SEARCH · Search NASA

Results for “generalized gradient approximations”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

All sources NASA NTRS DOE OSTI

DOE OSTI2024

Exploring interlayer coupling in the twisted bilayer PtTe 2

We have investigated interlayer interactions in the bilayer PtTe 2 system, which influence the electronic energy bands near the Fermi level. Our diffusion Monte Carlo (DMC) calculations for the high-symmetry bilayer stackings (AA, AB, AC) manifest distinct interlayer binding characteristics among the stacking modes by revealing significantly different interlayer separations depending on the stacking, which is critical to understanding the interlayer coupling of the twisted bilayers consisting of various local stacking arrangements. Furthermore, a comparison between the interlayer separations obtained from DMC and density functional theory (DFT) shows that meta-generalized gradient approximation (GGA)-based van der Waals–DFT results agree with DMC for different layer stackings, including twisted bilayers, but only the ground-state AA stacking matches well with GGA-based DFT predictions. This underscores the importance of accurate exchange-correlation potentials even for capturing the stacking-dependent interlayer binding properties. We further show that the variability in DFT-predicted interlayer separations is responsible for the large discrepancy of band structures in the 21 . 79 ∘ twisted bilayer PtTe 2 , affecting its classification as metallic or insulating. These results demonstrate the importance of obtaining a correct description of stacking-dependent interlayer coupling in modeling delicate bilayer systems at finite twists. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

DOE OSTI2025

Range-separated thermal hybrid exchange-correlation density functional for accurate band-gap calculations of warm dense matter

Here, in this study, we present a range-separated thermal hybrid exchange-correlation (XC) functional, termed RS-KDT0, which provides highly accurate band-gap predictions at elevated temperature while reducing the computational cost relative to thermal global hybrid functionals. At zero temperature, RS-KDT0 recovers the widely used ground-state range-separated hybrid functional HSE06. To assess its performance across temperature regimes, we conducted static calculations of electronic pressure, band gaps, and band structures. RS-KDT0 exhibits the same level of accuracy as HSE06 in the low-temperature regime and demonstrates improved agreement with finite-temperature GW calculations at elevated temperatures when compared to other thermal XC functionals such as the generalized gradient approximation (GGA)-level KDT16 and the global hybrid KDT0.

density functional theory↗

DOE OSTI2021

Photoelectrochemically Self Improving Si/GaN Photocathode: Figure 4a Raw Data

Calculated formation energy of (0001 ̅) c-plane GaN surfaces. The density-functional theory (DFT) calculations were performed with the generalized gradient approximation, using the plane-wave pseudopotential quantum-ESPRESSO package. Ultrasoft pseudopotentials were used to describe the interaction between valence electrons and ionic cores, where Ga 3d electrons were explicitly treated as valence electrons. The wave functions and electronic density were expanded in a plane-wave basis set truncated at a cutoff energy of 30 Ry and 240 Ry, respectively. The surface was modeled using a repeated slab geometry using a (2×2) unit cell with a thickness of seven GaN bilayers, where the Ga-terminated bottom side was passivated by pseudo-hydrogen with charge of 1.25e. In addition, the (1010) surface was modeled using 8 GaN atomic layers with a lateral dimension of 9.57 Å x 10.38 Å. A vacuum width of at least 15.0 Å was introduced between consecutive slabs, and a k-point mesh of 5x5x1 and 2x2x1 was used to sample the surface Brillouin zone for the polar and non-polar surfaces, respectively. Calculated formation energy of (0001 ̅) c-plane GaN surfaces with different oxygen configuration within the anion and cation-rich limits: ideal GaN surfaces of c-plane and m-plane; configurations with 100% replacement of nitrogen by oxygen on the surface c-plane and m-plane; 100% replacement of nitrogen by oxygen in the subsurface bilayer c-plane and m-plane; and configurations with 50% replacement of nitrogen of the surface and subsurface bilayers by oxygens c-plane and m-plane. In both cases, the ideal surface is chosen as the reference.

