Neutral Electronic Excitations:
|
|
- Kelley Briggs
- 5 years ago
- Views:
Transcription
1 Neutral Electronic Excitations: a Many-body approach to the optical absorption spectra Claudio Attaccalite Second Les Houches school in computational physics: ab-initio simulations in condensed matter
2 Motivations: +- hν Absorption Spectroscopy Many Body Effects!!!
3 Motivations(II):Absorption Spectroscopy Absorption linearly related to the Imaginary part of the MACROSCOPIC dielectric constant (frequency dependent)
4 Outline Response of the system to a perturbation Linear Response Regime How can we calculate the response of the system? Time Dependent DFT and Bethe Salpeter Equation Some applications and recent steps forward Conclusions
5 Spectroscopy
6 Theoretical Spectroscopy Propagation i Ψ=H +V ext (r,t )Ψ t1 [ Schrondinger eq. ] i + ei +V ext Gij (t 1, t 2 )=δ(t 1, t 2)+ Σ G Green's functions t1 i ρ(t )=[ H +V ext, ρ(t )] t HARD Correlation Density Matrix 2 i φ=(v h +V xc +V ext )φ +1 / 2 [ p+ A ( j) ] φ Current-DFT t i φ=(t +V h +V xc +V ext ) φ t TD-DFT 1 r r ' Σ(t 1, t 2) 2 3. ρ (r, r, r, r), ρ... V xc, A xc V xc
7 Linear Response Regime (I) The external potential induces a (time-dependent) density perturbation Kubo Formula (1957) ind δ ρ (r, t) ' ' χ ( r t, r t )= = i [δ ρ(r,t )δ ρ(r ' t ' )] δ φ ext (r ', t ' )
8 Linear Response Regime (II) The induced charge density results in a total potential via the V tot ( r t )=V ext ( r t )+ dt ' d r ' v ( r r ' )ρind ( r ' t ' ) Poisson equation. δ ρ(r,t ) δρ(r,t ) δ V tot (r ' ',t ' ') χ (r,r ', t t ')= = δv ext (r ',t ' ) δ V tot (r ' ', t ' ') δ V ext (r ', t ') Kubo Formula χ ( r t, r ' t ' )=χ 0 ( r t, r ' t ' )+ dt 1 dt 2 d r 1 d r 2 χ 0 ( r t, r 1 t 1) v ( r 1 r 2 ) χ ( r 2 t 2, r ' t ' ) ρind V ind ' χ 0 ( r, r )= V tot δ ρind ( r, t) Variation of the charge V tot ( r ' t ' ) Screening of the density w.r.t. The external perturbation total potential.
9 Linear Response Regime (III) The screening is described by the inverse of the microscopic δ V tot ( r t ) ϵ ( r t, r t )= δv ext ( r t ) 1 dielectric function ' ' =δ ( r r ' )+ dt ' ' d r ' ' v ( r r ' ' )χ ( r ' ', r ' ) Twofold physical meaning : Microscopic level: screening of the interaction between charge carriers in the system In the long wave length limit it determines the macroscopic dielectric function which gives rise to screening of the external perturbation The convolution integrals in real space can be reduced to products is Fourier space ϵ 1 G G ' (q, ω)=1+ v G (q)χ G G ' (q, ω) G=G '=0
10 Optical Absorption: Time Dependent DFT 1 2 [ + V eff (r, t)] ψi (r,t )=i ψi (r, t) 2 t N ρ(r,t )= ψi (r,t ) 2 i=1 V eff (r,t )=V H (r, t)+ V xc (r, t)+ V ext (r, t) Interacting System Petersilka et al. Int. J. Quantum Chem. 80, 584 (1996) δρi χ= δ V ext δρni χ0= δv eff... by using... δρ I =δρni χ δ V ext =χ 0 (δ V ext + δ V H + δv xc ) δ V H δ V xc χ=χ (1+ + ) δ V ext δ V ext 0 vχ Non Interacting System TDDFT is an exact f xc χ theory for neutral excitations! χ (q, ω)=χ 0 (q, ω)+ χ 0 (q, ω)(v+ f xc (q,ω)) χ (q,ω)
11 Why does paper turn yellow? Treasure map By comparing ultraviolet-visible reflectance spectra of ancient and artificially aged modern papers with ab- initio TD-DFT calculations, it was possible to identify and estimate the abundance of oxidized functional groups acting as chromophores and responsible of paper yellowing. yellowing A. Mosca Conte et al., Phys. Rev. Lett. 108, (2012)
12 Optical Absorption: Microscopic View (II) Elementary process of absorption: Photon creates a single e-h pair W= h 2π 2 ϕ e v ϕ δ(ϵi ϵ j ℏ ω) ℑϵ(ω) i j ℏ i, j Non Interacting Non Interacting Particles quasi-particles ϵi, ϵ j GW corrected ϵi, ϵ j Hartree, HF, DFT e Independent transitions energies
13 Optical Absorption: Microscopic View (III) Direct and indirect interactions between an e-h pair created by a photon Summing up all such interaction processes we get: L(r 1 t 1 ; r 2 t 2 ; r 3 t 3 ; r 4 t 4 )=L(1,2,3,4) The equation for L is the Bethe Salpeter Equation. The poles are the neutral excitations.
