Static subspace approximation for the evaluation of G0W0 quasiparticle energies within a sum-over-bands approach
Abstract
Many-body perturbation theory within the GW approach has been established as a quantitatively accurate approach for predicting the quasiparticle and excited-state properties of a wide variety of materials. However, the successful application of the method is often complicated by the computational complexity associated with the evaluation and inversion of the frequency-dependent dielectric matrix ε(ω). Here, we describe an approach to speed up the evaluation of the frequency-dependent part of ε(ω) in the traditional sum-over-states GW framework based on the low-rank approximation of the static dielectric matrix, a technique often used in GW implementations that are based on a starting mean field within density-functional perturbation theory. We show that the overall accuracy of the approach, independently from other calculation parameters, is solely determined by the threshold on the eigenvalues of the static dielectric matrix, ε(ω = 0) , and that it can yield orders-of-magnitude speed-ups in full-frequency G W calculations. In this work, we validate our implementation with several benchmark calculations ranging from bulk materials to systems with reduced dimensionality, and show that this technique allows one not only to study larger systems, but also to carefully consider the convergence of computationally demanding systems, such as ZnO, without relying on plasmon-polemore »
- Authors:
-
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
- Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division
- Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Sciences Division; Univ. du Quebec, Trois-Rivieres (Canada). Inst. de Recherche sur l'Hydrogene, Dept. de Chimie, Biochimie et Physique
- Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Molecular Foundry
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division; USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1530392
- Alternate Identifier(s):
- OSTI ID: 1501693
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 12; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; GW; Full Frequency; Contour Deformation; quasiparticle band structure
Citation Formats
Del Ben, Mauro, da Jornada, Felipe H., Antonius, Gabriel, Rangel, Tonatiuh, Louie, Steven G., Deslippe, Jack, and Canning, Andrew. Static subspace approximation for the evaluation of G0W0 quasiparticle energies within a sum-over-bands approach. United States: N. p., 2019.
Web. doi:10.1103/PhysRevB.99.125128.
Del Ben, Mauro, da Jornada, Felipe H., Antonius, Gabriel, Rangel, Tonatiuh, Louie, Steven G., Deslippe, Jack, & Canning, Andrew. Static subspace approximation for the evaluation of G0W0 quasiparticle energies within a sum-over-bands approach. United States. https://doi.org/10.1103/PhysRevB.99.125128
Del Ben, Mauro, da Jornada, Felipe H., Antonius, Gabriel, Rangel, Tonatiuh, Louie, Steven G., Deslippe, Jack, and Canning, Andrew. Mon .
"Static subspace approximation for the evaluation of G0W0 quasiparticle energies within a sum-over-bands approach". United States. https://doi.org/10.1103/PhysRevB.99.125128. https://www.osti.gov/servlets/purl/1530392.
@article{osti_1530392,
title = {Static subspace approximation for the evaluation of G0W0 quasiparticle energies within a sum-over-bands approach},
author = {Del Ben, Mauro and da Jornada, Felipe H. and Antonius, Gabriel and Rangel, Tonatiuh and Louie, Steven G. and Deslippe, Jack and Canning, Andrew},
abstractNote = {Many-body perturbation theory within the GW approach has been established as a quantitatively accurate approach for predicting the quasiparticle and excited-state properties of a wide variety of materials. However, the successful application of the method is often complicated by the computational complexity associated with the evaluation and inversion of the frequency-dependent dielectric matrix ε(ω). Here, we describe an approach to speed up the evaluation of the frequency-dependent part of ε(ω) in the traditional sum-over-states GW framework based on the low-rank approximation of the static dielectric matrix, a technique often used in GW implementations that are based on a starting mean field within density-functional perturbation theory. We show that the overall accuracy of the approach, independently from other calculation parameters, is solely determined by the threshold on the eigenvalues of the static dielectric matrix, ε(ω = 0) , and that it can yield orders-of-magnitude speed-ups in full-frequency G W calculations. In this work, we validate our implementation with several benchmark calculations ranging from bulk materials to systems with reduced dimensionality, and show that this technique allows one not only to study larger systems, but also to carefully consider the convergence of computationally demanding systems, such as ZnO, without relying on plasmon-pole models.},
doi = {10.1103/PhysRevB.99.125128},
journal = {Physical Review B},
number = 12,
volume = 99,
place = {United States},
year = {Mon Mar 18 00:00:00 EDT 2019},
month = {Mon Mar 18 00:00:00 EDT 2019}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 3 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Efficient dielectric matrix calculations using the Lanczos algorithm for fast many-body implementations
journal, March 2015
- Laflamme Janssen, Jonathan; Rousseau, Bruno; Côté, Michel
- Physical Review B, Vol. 91, Issue 12
Generalized Gradient Approximation Made Simple
journal, October 1996
- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
All-electron calculation based on the LAPW method: Application to wurtzite ZnO
journal, September 2002
- Usuda, Manabu; Hamada, Noriaki; Kotani, Takao
- Physical Review B, Vol. 66, Issue 12
Insights and challenges of applying the GW method to transition metal oxides
journal, October 2014
- Samsonidze, Georgy; Park, Cheol-Hwan; Kozinsky, Boris
- Journal of Physics: Condensed Matter, Vol. 26, Issue 47
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
Efficient implementation of the approximation within the all-electron FLAPW method
journal, March 2010
- Friedrich, Christoph; Blügel, Stefan; Schindlmayr, Arno
- Physical Review B, Vol. 81, Issue 12
Quantum Theory of the Dielectric Constant in Real Solids
journal, April 1962
- Adler, Stephen L.
