Materials Project Documentation
Return to materialsproject.org
  • Introduction
  • Frequently Asked Questions (FAQ)
    • Glossary of Terms
  • Changes and Updates
    • Database Versions
    • Website Changelog
  • Documentation Credit
  • Community
    • Getting Help
    • Getting Involved
      • Contributor Guide
      • Potential Collaborators
      • MP Community Software Ecosystem
    • Community Resources
    • Code of Conduct
  • Services
    • MPContribs
  • Methodology
    • Materials Methodology
      • Overview
      • Calculation Details
        • GGA/GGA+U Calculations
          • Parameters and Convergence
          • Hubbard U Values
          • Pseudo-potentials
        • r2SCAN Calculations
          • Parameters and Convergence
          • Pseudopotentials
      • Thermodynamic Stability
        • Energy Corrections
          • Anion and GGA/GGA+U Mixing
          • GGA/GGA+U/r2SCAN Mixing
        • Phase Diagrams (PDs)
        • Chemical Potential Diagrams (CPDs)
        • Finite Temperature Estimation
      • Electronic Structure
      • Phonon Dispersion
      • Diffraction Patterns
      • Aqueous Stability (Pourbaix)
      • Magnetic Properties
      • Elastic Constants
      • Piezoelectric Constants
      • Dielectric Constants
      • Equations of State (EOS)
      • X-ray Absorption Spectra (XAS)
      • Surface Energies
      • Grain Boundaries
      • Charge Density
      • Suggested Substrates
      • Related Materials
      • Optical absorption spectra
      • Alloys
    • Molecules Methodology
      • Overview
      • Calculation Details
      • Atomic Partial Charges
      • Atomic Partial Spins
      • Bonding
      • Metal Coordination and Binding
      • Natural Atomic and Molecular Orbitals
      • Redox and Electrochemical Properties
      • Molecular Thermodynamics
      • Vibrational Properties
      • Legacy Data
    • MOF Methodology
      • Calculation Parameters
        • DFT Parameters
        • Density Functionals
        • Pseudopotentials
        • DFT Workflow
  • Apps
    • Explore and Search Apps
      • Materials Explorer
        • Tutorial
      • Molecules Explorer
        • Tutorial
        • Legacy Data
      • Battery Explorer
        • Background
        • Tutorial
      • Synthesis Explorer
        • Background
        • Tutorial
      • Catalysis Explorer
        • Tutorial
      • MOF Explorer
        • Downloading the Data
        • Structure Details
          • QMOF IDs
          • Structure Sources
          • Finding MOFs by Common Name
          • Structural Fidelity
        • Property Definitions
          • SMILES, MOFid, and MOFkey
          • Pore Geometry
          • Topology
          • Electronic Structure
          • Population Analyses and Bond Orders
          • Symmetry
        • Version History
        • How to Cite
    • Analysis Apps
      • Phase Diagram
        • Background
        • Tutorials
        • FAQ
      • Pourbaix Diagram
        • Background
        • Tutorial
        • FAQ
      • Crystal Toolkit
        • Background
        • Tutorial
        • FAQ
      • Reaction Calculator
      • Interface Reactions
    • Characterization Apps
      • X-ray Absorption Spectra (XAS)
    • Explore Contributed Data
  • Downloading Data
    • How do I download the Materials Project database?
    • Using the API
      • Getting Started
      • Querying Data
      • Tips for Large Downloads
      • Examples
      • Advanced Usage
    • Differences between new and legacy API
    • Query and Download Contributed Data
    • AWS OpenData
  • Uploading Data
    • Contribute Data
  • Data Production
    • Data Workflows
    • Data Builders
Powered by GitBook
On this page
  • Hubbard U Values
  • Calibration and Values
  • Caveats
  • References

Was this helpful?

Edit on GitHub
Export as PDF
  1. Methodology
  2. Materials Methodology
  3. Calculation Details
  4. GGA/GGA+U Calculations

Hubbard U Values

Details on Hubbard U corrections used by the Materials Project

PreviousParameters and ConvergenceNextPseudo-potentials

Last updated 2 years ago

Was this helpful?