14 Derivation of the Bethe-Salpeter equation (1) What we want: δ V (1) ϵ (1,2)= δ U (2) 1 i=r i, t i... by using... V (1)=U (1) i ℏ d3 v (1,3)ρ(3) δ ρ(3) ϵ (1,2)=δ(1,2)+ d3 v (1,3) δ U (2) 1 The density is related to the Green's function by... by the identity... ρ(1) = i ℏ G(1,1+ ) δ G (1,2) G2 (1,3 ; 2,3 )=G(1,2)G(3,3 ) δ U (3) + + Reducible polarizability δ ρ(1) χ (1,2)= =i ℏ [G2 (1,2 ; 1+,2 + ) G(1,1+ )G(2,2+ )] δ U (2) χ (1,2)= i ℏ L(1,2 ; 1+,2+ ) two-particle correlation function G. Strinati, Rivista del Nuovo Cimento, 11, 1 (1988)
15 Derivation of the Bethe-Salpeter equation (2) What we have: [i ℏ h(1) U (1)]G(1,2) d4 Σ(3,4)G (4,2)=δ(1,2) t δ G (1,1+ ) δ ρ(1) χ (1,2)= i = = δ ρ(1)δ ρ(2) δ U (2) δ U (2) Using: δ G(1,4) δ G 1 (2,3) =L(1,5,4,6)= G(1,2) G(3,4) δ U (5,6) δ U (5,6) G 1 (1,2)=G(0) 1 (1,2) U (1)δ(1,2) Σ(1,2) Just the Dyson equation for G-1 Dyson equation
16 Derivation of the Bethe-Salpeter equation (3) L=L0+ L0 [ v+ δ Σ ] L δg Bethe-Salpeter Equation! 0 L (1,2,3,4)=G(1,4)G(2,3) Coulomb term Σ(1, 2)=G(1,2) v (2,1) => Screened Coulomb term Σ GW (1,2)= ig (1,2)W (2,1) Time-Dependent Hartree-Fock => Standard Bethe-Salpeter equation (Time-Dependent Screened Hartree-Fock) δ(g W ) L= L0 + L0 [ v ]L δg
17 Feynman's diagrams and Bethe-Salpeter equation L= L0 + L0 [ v W ] L L(1234)=L0 (1234)+ + L0 (1256)[v (57)δ (56)δ(78) W (56)δ(57)δ (68)] L(7834) = + Quasihole and quasielectron Intrinsc 4-point equation. It describes the (coupled) progation of two particles, the electron and the hole! Retardation effects are neglected W (1,2)=W (r 1, r 2 )δ(t 1,t 2 ) L(1,2,3,4)=L(r 1, r 2, r 3, r 4 ; t t 0)=L(1,2,3,4, ω)
18 Bethe-Salpeter equation (4-points - space and time) L(1,2,3,4)=L(r 1, r 2, r 3, r 4 ; t t 0)=L(1,2,3,4, ω) Should we invert the equation for L for each frequency??? H exc (n1 n2 ),(n3 n4 ) A (n3 n 4 ) λ =E λ A (n1 n2 ) λ We work in transition space...
19 Effective two particle Hamiltonian It corresponds to transitions at Pseudo-Hermitian positive absorption frequencies v. Tamm Dancoff!!! It corresponds to transitions at negative absorption frequencies v. ϵ M (ω)=1 lim v (q) q 0 v k q e i q r c k 2 λ vc, k E λ ω i η
20 Bethe Salpeter Equation Historical remarks First solution of BSE with dynamical effects: Shindo approximation JPSJ 29, 278(1970) Plane-waves implementation G. Onida et al. PRL 75, 818 (1995) 1974 First applications in solids: W. Hanke and L.J. Sham PRL 33, 582(1974) G. Strinati, H.J. Mattausch and W. Hanke PRL 45, 290 (1980)
21 Some results Bruneval et al., PRL 97, (2006) Strinati et al., Rivista del Nuovo Cimento 11, 1 (1988) Albrecht et al., PRL 80, 4510 (1998) Bruno et al., PRL 98, (2007) Tiago et al., PRB 70, (2004) V. Garbuio et al., PRL 97, (2006)
22 Excitons in nanoscale systems Frenkel excitons in photosynthesis Nanotubes/Nanowires Colloidal quantum dots Excitons in nanoscale systems Gregory D. Scholes, Garry Rumbles Nature Materials 5, (2006)
23 ... advances...
