$GW$ calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods
Abstract
In a recent paper we presented an approach to evaluate quasiparticle energies based on the spectral decomposition of the static dielectric matrix. This method does not require the calculation of unoccupied electronic states or the direct diagonalization of large dielectric matrices, and it avoids the use of plasmonpole models. The numerical accuracy of the approach is controlled by a single parameter, i.e., the number of eigenvectors used in the spectral decomposition of the dielectric matrix. Here we present a comprehensive validation of the method, encompassing calculations of ionization potentials and electron affinities of various molecules and of band gaps for several crystalline and disordered semiconductors. Lastly, we demonstrate the efficiency of our approach by carrying out $GW$ calculations for systems with several hundred valence electrons.
 Authors:

 Univ. of California, Davis, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Vietnam Academy of Science and Technology, Hanoi (Vietnam)
 Univ. of California, Davis, CA (United States); Univ. de Lorraine and CNRS, VandoeuvrelesNancy (France)
 Univ. of California, Davis, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1351134
 Alternate Identifier(s):
 OSTI ID: 1102164
 Report Number(s):
 LLNLJRNL613237
Journal ID: ISSN 10980121; PRBMDO
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review. B, Condensed Matter and Materials Physics
 Additional Journal Information:
 Journal Volume: 87; Journal Issue: 15; Journal ID: ISSN 10980121
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY
Citation Formats
Pham, T. Anh, Nguyen, Huy Viet, Rocca, Dario, and Galli, Giulia. GW calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods. United States: N. p., 2013.
Web. doi:10.1103/PhysRevB.87.155148.
Pham, T. Anh, Nguyen, Huy Viet, Rocca, Dario, & Galli, Giulia. GW calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods. United States. doi:10.1103/PhysRevB.87.155148.
Pham, T. Anh, Nguyen, Huy Viet, Rocca, Dario, and Galli, Giulia. Fri .
"GW calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods". United States. doi:10.1103/PhysRevB.87.155148. https://www.osti.gov/servlets/purl/1351134.
@article{osti_1351134,
title = {GW calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods},
author = {Pham, T. Anh and Nguyen, Huy Viet and Rocca, Dario and Galli, Giulia},
abstractNote = {In a recent paper we presented an approach to evaluate quasiparticle energies based on the spectral decomposition of the static dielectric matrix. This method does not require the calculation of unoccupied electronic states or the direct diagonalization of large dielectric matrices, and it avoids the use of plasmonpole models. The numerical accuracy of the approach is controlled by a single parameter, i.e., the number of eigenvectors used in the spectral decomposition of the dielectric matrix. Here we present a comprehensive validation of the method, encompassing calculations of ionization potentials and electron affinities of various molecules and of band gaps for several crystalline and disordered semiconductors. Lastly, we demonstrate the efficiency of our approach by carrying out GW calculations for systems with several hundred valence electrons.},
doi = {10.1103/PhysRevB.87.155148},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 15,
volume = 87,
place = {United States},
year = {2013},
month = {4}
}
Web of Science
Works referenced in this record:
SelfConsistent Equations Including Exchange and Correlation Effects
journal, November 1965
 Kohn, W.; Sham, L. J.
 Physical Review, Vol. 140, Issue 4A, p. A1133A1138
Electronic excitations in light absorbers for photoelectrochemical energy conversion: first principles calculations based on many body perturbation theory
journal, January 2013
 Ping, Yuan; Rocca, Dario; Galli, Giulia
 Chemical Society Reviews, Vol. 42, Issue 6
Electronic excitations: densityfunctional versus manybody Green’sfunction approaches
journal, June 2002
 Onida, Giovanni; Reining, Lucia; Rubio, Angel
 Reviews of Modern Physics, Vol. 74, Issue 2
New Method for Calculating the OneParticle Green's Function with Application to the ElectronGas Problem
journal, August 1965
 Hedin, Lars
 Physical Review, Vol. 139, Issue 3A
Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies
journal, October 1986
 Hybertsen, Mark S.; Louie, Steven G.
 Physical Review B, Vol. 34, Issue 8, p. 53905413
Reliability of Hybrid Functionals in Predicting Band Gaps
journal, November 2011
 Jain, Manish; Chelikowsky, James R.; Louie, Steven G.
 Physical Review Letters, Vol. 107, Issue 21
Band Offsets at the $\mathrm{Si}/{\mathrm{SiO}}_{2}$ Interface from ManyBody Perturbation Theory
journal, May 2008
 Shaltaf, R.; Rignanese, G. M.; Gonze, X.