photocathode↗

DOE OSTI2021

Photoelectrochemically Self Improving Si/GaN Photocathode: Figure 4b Raw Data

Calculated formation energy of (1010 ̅) m-plane GaN surfaces. The density-functional theory (DFT) calculations were performed with the generalized gradient approximation, using the plane-wave pseudopotential quantum-ESPRESSO package. Ultrasoft pseudopotentials were used to describe the interaction between valence electrons and ionic cores, where Ga 3d electrons were explicitly treated as valence electrons. The wave functions and electronic density were expanded in a plane-wave basis set truncated at a cutoff energy of 30 Ry and 240 Ry, respectively. The surface was modeled using a repeated slab geometry using a (2×2) unit cell with a thickness of seven GaN bilayers, where the Ga-terminated bottom side was passivated by pseudo-hydrogen with charge of 1.25e. In addition, the (1010) surface was modeled using 8 GaN atomic layers with a lateral dimension of 9.57 Å x 10.38 Å. A vacuum width of at least 15.0 Å was introduced between consecutive slabs, and a k-point mesh of 5x5x1 and 2x2x1 was used to sample the surface Brillouin zone for the polar and non-polar surfaces, respectively. Calculated formation energy of (1010 ̅) m-plane GaN surfaces with different oxygen configuration within the anion and cation-rich limits: ideal GaN surfaces of c-plane and m-plane; configurations with 100% replacement of nitrogen by oxygen on the surface c-plane and m-plane; 100% replacement of nitrogen by oxygen in the subsurface bilayer c-plane and m-plane; and configurations with 50% replacement of nitrogen of the surface and subsurface bilayers by oxygens c-plane and m-plane. In both cases, the ideal surface is chosen as the reference.

photocathode↗

DOE OSTI2023

Magnetic contributions to corundum-eskolaite and corundum-hematite phase equilibria: A DFT cluster expansion study

Magnetic contributions have the potential to significantly influence predicted phase stability within alloy and mineral mixing phase diagrams, yet have been historically challenging to incorporate due to a significant increase to phase space sampling. Here, in this work, we employ a computational protocol that includes spin orientation as an additional configurational component within multi-component cluster expansions between magnetic and non-magnetic metal oxide alloys [calculated using density functional theory (DFT) and the generalized gradient approximation]. This approach was used to determine the effect of magnetic contributions to corundum-eskolaite and corundum-hematite phase equilibria from first principles. Two-component cluster expansions of the magnetic components of eskolaite and hematite were first performed showing the ability of this method to properly calculate their respective magnetic properties. Two-component cluster expansions were then performed for non-magnetic Al(III) and ferromagnetic Cr(III) and Fe(III), and phase diagrams were calculated for later comparison. Finally, a non-magnetic Al(III) and “up” and “down” magnetic configurations for anti-ferromagnetic Cr(III) and Fe(III) were performed. Magnetic contributions to the calculated phase diagram for the corundumeskolaite system were shown to be inconsequential but are vital for accurate determination of the corundum-hematite solvus.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Adsorption and Growth of Organic Materials on Metal Surfaces

This work investigated extensively the role of van der Waals (vdWs) interactions, when incorporated self-consistently into density functional theory (DFT). The investigations follow two avenues: 1) screening of several vdWs schemes at the generalized gradient approximation (GGA), using adsorption of small and large organic molecules on a variety of metal surfaces; and 2) simulating the adsorption of 2D materials such as silicene and phosphorene on metal surfaces. This second avenue is done in connection were subject of experimental investigations. These investigations led us to the conclusion that, if the inclusion of the vdWs interactions improved the nature of the adsorption and brought some excellent agreements with the experimental observations of the adsorption geometries, there is still a lot to do when it comes to the changes to the electronic structure upon adsorption.

2D materials.↗

DOE OSTI2020

Many-Body Effects in FeN4 Center Embedded in Graphene

We introduce a computational approach to study porphyrin-like transition metal complexes, bridging density functional theory and exact many-body techniques, such as the density matrix renormalization group (DMRG). We first derive a multi-orbital Anderson impurity Hamiltonian starting from first principles considerations that qualitatively reproduce generalized gradient approximation (GGA)+U results when ignoring inter-orbital Coulomb repulsion U ′ and Hund exchange J. An exact canonical transformation is used to reduce the dimensionality of the problem and make it amenable to DMRG calculations, including all many-body terms (both intra- and inter-orbital), which are treated in a numerically exact way. We apply this technique to FeN 4 centers in graphene and show that the inclusion of these terms has dramatic effects: as the iron orbitals become single occupied due to the Coulomb repulsion, the inter-orbital interaction further reduces the occupation, yielding a non-monotonic behavior of the magnetic moment as a function of the interactions, with maximum polarization only in a small window at intermediate values of the parameters. Furthermore, U ′ changes the relative position of the peaks in the density of states, particularly on the iron d z 2 orbital, which is expected to affect the binding of ligands greatly.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Thermodynamics of Uranium Tri-Iodide from Density-Functional Theory