24 Beyond Tamm-Dancoff approximation! Mixed excitonic-plasmonic excitations in nanostructures (Nanoletters, 6, 257(2010)) Excited states of biological chromophores (J. Chem. Theory Comput., 6, (2010))
25 Ab-initio broadening in BSE Ab-Initio finite temperature excitons A. Marini PRL 101, (2008). Ab Initio Calculation of Optical Spectra of Liquids: Many-Body Effects in the Electronic Excitations of Water V. Garbuio et al., PRL 97, (2006).
26 Dynamical Excitonic Effects in Metals and Semiconductors The inclusion of the full dynamic screening in the BS equation complicates its numerical solution tremendously, but it is possible to perform an expansion in the dynamical part of the screened interaction. First solution of this problem the so-called Shindo approximation (J. Phys. Soc. Jpn. 29, 278(1970)) Dynamical effects in Sodium clusters Dynamical effects in metals and semiconductors A. Marini and R. Del sole PRL, 91, (2003). G. Pal et al. EPJ B 79, 327 (2011)
27 Non-linear response: frequency and time domain Second-order response Bethe-Salpeter equation (PRA, 83, (2011)) Real-time approach to the optical properties of solids and nanostructures: Time-dependent Bethe-Salpeter equation (PRB, 84, (2011))
28 References!!! Reviews: Application of the Green s functions method to the study of the optical properties of semiconductors Nuovo Cimento, vol 11, pg 1, (1988) G. Strinati Effects of the Electron Hole Interaction on the Optical Properties of Materials: the Bethe Salpeter Equation Physica Scripta, vol 109, pg 141, (2004) G. Bussi Electronic excitations: density-functional versus many-body Green's-function approaches RMP, vol 74, pg 601, (2002 ) G. Onida, L. Reining, and A. Rubio Books: On the web:
29 DFT meets Many-Body 29
30
31
32
33
34
35 .. with some algebra...
36 References!!! Reviews: Application of the Green s functions method to the study of the optical properties of semiconductors Nuovo Cimento, vol 11, pg 1, (1988) G. Strinati Effects of the Electron Hole Interaction on the Optical Properties of Materials: the Bethe Salpeter Equation Physica Scripta, vol 109, pg 141, (2004) G. Bussi Electronic excitations: density-functional versus many-body Green's-function approaches RMP, vol 74, pg 601, (2002 ) G. Onida, L. Reining, and A. Rubio Books: On the web:
37 37
38 Optical Absorption: Microscopic Limit δ ρni =χ 0 δ V tot 0 χ = ij ϕi (r) ϕ*j (r) ϕ*i (r ' ) ϕj (r ' ) ω (ϵi ϵ j )+ i η Hartree, Hartree-Fock, dft... Non Interacting System Absorption by independent Kohn-Sham particles =ℑ χ 0 = j D i 2 δ(ω (ϵ j ϵi )) ij 2 8π ϵ (ω)= 2 ω Particles are interacting! '' 2 ϕ e v ϕ δ (ϵi ϵ j ℏ ω) i j i, j
BSE and TDDFT at work
BSE and TDDFT at work Claudio Attaccalite http://abineel.grenoble.cnrs.fr/ CECAM Yambo School 2013 (Lausanne) Optical Absorption: Microscopic View Direct and indirect interactions between an e-h pair created
More informationLinear response theory and TDDFT
Linear response theory and TDDFT Claudio Attaccalite http://abineel.grenoble.cnrs.fr/ CECAM Yambo School 2013 (Lausanne) Motivations: +- hν Absorption Spectroscopy Many Body Effects!!! Motivations(II):Absorption
More informationLinear response to an electric field: absorption and energy-loss Independent particle, Local fields effects, and Time-Dependent DFT
Linear response to an electric field: absorption and energy-loss Independent particle, Local fields effects, and Time-Dependent DFT D. Sangalli Motivations: probe your system Scattering of Transmission
More informationPseudo-Hermitian eigenvalue equations in linear-response electronic-structure theory
1/11 Pseudo-Hermitian eigenvalue equations in linear-response electronic-structure theory Julien Toulouse Université Pierre & Marie Curie and CNRS, 4 place Jussieu, Paris, France Web page: www.lct.jussieu.fr/pagesperso/toulouse/
More informationThe GW approximation
The GW approximation Matteo Gatti European Theoretical Spectroscopy Facility (ETSF) LSI - Ecole Polytechnique & Synchrotron SOLEIL - France matteo.gatti@polytechnique.fr - http://etsf.polytechnique.fr
More informationIntroduction to Green functions, GW, and BSE
Introduction to Green functions, the GW approximation, and the Bethe-Salpeter equation Stefan Kurth 1. Universidad del País Vasco UPV/EHU, San Sebastián, Spain 2. IKERBASQUE, Basque Foundation for Science,
More informationTheoretical spectroscopy beyond quasiparticles