 Physical Review Letters, Vol. 100, Issue 18
Conserving $GW$ scheme for nonequilibrium quantum transport in molecular contacts
journal, March 2008
 Thygesen, Kristian S.; Rubio, Angel
 Physical Review B, Vol. 77, Issue 11
Optimal representation of the polarization propagator for largescale $GW$ calculations
journal, May 2009
 Umari, P.; Stenuit, Geoffrey; Baroni, Stefano
 Physical Review B, Vol. 79, Issue 20
Quasiparticle Band Gap of ZnO: High Accuracy from the Conventional ${G}^{0}{W}^{0}$ Approach
journal, September 2010
 Shih, BiChing; Xue, Yu; Zhang, Peihong
 Physical Review Letters, Vol. 105, Issue 14
Simple Approximate Physical Orbitals for $GW$ Quasiparticle Calculations
journal, October 2011
 Samsonidze, Georgy; Jain, Manish; Deslippe, Jack
 Physical Review Letters, Vol. 107, Issue 18
Electronic energy level alignment at metalmolecule interfaces with a $GW$ approach
journal, November 2011
 Tamblyn, Isaac; Darancet, Pierre; Quek, Su Ying
 Physical Review B, Vol. 84, Issue 20
Improving accuracy and efficiency of calculations of photoemission spectra within the manybody perturbation theory
journal, February 2012
 Nguyen, HuyViet; Pham, T. Anh; Rocca, Dario
 Physical Review B, Vol. 85, Issue 8
GW quasiparticle spectra from occupied states only
journal, March 2010
 Umari, P.; Stenuit, Geoffrey; Baroni, Stefano
 Physical Review B, Vol. 81, Issue 11
GW method with the selfconsistent Sternheimer equation
journal, March 2010
 Giustino, Feliciano; Cohen, Marvin L.; Louie, Steven G.
 Physical Review B, Vol. 81, Issue 11
Ab initio calculations of electronic excitations: Collapsing spectral sums
journal, July 2010
 Berger, J. A.; Reining, Lucia; Sottile, Francesco
 Physical Review B, Vol. 82, Issue 4
Band convergence and linearization error correction of allelectron $\mathit{GW}$ calculations: The extreme case of zinc oxide
journal, February 2011
 Friedrich, Christoph; Müller, Mathias C.; Blügel, Stefan
 Physical Review B, Vol. 83, Issue 8
Precise quasiparticle energies and HartreeFock bands of semiconductors and insulators
journal, May 1988
 von der Linden, Wolfgang; Horsch, Peter
 Physical Review B, Vol. 37, Issue 14
Metalinsulator transition in KohnSham theory and quasiparticle theory
journal, March 1989
 Godby, R. W.; Needs, R. J.
 Physical Review Letters, Vol. 62, Issue 10
Generalized plasmonpole model and plasmon band structures of crystals
journal, June 1993
 Engel, G. E.; Farid, Behnam
 Physical Review B, Vol. 47, Issue 23
${G}^{0}{W}^{0}$ band gap of ZnO: Effects of plasmonpole models
journal, December 2011
 Stankovski, M.; Antonius, G.; Waroquiers, D.
 Physical Review B, Vol. 84, Issue 24
Efficient calculation of exact exchange and RPA correlation energies in the adiabaticconnection fluctuationdissipation theory
journal, May 2009
 Nguyen, HuyViet; de Gironcoli, Stefano
 Physical Review B, Vol. 79, Issue 20
Selfconsistent HartreeFock and screenedexchange calculations in solids: Application to silicon
journal, September 1986
 Gygi, F.; Baldereschi, A.
 Physical Review B, Vol. 34, Issue 6
Dielectric Properties of Ice and Liquid Water from FirstPrinciples Calculations
journal, April 2008
 Lu, Deyu; Gygi, François; Galli, Giulia
 Physical Review Letters, Vol. 100, Issue 14
Iterative calculations of dielectric eigenvalue spectra
journal, June 2009
 Wilson, Hugh F.; Lu, Deyu; Gygi, François
 Physical Review B, Vol. 79, Issue 24
Efficient iterative method for calculations of dielectric matrices
journal, September 2008
 Wilson, Hugh F.; Gygi, François; Galli, Giulia
 Physical Review B, Vol. 78, Issue 11
Dielectric band structure of solids
journal, January 1979
 Baldereschi, A.; Tosatti, E.
