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Results for “Hubbard U correction”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Biased Spin-State Energetics of Fe(II) Molecular Complexes within Density-Functional Theory and the Linear-Response Hubbard U Correction

The spin-state energetics of six Fe(II) molecular complexes are computed using the linear-response Hubbard U approach within DFT. The adiabatic energy differences, ΔE H-L , between the high-spin (S = 2) and the low-spin (S = 0) states are computed and compared with accurate-coupled cluster-corrected CASPT2 results. We show that DFT+U fails in correctly capturing the ground state for strong-field ligands yielding ΔE H-L that are almost constant throughout the molecular series. This bias toward high spin together with the metal/ligand charge transfer upon U correction are here quantified and explained using molecular orbital diagrams involving both σ- and π-bonding interactions. Furthermore, with increasing ligand-field strengths this bias also increases owing to the stronger molecular character of the metal/ligand Kohn–Sham orbitals thus resulting in large deviations from the reference larger than 4 eV. Smaller values of U can be employed to mitigate this effect and recover the right energetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Structure and electronic properties of rare earth DOBDC metal–organic-frameworks

In our report, we apply density functional theory (DFT) to investigate rare-earth metal organic frameworks (RE-MOFs), RE 12 (μ 3 -OH) 16 (C 8 O 6 H 4 ) 8 (C 8 O 6 H 5 ) 4 (RE = Y, Eu, Tb, Yb), and characterize the level of theory needed to accurately predict structural and electronic properties in MOF materials with 4f-electrons. A two-step calculation approach of geometry optimization with spin-restricted DFT and large core potential (LCPs), and detailed electronic structures with spin-unrestricted DFT with a full valence potential + Hubbard U correction is investigated. Spin-restricted DFT with LCPs resulted in good agreement between experimental lattice parameters and optimized geometries, while a full valence potential is necessary for accurate representation of the electronic structure. The electronic structure of Eu-DOBDC MOF suggested a strong dependence on the treatment of highly localized 4f-electrons and spin polarization, as well as variation within a range of Hubbard corrections (U = 1–9 eV). For Hubbard corrected spin-unrestricted calculations, a U value of 1–4 eV maintains the non-metallic character of the band gap with slight deviations in f-orbital energetics. When compared with experimentally reported results, the importance of the full valence calculation and the Hubbard correction in correctly predicting the electronic structure is highlighted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Ni and Co Incorporation in Forsterite: A Density Functional Theory Study with Hubbard Correction

Ni and Co are critical elements for the world economy and modern technologies. Mafic and ultramafic deposits represent low-grade yet abundant alternatives to traditional Ni and Co ores. Here, in this work, density functional theory (DFT) with the Hubbard U correction (DFT+U) was used to simulate the incorporation of Ni and Co in forsterite (Mg 2 SiO 4 ), the Mg endmember of olivine, a common mineral in mafic and ultramafic rocks. Hubbard U terms for Ni and Co were parametrized using a series of oxide, hydroxide, carbonate, silicate, and sulfide minerals relevant to extraction and recovery of Ni and Co from mafic and ultramafic deposits. Electronic, energetic, magnetic, and structural properties were considered in the parametrization. For each of Ni and Co, an effective Hubbard correction (U eff ) value that optimized agreement with either experimental data or a hybrid exchange-correlation functional for all of the minerals considered is reported. DFT+U ab initio molecular dynamics (AIMD) simulations of Ni and Co incorporated into the M1 and M2 octahedral sites of forsterite were then performed. Ni and Co substitution in the M1 site was more energetically favorable than substitution in the M2 site, in agreement with published partition coefficients. AIMD trajectories were used to compute extended X-ray absorption fine structure (EXAFS) spectra of Ni in the M1 and M2 sites for direct fitting to a published experimental spectrum of Ni in a natural San Carlos olivine sample. The results of the fit indicated that ordering of Ni in the M1 site was not as strong at the low Ni concentrations relevant to mafic and ultramafic silicate minerals as that at the higher concentrations of the Ni-Mg olivine solid solutions studied to date.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Does DFT+U mimic hybrid density functionals?