A direct approach to the calculation of many-body Green s functions: Theoretical spectroscopy beyond quasiparticles Lucia Reining Palaiseau Theoretical Spectroscopy Group Palaiseau Theoretical Spectroscopy
More informationAndrea Marini. Introduction to the Many-Body problem (I): the diagrammatic approach
Introduction to the Many-Body problem (I): the diagrammatic approach Andrea Marini Material Science Institute National Research Council (Monterotondo Stazione, Italy) Zero-Point Motion Many bodies and
More informationAb initio calculation of the exchange-correlation kernel in extended systems
Ab initio calculation of the exchange-correlation kernel in extended systems Gianni Adragna, 1 Rodolfo Del Sole, 1 and Andrea Marini 2 1 Istituto Nazionale per la Fisica della Materia e Dipartimento di
More informationLinear-response excitations. Silvana Botti
from finite to extended systems 1 LSI, CNRS-CEA-École Polytechnique, Palaiseau, France 2 LPMCN, CNRS-Université Lyon 1, France 3 European Theoretical Spectroscopy Facility September 3, 2008 Benasque, TDDFT
More informationTime-dependent density functional theory
Time-dependent density functional theory E.K.U. Gross Max-Planck Institute for Microstructure Physics OUTLINE LECTURE I Phenomena to be described by TDDFT Some generalities on functional theories LECTURE
More informationMany-Body Perturbation Theory. Lucia Reining, Fabien Bruneval
, Fabien Bruneval Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France European Theoretical Spectroscopy Facility (ETSF) Belfast, 27.6.2007 Outline 1 Reminder 2 Perturbation Theory
More informationIntroduction to TDDFT
Introduction to TDDFT Linear-Response TDDFT in Frequency-Reciprocal space on a Plane-Waves basis: the DP (Dielectric Properties) code Valerio Olevano Institut Néel, CNRS, Grenoble European Theoretical
More informationMany-Body Perturbation Theory: (1) The GW Approximation
Many-Body Perturbation Theory: (1) The GW Approximation Michael Rohlfing Fachbereich Physik Universität Osnabrück MASP, June 29, 2012 Motivation Excited states: electrons, holes Equation of motion Approximations
More information297 K 297 K 83 K PRB 36, 4821 (1987) C. Tarrio, PRB 40, 7852 (1989)
Finite temperature calculations of the electronic and optical properties of solids and nanostructures: the role of electron-phonon coupling from Initio perspective Andrea Marini National Reserach Council
More informationJ. Paier, M. Marsman, G. Kresse, Kerstin Hummer. Computational Materials Physics Faculty of Physics University of Vienna. Funded by the Austrian FWF
J. Paier, M. Marsman, G. Kresse, Kerstin Hummer Computational Materials Physics Faculty of Physics University of Vienna Funded by the Austrian FWF Accurate calculation of optical absorption and electron
More informationarxiv:cond-mat/ v2 [cond-mat.other] 14 Apr 2006
Beyond time-dependent exact-exchange: the need for long-range correlation arxiv:cond-mat/0604358v2 [cond-mat.other] 14 Apr 2006 Fabien Bruneval 1,, Francesco Sottile 1,2,, Valerio Olevano 1,3, and Lucia
More informationCurrent density functional theory for optical spectra Boeij, P.L. de; Kootstra, F.; Berger, Johannes; Leeuwen, R. van; Snijders, J.G.
University of Groningen Current density functional theory for optical spectra Boeij, P.L. de; Kootstra, F.; Berger, Johannes; Leeuwen, R. van; Snijders, J.G. Published in: The Journal of Chemical Physics
More informationProgress & 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)
More informationTime Dependent Density Functional Theory. Francesco Sottile
Applications, limitations and... new frontiers Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France European Theoretical Spectroscopy Facility (ETSF) Vienna, 19 January 2007 /55 Outline
More informationTime-dependent density functional theory (TDDFT)
04/05/16 Hands-on workshop and Humboldt-Kolleg: Density-Functional Theory and Beyond - Basic Principles and Modern Insights Isfahan University of Technology, Isfahan, Iran, May 2 to 13, 2016 Time-dependent
More informationTime-dependent density functional theory (TDDFT)
Advanced Workshop on High-Performance & High-Throughput Materials Simulations using Quantum ESPRESSO ICTP, Trieste, Italy, January 16 to 27, 2017 Time-dependent density functional theory (TDDFT) Ralph