 Solid State Communications, Vol. 29, Issue 3
Dielectric band structure of crystals: General properties and calculations for silicon
journal, July 1981
 Car, R.; Tosatti, E.; Baroni, S.
 Physical Review B, Vol. 24, Issue 2
Ab initio static dielectric matrices from the densityfunctional approach. I. Formulation and application to semiconductors and insulators
journal, April 1987
 Hybertsen, Mark S.; Louie, Steven G.
 Physical Review B, Vol. 35, Issue 11
Turbo charging timedependent densityfunctional theory with Lanczos chains
journal, April 2008
 Rocca, Dario; Gebauer, Ralph; Saad, Yousef
 The Journal of Chemical Physics, Vol. 128, Issue 15
SpaceTime Method for Ab Initio Calculations of SelfEnergies and Dielectric Response Functions of Solids
journal, March 1995
 Rojas, H. N.; Godby, R. W.; Needs, R. J.
 Physical Review Letters, Vol. 74, Issue 10
The GW spacetime method for the selfenergy of large systems
journal, March 1999
 Rieger, Martin M.; Steinbeck, L.; White, I. D.
 Computer Physics Communications, Vol. 117, Issue 3
QUANTUM ESPRESSO: a modular and opensource software project for quantum simulations of materials
journal, September 2009
 Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola
 Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502
A firstprinciples study of weakly bound molecules using exact exchange and the random phase approximation
journal, January 2010
 Nguyen, HuyViet; Galli, Giulia
 The Journal of Chemical Physics, Vol. 132, Issue 4
van der Waals Interactions in Molecular Assemblies from FirstPrinciples Calculations
journal, February 2010
 Li, Yan; Lu, Deyu; Nguyen, HuyViet
 The Journal of Physical Chemistry A, Vol. 114, Issue 4
Generalized Gradient Approximation Made Simple
journal, October 1996
 Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
 Physical Review Letters, Vol. 77, Issue 18, p. 38653868
Firstprinciples $\mathit{GW}$ calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
journal, March 2011
 Blase, X.; Attaccalite, C.; Olevano, V.
 Physical Review B, Vol. 83, Issue 11
The GW Method for Quantum Chemistry Applications: Theory and Implementation
journal, December 2012
 van Setten, M. J.; Weigend, F.; Evers, F.
 Journal of Chemical Theory and Computation, Vol. 9, Issue 1
Assessment of Gaussian2 and density functional theories for the computation of enthalpies of formation
journal, January 1997
 Curtiss, Larry A.; Raghavachari, Krishnan; Redfern, Paul C.
 The Journal of Chemical Physics, Vol. 106, Issue 3
ABINIT: Firstprinciples approach to material and nanosystem properties
journal, December 2009
 Gonze, X.; Amadon, B.; Anglade, P. M.
 Computer Physics Communications, Vol. 180, Issue 12
Rationale for mixing exact exchange with density functional approximations
journal, December 1996
 Perdew, John P.; Ernzerhof, Matthias; Burke, Kieron
 The Journal of Chemical Physics, Vol. 105, Issue 22, p. 99829985
Toward reliable density functional methods without adjustable parameters: The PBE0 model
journal, April 1999
 Adamo, Carlo; Barone, Vincenzo
 The Journal of Chemical Physics, Vol. 110, Issue 13
Hybrid functionals based on a screened Coulomb potential
journal, May 2003
 Heyd, Jochen; Scuseria, Gustavo E.; Ernzerhof, Matthias
 The Journal of Chemical Physics, Vol. 118, Issue 18
Selfinteraction correction to densityfunctional approximations for manyelectron systems
journal, May 1981
 Perdew, J. P.; Zunger, Alex
 Physical Review B, Vol. 23, Issue 10, p. 50485079
Fully selfconsistent GW calculations for molecules
journal, February 2010
 Rostgaard, C.; Jacobsen, K. W.; Thygesen, K. S.
 Physical Review B, Vol. 81, Issue 8
Benchmarking the Starting Points of the GW Approximation for Molecules
journal, December 2012
 Bruneval, Fabien; Marques, Miguel A. L.
 Journal of Chemical Theory and Computation, Vol. 9, Issue 1
Efficient Band Gap Prediction for Solids
journal, November 2010
 Chan, M. K. Y.; Ceder, G.