Here, this work examines the question of how a Hubbard U correction to a local exchange–correlation functional compares with adding Hartree–Fock exchange to a local functional for both solid-state and molecular properties. We compute a solid-state property, namely the band gap, and thermochemical molecular properties, in particular main-group bond energies, transition-metal–ligand bond energies, and barrier heights, to elucidate whether the DFT+U method mimics hybrid DFT. We find that a calculation with a Hubbard U correction may or may not mimic a hybrid functional – depending on the atom, the subshell, and the property to which it is applied. For band gaps, we find that adding a Hubbard U correction to the valence d orbitals of transition metals increases the band gap, which thereby gets closer to the experimental value, while adding a Hubbard U correction to valence s or p orbitals of main group elements need not always increase the band gap. For molecular thermochemistry, we find that adding a Hubbard U correction to a local density functional need not have the same effect as adding Hartree–Fock exchange to a local density functional. For example when compared to a local DFT, hybrid DFT increases the barrier height in all cases, but DFT+U does not always increase the barrier height. For the band gaps of transition metal monoxides, the Hubbard-corrected results lowered the mean errors significantly and were comparable to what could be achieved with a much more expensive hybrid functional, but for reaction barrier heights and bond energies the Hubbard correction can lower the mean error by approximately a kcal/mol. As part of the analysis, we also compare VASP and Gaussian 09 calculations for the same density functional.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Altermagnetic behavior in OsO2: Parallels with RuO2

This dataset contains input and output files from DFT simulations used to reproduce the electronic and phonon band structures of bulk OsO₂ and RuO₂. The files include data from initial electronic structure and phonon calculations performed with Hubbard-U correction (i.e., Antiferromagnetic, AFM) and without Hubbard-U correction (i.e., Non-magnetic, NM). The electronic structure calculations are provided both with and without spin-orbit coupling (SOC). The computed electronic properties are compared with existing literature, while the calculated phonon density of states (PhDOS) is compared with experimental PhDOS.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Assessing Hubbard-corrected AM05+ U and PBEsol+ U density functionals for strongly correlated oxides CeO 2 and Ce 2 O 3

The structure–property relationships of bulk CeO 2 and Ce 2 O 3 have been investigated using AM05 and PBEsol exchange–correlation functionals within the frameworks of Hubbard-corrected density functional theory (DFT+ U ) and density functional perturbation theory (DFPT+ U ). Compared with conventional PBE+ U , RPBE+ U , PW91+ U and LDA+ U functionals, AM05+ U and PBEsol+ U describe experimental crystalline parameters and properties of CeO 2 and Ce 2 O 3 with superior accuracy, especially when + U is chosen close to its value derived by the linear-response approach. Lastly, the present findings call for a reexamination of some of the problematic oxide materials featuring strong f- and d-electron correlation using AM05+ U and PBEsol+ U .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Data-driven approach to parameterize SCAN + U for an accurate description of 3 d transition metal oxide thermochemistry

Semilocal density-functional theory (DFT) methods exhibit significant errors for the phase diagrams of transition-metal oxides that are caused by an incorrect description of molecular oxygen and the large self-interaction error in materials with strongly localized electronic orbitals. Empirical and semiempirical corrections based on the DFT + U method can reduce these errors, but the parameterization and validation of the correction terms remains an on-going challenge. Here we develop a systematic methodology to determine the parameters and to statistically assess the results by considering interlinked thermochemical data across a set of transition metal compounds. We consider three interconnected levels of correction terms: (1) a constant oxygen binding correction, (2) Hubbard-U correction, and (3) DFT/DFT + U compatibility correction. The parameterization is expressed as a unified optimization problem. We demonstrate this approach for 3d transition metal oxides, considering a target set of binary and ternary oxides. With a total of 37 measured formation enthalpies taken from the literature, the dataset is augmented by the reaction energies of 1710 unique reactions that were derived from the formation energies by systematic enumeration. To ensure a balanced dataset across the available data, the reactions were grouped by their similarity using clustering and suitably weighted. The parameterization is validated using leave-one-out cross validation (CV), a standard technique for the validation of statistical models. We apply the methodology to the strongly constrained and appropriately normed (SCAN) density functional. Based on the CV score, the error of binary (ternary) oxide formation energies is reduced by 40% (75%) to 0.10 (0.03) eV/atom. A simplified correction scheme that does not involve SCAN/SCAN + U compatibility terms still achieves an error reduction of 30% (25%). The method and tools demonstrated here can be applied to other classes of materials or to parameterize the corrections to optimize DFT + U performance for other target physical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Localizing Holes as Polarons and Predicting Band Gaps, Defect Levels, and Delithiation Energies of Solid-State Materials with a Local Exchange-Correlation Functional