More informationTheoretical Framework for Electronic & Optical Excitations, the GW & BSE Approximations and Considerations for Practical Calculations
Theoretical Framework for Electronic & Optical Excitations, the GW & BSE Approximations and Considerations for Practical Calculations Mark S Hybertsen Center for Functional Nanomaterials Brookhaven National
More informationSpectroscopy of nanostructures: from optics to transport
Spectroscopy of nanostructures: from optics to transport Angel Rubio NanoBio Spectroscopy Group, Dpto. Física de Materiales, Universidad del País Vasco, Centro Mixto CSIC UPV/EHU and DIPC Edificio Korta,
More informationBeyond time-dependent exact exchange: The need for long-range correlation
THE JOURNAL OF CHEMICAL PHYSICS 124, 144113 2006 Beyond time-dependent exact exchange: The need for long-range correlation Fabien Bruneval a European Theoretical Spectroscopy Facility (ETSF), Laboratoire
More informationOptical Properties of Solid from DFT
Optical Properties of Solid from DFT 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India & Center for Materials Science and Nanotechnology, University of Oslo, Norway http://folk.uio.no/ravi/cmt15
More informationAndré 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
More informationAb Initio theories to predict ARPES Hedin's GW and beyond
Ab Initio theories to predict ARPES Hedin's GW and beyond Valerio Olevano Institut NEEL, CNRS, Grenoble, France and European Theoretical Spectroscopy Facility Many thanks to: Matteo Gatti, Pierre Darancet,
More informationElectronic Excitation Energies of Molecular Systems from the Bethe Salpeter Equation
8 Electronic Excitation Energies of Molecular Systems from the Bethe Salpeter Equation Example of the H Molecule Elisa Rebolini, Julien Toulouse, and Andreas Savin CONTENTS 8. Introduction... 67 8. Review
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 informationMulti-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
More informationThe frequency-dependent Sternheimer equation in TDDFT
The frequency-dependent Sternheimer equation in TDDFT A new look into an old equation Miguel A. L. Marques 1 Centre for Computational Physics, University of Coimbra, Portugal 2 LPMCN, Université Claude
More informationVASP: Dielectric response Perturbation theory, linear response, and finite electric fields
VASP: Dielectric response Perturbation theory, linear response, and finite electric fields University of Vienna, Faculty of Physics and Center for Computational Materials Science, Vienna, Austria Outline
More informationMicroscopic-Macroscopic connection. Silvana Botti
relating experiment and theory European Theoretical Spectroscopy Facility (ETSF) CNRS - Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France Temporary Address: Centre for Computational
More informationTime-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
More informationElectronic excitations in materials for solar cells
Electronic excitations in materials for solar cells beyond standard density functional theory Silvana Botti 1 LSI, École Polytechnique-CNRS-CEA, Palaiseau, France 2 LPMCN, CNRS-Université Lyon 1, France
More informationEnergy dependence of the exchange-correlation kernel of time-dependent density functional theory: A simple model for solids
Energy dependence of the exchange-correlation kernel of time-dependent density functional theory: A simple model for solids Silvana Botti, Armel Fourreau, François Nguyen, Yves-Olivier Renault, Francesco
More informationThe GW Approximation. Manish Jain 1. July 8, Department of Physics Indian Institute of Science Bangalore 1/36
1/36 The GW Approximation Manish Jain 1 Department of Physics Indian Institute of Science Bangalore July 8, 2014 Ground-state properties 2/36 Properties that are intrinsic to a system with all its electrons
More informationOptical Properties of Semiconductors. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India
Optical Properties of Semiconductors 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India http://folk.uio.no/ravi/semi2013 Light Matter Interaction Response to external electric
More informationTheory, Interpretation and Applications of X-ray Spectra*
REU Seminar University of Washington 27 July, 2015 Theory, Interpretation and Applications of X-ray Spectra* J. J. Rehr et al. A theoretical horror story Starring Fernando Vila & Anatoly Frenkel with J.
