WITH χ KS CONTAIN ALL THE BASIC CHEMICAL AND PHYSICAL FORCES - II RPA vdw (Casimir-Polder): E.g. for isolated spherical systems in the dipolar approx, This is the exact result from perturbation theory except A A RPA Result does not appear to be true for RPA+approx f xc! JFD pp in 'Topics in condensed matter physics', Ed. M.P. Das, (Nova, NY 1994, ISBN ) ( Hard to get: reproduced in cond-mat/ )
30 vdw energy: well separated systems a R R >> a Make multipolar expansion of and 1 R 2 isotropic case Dipole resp of 2
31 SOME LESS-KNOWN WAYS TO GO BEYOND RPA IN ACFDT Range-separated energy functionals Started with Savin et al 1980 s (short-ranged LDA with long-ranged CI) Split bare Coulomb interaction W=W short range +W long range Treat SR by DFT, LR by another method (perturbation, ACF/FDT.) Kohn, Meir, Makarov PRL 1998: rigorous SR/LR separation for ACF/FDT Angyan, Savin, Toulouse et al : another aproach, using 2 nd order pert. for LR part, and recently RPA RPA/x correlation for long ranged part. Also TD. More empirical hybrids: Goursot, Elstner Energy optimized f xc The "Energy optimized Fxc" (Dobson, Wang PRB 2000) was designed to be local and frequency independent, but to give correct Ec via ACFDT for hom. gas. A spatially nonlocal version was given in Jung et al PRB 04
32 Petersilka, Gossmann, Gross TD OEP
33 Performance of fxc kernels for atom-atom C6
34 Performance of fxc kernels for atom-atom C6
35
36 VERY NONLOCAL f xc [n] IN 2 ISOLATED SUBSYSTEMS?: DIMER VS GEN CASIMIR-POLDER CALCULATION OF VDW ENERGY Gen. nonoverlapping finite systems 1 2 R Casimir-Polder, O(W 122 ): W 21 E vdw = = 0 dutr{χ 11 W 12 χ 22 W 21 } W 12 ACFDT Dimer Calc: E tot xc = 0 1 d λ Then find R-dependent part as R These two approaches must give the same result if exact response fns are used. But in approx theories (eg ACFDT-TDDFT incl short-ranged f xc ) they MAY NOT Can show the two calculations give the same result if f xc = 0 (JFD 94, arxiv 03)
37 SPECTATOR EFFECTS ON f xc IN VdW GEOMETRY (2 SEPARATED SYSTEMS)? f xc (r 1,r 1 ) depends on the presence of a distant system 2, because Coulomb interaction between electrons in system 1 is screened by system Lowest term in RPA correlation energy of system 1 alone Lowest spectator term in RPA energy of coupled systems. Included in RPA dimer calc Not incl in RPA-dimer or RPA-GCP Lowest terms beyond RPA for energy of system 1 alone (includes system 1 self -energy, would involve f xc (r 1,r 1 ) in DFT) 1 2 Lowest spectator terms in beyond -RPA energy of coupled systems.
38 CASIMIR POLDER ENERGY GETS ALL THESE SPECTATOR TERMS WHEN FULL χ 11 OF ISOLATED SYSTEM 1 IS USED 1 2 = A term in χ Lowest spectator terms in beyond -RPA energy of coupled systems. = 1 2 The beyond-rpa spectator diagrams on the left (copied from the previous slide) can be rearranged geometrically to be recognizable as terms in the Casimir -Polder energy expansion (on the right above).
39 SAME IDEAS SHOW THAT F xc IN DIMER CALC HAS LONG-RA DENS DEP Spectator terms arise when system 2 screens the interaction between electrons that are both located in system 1. How does the lowest order spectator self energy contribution to χ 11 contribute to f xc (r 1,r 1 ) in the DIMER calculation? Lowest terms beyond RPA for density response of system 1 alone (includes system 1 self -energy, and an exchange term of lowest RPA diagram this would involve f xc (r 1,r 1 ) in DFT) Lowest spectator terms in beyond-rpa dens-dens response of system.1 to fields applied inside system 1
40 AN EXPLICIT EXPRESSION FOR NONLOCAL-N-DEP f xc IN DIMER CALC? In the above the frequency convolutions and integrations have not been displayed. Perhaps by expanding the LHS to 2nd order in V12 we can get an explicit expression for the lowest-order spectator contribution to fxc11.
