Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Density gradient function”

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.

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

At least 109 records · Page 6

Predicting band gaps and band-edge positions of oxide perovskites using density functional theory and machine learning

Density functional theory (DFT) within the local or semilocal density approximations, i.e., the local density approximation (LDA) or generalized gradient approximation (GGA), has become a workhorse in the electronic structure theory of solids, being extremely fast and reliable for energetics and structural properties, yet remaining highly inaccurate for predicting band gaps of semiconductors and insulators. The accurate prediction of band gaps using first-principles methods is time consuming, requiring hybrid functionals, quasiparticle GW, or quantum Monte Carlo methods. Efficiently correcting DFT-LDA/GGA band gaps and unveiling the main chemical and structural factors involved in this correction is desirable for discovering novel materials in high-throughput calculations. In this direction, we, in this study, use DFT and machine learning techniques to correct band gaps and band-edge positions of a representative subset of ABO 3 perovskite oxides. Relying on the results of HSE06 hybrid functional calculations as target values of band gaps, we find a systematic band-gap correction of ~1.5 eV for this class of materials, where ~1 eV comes from downward shifting the valence band and ~0.5 eV from uplifting the conduction band. The main chemical and structural factors determining the band-gap correction are determined through a feature selection procedure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

An error-in-constitutive equations strategy for topology optimization for frequency-domain dynamics

This paper presents a topology optimization formulation for frequency-domain dynamics to reduce solution dependence upon initial guess and considered loading conditions. Due to resonance phenomena in undamped steady-state dynamics, objectives measuring dynamic response possess many local minima that may represent poor solutions to a design problem, an issue exacerbated for design with respect to multiple frequencies. In this work, we propose an extension of the modified error-in-constitutive-equations (MECE) method, used previously in material identification inverse problems, as a new approach for frequency-domain dynamics topology optimization to mitigate these issues. The main idea of the proposed framework is to incorporate an additional penalty-like term in the objective function that measures the discrepancy in the constitutive relations between stresses and strains and between inertial forces and displacements. Then, the design problem is cast within a PDE-constrained optimization formulation in which we seek displacements, stresses, inertial forces, and a density-field solution that minimize our new objective subject to conservation of linear momentum plus some additional constraints. We show that this approach yields superior designs to conventional gradient-based optimization approaches that solely use a functional of displacements as the objective, while strictly enforcing the constitutive equations. The MECE strategy integrates into a density-based topology optimization scheme for void–solid or two-phase material structural design. We highlight the merits of our approach in a variety of scenarios for direct frequency response design, considering multiple frequency load cases and structural objectives.

42 ENGINEERING↗

Vertical detachment energies of ammonia cluster anions using self-interaction-corrected methods

Systems with weakly bound extra electrons impose great challenges to semilocal density functional approximations (DFAs), which suffer from self-interaction errors. Small ammonia clusters are one such example of weakly bound anions where the extra electron is weakly bound. We applied two self-interaction correction (SIC) schemes, viz., the well-known Perdew–Zunger and the recently developed locally scaled SIC (LSIC) with the local spin density approximation (LSDA), Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation (GGA), and the SCAN meta-GGA functionals to calculate the vertical detachment energies (VDEs) of small ammonia cluster anions (NH3)n–. Our results show that the LSIC significantly reduces the errors in calculations of VDE with LSDA and PBE-GGA functionals leading to better agreement with the reference values calculated with coupled cluster singles and doubles with perturbative triples [CCSD(T)]. Accurate prediction of VDE as an absolute of the highest occupied molecular orbital (HOMO) is challenging for DFAs. Our results show that VDEs estimated from the negative of HOMO eigenvalues with the LSIC-LSDA and Perdew–Zunger SIC-PBE are within 11 meV of the reference CCSD(T) results. Here, the LSIC method performs consistently well for the VDE estimates, from both the total energy differences and the absolute HOMO eigenvalues.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

First-principles study of L -shell iron and chromium opacity at stellar interior temperatures

