Reproducibility in G0W0 calculations for solids

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.

doi:10.1016/j.cpc.2020.107242

Title: 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 »« less

Authors:

^[1]; Del Ben, Mauro ^[2]; Varsano, Daniele ^[3]; Antonius, Gabriel ^[4]; Bruneval, Fabien ^[5]; da Jornada, Felipe H. ^[6];

^[7];

^[8];

^[8]; Canning, Andrew ^[2];

^[3];

^[9];

^[10]; Deslippe, Jack ^[11]; Louie, Steven G. ^[12]; Neaton, Jeffrey B. ^[13]

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:: Wed Mar 04 00:00:00 EST 2020

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.

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                    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

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                    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.

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@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}

}

Copy to clipboard

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Title: Reproducibility in G0W0 calculations for solids

Abstract

Citation Formats

New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem journal, August 1965

Generalized Kohn-Sham schemes and the band-gap problem journal, February 1996

First-Principles Theory of Quasiparticles: Calculation of Band Gaps in Semiconductors and Insulators journal, September 1985

Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies journal, October 1986

The GW method journal, March 1998

Electronic excitations: density-functional versus many-body Green’s-function approaches journal, June 2002

Band Offsets at the Si / SiO 2 Interface from Many-Body Perturbation Theory journal, May 2008

G 0 W 0 band gap of ZnO: Effects of plasmon-pole models journal, December 2011

Effects of plasmon pole models on the G0W0 electronic structure of various oxides journal, September 2012

Role of the plasmon-pole model in the G W approximation journal, September 2013

Predictive G W calculations using plane waves and pseudopotentials journal, August 2014

The electronic structures of the thin films of InVO4 and TiO2 by first principles calculations journal, December 2003

Self-energy and excitonic effects in the electronic and optical properties of TiO 2 crystalline phases journal, July 2010

First-principles DFT + G W study of oxygen vacancies in rutile TiO 2 journal, February 2014

Band convergence and linearization error correction of all-electron GW calculations: The extreme case of zinc oxide journal, February 2011

Erratum: Band convergence and linearization error correction of all-electron G W calculations: The extreme case of zinc oxide [Phys. Rev. B10.1103/PhysRevB.83.081101 83 , 081101(R) (2011)] journal, July 2011

Efficient G W calculations for SnO 2 , ZnO, and rubrene: The effective-energy technique journal, February 2012

Insights and challenges of applying the GW method to transition metal oxides journal, October 2014

Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions journal, May 2012

The GW -Method for Quantum Chemistry Applications: Theory and Implementation journal, December 2012

GW 100: A Plane Wave Perspective for Small Molecules journal, January 2017

GW 100: Benchmarking G 0 W 0 for Molecular Systems journal, November 2015

Recent developments in the ABINIT software package journal, August 2016

BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures journal, June 2012

yambo: An ab initio tool for excited state calculations journal, August 2009

Metal-insulator transition in Kohn-Sham theory and quasiparticle theory journal, March 1989

Evaluation of quasiparticle energies for semiconductors without inversion symmetry journal, August 1989

Electronic properties of interfaces and defects from many-body perturbation theory: Recent developments and applications journal, January 2011

Large-scale GW calculations on pre-exascale HPC systems journal, February 2019

Implementation and performance of the frequency-dependent G W method within the PAW framework journal, July 2006

Numerical integration for ab initio many-electron self energy calculations within the GW approximation journal, April 2015

Ab initio static dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators journal, April 1987

Ab initio calculation of the macroscopic dielectric constant in silicon journal, May 1986

Self-consistent Hartree-Fock and screened-exchange calculations in solids: Application to silicon journal, September 1986

Microscopic Theory of Force Constants in the Adiabatic Approximation journal, January 1970

Hartree-Fock LAPW approach to the electronic properties of periodic systems journal, August 1993

General treatment of the singularities in Hartree-Fock and exact-exchange Kohn-Sham methods for solids journal, May 2007