Here, we assess the performance of seven exchange–correlation functionals (some with and some without a Hubbard U correction) for their ability (i) to predict band gaps of silicon, diamond, and Li-ion battery cathode materials, (ii) to localize hole polarons and predict delithiation energies in Li-ion battery cathode materials, and (iii) to predict transition levels of charge carriers of doped silicon and diamond. Both local and hybrid exchange–correlation functionals were tested. The local functionals tend to underestimate band gaps and delocalize polarons. The hybrid functionals very often give a good description of both properties, but they may not be practical for calculations involving large unit cells, large ensembles, or dynamics, and therefore a local functional with a Hubbard U correction is often used (giving the method called DFT+U), where the value of a parameter U is adjusted according to the system and the property being investigated. Keeping in mind the importance of computational cost and the undesirability of having to adjust an empirical parameter for each system or property of interest, we recently developed a local functional, namely HLE17, to try to accurately predict band gaps and excitation energies, and we validated it using mostly main-group solids and molecules. Here we test the performance of HLE17 for its ability to predict band gaps and localize polarons in other solid-state materials, and we compare its performance to that of popular local functionals (PBE, PBEsol, and TPSS), a range-separated hybrid functional with screened exchange (HSE06), and DFT+U. We find that HLE17 predicts more accurate band gaps than other local functionals and can localize holes as polarons, which other local functionals usually fail to do, and for a number of cases it is comparable in performance quality to Hubbard-corrected functionals without the need for system-specific parametrization and to hybrid functionals without the high cost. Because HLE17 does not predict accurate lattice constants, we use the single-point method of quantum chemistry, where the geometry is optimized with one functional and the band gap is calculated with HLE17, or we perform calculations with the lattice constants obtained by TPSS and both the fractional intracell coordinates and the electronic structure obtained by HLE17 (a new method denoted HLE17\\TPSS). In particular, we performed calculations by HLE17//TPSS, HLE17//HSE06, HLE17//DFT+U, and HLE17\\TPSS, and these methods usually agree well with each other and give values similar to experiment.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Machine learning the Hubbard U parameter in DFT+U using Bayesian optimization

Abstract Within density functional theory (DFT), adding a Hubbard U correction can mitigate some of the deficiencies of local and semi-local exchange-correlation functionals, while maintaining computational efficiency. However, the accuracy of DFT+U largely depends on the chosen Hubbard U values. We propose an approach to determining the optimal U parameters for a given material by machine learning. The Bayesian optimization (BO) algorithm is used with an objective function formulated to reproduce the band structures produced by more accurate hybrid functionals. This approach is demonstrated for transition metal oxides, europium chalcogenides, and narrow-gap semiconductors. The band structures obtained using the BO U values are in agreement with hybrid functional results. Additionally, comparison to the linear response (LR) approach to determining U demonstrates that the BO method is superior.

Chemistry↗
DOE OSTI2016

First-principles Hubbard U approach for small molecule binding in metal-organic frameworks

We apply first-principles approaches with Hubbard U corrections for calculation of small molecule binding energetics to open-shell transition metal atoms in metal-organic frameworks (MOFs). Using density functional theory with van der Waals dispersion-corrected functionals, we determine Hubbard U values ab initio through an established linear response procedure for M-MOF-74, for a number of different metal centers (M = Ti, V, Cr, Mn, Fe, Co, Ni, and Cu). While our ab initio U values differ from those used in previous work, we show that they result in lattice parameters and electronic contributions to CO{sub 2}-MOF binding energies that lead to excellent agreement with experiments and previous results, yielding lattice parameters within 3%. In addition, U-dependent calculations for an example system, Co-MOF-74, suggest that the CO{sub 2} binding energy grows monotonically with the value of Hubbard U, with the binding energy shifting 4 kJ/mol (or 0.041 eV) over the range of U = 0-5.4 eV. These results provide insight into an approximate but computationally efficient means for calculation of small molecule binding energies to open-shell transition metal atoms in MOFs and suggest that the approach can be predictive with good accuracy, independent of the cations used and the availability of experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Interplay between London Dispersion, Hubbard U , and Metastable States for Uranium Compounds