- Physical Review, Vol. 126, Issue 2
Erratum: Optical Spectrum of : Many-Body Effects and Diversity of Exciton States [Phys. Rev. Lett. 111 , 216805 (2013)]
journal, September 2015
- Qiu, Diana Y.; da Jornada, Felipe H.; Louie, Steven G.
- Physical Review Letters, Vol. 115, 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
Efficient calculations for SnO , ZnO, and rubrene: The effective-energy technique
journal, February 2012
- Berger, J. A.; Reining, Lucia; Sottile, Francesco
- Physical Review B, Vol. 85, Issue 8
Angle-resolved photoemission and quasiparticle calculation of ZnO: The need for band shift in oxide semiconductors
journal, December 2012
- Lim, Linda Y.; Lany, Stephan; Chang, Young Jun
- Physical Review B, Vol. 86, Issue 23
BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures
journal, June 2012
- Deslippe, Jack; Samsonidze, Georgy; Strubbe, David A.
- Computer Physics Communications, Vol. 183, Issue 6
QUANTUM ESPRESSO: a modular and open-source 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
Effects of plasmon pole models on the G0W0 electronic structure of various oxides
journal, September 2012
- Miglio, A.; Waroquiers, D.; Antonius, G.
- The European Physical Journal B, Vol. 85, Issue 9
molgw 1: Many-body perturbation theory software for atoms, molecules, and clusters
journal, November 2016
- Bruneval, Fabien; Rangel, Tonatiuh; Hamed, Samia M.
- Computer Physics Communications, Vol. 208
Stochastic GW Calculations for Molecules
journal, September 2017
- Vlček, Vojtěch; Rabani, Eran; Neuhauser, Daniel
- Journal of Chemical Theory and Computation, Vol. 13, Issue 10
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. 5390-5413
Implementation of an all-electron 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
Self-energy operators and exchange-correlation potentials in semiconductors
journal, June 1988
- Godby, R. W.; Schlüter, M.; Sham, L. J.
- Physical Review B, Vol. 37, Issue 17
Optimized norm-conserving Vanderbilt pseudopotentials
journal, August 2013
- Hamann, D. R.
- Physical Review B, Vol. 88, Issue 8
Optical Spectrum of : Many-Body Effects and Diversity of Exciton States
journal, November 2013
- Qiu, Diana Y.; da Jornada, Felipe H.; Louie, Steven G.
- Physical Review Letters, Vol. 111, Issue 21
Ionization Potentials of Solids: The Importance of Vertex Corrections
journal, March 2014
- Grüneis, Andreas; Kresse, Georg; Hinuma, Yoyo
- Physical Review Letters, Vol. 112, Issue 9
Truncation of periodic image interactions for confined systems
journal, June 2006
- Ismail-Beigi, Sohrab
- Physical Review B, Vol. 73, Issue 23
Electronic properties of interfaces and defects from many-body perturbation theory: Recent developments and applications
journal, January 2011
- Giantomassi, M.; Stankovski, M.; Shaltaf, R.
- physica status solidi (b), Vol. 248, Issue 2
Reproducibility in density functional theory calculations of solids
journal, March 2016
- Lejaeghere, K.; Bihlmayer, G.; Bjorkman, T.
- Science, Vol. 351, Issue 6280
Dielectric band structure of solids
journal, January 1979
- Baldereschi, A.; Tosatti, E.
- Solid State Communications, Vol. 29, Issue 3
Self-consistent Hartree-Fock and screened-exchange calculations in solids: Application to silicon
journal, September 1986
- Gygi, F.; Baldereschi, A.
- Physical Review B, Vol. 34, Issue 6
A brief introduction to the ABINIT software package
journal, January 2005
- Gonze, Xavier
- Zeitschrift für Kristallographie - Crystalline Materials, Vol. 220, Issue 5/6
Analysis of numerical methods for evaluating the Fock exchange integral in a plane-wave basis
journal, September 2011
- Holzwarth, N. A. W.; Xu, Xiao
- Physical Review B, Vol. 84, Issue 11
Metal-insulator transition in Kohn-Sham theory and quasiparticle theory
journal, March 1989
- Godby, R. W.; Needs, R. J.
