Exploring DFT+U parameter space with a Bayesian calibration assisted by Markov chain Monte Carlo sampling

Tavadze, Pedram; Boucher, Reese; Avendaño-Franco, Guillermo; Kocan, Keenan X.; Singh, Sobhit; Dovale-Farelo, Viviana; Ibarra-Hernández, Wilfredo; Johnson, Matthew B.; Mebane, David S.; Romero, Aldo H.

doi:10.1038/s41524-021-00651-0

Title: Exploring DFT+U parameter space with a Bayesian calibration assisted by Markov chain Monte Carlo sampling

Abstract

Abstract The density-functional theory is widely used to predict the physical properties of materials. However, it usually fails for strongly correlated materials. A popular solution is to use the Hubbard correction to treat strongly correlated electronic states. Unfortunately, the values of the Hubbard U and J parameters are initially unknown, and they can vary from one material to another. In this semi-empirical study, we explore the U and J parameter space of a group of iron-based compounds to simultaneously improve the prediction of physical properties (volume, magnetic moment, and bandgap). We used a Bayesian calibration assisted by Markov chain Monte Carlo sampling for three different exchange-correlation functionals (LDA, PBE, and PBEsol). We found that LDA requires the largest U correction. PBE has the smallest standard deviation and its U and J parameters are the most transferable to other iron-based compounds. Lastly, PBE predicts lattice parameters reasonably well without the Hubbard correction.

Authors:

; Boucher, Reese; Avendaño-Franco, Guillermo; Kocan, Keenan X.; Singh, Sobhit;

; Ibarra-Hernández, Wilfredo; Johnson, Matthew B.;

; Romero, Aldo H.

Publication Date:: 2021-11-11

Sponsoring Org.:: USDOE

OSTI Identifier:: 1829908

Resource Type:: Published Article

Journal Name:: npj Computational Materials

Additional Journal Information:: Journal Name: npj Computational Materials Journal Volume: 7 Journal Issue: 1; Journal ID: ISSN 2057-3960

Publisher:: Nature Publishing Group

Country of Publication:: United Kingdom

Language:: English

Citation Formats


                    Tavadze, Pedram, Boucher, Reese, Avendaño-Franco, Guillermo, Kocan, Keenan X., Singh, Sobhit, Dovale-Farelo, Viviana, Ibarra-Hernández, Wilfredo, Johnson, Matthew B., Mebane, David S., and Romero, Aldo H. Exploring DFT+U parameter space with a Bayesian calibration assisted by Markov chain Monte Carlo sampling.  United Kingdom: N. p., 2021. 
Web.  doi:10.1038/s41524-021-00651-0.

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                    Tavadze, Pedram, Boucher, Reese, Avendaño-Franco, Guillermo, Kocan, Keenan X., Singh, Sobhit, Dovale-Farelo, Viviana, Ibarra-Hernández, Wilfredo, Johnson, Matthew B., Mebane, David S., & Romero, Aldo H. Exploring DFT+U parameter space with a Bayesian calibration assisted by Markov chain Monte Carlo sampling.  United Kingdom.  https://doi.org/10.1038/s41524-021-00651-0

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                    Tavadze, Pedram, Boucher, Reese, Avendaño-Franco, Guillermo, Kocan, Keenan X., Singh, Sobhit, Dovale-Farelo, Viviana, Ibarra-Hernández, Wilfredo, Johnson, Matthew B., Mebane, David S., and Romero, Aldo H. Thu .  
"Exploring DFT+U parameter space with a Bayesian calibration assisted by Markov chain Monte Carlo sampling".  United Kingdom.  https://doi.org/10.1038/s41524-021-00651-0.

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@article{osti_1829908,

  title        = {Exploring DFT+U parameter space with a Bayesian calibration assisted by Markov chain Monte Carlo sampling},

  author       = {Tavadze, Pedram and Boucher, Reese and Avendaño-Franco, Guillermo and Kocan, Keenan X. and Singh, Sobhit and Dovale-Farelo, Viviana and Ibarra-Hernández, Wilfredo and Johnson, Matthew B. and Mebane, David S. and Romero, Aldo H.},

