Reproducibility in G0W0 calculations for solids
Abstract
Ab initio many-body perturbation theory within the GW approximation is a Green's function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become an increasingly standard approach, Kohn–Sham eigenenergies, generated from a DFT calculation with a strategically-chosen exchange–correlation functional “starting point”, are used to construct G and W, and then perturbatively corrected by the resultant GW self-energy. In practice, there are several ways to construct the GW self-energy, and these can lead to variations in predicted quasiparticle energies. For example, for ZnO and TiO2, the GW fundamental gaps reported in the literature can vary by more than 1 eV depending on the GW code used. In this work, we calculate and analyze GW quasiparticle (QP) energies of these and other systems with three different GW codes: BERKELEYGW, ABINIT and YAMBO. Through a systematic analysis of the GW implementation of these three codes, we identify the primary origin of major discrepancies between codes reported in prior literature to be the different implementations the Coulomb divergence in the Fock exchange term and the frequency integration scheme of the GW self-energy. We then eliminate these discrepancies by using common numerical methods and algorithms, demonstrating that the samemore »
- Authors:
-
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- European Theoretical Spectroscopy Facility (ETSF) (Belgium); Consiglio Nazionale delle Ricerche (CNR), Modena (Italy). Istituto Nanoscienze (CNR-NANO)
- Univ. of Quebec a Trois-Rivieres, QC (Canada); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
- Univ. Paris-Saclay, Gif-sur-Yvette (France); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
- Stanford Univ., CA (United States); Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Univ. catholique de Louvain (Belgium); Interuniversity Microelectronics Centre (IMEC), Leuven (Belgium); European Theoretical Spectroscopy Facility (ETSF) (Belgium)
- Univ. of Dublin (Ireland)
- European Theoretical Spectroscopy Facility (ETSF) (Belgium); National Research Council (CNR), Montelibretti (Italy)
- European Theoretical Spectroscopy Facility (ETSF) (Belgium); Univ. catholique de Louvain (Belgium)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Kavli Energy NanoScience Institute, Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1647622
- Alternate Identifier(s):
- OSTI ID: 1633342
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Physics Communications
- Additional Journal Information:
- Journal Volume: 255; Journal ID: ISSN 0010-4655
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE
Citation Formats
Rangel, Tonatiuh, Del Ben, Mauro, Varsano, Daniele, Antonius, Gabriel, Bruneval, Fabien, da Jornada, Felipe H., van Setten, Michiel J., Orhan, Okan K., O’Regan, David D., Canning, Andrew, Ferretti, Andrea, Marini, Andrea, Rignanese, Gian-Marco, Deslippe, Jack, Louie, Steven G., and Neaton, Jeffrey B. Reproducibility in G0W0 calculations for solids. United States: N. p., 2020.
Web. doi:10.1016/j.cpc.2020.107242.
Rangel, Tonatiuh, Del Ben, Mauro, Varsano, Daniele, Antonius, Gabriel, Bruneval, Fabien, da Jornada, Felipe H., van Setten, Michiel J., Orhan, Okan K., O’Regan, David D., Canning, Andrew, Ferretti, Andrea, Marini, Andrea, Rignanese, Gian-Marco, Deslippe, Jack, Louie, Steven G., & Neaton, Jeffrey B. Reproducibility in G0W0 calculations for solids. United States. https://doi.org/10.1016/j.cpc.2020.107242
Rangel, Tonatiuh, Del Ben, Mauro, Varsano, Daniele, Antonius, Gabriel, Bruneval, Fabien, da Jornada, Felipe H., van Setten, Michiel J., Orhan, Okan K., O’Regan, David D., Canning, Andrew, Ferretti, Andrea, Marini, Andrea, Rignanese, Gian-Marco, Deslippe, Jack, Louie, Steven G., and Neaton, Jeffrey B. Wed .
"Reproducibility in G0W0 calculations for solids". United States. https://doi.org/10.1016/j.cpc.2020.107242. https://www.osti.gov/servlets/purl/1647622.