- Physical Review Letters, Vol. 62, Issue 10
Erratum: Band convergence and linearization error correction of all-electron calculations: The extreme case of zinc oxide [Phys. Rev. B10.1103/PhysRevB.83.081101 83 , 081101(R) (2011)]
journal, July 2011
- Friedrich, Christoph; Müller, Mathias C.; Blügel, Stefan
- Physical Review B, Vol. 84, Issue 3
A reciprocal space based method for treating long range interactions in ab initio and force-field-based calculations in clusters
journal, February 1999
- Martyna, Glenn J.; Tuckerman, Mark E.
- The Journal of Chemical Physics, Vol. 110, Issue 6
Generalized plasmon-pole model and plasmon band structures of crystals
journal, June 1993
- Engel, G. E.; Farid, Behnam
- Physical Review B, Vol. 47, Issue 23
GW method with the self-consistent Sternheimer equation
journal, March 2010
- Giustino, Feliciano; Cohen, Marvin L.; Louie, Steven G.
- Physical Review B, Vol. 81, Issue 11
band gap of ZnO: Effects of plasmon-pole models
journal, December 2011
- Stankovski, M.; Antonius, G.; Waroquiers, D.
- Physical Review B, Vol. 84, Issue 24
GW quasiparticle spectra from occupied states only
journal, March 2010
- Umari, P.; Stenuit, Geoffrey; Baroni, Stefano
- Physical Review B, Vol. 81, Issue 11
Efficient pseudopotentials for plane-wave calculations
journal, January 1991
- Troullier, N.; Martins, José Luriaas
- Physical Review B, Vol. 43, Issue 3
Low rank approximation in G 0 W 0 calculations
journal, June 2016
- Shao, MeiYue; Lin, Lin; Yang, Chao
- Science China Mathematics, Vol. 59, Issue 8
Efficient calculation of the exact exchange energy in periodic systems using a truncated Coulomb potential
journal, May 2008
- Spencer, James; Alavi, Ali
- Physical Review B, Vol. 77, Issue 19
Screening and many-body effects in two-dimensional crystals: Monolayer
journal, June 2016
- Qiu, Diana Y.; da Jornada, Felipe H.; Louie, Steven G.
- Physical Review B, Vol. 93, Issue 23
Band structure of gold from many-body perturbation theory
journal, September 2012
- Rangel, T.; Kecik, D.; Trevisanutto, P. E.
- Physical Review B, Vol. 86, Issue 12
Dielectric Constant with Local Field Effects Included
journal, January 1963
- Wiser, Nathan
- Physical Review, Vol. 129, Issue 1
Large-scale GW calculations on pre-exascale HPC systems
journal, February 2019
- Del Ben, Mauro; da Jornada, Felipe H.; Canning, Andrew
- Computer Physics Communications, Vol. 235
GW 100: A Plane Wave Perspective for Small Molecules
journal, January 2017
- Maggio, Emanuele; Liu, Peitao; van Setten, Michiel J.
- Journal of Chemical Theory and Computation, Vol. 13, Issue 2
GW in the Gaussian and Plane Waves Scheme with Application to Linear Acenes
journal, July 2016
- Wilhelm, Jan; Del Ben, Mauro; Hutter, Jürg
- Journal of Chemical Theory and Computation, Vol. 12, Issue 8
Role of the plasmon-pole model in the approximation
journal, September 2013
- Larson, Paul; Dvorak, Marc; Wu, Zhigang
- Physical Review B, Vol. 88, Issue 12
Improving accuracy and efficiency of calculations of photoemission spectra within the many-body perturbation theory
journal, February 2012
- Nguyen, Huy-Viet; Pham, T. Anh; Rocca, Dario
- Physical Review B, Vol. 85, Issue 8
Nonuniform sampling schemes of the Brillouin zone for many-electron perturbation-theory calculations in reduced dimensionality
journal, January 2017
- da Jornada, Felipe H.; Qiu, Diana Y.; Louie, Steven G.
- Physical Review B, Vol. 95, Issue 3
Band convergence and linearization error correction of all-electron calculations: The extreme case of zinc oxide
journal, February 2011
- Friedrich, Christoph; Müller, Mathias C.; Blügel, Stefan
- Physical Review B, Vol. 83, Issue 8
Special points for Brillouin-zone integrations
journal, June 1976
- Monkhorst, Hendrik J.; Pack, James D.