  abstractNote = {Abstract The density-functional theory is widely used to predict the physical properties of materials. However, it usually fails for strongly correlated materials. A popular solution is to use the Hubbard correction to treat strongly correlated electronic states. Unfortunately, the values of the Hubbard U and J parameters are initially unknown, and they can vary from one material to another. In this semi-empirical study, we explore the U and J parameter space of a group of iron-based compounds to simultaneously improve the prediction of physical properties (volume, magnetic moment, and bandgap). We used a Bayesian calibration assisted by Markov chain Monte Carlo sampling for three different exchange-correlation functionals (LDA, PBE, and PBEsol). We found that LDA requires the largest U correction. PBE has the smallest standard deviation and its U and J parameters are the most transferable to other iron-based compounds. Lastly, PBE predicts lattice parameters reasonably well without the Hubbard correction.},

  doi          = {10.1038/s41524-021-00651-0},

  journal      = {npj Computational Materials},

  number       = 1,

  volume       = 7,

  place        = {United Kingdom},

  year         = {2021},

  month        = {11}

}

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Title: Exploring DFT+U parameter space with a Bayesian calibration assisted by Markov chain Monte Carlo sampling

Abstract

Citation Formats

Libxc: A library of exchange and correlation functionals for density functional theory journal, October 2012

Projector augmented-wave method journal, December 1994

Hybrid functionals based on a screened Coulomb potential journal, May 2003

Effective Coulomb interaction in transition metals from constrained random-phase approximation journal, March 2011

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional journal, November 2005

Enhanced room-temperature magnetocaloric effect and tunable magnetic response in Ga-and Ge-substituted AlFe2B2 journal, March 2019

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials journal, September 2009

Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory journal, March 2004

When Density Functional Approximations Meet Iron Oxides journal, September 2016

RESPACK: An ab initio tool for derivation of effective low-energy model of material journal, April 2021

Communication: Effect of the orbital-overlap dependence in the meta generalized gradient approximation journal, August 2012

From ultrasoft pseudopotentials to the projector augmented-wave method journal, January 1999

Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study journal, January 1998

Perspective: Treating electron over-delocalization with the DFT+U method journal, June 2015

Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators journal, August 1995

A new mixing of Hartree–Fock and local density‐functional theories journal, January 1993

Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs journal, December 2008

The density functional formalism, its applications and prospects journal, July 1989

TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials journal, July 2016

A self-consistent Hubbard U density-functional theory approach to the addition-elimination reactions of hydrocarbons on bare FeO+ journal, October 2008

Hybrid exchange correlation functionals and potentials: Concept elaboration journal, January 2007

Ab initiomolecular dynamics for liquid metals journal, January 1993

First-principle electronic structure calculations for magnetic moment in iron-based superconductors: An LSDA+negative U study journal, October 2009

Density Functional Theory of Electronic Structure journal, January 1996

Method for locating low-energy solutions within DFT + U journal, November 2010

Wüstite: electric, thermodynamic and optical properties of FeO journal, May 2012

J dependence in the LSDA + U treatment of noncollinear magnets journal, December 2010

On optimal and data-based histograms journal, January 1979

On the room temperature multiferroic BiFeO3: magnetic, dielectric and thermal properties journal, June 2010

Recent developments in libxc — A comprehensive library of functionals for density functional theory journal, January 2018

Self-Consistent Equations Including Exchange and Correlation Effects journal, November 1965

Crystal structure and isothermal compression of Fe2O3, Cr2O3, and V2O3 to 50 kbars journal, January 1980

Occupation matrix control of d- and f-electron localisations using DFT + U journal, January 2014

Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals journal, April 2017

A density functional (PBE, PBEsol, HSE06) study of the structural, electronic and optical properties of the ternary compounds AgAlX2 (X = S, Se, Te) journal, May 2015

Hubbard parameters from density-functional perturbation theory journal, August 2018

Systematic study of first-row transition-metal diatomic molecules: A self-consistent DFT+U approach journal, September 2010

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density journal, January 1988

Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set journal, July 1996

Magnetism and crystal structure in orthorhombic Fe 2 P: a theoretical and experimental study journal, January 1995

Implementation of the projector augmented-wave LDA+U method: Application to the electronic structure of NiO journal, December 2000

Performance of six functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in the simulation of vibrational and dielectric properties of crystalline compounds. The case of forsterite Mg2SiO4 journal, April 2011

Magnetic and structural properties of ferromagnetic Fe 5 PB 2 and Fe 5 SiB 2 and effects of Co and Mn substitutions journal, October 2015

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set journal, October 1996

PyVista: 3D plotting and mesh analysis through a streamlined interface for the Visualization Toolkit (VTK) journal, May 2019

Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces journal, April 2008

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation journal, September 1992

Electrical and optical properties of FeO journal, January 1975

A local exchange-correlation potential for the spin polarized case. i journal, July 1972