Efficient calculation of the exact exchange energy in periodic systems using a truncated Coulomb potential journal, May 2008

Exact Coulomb cutoff technique for supercell calculations journal, May 2006

Truncation of periodic image interactions for confined systems journal, June 2006

Ab Initio Calculation of Self-Energy Effects on Optical Properties of GaAs(110) journal, December 1998

Optimized norm-conserving Vanderbilt pseudopotentials journal, August 2013

Generalized Gradient Approximation Made Simple journal, October 1996

Influence of the Core-Valence Interaction and of the Pseudopotential Approximation on the Electron Self-Energy in Semiconductors journal, September 2008

Band structure of gold from many-body perturbation theory journal, September 2012

Theory and computation of hot carriers generated by surface plasmon polaritons in noble metals journal, June 2015

Relativistic separable dual-space Gaussian pseudopotentials from H to Rn journal, August 1998

Parameter-Free Calculation of Response Functions in Time-Dependent Density-Functional Theory journal, July 2003

All-electron GW calculation based on the LAPW method: Application to wurtzite ZnO journal, September 2002

Angle-resolved photoemission and quasiparticle calculation of ZnO: The need for d band shift in oxide semiconductors journal, December 2012

Strong Renormalization of the Electronic Band Gap due to Lattice Polarization in the G W Formalism journal, May 2013

Isotope effects on the optical spectra of semiconductors journal, November 2005

Correlation effects on electron-phonon coupling in semiconductors: Many-body theory along thermal lines journal, March 2016

Photoemission and Bremsstrahlung Isochromat Spectroscopy Studies of TiO 2 (Rutile) and SrTiO 3 journal, January 1994

Electronic properties of ultrathin Cu and Fe films on TiO 2 (110) studied by photoemission and inverse photoemission journal, October 1994

Effect of temperature on isotopic mass dependence of excitonic band gaps in semiconductors: ZnO journal, May 2007

The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table journal, May 2018

Optimized pseudopotentials journal, January 1990

Coulomb-hole summations and energies for G W calculations with limited number of empty orbitals: A modified static remainder approach journal, April 2013

Title: Reproducibility in G₀W₀ calculations for solids

New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem
journal, August 1965

Generalized Kohn-Sham schemes and the band-gap problem
journal, February 1996

First-Principles Theory of Quasiparticles: Calculation of Band Gaps in Semiconductors and Insulators
journal, September 1985

Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies
journal, October 1986

The GW method
journal, March 1998

Electronic excitations: density-functional versus many-body Green’s-function approaches
journal, June 2002

Band Offsets at the $Si / {SiO}_{2}$ Interface from Many-Body Perturbation Theory
journal, May 2008

$G^{0} W^{0}$ band gap of ZnO: Effects of plasmon-pole models
journal, December 2011

Effects of plasmon pole models on the G0W0 electronic structure of various oxides
journal, September 2012

Role of the plasmon-pole model in the $G W$ approximation
journal, September 2013

Predictive $G W$ calculations using plane waves and pseudopotentials
journal, August 2014

The electronic structures of the thin films of InVO4 and TiO2 by first principles calculations
journal, December 2003

Self-energy and excitonic effects in the electronic and optical properties of ${TiO}_{2}$ crystalline phases
journal, July 2010

First-principles $DFT + G W$ study of oxygen vacancies in rutile ${TiO}_{2}$
journal, February 2014

Band convergence and linearization error correction of all-electron $GW$ calculations: The extreme case of zinc oxide
journal, February 2011

Erratum: Band convergence and linearization error correction of all-electron $G W$ calculations: The extreme case of zinc oxide [Phys. Rev. B10.1103/PhysRevB.83.081101 83 , 081101(R) (2011)]
journal, July 2011

Efficient $G W$ calculations for SnO $_{2}$ , ZnO, and rubrene: The effective-energy technique
journal, February 2012

Insights and challenges of applying the GW method to transition metal oxides
journal, October 2014