High-throughput computational studies of lanthanide and actinide chemistry with density-functional theory are complicated by the need for Hubbard U corrections, which ensure localization of the f-electrons, but can lead to metastable states. This work presents a systematic investigation of the effects of both Hubbard U value and metastable states on the predicted structural and thermodynamic properties of four uranium compounds central to the field of nuclear fuels: UC, UN, UO 2 , and UCl 3 . We also assess the impact of the exchange-hole dipole moment (XDM) dispersion correction on the computed properties. Overall, the choice of Hubbard U value and inclusion of a dispersion correction cause larger variations in the computed geometric properties than result from metastable states. Further, the weak dependence of structure optimization on metastable states should simplify future high-throughput calculations on actinides. Conversely, addition of the dispersion correction is found to offset the repulsion introduced by the Hubbard U term and provides greatly improved agreement with experiment for both cell volumes and heats of formation. The XDM dispersion correction is largely invariant to the chosen U value, making it a robust dispersion correction for actinide systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT

Density functional theory (DFT) is widely applied to both molecules and materials, but well known energetic delocalization and static correlation errors in practical exchange-correlation approximations limit quantitative accuracy. Common methods that correct energetic delocalization errors, such as the Hubbard U correction in DFT+U or Hartree-Fock exchange in global hybrids, do so at the cost of worsening static correlation errors. We recently introduced an alternate approach [Bajaj et al., J. Chem. Phys. 147, 191101 (2017)] known as judiciously modified DFT (jmDFT), wherein the deviation from exact behavior of semilocal functionals over both fractional spin and charge, i.e., the so-called flat plane, was used to motivate functional forms of second order analytic corrections. In this work, we introduce fully nonempirical expressions for all four coefficients in a DFT+U+J-inspired form of jmDFT, where all coefficients are obtained only from energies and eigenvalues of the integer-electron systems. We show good agreement for U and J coefficients obtained nonempirically as compared with the results of numerical fitting in a jmDFT U+J/J' correction. Incorporating the fully nonempirical jmDFT correction reduces and even eliminates the fractional spin error at the same time as eliminating the energetic delocalization error. We show that this approach extends beyond s-electron systems to higher angular momentum cases including p- and d-electrons. Finally, we diagnose some shortcomings of the current jmDFT approach that limit its ability to improve upon DFT results for cases such as weakly bound anions due to poor underlying semilocal functional behavior.

Delocalization↗
DOE OSTI2016

Magnetic BiMn-α phase synthesis prediction: First-principles calculation, thermodynamic modeling and nonequilibrium chemical partitioning

BiMn-α is promising permanent magnet. Due to its peritectic formation feature, there is a synthetic challenge to produce single BiMn-α phase. The objective of this study is to assess driving force for crystalline phase pathways under far-from-equilibrium conditions. First-principles calculations with Hubbard U correction are performed to provide a robust description of the thermodynamic behavior. The energetics associated with various degrees of the chemical partitioning are quantified to predict temperature, magnetic field, and time dependence of the phase selection. By assessing the phase transformation under the influence of the chemical partitioning, temperatures, and cooling rate from our calculations, we suggest that it is possible to synthesize the magnetic BiMn-α compound in a congruent manner by rapid solidification. The external magnetic field enhances the stability of the BiMn-α phase. In conclusion, the compositions of the initial compounds from these highly driven liquids can be far from equilibrium.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

First-principles study of the electronic structure and the Fermi surface in rare-earth filled skutterudites R Pt 4 Ge 12

Experiments on rare-earth filled skutterudites demonstrate an intriguing array of thermodynamic, transport, and superconducting properties, and bring to fore theoretical challenges posed by f-electron systems. First-principle calculations based density functional theory and its extensions for strongly correlated systems such as the Hubbard U correction, provide valuable information about electronic structure that can be used to understand experiments. We present a comprehensive study of the electronic structure and Fermi surface of a series of rare-earth filled skutterudites, RPt 4 Ge 12 (where R = La, Ce, Pr), aimed at shedding light on: consequences of progressive increase of f-orbital occupancy in the series; the effects of the Hubbard parameter U; and the Fermi surfaces, band structures, and densities of states. The calculated Fermi surfaces may be relevant to the question of multiband versus single-band superconductivity. Computed densities of states qualitatively explain the available resonant photoemission spectroscopy experiments, and (together with available specific heat measurements) provide estimates of the effective masses. We also show the existence of pseudogaps in the total density of states which may be relevant for the thermoelectric properties of these systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