@article{osti_1647622,
title = {Reproducibility in G0W0 calculations for solids},
author = {Rangel, Tonatiuh and Del Ben, Mauro and Varsano, Daniele and Antonius, Gabriel and Bruneval, Fabien and da Jornada, Felipe H. and van Setten, Michiel J. and Orhan, Okan K. and O’Regan, David D. and Canning, Andrew and Ferretti, Andrea and Marini, Andrea and Rignanese, Gian-Marco and Deslippe, Jack and Louie, Steven G. and Neaton, Jeffrey B.},
abstractNote = {Ab initio many-body perturbation theory within the GW approximation is a Green's function formalism widely used in the calculation of quasiparticle excitation energies of solids. In what has become an increasingly standard approach, Kohn–Sham eigenenergies, generated from a DFT calculation with a strategically-chosen exchange–correlation functional “starting point”, are used to construct G and W, and then perturbatively corrected by the resultant GW self-energy. In practice, there are several ways to construct the GW self-energy, and these can lead to variations in predicted quasiparticle energies. For example, for ZnO and TiO2, the GW fundamental gaps reported in the literature can vary by more than 1 eV depending on the GW code used. In this work, we calculate and analyze GW quasiparticle (QP) energies of these and other systems with three different GW codes: BERKELEYGW, ABINIT and YAMBO. Through a systematic analysis of the GW implementation of these three codes, we identify the primary origin of major discrepancies between codes reported in prior literature to be the different implementations the Coulomb divergence in the Fock exchange term and the frequency integration scheme of the GW self-energy. We then eliminate these discrepancies by using common numerical methods and algorithms, demonstrating that the same quasiparticle energies for a given material can be obtained with different codes, within numerical differences ascribable to the technical details of the underling implementations. This work will be important for users and developers in assessing the precision of future GW applications and methods.},
doi = {10.1016/j.cpc.2020.107242},
journal = {Computer Physics Communications},
number = ,
volume = 255,
place = {United States},
year = {Wed Mar 04 00:00:00 EST 2020},
month = {Wed Mar 04 00:00:00 EST 2020}
}
Web of Science
Works referenced in this record:
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
Generalized Kohn-Sham schemes and the band-gap problem
journal, February 1996
- Seidl, A.; Görling, A.; Vogl, P.
- Physical Review B, Vol. 53, Issue 7
First-Principles Theory of Quasiparticles: Calculation of Band Gaps in Semiconductors and Insulators
journal, September 1985
- Hybertsen, Mark S.; Louie, Steven G.
- Physical Review Letters, Vol. 55, Issue 13
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
The GW method
journal, March 1998
- Aryasetiawan, F.; Gunnarsson, O.
- Reports on Progress in Physics, Vol. 61, Issue 3
Electronic excitations: density-functional versus many-body Green’s-function approaches
journal, June 2002
- Onida, Giovanni; Reining, Lucia; Rubio, Angel
- Reviews of Modern Physics, Vol. 74, Issue 2
Band Offsets at the Interface from Many-Body Perturbation Theory
journal, May 2008
- Shaltaf, R.; Rignanese, G. -M.; Gonze, X.
- Physical Review Letters, Vol. 100, Issue 18
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
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
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
Predictive calculations using plane waves and pseudopotentials
journal, August 2014
- Klimeš, Jiří; Kaltak, Merzuk; Kresse, Georg
- Physical Review B, Vol. 90, Issue 7
The electronic structures of the thin films of InVO4 and TiO2 by first principles calculations
journal, December 2003
- Oshikiri, M.; Boero, M.; Ye, J.
- Thin Solid Films, Vol. 445, Issue 2
Self-energy and excitonic effects in the electronic and optical properties of crystalline phases
journal, July 2010
- Chiodo, Letizia; García-Lastra, Juan Maria; Iacomino, Amilcare
- Physical Review B, Vol. 82, Issue 4
First-principles study of oxygen vacancies in rutile
journal, February 2014
- Malashevich, Andrei; Jain, Manish; Louie, Steven G.
- Physical Review B, Vol. 89, Issue 7
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
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
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
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
Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions
journal, May 2012
- Ren, Xinguo; Rinke, Patrick; Blum, Volker
- New Journal of Physics, Vol. 14, Issue 5
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
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 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
Recent developments in the ABINIT software package
journal, August 2016
- Gonze, X.; Jollet, F.; Abreu Araujo, F.
- Computer Physics Communications, Vol. 205
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
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
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
Evaluation of quasiparticle energies for semiconductors without inversion symmetry
journal, August 1989
- Zhang, S. B.; Tománek, D.; Cohen, Marvin L.