Matplotlib: A 2D Graphics Environment journal, January 2007

X-ray spectroscopic study of BaFeO 3 thin films: An Fe 4 + ferromagnetic insulator journal, March 2015

DMFTwDFT: An open-source code combining Dynamical Mean Field Theory with various density functional theory packages journal, April 2021

Mixed magnetic phase in 6 H -type BaFeO 3−δ journal, February 2007

Systematic beyond-DFT study of binary transition metal oxides journal, November 2019

HLE16: A Local Kohn–Sham Gradient Approximation with Good Performance for Semiconductor Band Gaps and Molecular Excitation Energies journal, January 2017

Magnetic properties of hexagonal and cubic Fe 3 Ge journal, November 1976

Band gap measurement of SrFeO3−δ by ultraviolet photoelectron spectroscopy and photovoltage method journal, January 2012

Phase analysis of AlFe 2 B 2 by synchrotron X-ray diffraction, magnetic and Mössbauer studies journal, April 2017

Density-functional exchange-energy approximation with correct asymptotic behavior journal, September 1988

Performance of various density-functional approximations for cohesive properties of 64 bulk solids journal, June 2018

Efficient lattice dynamics calculations for correlated materials with DFT + DMFT journal, December 2020

Structure and magnetic properties of single‐crystal Fe/Au(100) superlattices synthesized using RHEED oscillation journal, May 1990

Applications of DFT + DMFT in Materials Science journal, July 2019

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U method journal, January 1997

Electronic structure calculations with dynamical mean-field theory journal, August 2006

Ab initio evaluation of Coulomb and exchange parameters for DFT + U calculations journal, October 2007

Hubbard U and Hund exchange J in transition metal oxides: Screening versus localization trends from constrained random phase approximation journal, October 2012

Strongly Constrained and Appropriately Normed Semilocal Density Functional journal, July 2015

Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure conference, January 2004

Linear response approach to the calculation of the effective interaction parameters in the LDA + U method journal, January 2005

Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems journal, July 2013

SciPy 1.0: fundamental algorithms for scientific computing in Python journal, February 2020

Generalized gradient approximation for the exchange-correlation hole of a many-electron system journal, December 1996

The magnetic structure of SrFeO3 calculated within LDA journal, February 1995

Hubbard model in infinite dimensions journal, March 1992

Toward a predictive theory of correlated materials journal, July 2018

Calculations of Hubbard U from first-principles journal, September 2006

Libxc: A library of exchange and correlation functionals for density functional theory
journal, October 2012

Projector augmented-wave method
journal, December 1994

Hybrid functionals based on a screened Coulomb potential
journal, May 2003

Effective Coulomb interaction in transition metals from constrained random-phase approximation
journal, March 2011

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional
journal, November 2005

Enhanced room-temperature magnetocaloric effect and tunable magnetic response in Ga-and Ge-substituted AlFe2B2
journal, March 2019

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009

Strongly Correlated Materials: Insights From Dynamical Mean-Field Theory
journal, March 2004

When Density Functional Approximations Meet Iron Oxides
journal, September 2016

RESPACK: An ab initio tool for derivation of effective low-energy model of material
journal, April 2021

Communication: Effect of the orbital-overlap dependence in the meta generalized gradient approximation
journal, August 2012

From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999

Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study
journal, January 1998

Perspective: Treating electron over-delocalization with the DFT+U method
journal, June 2015

Density-functional theory and strong interactions: Orbital ordering in Mott-Hubbard insulators
journal, August 1995

A new mixing of Hartree–Fock and local density‐functional theories
journal, January 1993

Assessment of correction methods for the band-gap problem and for finite-size effects in supercell defect calculations: Case studies for ZnO and GaAs
journal, December 2008

The density functional formalism, its applications and prospects
journal, July 1989

TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials
journal, July 2016

A self-consistent Hubbard U density-functional theory approach to the addition-elimination reactions of hydrocarbons on bare FeO+
journal, October 2008

Hybrid exchange correlation functionals and potentials: Concept elaboration
journal, January 2007

Ab initiomolecular dynamics for liquid metals
journal, January 1993

First-principle electronic structure calculations for magnetic moment in iron-based superconductors: An LSDA+negative U study
journal, October 2009

Density Functional Theory of Electronic Structure
journal, January 1996

Method for locating low-energy solutions within $DFT + U$
journal, November 2010

Wüstite: electric, thermodynamic and optical properties of FeO
journal, May 2012

$J$ dependence in the $LSDA + U$ treatment of noncollinear magnets
journal, December 2010