Recently developed free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter has been applied for studying L-shell opacity of iron and chromium at T = 182 eV. We use Mermin–Kohn–Sham density functional theory with a ground-state and a fully temperature-dependent generalized gradient approximation exchange-correlation (XC) functionals. It is demonstrated that the role of XC at such a high-T is negligible due to the total free-energy of interacting system being dominated by the noninteracting free-energy term in agreement with estimations for the homogeneous electron gas. Furthermore, our DFT predictions are compared to the radiative emissivity and opacity of dense plasmas model, to the real-space Greens function method, and to experimental measurements. Good agreement is found between all three theoretical methods, and in the bound–continuum region for Cr when compared to the experiment, while the discrepancy between direct DFT calculations and the experiment for Fe remains essentially the same as for plasma-physics models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Mott vs Kondo: Influence of various density functional based methods on the Ce isostructural phase transition mechanism

The cerium iso-structural phase transition (γ–α) is dominated by f-electron localization changes that results in a magnetic ordering change and a volume collapse. Generally, these physics are difficult to capture with ab initio and first principles methods. However, previous works have shown various methods to be successful in predicting at least some of the physics of the γ to α phase transition. Therefore, here, we perform a broad survey of density functional based methods across three levels of theory and types of functions [GGA (generalized gradient approximation), MetaGGA, and hybrid functionals] and compare the results, focusing on hydrostatic compression across the phase boundary at zero kelvin. For the methods that best reproduce experimental results, we directly probe the predicted mechanisms and frame the results in the Mott/Kondo debate, assessing how the underlying methods and assumptions of different functionals can assess the physical drivers in the phase transition, providing insight into the governing processes of this unique phase transition.

36 MATERIALS SCIENCE↗

Sensitivity of the electronic and magnetic structures of cuprate superconductors to density functional approximations

Abstract We discuss the crystal, electronic, and magnetic structures of La 2− x Sr x CuO 4 (LSCO) for x = 0.0 and x = 0.25 employing 13 density functional approximations, representing the local, semi-local, and hybrid exchange-correlation approximations within the Perdew–Schmidt hierarchy. The meta-generalized gradient approximation (meta-GGA) class of functionals is found to perform well in capturing the key properties of LSCO, a prototypical high-temperature cuprate superconductor. In contrast, the localspin-density approximation, GGA, and the hybrid density functional fail to capture the metal-insulator transition under doping.

36 MATERIALS SCIENCE↗

Free-energy orbital-free density functional theory: recent developments, perspective, and outlook

By summarizing the constraint-based development of orbital-free free-energy density functional approximations, we provide a perspective on progress over the last 15 years, the limitations of existing functionals, and the challenges awaiting resolution. We outline the chronology of the development of noninteracting and exchange-correlation free-energy orbital-free functionals and summarize the theoretical basis of existing local density approximation, second-order approximation, generalized gradient approximation (GGA), and meta-GGAs. We discuss limitations and challenges such as problems with thermodynamic derivatives, free-energy nonadditivity and the closely related issue of all-electron versus valence-only local pseudo-potential performance.

74 ATOMIC AND MOLECULAR PHYSICS↗

Examination of How Well Long-Range-Corrected Density Functionals Satisfy the Ionization Energy Theorem