More informationTime Dependent Density Functional Theory. Francesco Sottile
An Introduction Laboratoire des Solides Irradiés Ecole Polytechnique, Palaiseau - France European Theoretical Spectroscopy Facility (ETSF) Belfast, 29 Jun 2007 Outline 1 Introduction: why TD-DFT? 2 (Just)
More informationarxiv:cond-mat/ v1 [cond-mat.mtrl-sci] 10 May 2006
Optical excitations in organic molecules, clusters and defects studied by first-principles Green s function methods arxiv:cond-mat/65248v [cond-mat.mtrl-sci] May 26 Murilo L. Tiago (a) and James R. Chelikowsky
More informationExcited state dynamics of nanostructures and extended systems within TDDFT
Excited state dynamics of nanostructures and extended systems within TDDFT Angel Rubio Dpto. de Física de Materiales, Universidad del País Vasco, Donostia International Physics Center (DIPC), and Centro
More informationCore-level Spectroscopies with FEFF9 and OCEAN
Soleil Theory Day Synchrotron SOLEIL, Grand Amphi 6/5/2014 Core-level Spectroscopies with FEFF9 and OCEAN J. J. Rehr 1,4 K. Gilmore, 2,4 J. Kas, 1 J. Vinson, 3 E. Shirley 3 1 University of Washington,
More informationFaddeev Random Phase Approximation (FRPA) Application to Molecules
Faddeev Random Phase Approximation (FRPA) Application to Molecules Matthias Degroote Center for Molecular Modeling (CMM) Ghent University INT 2011 Spring Program Fermions from Cold Atoms to Neutron Stars:
More informationRabi oscillations within TDDFT: the example of the 2 site Hubbard model
Rabi oscillations within TDDFT: the example of the 2 site Hubbard model Johanna I. Fuks, H. Appel, Mehdi,I.V. Tokatly, A. Rubio Donostia- San Sebastian University of Basque Country (UPV) Outline Rabi oscillations
More informationMicroscopic-macroscopic connection
icroscopic-macroscopic connection Valérie Véniard ETSF France Laboratoire des Solides Irradiés Ecole Polytechniue CEA-DS CNRS 91128 Palaiseau France Outline 1. Introduction: which uantities do we need
More informationOptical Properties with Wien2k
Optical Properties with Wien2k Elias Assmann Vienna University of Technology, Institute for Solid State Physics WIEN2013@PSU, Aug 13 Menu 1 Theory Screening in a solid Calculating ϵ: Random-Phase Approximation
More informationApplications of Time-Dependent Density Functional Theory
Physica Scripta. Vol. T109, 54 60, 2004 Applications of Time-Dependent Density Functional Theory Silvana Botti Laboratiore des Solides Irradiés, CNRS-CEA-E cole Polytechnique, F-91128 Palaiseau, France
More informationAb Initio Calculations for Large Dielectric Matrices of Confined Systems Serdar Ö güt Department of Physics, University of Illinois at Chicago, 845 We
Ab Initio Calculations for Large Dielectric Matrices of Confined Systems Serdar Ö güt Department of Physics, University of Illinois at Chicago, 845 West Taylor Street (M/C 273), Chicago, IL 60607 Russ
More informationPlan of the lectures
Plan of the lectures 1. Introductory remarks on metallic nanostructures Relevant quantities and typical physical parameters Applications. Linear electron response: Mie theory and generalizations 3. Nonlinear
More informationOptical & Transport Properties of Carbon Nanotubes II
Optical & Transport Properties of Carbon Nanotubes II Duncan J. Mowbray Nano-Bio Spectroscopy Group European Theoretical Spectroscopy Facility (ETSF) Donostia International Physics Center (DIPC) Universidad
More informationTime-dependent density functional theory
Time-dependent density functional theory E.K.U. Gross Max-Planck Institute of Microstructure Physics Halle (Saale) OUTLINE Phenomena to be described by TDDFT Basic theorems of TDDFT Approximate xc functionals:
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 informationMultiple Exciton Generation in Si and Ge Nanoparticles with High Pressure Core Structures
Multiple Exciton Generation in Si and Ge Nanoparticles with High Pressure Core Structures S. Wippermann, M. Vörös, D. Rocca, A. Gali, G. Zimanyi, G. Galli NanoMatFutur DPG-214, 4/3/214 Multiple Exciton
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 informationCumulant Green s function approach for excited state and thermodynamic properties of cool to warm dense matter
HoW exciting! Workshop Humboldt University Berlin 7 August, 2018 Cumulant Green s function approach for excited state and thermodynamic properties of cool to warm dense matter J. J. Rehr & J. J. Kas University
More informationGW quasiparticle energies
Chapter 4 GW quasiparticle energies Density functional theory provides a good description of ground state properties by mapping the problem of interacting electrons onto a KS system of independent particles
More informationOptical Anisotropy of Quantum Disks in the External Static Magnetic Field
Vol. 114 (2008) ACTA PHYSICA POLONICA A No. 5 Proc. XXXVII International School of Semiconducting Compounds, Jaszowiec 2008 Optical Anisotropy of Quantum Disks in the External Static Magnetic Field P.