 Physical Review Letters, Vol. 105, Issue 19
Resolutionofidentity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atomcentered orbital basis functions
journal, May 2012
 Ren, Xinguo; Rinke, Patrick; Blum, Volker
 New Journal of Physics, Vol. 14, Issue 5
Ab initio calculation of the macroscopic dielectric constant in silicon
journal, May 1986
 Baroni, Stefano; Resta, Raffaele
 Physical Review B, Vol. 33, Issue 10
Meanvalue point and dielectric properties of semiconductors and insulators
journal, June 1978
 Baldereschi, A.; Tosatti, E.
 Physical Review B, Vol. 17, Issue 12
Spectral properties of quasiparticles in a semiconductor
journal, October 1997
 Fleszar, A.; Hanke, W.
 Physical Review B, Vol. 56, Issue 16
Exactexchangebased quasiparticle calculations
journal, September 2000
 Aulbur, Wilfried G.; Städele, Martin; Görling, Andreas
 Physical Review B, Vol. 62, Issue 11
Quasiparticle bandstructure calculations for C, Si, Ge, GaAs, and SiC using Gaussianorbital basis sets
journal, December 1993
 Rohlfing, Michael; Krüger, Peter; Pollmann, Johannes
 Physical Review B, Vol. 48, Issue 24
Electronic and spectroscopic properties of the hydrogenterminated Si(111) surface from ab initio calculations
journal, July 2010
 Li, Yan; Galli, Giulia
 Physical Review B, Vol. 82, Issue 4
Implementation of an allelectron GW approximation based on the projector augmented wave method without plasmon pole approximation: Application to Si, SiC, AlAs, InAs, NaH, and KH
journal, April 2003
 Lebègue, S.; Arnaud, B.; Alouani, M.
 Physical Review B, Vol. 67, Issue 15
Microscopic modeling of the dielectric properties of silicon nitride
journal, July 2011
 Pham, T. Anh; Li, Tianshu; Shankar, Sadasivan
 Physical Review B, Vol. 84, Issue 4
Firstprinciples investigations of the dielectric properties of crystalline and amorphous Si3N4 thin films
journal, February 2010
 Pham, T. Anh; Li, Tianshu; Shankar, Sadasivan
 Applied Physics Letters, Vol. 96, Issue 6
Optical properties, band gap, and surface roughness of Si3N4
journal, February 1977
 Bauer, J.
 Physica Status Solidi (a), Vol. 39, Issue 2
Phonons and related crystal properties from densityfunctional perturbation theory
journal, July 2001
 Baroni, Stefano; de Gironcoli, Stefano; Dal Corso, Andrea
 Reviews of Modern Physics, Vol. 73, Issue 2
Works referencing / citing this record:
Comparing timedependent density functional theory with manybody perturbation theory for semiconductors: Screened rangeseparated hybrids and the $GW$ plus BetheSalpeter approach
journal, June 2019
 Wing, Dahvyd; Haber, Jonah B.; Noff, Roy
 Physical Review Materials, Vol. 3, Issue 6
Design of defect spins in piezoelectric aluminum nitride for solidstate hybrid quantum technologies
journal, February 2016
 Seo, Hosung; Govoni, Marco; Galli, Giulia
 Scientific Reports, Vol. 6, Issue 1
Comparing timedependent density functional theory with manybody perturbation theory for semiconductors: Screened rangeseparated hybrids and the $GW$ plus BetheSalpeter approach
journal, June 2019
 Wing, Dahvyd; Haber, Jonah B.; Noff, Roy
 Physical Review Materials, Vol. 3, Issue 6
The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy
journal, July 2019
 Golze, Dorothea; Dvorak, Marc; Rinke, Patrick
 Frontiers in Chemistry, Vol. 7
Ab initio simulations of liquid electrolytes for energy conversion and storage
journal, October 2018
 Pham, Tuan Anh
 International Journal of Quantum Chemistry, Vol. 119, Issue 1
Re‐weighted random series path integral simulations of molecular clusters: Applications to lithium solvated by a mixed Stockmayer cluster
journal, December 2018
 Hyers, Matthew J.; Fodor, Alex M.; Bierwisch, Dominic K.