41
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
Supplementary Figure 1(a) The trajectory of the levitated pyrolytic graphite test sample (blue curve) and
Supplementary Figure 1(a) The trajectory of the levitated pyrolytic graphite test sample (blue curve) and the envelope from free vibration theory (red curve). (b) The FFT of the displacement-time curve
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
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
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
Assessment 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
Evaluating van der Waals energies from dielectric response functions
Evaluating van der Waals energies from dielectric response functions Deyu Lu Department of chemistry, UC Davis Electronic structure workshop, Davis, CA 06/23/2009 Motivation vdw forces play important roles
Théorie 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
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
Many-body dispersion interactions between semiconducting wires
Many-body dispersion interactions between semiconducting wires Alston J. Misquitta TCM Group, Cavendish Laboratory University of Cambridge 26 th July, 2010 Collaborators James Spencer (Imperial College,
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
The Gutzwiller Density Functional Theory
The Gutzwiller Density Functional Theory Jörg Bünemann, BTU Cottbus I) Introduction 1. Model for an H 2 -molecule 2. Transition metals and their compounds II) Gutzwiller variational theory 1. Gutzwiller
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
Convergence behavior of RPA renormalized many-body perturbation theory
Convergence behavior of RPA renormalized many-body perturbation theory Understanding why low-order, non-perturbative expansions work Jefferson E. Bates, Jonathon Sensenig, Niladri Sengupta, & Adrienn Ruzsinszky
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
QMC in the Apuan Alps IV Vallico Sotto, 28th July 2008
Van der Waals forces in graphitic nanostructures Norbert Nemec QMC in the Apuan Alps IV Vallico Sotto, 28th July 2008 1 History Johannes Diderik van der Waals (1837-1923): Postulation of intermolecular
Van der Waals density functional applied to adsorption systems
Van der Waals density functional applied to adsorption systems Ikutaro Hamada Advanced Institute for Materials Research (AIMR) Tohoku University Contents Introduction The van der Waals density functional
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
Multi-Scale Modeling from First Principles
m mm Multi-Scale Modeling from First Principles μm nm m mm μm nm space space Predictive modeling and simulations must address all time and Continuum Equations, densityfunctional space scales Rate Equations
The Self Interaction Correction revisited
The Self Interaction Correction revisited Explicit dynamics of clusters and molecules under irradiation Spectroscopic accuracy at low energy SIC problem : one electron interacts with its own mean-field!
The Nature of the Interlayer Interaction in Bulk. and Few-Layer Phosphorus
Supporting Information for: The Nature of the Interlayer Interaction in Bulk and Few-Layer Phosphorus L. Shulenburger, A.D. Baczewski, Z. Zhu, J. Guan, and D. Tománek, Sandia National Laboratories, Albuquerque,
Time-Dependent Density-Functional Theory
Summer School on First Principles Calculations for Condensed Matter and Nanoscience August 21 September 3, 2005 Santa Barbara, California Time-Dependent Density-Functional Theory X. Gonze, Université Catholique
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
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,
Introduction to Density Functional Theory
1 Introduction to Density Functional Theory 21 February 2011; V172 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT 2 3 4 Ab initio Computational
van der Waals dispersion power laws for cleavage, exfoliation and stretching in multi-scale, layered systems Abstract
van der Waals dispersion power laws for cleavage, exfoliation and stretching in multi-scale, layered systems Tim Gould, Evan Gray, and John F. Dobson Nanoscale Science and Technology Centre, Nathan campus,
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
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,
Preface Introduction to the electron liquid
Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2
DFT EXERCISES. FELIPE CERVANTES SODI January 2006
DFT EXERCISES FELIPE CERVANTES SODI January 2006 http://www.csanyi.net/wiki/space/dftexercises Dr. Gábor Csányi 1 Hydrogen atom Place a single H atom in the middle of a largish unit cell (start with a
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
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
Progress & challenges with Luttinger-Ward approaches for going beyond DFT
Progress & challenges with Luttinger-Ward approaches for going beyond DFT Sohrab Ismail-Beigi Yale University Dept. of Applied Physics and Physics & CRISP (NSF MRSEC) Ismail-Beigi, Phys. Rev. B (2010)
Calculation of dispersion energies. Author. Published. Journal Title DOI. Copyright Statement. Downloaded from. Griffith Research Online
Calculation of dispersion energies Author Dobson, John, Gould, Tim Published 2012 Journal Title Journal of Physics: Condensed Matter DOI https://doi.org/10.1088/0953-8984/24/7/073201 Copyright Statement
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,
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
Density 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
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.