On optimal and data-based histograms
journal, January 1979

On the room temperature multiferroic BiFeO3: magnetic, dielectric and thermal properties
journal, June 2010

Recent developments in libxc — A comprehensive library of functionals for density functional theory
journal, January 2018

Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965

Crystal structure and isothermal compression of Fe2O3, Cr2O3, and V2O3 to 50 kbars
journal, January 1980

Occupation matrix control of d- and f-electron localisations using DFT + U
journal, January 2014

Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals
journal, April 2017

A density functional (PBE, PBEsol, HSE06) study of the structural, electronic and optical properties of the ternary compounds AgAlX2 (X = S, Se, Te)
journal, May 2015

Hubbard parameters from density-functional perturbation theory
journal, August 2018

Systematic study of first-row transition-metal diatomic molecules: A self-consistent DFT+U approach
journal, September 2010

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
journal, January 1988

Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
journal, July 1996

Magnetism and crystal structure in orthorhombic Fe ₂ P: a theoretical and experimental study
journal, January 1995

Implementation of the projector augmented-wave LDA+U method: Application to the electronic structure of NiO
journal, December 2000

Performance of six functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in the simulation of vibrational and dielectric properties of crystalline compounds. The case of forsterite Mg2SiO4
journal, April 2011

Magnetic and structural properties of ferromagnetic Fe ₅ PB ₂ and Fe ₅ SiB ₂ and effects of Co and Mn substitutions
journal, October 2015

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996

PyVista: 3D plotting and mesh analysis through a streamlined interface for the Visualization Toolkit (VTK)
journal, May 2019

Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
journal, April 2008

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation
journal, September 1992

Electrical and optical properties of FeO
journal, January 1975

A local exchange-correlation potential for the spin polarized case. i
journal, July 1972

Matplotlib: A 2D Graphics Environment
journal, January 2007

X-ray spectroscopic study of $BaFeO_{3}$ thin films: An ${Fe}^{4 +}$ ferromagnetic insulator
journal, March 2015

DMFTwDFT: An open-source code combining Dynamical Mean Field Theory with various density functional theory packages
journal, April 2021

Mixed magnetic phase in 6 H -type BaFeO _3−δ
journal, February 2007

Systematic beyond-DFT study of binary transition metal oxides
journal, November 2019

HLE16: A Local Kohn–Sham Gradient Approximation with Good Performance for Semiconductor Band Gaps and Molecular Excitation Energies
journal, January 2017

Magnetic properties of hexagonal and cubic Fe ₃ Ge
journal, November 1976

Band gap measurement of SrFeO3−δ by ultraviolet photoelectron spectroscopy and photovoltage method
journal, January 2012

Phase analysis of AlFe 2 B 2 by synchrotron X-ray diffraction, magnetic and Mössbauer studies
journal, April 2017

Density-functional exchange-energy approximation with correct asymptotic behavior
journal, September 1988

Performance of various density-functional approximations for cohesive properties of 64 bulk solids
journal, June 2018

Efficient lattice dynamics calculations for correlated materials with $DFT + DMFT$
journal, December 2020

Structure and magnetic properties of single‐crystal Fe/Au(100) superlattices synthesized using RHEED oscillation
journal, May 1990

Applications of DFT + DMFT in Materials Science
journal, July 2019

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U method
journal, January 1997

Electronic structure calculations with dynamical mean-field theory
journal, August 2006

Ab initio evaluation of Coulomb and exchange parameters for $DFT + U$ calculations
journal, October 2007

Hubbard $U$ and Hund exchange $J$ in transition metal oxides: Screening versus localization trends from constrained random phase approximation
journal, October 2012

Strongly Constrained and Appropriately Normed Semilocal Density Functional
journal, July 2015

Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure
conference, January 2004

Linear response approach to the calculation of the effective interaction parameters in the $LDA + U$ method
journal, January 2005

Hubbard-corrected DFT energy functionals: The LDA+U description of correlated systems
journal, July 2013

SciPy 1.0: fundamental algorithms for scientific computing in Python
journal, February 2020

Generalized gradient approximation for the exchange-correlation hole of a many-electron system
journal, December 1996

The magnetic structure of SrFeO3 calculated within LDA
journal, February 1995

Hubbard model in infinite dimensions
journal, March 1992

Toward a predictive theory of correlated materials
journal, July 2018

Calculations of Hubbard $U$ from first-principles
journal, September 2006

On the ferromagnetism of AlFe2B2
journal, August 2011

Metal–insulator transition in helical SrFeO3− antiferromagnet
journal, October 2004

Special points for Brillouin-zone integrations
journal, June 1976