 International Journal of Quantum Chemistry, Vol. 119, Issue 13
Modelling heterogeneous interfaces for solar water splitting
journal, January 2017
 Pham, Tuan Anh; Ping, Yuan; Galli, Giulia
 Nature Materials, Vol. 16, Issue 4
Speeding up GW Calculations to Meet the Challenge of Large Scale Quasiparticle Predictions
journal, November 2016
 Gao, Weiwei; Xia, Weiyi; Gao, Xiang
 Scientific Reports, Vol. 6, Issue 1
Dimensionality and anisotropicity dependence of radiative recombination in nanostructured phosphorene
journal, January 2019
 Wu, Feng; Rocca, Dario; Ping, Yuan
 Journal of Materials Chemistry C, Vol. 7, Issue 41
Communication: Electronic structure of the solvated chloride anion from first principles molecular dynamics
journal, May 2013
 Zhang, Cui; Pham, Tuan Anh; Gygi, François
 The Journal of Chemical Physics, Vol. 138, Issue 18
GW and BetheSalpeter study of small water clusters
journal, January 2016
 Blase, Xavier; Boulanger, Paul; Bruneval, Fabien
 The Journal of Chemical Physics, Vol. 144, Issue 3
Combining the GW formalism with the polarizable continuum model: A statespecific nonequilibrium approach
journal, April 2016
 Duchemin, Ivan; Jacquemin, Denis; Blase, Xavier
 The Journal of Chemical Physics, Vol. 144, Issue 16
Allelectron ab initio BetheSalpeter equation approach to neutral excitations in molecules with numeric atomcentered orbitals
journal, January 2020
 Liu, Chi; Kloppenburg, Jan; Yao, Yi
 The Journal of Chemical Physics, Vol. 152, Issue 4
Improving the efficiency of G _{0} W _{0} calculations with approximate spectral decompositions of dielectric matrices
journal, December 2019
 Yang, Han; Govoni, Marco; Galli, Giulia
 The Journal of Chemical Physics, Vol. 151, Issue 22
Ab initio SternheimerGW method for quasiparticle calculations using plane waves
journal, August 2013
 Lambert, Henry; Giustino, Feliciano
 Physical Review B, Vol. 88, Issue 7
Probing the electronic structure of liquid water with manybody perturbation theory
journal, February 2014
 Pham, T. Anh; Zhang, Cui; Schwegler, Eric
 Physical Review B, Vol. 89, Issue 6
Selfconsistent hybrid functional for condensed systems
journal, May 2014
 Skone, Jonathan H.; Govoni, Marco; Galli, Giulia
 Physical Review B, Vol. 89, Issue 19
Allelectron selfconsistent $GW$ in the Matsubaratime domain: Implementation and benchmarks of semiconductors and insulators
journal, March 2016
 Chu, IekHeng; Trinastic, Jonathan P.; Wang, YunPeng
 Physical Review B, Vol. 93, Issue 12
Excitation spectra of aromatic molecules within a realspace $GW$ BSE formalism: Role of selfconsistency and vertex corrections
journal, August 2016
 Hung, Linda; da Jornada, Felipe H.; SoutoCasares, Jaime
 Physical Review B, Vol. 94, Issue 8
Electronic structure of Na, K, Si, and LiF from selfconsistent solution of Hedin's equations including vertex corrections
journal, October 2016
 Kutepov, Andrey L.
 Physical Review B, Vol. 94, Issue 15
Accurate description of charged excitations in molecular solids from embedded manybody perturbation theory
journal, January 2018
 Li, Jing; D'Avino, Gabriele; Duchemin, Ivan
 Physical Review B, Vol. 97, Issue 3
Spectral properties from Matsubara Green's function approach: Application to molecules
journal, March 2018
 Schüler, M.; Pavlyukh, Y.
 Physical Review B, Vol. 97, Issue 11
Solar Nanocomposites with Complementary Charge Extraction Pathways for Electrons and Holes: Si Embedded in ZnS
journal, March 2014
 Wippermann, Stefan; Vörös, Márton; Gali, Adam
 Physical Review Letters, Vol. 112, Issue 10
Breaking the Theoretical Scaling Limit for Predicting Quasiparticle Energies: The Stochastic $GW$ Approach
journal, August 2014
 Neuhauser, Daniel; Gao, Yi; Arntsen, Christopher
 Physical Review Letters, Vol. 113, Issue 7
Firstprinciples engineering of charged defects for twodimensional quantum technologies
journal, December 2017
 Wu, Feng; Galatas, Andrew; Sundararaman, Ravishankar
 Physical Review Materials, Vol. 1, Issue 7
Fundamental principles for calculating charged defect ionization energies in ultrathin twodimensional materials
journal, December 2018
 Smart, Tyler J.; Wu, Feng; Govoni, Marco
 Physical Review Materials, Vol. 2, Issue 12