More informationThe Electronic Structure of Dye- Sensitized TiO 2 Clusters from Many- Body Perturbation Theory
The Electronic Structure of Dye- Sensitized TiO 2 Clusters from Many- Body Perturbation Theory Noa Marom Center for Computational Materials Institute for Computational Engineering and Sciences The University
More informationX-ray Spectroscopy Theory Lectures
TIMES Lecture Series SIMES-SLAC-Stanford Winter, 2017 X-ray Spectroscopy Theory Lectures J. J. Rehr I. Introduction to the Theory of X-ray spectra II. Real-space Green's function Theory and FEFF III. Inelastic
More informationAb 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
More informationChapter 3 The Microscopic Description of a Macroscopic Experiment
Chapter 3 The Microscopic Description of a Macroscopic Experiment Silvana Botti and Matteo Gatti 3.1 Introduction The interaction between electromagnetic radiation (or particles) and matter creates elementary
More informationGW-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
More informationIntroduction to many-body Green-function theory
Introduction to many-body Green-function theory Julien Toulouse Laboratoire de Chimie Théorique Université Pierre et Marie Curie et CNRS, 75005 Paris, France julien.toulouse@upmc.fr July 15, 2015 Contents
More informationThe frequency-dependent Sternheimer equation in TDDFT
The frequency-dependent Sternheimer equation in TDDFT A new look into an old equation Miguel A. L. Marques 1 Centre for Computational Physics, University of Coimbra, Portugal 2 European Theoretical Spectroscopy
More information[ ( )] + ρ VIII. NONLINEAR OPTICS -- QUANTUM PICTURE: 45 THE INTERACTION OF RADIATION AND MATTER: QUANTUM THEORY PAGE 88
THE INTERACTION OF RADIATION AND MATTER: QUANTUM THEORY PAGE 88 VIII. NONLINEAR OPTICS -- QUANTUM PICTURE: 45 A QUANTUM MECHANICAL VIEW OF THE BASICS OF N ONLINEAR OPTICS 46 In what follows we draw on
More informationAdvanced TDDFT II. II. Frequency-Dependent Kernels: Double Excitations. f xc
Advanced TDDFT II II. Frequency-Dependent Kernels: Double Excitations f xc Neepa T. Maitra Hunter College and the Graduate Center of the City University of New York Plan -- Double-Excitations in TDDFT
More informationQuantum Quenches in Extended Systems
Quantum Quenches in Extended Systems Spyros Sotiriadis 1 Pasquale Calabrese 2 John Cardy 1,3 1 Oxford University, Rudolf Peierls Centre for Theoretical Physics, Oxford, UK 2 Dipartimento di Fisica Enrico
More informationIII. Inelastic losses and many-body effects in x-ray spectra
TIMES Lecture Series SIMES-SLAC-Stanford March 2, 2017 III. Inelastic losses and many-body effects in x-ray spectra J. J. Rehr TALK: Inelastic losses and many-body effects in x-ray spectra Inelastic losses
More informationSpeeding up the solution of the Bethe-Salpeter equation by a double-grid method and Wannier interpolation
Speeding up the solution of the Bethe-Salpeter equation by a double-grid method and Wannier interpolation David Kammerlander, 1,2, Silvana Botti, 3 Miguel A. L Marques, 4 Andrea Marini, 4 and Claudio Attaccalite
More informationElectronic band structure, sx-lda, Hybrid DFT, LDA+U and all that. Keith Refson STFC Rutherford Appleton Laboratory
Electronic band structure, sx-lda, Hybrid DFT, LDA+U and all that Keith Refson STFC Rutherford Appleton Laboratory LDA/GGA DFT is good but... Naive LDA/GGA calculation severely underestimates band-gaps.
More informationCondensed matter physics FKA091
Condensed matter physics FKA091 Ermin Malic Department of Physics Chalmers University of Technology Henrik Johannesson Department of Physics University of Gothenburg Teaching assistants: Roland Jago &
More informationSupplementary Materials
Supplementary Materials Sample characterization The presence of Si-QDs is established by Transmission Electron Microscopy (TEM), by which the average QD diameter of d QD 2.2 ± 0.5 nm has been determined
More informationMD simulation: output
Properties MD simulation: output Trajectory of atoms positions: e. g. diffusion, mass transport velocities: e. g. v-v autocorrelation spectrum Energies temperature displacement fluctuations Mean square
More informationReal space investigation of local field effects on surfaces
Real space investigation of local field effects on surfaces Nicolas Tancogne-Dejean, Valérie Véniard Laboratoire des Solides Irradiés,Ecole Polytechnique, CNRS, CEA/DSM European Theoretical Spectroscopy
More informationMBPT and TDDFT Theory and Tools for Electronic-Optical Properties Calculations in Material Science
MBPT and TDDFT Theory and Tools for Electronic-Optical Properties Calculations in Material Science Dott.ssa Letizia Chiodo Nano-bio Spectroscopy Group & ETSF - European Theoretical Spectroscopy Facility,
More informationTheoretical spectroscopy
Theoretical spectroscopy from basic developments to real-world applications M. A. L. Marques http://www.tddft.org/bmg/ 1 LPMCN, CNRS-Université Lyon 1, France 2 European Theoretical Spectroscopy Facility
More informationSemiconducting nano-composites for solar energy conversion: insights from ab initio calculations. S. Wippermann, G. Galli