- Physical Review B, Vol. 13, Issue 12, p. 5188-5192
GW 100: Benchmarking G 0 W 0 for Molecular Systems
journal, November 2015
- van Setten, Michiel J.; Caruso, Fabio; Sharifzadeh, Sahar
- Journal of Chemical Theory and Computation, Vol. 11, Issue 12
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem
journal, August 1965
- Hedin, Lars
- Physical Review, Vol. 139, Issue 3A
Quasiparticle band-structure calculations for C, Si, Ge, GaAs, and SiC using Gaussian-orbital basis sets
journal, December 1993
- Rohlfing, Michael; Krüger, Peter; Pollmann, Johannes
- Physical Review B, Vol. 48, Issue 24
Quasiparticle Electronic Structure of Copper in the Approximation
journal, December 2001
- Marini, Andrea; Onida, Giovanni; Del Sole, Rodolfo
- Physical Review Letters, Vol. 88, Issue 1
All-electron mixed basis calculations of and ZnO crystals
journal, April 2016
- Zhang, Ming; Ono, Shota; Nagatsuka, Naoki
- Physical Review B, Vol. 93, Issue 15
Spectral properties of quasiparticles in a semiconductor
journal, October 1997
- Fleszar, A.; Hanke, W.
- Physical Review B, Vol. 56, Issue 16
Predictive calculations using plane waves and pseudopotentials
journal, August 2014
- Klimeš, Jiří; Kaltak, Merzuk; Kresse, Georg
- Physical Review B, Vol. 90, Issue 7
FHI-gap: A code based on the all-electron augmented plane wave method
journal, February 2013
- Jiang, Hong; Gómez-Abal, Ricardo I.; Li, Xin-Zheng
- Computer Physics Communications, Vol. 184, Issue 2
Quasiparticle semiconductor band structures including spin–orbit interactions
journal, February 2013
- Malone, Brad D.; Cohen, Marvin L.
- Journal of Physics: Condensed Matter, Vol. 25, Issue 10
How dielectric screening in two-dimensional crystals affects the convergence of excited-state calculations: Monolayer MoS
journal, December 2013
- Hüser, Falco; Olsen, Thomas; Thygesen, Kristian S.
- Physical Review B, Vol. 88, Issue 24
Optimization algorithm for the generation of ONCV pseudopotentials
journal, November 2015
- Schlipf, Martin; Gygi, François
- Computer Physics Communications, Vol. 196
Iterative calculations of dielectric eigenvalue spectra
journal, June 2009
- Wilson, Hugh F.; Lu, Deyu; Gygi, François
- Physical Review B, Vol. 79, Issue 24
calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods
journal, April 2013
- Pham, T. Anh; Nguyen, Huy-Viet; Rocca, Dario
- Physical Review B, Vol. 87, Issue 15
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
Ab initio electronic relaxation times and transport in noble metals
journal, October 2016
- Mustafa, Jamal I.; Bernardi, Marco; Neaton, Jeffrey B.
- Physical Review B, Vol. 94, Issue 15
Large Scale GW Calculations
journal, May 2015
- Govoni, Marco; Galli, Giulia
- Journal of Chemical Theory and Computation, Vol. 11, Issue 6
General treatment of the singularities in Hartree-Fock and exact-exchange Kohn-Sham methods for solids
journal, May 2007
- Carrier, Pierre; Rohra, Stefan; Görling, Andreas
- Physical Review B, Vol. 75, Issue 20
Photoemission experiments on copper
journal, October 1984
- Courths, R.; Hüfner, S.
- Physics Reports, Vol. 112, Issue 2
yambo: An ab initio tool for excited state calculations
journal, August 2009
- Marini, Andrea; Hogan, Conor; Grüning, Myrta
- Computer Physics Communications, Vol. 180, Issue 8
Implementation and performance of the frequency-dependent method within the PAW framework
journal, July 2006
- Shishkin, M.; Kresse, G.
- Physical Review B, Vol. 74, Issue 3
SaX: An open source package for electronic-structure and optical-properties calculations in the GW approximation
journal, August 2009
- Martin-Samos, Layla; Bussi, Giovanni
- Computer Physics Communications, Vol. 180, Issue 8
Local field effects and the dielectric response matrix of insulators: A model
journal, May 1974
- Johnson, David Linton
- Physical Review B, Vol. 9, Issue 10
Precise quasiparticle energies and Hartree-Fock bands of semiconductors and insulators
journal, May 1988
- von der Linden, Wolfgang; Horsch, Peter
- Physical Review B, Vol. 37, Issue 14
The GW space-time method for the self-energy of large systems
journal, March 1999
- Rieger, Martin M.; Steinbeck, L.; White, I. D.
- Computer Physics Communications, Vol. 117, Issue 3
Effect of temperature on isotopic mass dependence of excitonic band gaps in semiconductors: ZnO
journal, May 2007
- Alawadhi, H.; Tsoi, S.; Lu, X.
- Physical Review B, Vol. 75, Issue 20