Resolution-of-identity approach to Hartree–Fock, hybrid density functionals, RPA, MP2 and GW with numeric atom-centered orbital basis functions
journal, May 2012

The GW -Method for Quantum Chemistry Applications: Theory and Implementation
journal, December 2012

GW 100: A Plane Wave Perspective for Small Molecules
journal, January 2017

GW 100: Benchmarking G ₀ W ₀ for Molecular Systems
journal, November 2015

Recent developments in the ABINIT software package
journal, August 2016

BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures
journal, June 2012

yambo: An ab initio tool for excited state calculations
journal, August 2009

Metal-insulator transition in Kohn-Sham theory and quasiparticle theory
journal, March 1989

Evaluation of quasiparticle energies for semiconductors without inversion symmetry
journal, August 1989

Electronic properties of interfaces and defects from many-body perturbation theory: Recent developments and applications
journal, January 2011

Large-scale GW calculations on pre-exascale HPC systems
journal, February 2019

Implementation and performance of the frequency-dependent $G W$ method within the PAW framework
journal, July 2006

Numerical integration for ab initio many-electron self energy calculations within the GW approximation
journal, April 2015

Ab initio static dielectric matrices from the density-functional approach. I. Formulation and application to semiconductors and insulators
journal, April 1987

Ab initio calculation of the macroscopic dielectric constant in silicon
journal, May 1986

Self-consistent Hartree-Fock and screened-exchange calculations in solids: Application to silicon
journal, September 1986

Microscopic Theory of Force Constants in the Adiabatic Approximation
journal, January 1970

Hartree-Fock LAPW approach to the electronic properties of periodic systems
journal, August 1993

General treatment of the singularities in Hartree-Fock and exact-exchange Kohn-Sham methods for solids
journal, May 2007

Efficient calculation of the exact exchange energy in periodic systems using a truncated Coulomb potential
journal, May 2008

Exact Coulomb cutoff technique for supercell calculations
journal, May 2006

Truncation of periodic image interactions for confined systems
journal, June 2006

Ab Initio Calculation of Self-Energy Effects on Optical Properties of GaAs(110)
journal, December 1998

Optimized norm-conserving Vanderbilt pseudopotentials
journal, August 2013

Generalized Gradient Approximation Made Simple
journal, October 1996

Influence of the Core-Valence Interaction and of the Pseudopotential Approximation on the Electron Self-Energy in Semiconductors
journal, September 2008

Band structure of gold from many-body perturbation theory
journal, September 2012

Theory and computation of hot carriers generated by surface plasmon polaritons in noble metals
journal, June 2015

Relativistic separable dual-space Gaussian pseudopotentials from H to Rn
journal, August 1998

Parameter-Free Calculation of Response Functions in Time-Dependent Density-Functional Theory
journal, July 2003

All-electron $GW$ calculation based on the LAPW method: Application to wurtzite ZnO
journal, September 2002

Angle-resolved photoemission and quasiparticle calculation of ZnO: The need for $d$ band shift in oxide semiconductors
journal, December 2012

Strong Renormalization of the Electronic Band Gap due to Lattice Polarization in the $G W$ Formalism
journal, May 2013

Isotope effects on the optical spectra of semiconductors
journal, November 2005

Correlation effects on electron-phonon coupling in semiconductors: Many-body theory along thermal lines
journal, March 2016

Photoemission and Bremsstrahlung Isochromat Spectroscopy Studies of TiO ₂ (Rutile) and SrTiO ₃
journal, January 1994

Electronic properties of ultrathin Cu and Fe films on ${TiO}_{2}$ (110) studied by photoemission and inverse photoemission
journal, October 1994

Effect of temperature on isotopic mass dependence of excitonic band gaps in semiconductors: ZnO
journal, May 2007

The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table
journal, May 2018

Optimized pseudopotentials
journal, January 1990

Coulomb-hole summations and energies for $G W$ calculations with limited number of empty orbitals: A modified static remainder approach
journal, April 2013