Semiconducting nano-composites for solar energy conversion: insights from ab initio calculations S. Wippermann, G. Galli ICAMP-12, 08/10/2012 Search for materials to harvest light: Desperately seeking
More informationGW+BSE Robert Laskowski
GW+BSE Robert Laskowski rolask@ihpc.a star.edu.sg Institute of High Performance Computing Singapore outline Thanks to Hong Jiang from College of Chemistry, Peking University, contributing GW package, and
More informationPhotoelectronic properties of chalcopyrites for photovoltaic conversion:
Photoelectronic properties of chalcopyrites for photovoltaic conversion: self-consistent GW calculations Silvana Botti 1 LSI, CNRS-CEA-École Polytechnique, Palaiseau, France 2 LPMCN, CNRS-Université Lyon
More informationf xc Advanced TDDFT PDF Created with deskpdf PDF Writer - Trial :: II. Frequency-Dependent Kernels: Double Excitations
Advanced TDDFT II. Frequency-Dependent Kernels: Double Excitations f xc Neepa T. Maitra Hunter College and the Graduate Center of the City University of New York First, quick recall of how we get excitations
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 informationReview Time-Dependent Density-Functional Theory and Excitons in Bulk and Two-Dimensional Semiconductors
Review Time-Dependent Density-Functional Theory and Excitons in Bulk and Two-Dimensional Semiconductors Volodymyr Turkowski 1, *, Naseem Ud Din 1 and Talat S. Rahman 1,2 1 Department of Physics, University
More informationTime-dependent density functional theory
Time-dependent density functional theory E.K.U. Gross Max-Planck Institute for Microstructure Physics OUTLINE LECTURE I Phenomena to be described by TDDFT LECTURE II Review of ground-state DFT LECTURE
More informationModeling of Transport and Gain in Quantum Cascade Lasers
Modeling of Transport and Gain in Quantum Cascade Lasers Andreas Wacker in collaboration with: M.P. Pereira Jr., NMRC, Cork p.1 Introduction p.2 The Challenge: Intersubband Lasing tunneling Kazarinov and
More informationOptical properties by wien2k
Optical properties by wien2k Robert Laskowski rolask@ihpc.a star.edu.sg Institute of High Performance Computing Singapore outline Basics, formalism What, how? optic, joint, tetra. inputs / outputs, examples
More informationTheory and Parameter Free Calculations of EELS and X-ray Spectra
M&M Conference Columbus, OH 24-28 June, 2016 Theory and Parameter Free Calculations of EELS and X-ray Spectra J.J. Rehr 1, J. J. Kas 1, K. Jorissen 2, and F. Vila 1 1 Department of Physics, University
More informationOptical properties by wien2k
Optical properties by wienk Robert Laskowski rolask@ihpc.a star.edu.sg Institute of High Performance Computing Singapore outline Theory: independent particle approximation optic, joint, tetra. inputs /
More informationTime-dependent density functional theory
Time-dependent density functional theory E.K.U. Gross Max-Planck Institute of Microstructure Physics Halle (Saale) OUTLINE Phenomena to be described by TDDFT: Matter in weak and strong laser fields Basic
More informationIV. Calculations of X-ray Spectra in Real-space and Real-time. J. J. Rehr
TIMES Lecture Series SLAC-Stanford U March 2, 2017 IV. Calculations of X-ray Spectra in Real-space and Real-time J. J. Rehr Calculations of X-ray Spectra in Real-space and Real-time Goal: Real-space, real
More informationPreface 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
More informationOptical and electronic properties of Copper and Silver: from Density Functional Theory to Many Body Effects
Facoltà di Scienze Matematiche Fisiche e Naturali Optical and electronic properties of Copper and Silver: from Density Functional Theory to Many Body Effects Andrea Marini Il supervisori Prof. Rodolfo
More informationAdvanced TDDFT II. Double Excitations in TDDFT
Advanced TDDFT II. Double Excitations in TDDFT f xc Neepa T. Maitra Hunter College and the Graduate Center of the City University of New York First, quick recall of how we get excitations in TDDFT: Linear
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 informationAb-initio modeling of opto-electronic properties of molecules in solvents and in proximity to a semiconductor nanoparticle
Ab-initio modeling of opto-electronic properties of molecules in solvents and in proximity to a semiconductor nanoparticle Alain Delgado (a,b), Stefano Corni (b), Carlo Andrea Rozzi (b) Stefano Pittalis
More informationThe 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
More informationarxiv: v1 [cond-mat.mtrl-sci] 6 Jun 2007
Optical properties of graphene nanoribbons: the role of many-body effects arxiv:76.916v1 [cond-mat.mtrl-sci] 6 Jun 7 Deborah Prezzi, 1,, Daniele Varsano, 1 Alice Ruini, 1, Andrea Marini, 3 and Elisa Molinari
More informationExcitation Dynamics in Quantum Dots. Oleg Prezhdo U. Washington, Seattle
Excitation Dynamics in Quantum Dots Oleg Prezhdo U. Washington, Seattle Warwick August 27, 2009 Outline Time-Domain Density Functional Theory & Nonadiabatic Molecular Dynamics Quantum backreaction, surface
More informationTheory and Calculation of X-ray spectra. J. J. Kas
Theory and Calculation of X-ray spectra J. J. Kas Theoretical Spectroscopy Calculations GOAL: Next Generation Theory for Next Generation X-ray Sources TALK I Introduction II State-of-the-art III Next generation
More information