GW Many-Body Theory for Electronic Structure. Rex Godby
GW Many-Body Theory for Electronic Structure Rex Godby Outline Lecture 1 (Monday) Introduction to MBPT The GW approximation (non-sc and SC) Implementation of GW Spectral properties Lecture 2 (Tuesday)
Electronic 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
Density 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
Density 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)
Density Functional Theory. Martin Lüders Daresbury Laboratory
Density Functional Theory Martin Lüders Daresbury Laboratory Ab initio Calculations Hamiltonian: (without external fields, non-relativistic) impossible to solve exactly!! Electrons Nuclei Electron-Nuclei
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
Improved Electronic Structure and Optical Properties of sp-hybridized Semiconductors Using LDA+U SIC
286 Brazilian Journal of Physics, vol. 36, no. 2A, June, 2006 Improved Electronic Structure and Optical Properties of sp-hybridized Semiconductors Using LDA+U SIC Clas Persson and Susanne Mirbt Department
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
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
Chapter 3. Crystal Binding
Chapter 3. Crystal Binding Energy of a crystal and crystal binding Cohesive energy of Molecular crystals Ionic crystals Metallic crystals Elasticity What causes matter to exist in three different forms?
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
GW-like approaches to quantum transport. Rex Godby
GW-like approaches to quantum transport Rex Godby Outline Introduction to the quantum transport problem Ab initio quantum conductance in the presence of e e interaction (TDDFT / MBPT) 2 + Bothersome aspects
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
The electronic structure of materials 2 - DFT
Quantum mechanics 2 - Lecture 9 December 19, 2012 1 Density functional theory (DFT) 2 Literature Contents 1 Density functional theory (DFT) 2 Literature Historical background The beginnings: L. de Broglie
Many electrons: Density functional theory Part II. Bedřich Velický VI.
Many electrons: Density functional theory Part II. Bedřich Velický velicky@karlov.mff.cuni.cz VI. NEVF 514 Surface Physics Winter Term 013-014 Troja 1 st November 013 This class is the second devoted to
Adiabatic connection for near degenerate excited states
PHYSICAL REVIEW A 69, 052510 (2004) Adiabatic connection for near degenerate excited states Fan Zhang Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey
Dispersion 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/
Van der Waals Density Functional Theory with Applications
Van der Waals Density Functional Theory with Applications D. C. Langreth, 1 M. Dion, 1 H. Rydberg, 2 E. Schröder, 2 P. Hyldgaard, 2 and B. I. Lundqvist 2 1 Department of Physics & Astronomy and Center
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
Introduction 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
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
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.
Binding energy of bilayer graphene and Electronic properties of oligoynes
Binding energy of bilayer graphene and Electronic properties of oligoynes E. Mostaani and N. Drummond Thursday, 31 July 2014 Van der Waals interaction Important contributions to the description of binding
Ab initio Electronic Structure
Ab initio Electronic Structure M. Alouani IPCMS, UMR 7504, Université Louis Pasteur, Strasbourg France http://www-ipcms.u-strasbg.fr In coll. with: B. Arnaud, O. Bengone, Y. Dappe, and S. Lebègue 1965
Introduction 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_
Lecture. Ref. Ihn Ch. 3, Yu&Cardona Ch. 2
Lecture Review of quantum mechanics, statistical physics, and solid state Band structure of materials Semiconductor band structure Semiconductor nanostructures Ref. Ihn Ch. 3, Yu&Cardona Ch. 2 Reminder
Is the homogeneous electron gas homogeneous?
Is the homogeneous electron gas homogeneous? Electron gas (jellium): simplest way to view a metal homogeneous and normal Hartree-Fock: simplest method for many-electron systems a single Slater determinant
Towards ab initio device Design via Quasiparticle self-consistent GW theory
Towards ab initio device Design via Quasiparticle self-consistent GW theory Mark van Schilfgaarde and Takao Kotani Arizona State University Limitations to the local density approximation, the GW approximation
André Schleife Department of Materials Science and Engineering
André Schleife Department of Materials Science and Engineering Yesterday you (should have) learned this: http://upload.wikimedia.org/wikipedia/commons/e/ea/ Simple_Harmonic_Motion_Orbit.gif 1. deterministic
Table of Contents. Table of Contents Spin-orbit splitting of semiconductor band structures
Table of Contents Table of Contents Spin-orbit splitting of semiconductor band structures Relavistic effects in Kohn-Sham DFT Silicon band splitting with ATK-DFT LSDA initial guess for the ground state
Quantum Transport: electron-electron and electron-phonon effects. Rex Godby
Quantum Transport: electron-electron and electron-phonon effects Rex Godby Outline Introduction to the quantum transport problem Ab initio quantum conductance in the presence of e-e interaction (TDDFT
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
Neutral Electronic Excitations:
Neutral Electronic Excitations: a Many-body approach to the optical absorption spectra Claudio Attaccalite http://abineel.grenoble.cnrs.fr/ Second Les Houches school in computational physics: ab-initio
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
High pressure core structures of Si nanoparticles for solar energy conversion
High pressure core structures of Si nanoparticles for solar energy conversion S. Wippermann, M. Vörös, D. Rocca, A. Gali, G. Zimanyi, G. Galli [Phys. Rev. Lett. 11, 4684 (213)] NSF/Solar DMR-135468 NISE-project
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
Electron Interactions and Nanotube Fluorescence Spectroscopy C.L. Kane & E.J. Mele
Electron Interactions and Nanotube Fluorescence Spectroscopy C.L. Kane & E.J. Mele Large radius theory of optical transitions in semiconducting nanotubes derived from low energy theory of graphene Phys.