Density-functional theory (DFT) is employed to investigate the thermodynamic and ground-state properties of bulk uranium tri-iodide, UI3. The theory is fully relativistic and electron correlations, beyond the DFT and generalized gradient approximation, are addressed with orbital polarization. The electronic structure indicates anti-ferromagnetism, in agreement with neutron diffraction, with band gaps and a non-metallic system. Furthermore, the formation energy, atomic volume, crystal structure, and heat capacity are calculated in reasonable agreement with experiments, whereas for the elastic constants experimental data are unavailable for comparison. The thermodynamical properties are modeled within a quasi-harmonic approximation and the heat capacity and Gibbs free energy as functions of temperature agree with available calculation of phase diagram (CALPHAD) thermodynamic assessment of the experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Construction of meta-GGA functionals through restoration of exact constraint adherence to regularized SCAN functionals

The strongly constrained and appropriately normed (SCAN) meta-GGA exchange–correlation functional is constructed as a chemical environment-determined interpolation between two separate energy densities: one describes single-orbital electron densities accurately and another describes slowly varying densities accurately. To conserve constraints known for the exact exchange–correlation functional, the derivatives of this interpolation vanish in the slowly varying limit. While theoretically convenient, this choice introduces numerical challenges that degrade the functional’s efficiency. We have recently reported a modification to the SCAN meta-GGA, termed restored-regularized-SCAN (r 2 SCAN) , that introduces two regularizations into SCAN, which improve its numerical performance at the expense of not recovering the fourth order term of the slowly varying density gradient expansion for exchange. Here, we show the derivation of a progression of density functional approximations [regularized SCAN (rSCAN), r++SCAN, r 2 SCAN, and r 4 SCAN] with increasing adherence to exact conditions while maintaining a smooth interpolation. The greater smoothness of r 2 SCAN seems to lead to better general accuracy than the additional exact constraint of SCAN or r 4 SCAN does.

, correlation energy↗

DOE OSTI2021

Proof-of-concept of a reinforcement learning framework for wind farm energy capture maximization in time-varying wind

Here, we present a proof-of-concept distributed reinforcement learning framework for wind farm energy capture maximization. The algorithm we propose uses Q-Learning in a wake-delayed wind farm environment and considers time-varying, though not yet fully turbulent, wind inflow conditions. These algorithm modifications are used to create the Gradient Approximation with Reinforcement Learning and Incremental Comparison (GARLIC) framework for optimizing wind farm energy capture in time-varying conditions, which is then compared to the FLOw Redirection and Induction in Steady State (FLORIS) static lookup table wind farm controller baseline.

17 WIND ENERGY↗

DOE OSTI2022

Testing the r 2 SCAN Density Functional for the Thermodynamic Stability of Solids with and without a van der Waals Correction

Not Available

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Accelerating defect predictions in semiconductors using graph neural networks

First-principles computations reliably predict the energetics of point defects in semiconductors but are constrained by the expense of using large supercells and advanced levels of theory. Machine learning models trained on computational data, especially ones that sufficiently encode defect coordination environments, can be used to accelerate defect predictions. Here, we develop a framework for the prediction and screening of native defects and functional impurities in a chemical space of group IV, III–V, and II–VI zinc blende semiconductors, powered by crystal Graph-based Neural Networks (GNNs) trained on high-throughput density functional theory (DFT) data. Using an innovative approach of sampling partially optimized defect configurations from DFT calculations, we generate one of the largest computational defect datasets to date, containing many types of vacancies, self-interstitials, anti-site substitutions, impurity interstitials and substitutions, as well as some defect complexes. We applied three types of established GNN techniques, namely crystal graph convolutional neural network, materials graph network, and Atomistic Line Graph Neural Network (ALIGNN), to rigorously train models for predicting defect formation energy (DFE) in multiple charge states and chemical potential conditions. We find that ALIGNN yields the best DFE predictions with root mean square errors around 0.3 eV, which represents a prediction accuracy of 98% given the range of values within the dataset, improving significantly on the state-of-the-art. We further show that GNN-based defective structure optimization can take us close to DFT-optimized geometries at a fraction of the cost of full DFT. The current models are based on the semi-local generalized gradient approximation-Perdew–Burke–Ernzerhof (PBE) functional but are highly promising because of the correlation of computed energetics and defect levels with higher levels of theory and experimental data, the accuracy and necessity of discovering novel metastable and low energy defect structures at the PBE level of theory before advanced methods could be applied, and the ability to train multi-fidelity models in the future with new data from non-local functionals. The DFT-GNN models enable prediction and screening across thousands of hypothetical defects based on both unoptimized and partially optimized defective structures, helping identify electronically active defects in technologically important semiconductors.