Hubbard U Values

It is well-known that first principles calculations within the local density approximation (LDA) or generalized gradient approximation (GGA) lead to considerable error in calculated redox reaction energies of many transition metal compounds. This error arises from the self-interaction error in LDA and GGA, which is not canceled out in redox reactions where an electron is transferred between significantly different environments, such as between a metal and a transition metal or between a transition metal and oxygen or fluorine. Extensive discussion of this issue can be found in the following works.

In the Materials Project, we have calibrated UUU values for many transition metals of interest using the approach outlined in Wang et al.'s work . At the present moment, UUU values have only been calibrated for transition metal oxide systems. UUU values were calibrated for the following elements: Co\text{Co}Co, Cr\text{Cr}Cr, Fe\text{Fe}Fe, Mn\text{Mn}Mn, Mo\text{Mo}Mo, Ni\text{Ni}Ni, V\text{V}V and W\text{W}W. The choice of systems to which we apply UUU was largely determined by our experience and by systematic benchmarking. It is very likely that we will expand calibration of UUU values to more chemical systems in the future.

In the Materials Project, for an oxide or fluoride material with a transition element listed previously, with the VASP input settings constructed according to the logic defined in .

Note that for fluorides, the UUU value gets set to the one calibrated from the oxide system, although in principle our architecture allows different UUU values to be set for oxides and fluorides respectively.

Calibration and Values

The UUU values were obtained by fitting to experimental binary formation enthalpies as described in Wang et al.'s work. This method is simple yet accurately reproduces phase stabilities. A least squares method of obtaining the correct UUU value was used, as follows:

  1. For each non-overlapping formation energy reaction considered, we find the region where the formation energy error passes zero. For the V-O\text{V-O}V-O system, this includes the following:

    • 2V2O3+O2→4VO22\text{V}_2\text{O}_3 + \text{O}_2 \rightarrow 4 \text{VO}_22V2​O3​+O2​→4VO2​

    • 4VO2+O2→2V2O54 \text{VO}_2 + \text{O}_2 \rightarrow 2\text{V}_2\text{O}_54VO2​+O2​→2V2​O5​

  2. For each formation energy region identified, we fit the linear equation to the final UUU range. In the case of V\text{V}V, we will have two sets of (m,c)(m,c)(m,c).

  3. We find the U value that minimizes the sum of square Error / Redox.

  4. In the case of V\text{V}V, we get a UUU value of 3.25.

The full list of U values used is described in the table below. For oxides and fluorides containing any of the elements, only GGA+U calculations are performed.

Element
System
Fitting Reaction
Redox Couple
Calibrated U (eV)
Comments

Co

Oxides

3.32

Cr

Oxides

3.7

Fe

Oxides

5.3

Mn

Oxides

3.9

Mo

Oxides

4.38

Ni

Oxides

6.2

V

Oxides

3.25

W

Oxides

6.2

Caveats

References

[5]: M. Wang, A. Navrotsky Enthalpy of formation of LiNiO2, LiCoO2 and their solid solution, LiNi1-xCoxO2, Solid State Ionics, vol. 166, no. 1-2, pp. 167-173, Jan. 2004.

was explicitly excluded from calibration set due to the large number of atoms in its unit cell.

Binary formation energies are not readily available for Ni. The Ni U calibration was performed using a ternary oxide formation energy.

was explicitly excluded from calibration due to its known metallic nature.

The U values are calibrated for phase stability analyses, and should be used with care if applied to obtain other properties such as band structures. Also, the U values depend on the pseudopotential used. Further, typically, U values should be site specific, however in our approach, U values were applied to all sites with an element listed above, and only to the d-orbitals. A discussion of the pseudopotentials used in the Materials Project can be found .

[1]: F. Zhou, M. Cococcioni, C. A. Marianetti, D. Morgan and G. Ceder. First-principles prediction of redox potentials in transition-metal compounds with LDA+U. Physical Review B, 2004, 70, 235121.

[2]: M. Cococcioni, S. de Gironcoli, Linear response approach to the calculation of the effective interaction parameters in the LDA+U method. Physical Review B, 2005, 71, 035105.