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
lectures accompanying the book: Solid State Physics: An Introduction, by Philip ofmann (2nd edition 2015, ISBN-10: 3527412824, ISBN-13: 978-3527412822, Wiley-VC Berlin. www.philiphofmann.net 1 Bonds between
Comparison of exchange-correlation functionals: from LDA to GGA and beyond
Comparison of ehange-correlation functionals: from LDA to GGA and beyond Martin Fuchs Fritz-Haber-Institut der MPG, Berlin, Germany Density-Functional Theory Calculations for Modeling Materials and Bio-Molecular
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
Outline. Introduction: graphene. Adsorption on graphene: - Chemisorption - Physisorption. Summary
Outline Introduction: graphene Adsorption on graphene: - Chemisorption - Physisorption Summary 1 Electronic band structure: Electronic properties K Γ M v F = 10 6 ms -1 = c/300 massless Dirac particles!
Practical Guide to Density Functional Theory (DFT)
Practical Guide to Density Functional Theory (DFT) Brad Malone, Sadas Shankar Quick recap of where we left off last time BD Malone, S Shankar Therefore there is a direct one-to-one correspondence between
1 Back to the ground-state: electron gas
1 Back to the ground-state: electron gas Manfred Lein and Eberhard K. U. Gross 1.1 Introduction In this chapter, we explore how concepts of time-dependent density functional theory can be useful in the
Kohn Sham density functional theory [1 3] is. Role of the Exchange Correlation Energy: Nature s Glue STEFAN KURTH, JOHN P. PERDEW.
![Kohn Sham density functional theory [1 3] is. Role of the Exchange Correlation Energy: Nature s Glue STEFAN KURTH, JOHN P. PERDEW.](/thumbs/80/82235561.jpg "Kohn Sham density functional theory [1 3] is. Role of the Exchange Correlation Energy: Nature s Glue STEFAN KURTH, JOHN P. PERDEW.")
Role of the Exchange Correlation Energy: Nature s Glue STEFAN KURTH, JOHN P. PERDEW Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118 Received 11 March 1999;
7/29/2014. 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
v(r i r j ) = h(r i )+ 1 N
Chapter 1 Hartree-Fock Theory 1.1 Formalism For N electrons in an external potential V ext (r), the many-electron Hamiltonian can be written as follows: N H = [ p i i=1 m +V ext(r i )]+ 1 N N v(r i r j
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
QMC 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.
Electronic structure of correlated electron systems. G.A.Sawatzky UBC Lecture
Electronic structure of correlated electron systems G.A.Sawatzky UBC Lecture 6 011 Influence of polarizability on the crystal structure Ionic compounds are often cubic to maximize the Madelung energy i.e.
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
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
PBS: FROM SOLIDS TO CLUSTERS
PBS: FROM SOLIDS TO CLUSTERS E. HOFFMANN AND P. ENTEL Theoretische Tieftemperaturphysik Gerhard-Mercator-Universität Duisburg, Lotharstraße 1 47048 Duisburg, Germany Semiconducting nanocrystallites like
Today: Thursday, April 30. Examples of applications of the Baym-Kadanoff theory for the polarization propagator: Approximations for the self-energy:
Thursday, April 30 Today: Examples of applications of the Baym-Kadanoff theory for the polarization propagator: Free propagator Random Phase Approximation Extended (2p2h) RPA Approximations for the self-energy:
Density 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
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
Performance ofhybrid density functional methods,screened exchange and EXX-OEP methodsin the PAW approach p.1/26
Performance of hybrid density functional methods, screened exchange and EXX-OEP methods in the PAW approach Georg Kresse, J Paier, R Hirschl, M Marsmann Institut für Materialphysik and Centre for Computational
Introduction of XPS Absolute binding energies of core states Applications to silicene
Core level binding energies in solids from first-principles Introduction of XPS Absolute binding energies of core states Applications to silicene arxiv:1607.05544 arxiv:1610.03131 Taisuke Ozaki and Chi-Cheng
Excitation energies of dissociating H 2 : A problematic case for the adiabatic approximation of time-dependent density functional theory
JOURNAL OF CHEMICAL PHYSICS VOLUME 113, NUMBER 19 15 NOVEMBER 2000 Eitation energies of dissociating H 2 : A problematic case for the adiabatic approximation of time-dependent density functional theory
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