- Physical Review B, Vol. 40, Issue 5
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
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
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
Numerical integration for ab initio many-electron self energy calculations within the GW approximation
journal, April 2015
- Liu, Fang; Lin, Lin; Vigil-Fowler, Derek
- Journal of Computational Physics, Vol. 286
Ab initio static dielectric matrices from the density-functional 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
Ab initio calculation of the macroscopic dielectric constant in silicon
journal, May 1986
- Baroni, Stefano; Resta, Raffaele
- Physical Review B, Vol. 33, Issue 10
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
Microscopic Theory of Force Constants in the Adiabatic Approximation
journal, January 1970
- Pick, Robert M.; Cohen, Morrel H.; Martin, Richard M.
- Physical Review B, Vol. 1, Issue 2
Hartree-Fock LAPW approach to the electronic properties of periodic systems
journal, August 1993
- Massidda, S.; Posternak, M.; Baldereschi, A.
- Physical Review B, Vol. 48, Issue 8
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
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
Exact Coulomb cutoff technique for supercell calculations
journal, May 2006
- Rozzi, Carlo A.; Varsano, Daniele; Marini, Andrea
- Physical Review B, Vol. 73, Issue 20
Truncation of periodic image interactions for confined systems
journal, June 2006
- Ismail-Beigi, Sohrab
- Physical Review B, Vol. 73, Issue 23
Ab Initio Calculation of Self-Energy Effects on Optical Properties of GaAs(110)
journal, December 1998
- Pulci, Olivia; Onida, Giovanni; Del Sole, Rodolfo
- Physical Review Letters, Vol. 81, Issue 24
Optimized norm-conserving Vanderbilt pseudopotentials
journal, August 2013
- Hamann, D. R.
- Physical Review B, Vol. 88, Issue 8
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
Influence of the Core-Valence Interaction and of the Pseudopotential Approximation on the Electron Self-Energy in Semiconductors
journal, September 2008
- Gómez-Abal, Ricardo; Li, Xinzheng; Scheffler, Matthias
- Physical Review Letters, Vol. 101, Issue 10
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
Theory and computation of hot carriers generated by surface plasmon polaritons in noble metals
journal, June 2015
- Bernardi, Marco; Mustafa, Jamal; Neaton, Jeffrey B.
- Nature Communications, Vol. 6, Issue 1
Relativistic separable dual-space Gaussian pseudopotentials from H to Rn
journal, August 1998
- Hartwigsen, C.; Goedecker, S.; Hutter, J.
- Physical Review B, Vol. 58, Issue 7
Parameter-Free Calculation of Response Functions in Time-Dependent Density-Functional Theory
journal, July 2003
- Sottile, Francesco; Olevano, Valerio; Reining, Lucia
- Physical Review Letters, Vol. 91, Issue 5
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
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
Strong Renormalization of the Electronic Band Gap due to Lattice Polarization in the Formalism
journal, May 2013
- Botti, Silvana; Marques, Miguel A. L.
- Physical Review Letters, Vol. 110, Issue 22
Isotope effects on the optical spectra of semiconductors
journal, November 2005
- Cardona, Manuel; Thewalt, M. L. W.
- Reviews of Modern Physics, Vol. 77, Issue 4
Correlation effects on electron-phonon coupling in semiconductors: Many-body theory along thermal lines
journal, March 2016
- Monserrat, Bartomeu
- Physical Review B, Vol. 93, Issue 10
Photoemission and Bremsstrahlung Isochromat Spectroscopy Studies of TiO 2 (Rutile) and SrTiO 3
journal, January 1994
- Tezuka, Yasuhisa; Shin, Shik; Ishii, Takehiko
- Journal of the Physical Society of Japan, Vol. 63, Issue 1
Electronic properties of ultrathin Cu and Fe films on (110) studied by photoemission and inverse photoemission
journal, October 1994
- See, A. K.; Bartynski, R. A.
- Physical Review B, Vol. 50, Issue 16
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
The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
journal, May 2018
- van Setten, M. J.; Giantomassi, M.; Bousquet, E.
- Computer Physics Communications, Vol. 226
Optimized pseudopotentials
journal, January 1990
- Rappe, Andrew M.; Rabe, Karin M.; Kaxiras, Efthimios
- Physical Review B, Vol. 41, Issue 2
Coulomb-hole summations and energies for calculations with limited number of empty orbitals: A modified static remainder approach
journal, April 2013
- Deslippe, Jack; Samsonidze, Georgy; Jain, Manish
- Physical Review B, Vol. 87, Issue 16