[3]: L. Wang, T. Maxisch, & G. Ceder. Oxidation energies of transition metal oxides within the GGA+U framework. Physical Review B. 2006, 73, 195107,

[4]: A. Jain, G. Hautier, S. P. Ong, C. Moore, C. Fischer, K. A. Persson, & G. Ceder. Formation enthalpies by mixing GGA and GGA + U calculations. Physical Review B, 2011, 84(4), 045115.

6CoO+O2→2Co3O46\text{CoO} + \text{O}_2 \rightarrow 2 \text{Co}_3\text{O}_46CoO+O2​→2Co3​O4​
Co2+→Co2.67+\text{Co}^{2+} \rightarrow\text{Co}^{2.67+}Co2+→Co2.67+
2/3Cr2O3+O2→4/3CrO32/3\text{Cr}_2 \text{O}_3 + \text{O}_2 \rightarrow 4/3 \text{CrO}_32/3Cr2​O3​+O2​→4/3CrO3​
Cr3+→Cr6+\text{Cr}^{3+} \rightarrow \text{Cr}^{6+}Cr3+→Cr6+
6FeO+O2→2Fe3O46\text{FeO} + \text{O}_2 \rightarrow 2 \text{Fe}_3 \text{O}_46FeO+O2​→2Fe3​O4​
4Fe3O4+O2→6Fe2O34\text{Fe}_3\text{O}_4 +\text{O}_2 \rightarrow 6 \text{Fe}_2 \text{O}_34Fe3​O4​+O2​→6Fe2​O3​
Fe2+→Fe2.67+\text{Fe}^{2+} \rightarrow \text{Fe}^{2.67+}Fe2+→Fe2.67+
Fe2.67+→Fe3+\text{Fe}^{2.67+} \rightarrow \text{Fe}^{3+}Fe2.67+→Fe3+
6MnO+O2→2Mn3O46 \text{MnO} + \text{O}_2 \rightarrow 2 \text{Mn}_3\text{O}_46MnO+O2​→2Mn3​O4​
Mn3O4+O2→3MnO2\text{Mn}_3\text{O}_4 + \text{O}_2\rightarrow 3 \text{MnO}_2Mn3​O4​+O2​→3MnO2​
Mn2+→Mn2.67+\text{Mn}^{2+} \rightarrow \text{Mn}^{2.67+}Mn2+→Mn2.67+
Mn2.67+→Mn4+\text{Mn}^{2.67+} \rightarrow \text{Mn}^{4+}Mn2.67+→Mn4+
Mn2O3\text{Mn}_2\text{O}_3Mn2​O3​
2MoO2+O2→2MnO32 \text{MoO}_2 + \text{O}_2 \rightarrow 2 \text{MnO}_32MoO2​+O2​→2MnO3​
Mo4+→Mo6+\text{Mo}^{4+} \rightarrow \text{Mo}^{6+}Mo4+→Mo6+
Li2O+2NiO+1/2O2→2LiNiO2\text{Li}_2 \text{O} + 2\text{NiO} + 1/2 \text{O}_2 \rightarrow 2 \text{LiNiO}_2Li2​O+2NiO+1/2O2​→2LiNiO2​
Ni2+→Ni3+\text{Ni}^{2+} \rightarrow \text{Ni}^{3+}Ni2+→Ni3+
2V2O3+O2→4VO22 \text{V}_2 \text{O}_3 + \text{O}_2 \rightarrow 4 \text{VO}_22V2​O3​+O2​→4VO2​
4VO2+O2→2V2O54 \text{VO}_2 + \text{O}_2 \rightarrow 2 \text{V}_2 \text{O}_54VO2​+O2​→2V2​O5​
V3+→V4+\text{V}^{3+} \rightarrow \text{V}^{4+}V3+→V4+
V4+→V5+\text{V}^{4+} \rightarrow \text{V}^{5+}V4+→V5+
VO\text{VO}VO
2WO2+O2→2WO32 \text{WO}_2 + \text{O}_2 \rightarrow 2 \text{WO}_32WO2​+O2​→2WO3​
W4+→W6+\text{W}^{4+} \rightarrow \text{W}^{6+}W4+→W6+
here
doi:10.1103/PhysRevB.70.235121
doi:10.1103/PhysRevB.71.035105
doi:10.1103/PhysRevB.73.195107
doi:10.1103/PhysRevB.84.045115
pymatgen
[1-4]
[5]
[5]