Rahman, Md Habibur (ORCID:000000027705984X)↗

DOE OSTI2024

How well do one-electron self-interaction-correction methods perform for systems with fractional electrons?

Recently developed locally scaled self-interaction correction (LSIC) is a one-electron SIC method that, when used with a ratio of kinetic energy densities (z σ ) as iso-orbital indicator, performs remarkably well for both thermochemical properties as well as for barrier heights overcoming the paradoxical behavior of the well-known Perdew–Zunger self-interaction correction (PZSIC) method. In this work, we examine how well the LSIC method performs for the delocalization error. Our results show that both LSIC and PZSIC methods correctly describe the dissociation of $H$$^{+}_{2}$ and $H$$^{+}_{2}$ but LSIC is overall more accurate than the PZSIC method. Likewise, in the case of the vertical ionization energy of an ensemble of isolated He atoms, the LSIC and PZSIC methods do not exhibit delocalization errors. For the fractional charges, both LSIC and PZSIC significantly reduce the deviation from linearity in the energy vs number of electrons curve, with PZSIC performing superior for C, Ne, and Ar atoms while for Kr they perform similarly. The LSIC performs well at the endpoints (integer occupations) while substantially reducing the deviation. The dissociation of LiF shows both LSIC and PZSIC dissociate into neutral Li and F but only LSIC exhibits charge transfer from Li + to F – at the expected distance from the experimental data and accurate ab initio data. Overall, both the PZSIC and LSIC methods reduce the delocalization errors substantially.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Orbital dependent complications for close vs well-separated electrons in diradicals

We investigate two limits in open-shell diradical systems: O3, in which the interesting orbitals are in close proximity to one another, and (C21H13)2, where there is a significant spatial separation between the two orbitals. In accord with earlier calculations, we find that standard density-functional approximations do not predict the open-shell character for the former case but uniformly predict the open-shell character for the latter case. We trace the qualitatively incorrect behavior in O3 predicted by these standard density functional approximations to self-interaction error and use the Fermi–Löwdin-orbital-self-interaction-corrected formalism to determine accurate triplet, closed-shell singlet, and open-shell broken-spin-symmetry electronic configurations. Analysis of the resulting many-electron overlap matrices allows us to unambiguously show that the broken-spin-symmetry configurations do not participate in the representation of the Ms = 0 triplet states and allows us to reliably extract the singlet–triplet splitting in O3 by analyzing the energy as a function of Fermi-orbital-descriptor permutations. The results of these analyses predict the percentage of open-shell character in O3, which agrees well with conventional wavefunction-based methods. While these techniques are expected to be required in cases near the Coulson–Fischer point, we find that they will be less necessary in diradical systems with well-separated electrons, such as (C21H13)2. Results based on energies from self-interaction-corrected generalized gradient, local density, and Hartree–Fock approximations and experimental results are in generally good agreement for O3. These results help form the basis for deriving extended Heisenberg-like Hamiltonians that are needed for descriptions of molecular magnets when there are competing low-energy electronic configurations.

Chemistry↗

DOE OSTI2020

Self-interaction error overbinds water clusters but cancels in structural energy differences

Here, we gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi–Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew–Burke–Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction–corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/ H 2 O from about 42 meV/ H 2 O for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction–corrected SCAN. These findings suggest that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1987

Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers

Applying a finite difference approximation to a biharmonic equation results in a very ill-conditioned system of equations. This paper examines the conjugate gradient method used in conjunction with the generalized and approximate polynomial preconditionings for solving such linear systems. An approximate polynomial preconditioning is introduced, and is shown to be more efficient than the generalized polynomial preconditionings. This new technique provides a simple but effective preconditioning polynomial, which is based on another coefficient matrix rather than the original matrix operator as commonly used.

Wong, Yau Shu↗

NASA NTRS1983

Structural optimization - Challenges and opportunities

A review of developments in structural optimization techniques and their interface with growing computer capabilities is presented. Structural design steps comprise functional definition of an object, an evaluation phase wherein external influences are quantified, selection of the design concept, material, object geometry, and the internal layout, and quantification of the physical characteristics. Optimization of a fully stressed design is facilitated by use of nonlinear mathematical programming which permits automated definition of the physics of a problem. Design iterations terminate when convergence is acquired between mathematical and physical criteria. A constrained minimum algorithm has been formulated using an Augmented Lagrangian approach and a generalized reduced gradient to obtain fast convergence. Various approximation techniques are mentioned. The synergistic application of all the methods surveyed requires multidisciplinary teamwork during a design effort.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1984

Structural optimization: Challenges and opportunities

Sobieszczanski-Sobieski, J.↗