For this work, we calculated the vertical ionization energies (VIE) of 99 species in two ways to examine the accuracy of several long-range-corrected (LC) hybrid meta functionals in comparison with a gradient approximation (GA), global hybrids, and doubly hybrids. In the category of LC functionals, we examined both those with meta ingredients (i.e., that depend on the kinetic energy density) and those without them. The LC-hybrid meta functionals examined are M11, revM11, M11plus, and ωB97M-V. The reference data used to assess accuracy consist of 95 molecules and 4 atoms in the GW100 set. The two methods studied are the ΔSCF method (involving the difference of neutral and cation self-consistent field (SCF) energies) and the ionization energy theorem (involving the orbital energy of the highest occupied molecular orbital, HOMO). We calculated linear correlation coefficients (r 2 ) and mean absolute deviations (MADs) between each approach and the reference VIE value from the CCSD(T)/def2-TZVPP level of theory. We compared the new LC-hybrid meta calculations to calculations with the 10 functionals in a previous VIE study by Brémond et al. and to the calculations with LC-BLYP (LC-Becke, Lee–Yang–Parr), CAM-B3LYP (Coulomb-attenuating-method Becke-3-parameter Lee–Yang–Parr), LC-ωHPBE, and ωB97X-D. The results show that Minnesota LC-hybrid meta functionals have the smallest mean absolute deviation of ionization energy theorem VIEs with the reference data; the LC-ωHPBE functional also does quite well in this test. This is very encouraging and indicates that LC-hybrid meta functionals would be the best starting points for the tuning strategy that has been shown to be a very good procedure for improving time-dependent density functional calculations, and it also helps explain the good success of LC-hybrid meta functionals for molecular excitation energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Carbon nanotube thermoelectric devices by direct printing: Toward wearable energy converters

Thermoelectric devices convert thermal energy to electrical energy and are particularly well-suited for energy harvesting from waste heat. Even as the number of electronic devices used in daily life proliferates, technical advances diminish the average power such devices require to perform a given function. Here, localized thermal gradients that abound in our living environments, despite having modest energy densities, are therefore becoming increasingly viable and attractive to power such devices. With this motivation, we report the design, fabrication, and characterization of single-wall carbon nanotube thermoelectric devices (CNT-TDs) on flexible polyimide substrates as a basis for wearable energy converters. Our aqueous-solution-based film fabrication process could enable readily scalable, low-cost TDs; here, we demonstrate CNT-hydroxypropyl cellulose (HPC) composite thermoelectric films by aerosol jet printing. The electrical conductivity of the composite films is controlled through the number of CNT/HPC layers printed in combination with control of the annealing conditions.

30 DIRECT ENERGY CONVERSION↗

Self-consistent implementation of locally scaled self-interaction-correction method

Recently proposed local self-interaction correction (LSIC) method is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange–correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew–Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn–Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional and barrier heights of the BH6 database better than some of the most widely used hybrid functionals. The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). Furthermore, this work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Laplacian-level meta-generalized gradient approximation for solid and liquid metals

In this work, we derive and motivate a Laplacian-level, orbital-free meta-generalized-gradient approximation (LL-MGGA) for the exchange-correlation energy, targeting accurate ground-state properties of sp and sd metallic condensed matter, in which the density functional for the exchange-correlation energy is only weakly nonlocal due to perfect long-range screening. Our model for the orbital-free kinetic energy density restores the fourth-order gradient expansion for exchange to the r 2 SCAN meta-GGA [Furness et al., J. Phys. Chem. Lett. 11, 8208 (2020)], yielding a LL-MGGA we call OFR2. OFR2 matches the accuracy of SCAN for prediction of common lattice constants and improves the equilibrium properties of alkali metals, transition metals, and intermetallics that were degraded relative to the PBE GGA values by both SCAN and r 2 SCAN. We compare OFR2 to the r 2 SCAN -L LL-MGGA [Mejia-Rodriguez and Trickey, Phys. Rev. B 102, 121109(R) (2020)] and show that OFR2 tends to outperform r 2 SCAN -L for the equilibrium properties of solids, but r 2 SCAN -L much better describes the atomization energies of molecules than OFR2 does. For best accuracy in molecules and nonmetallic condensed matter, we continue to recommend SCAN and r 2 SCAN. Numerical performance is discussed in detail, and our paper provides an outlook to machine learning.

36 MATERIALS SCIENCE↗

Lattice Structure and Dynamics of Sparse Molecular Crystals: OsO 4 and RuO 4

OsO 4 and RuO 4 are molecular oxides with unique tetrameric structures and rare +8 oxidation states. Accurately modeling their properties remains challenging for density functional theory (DFT) due to weak intertetramer interactions, which standard functionals fail to capture. Here, in this work, we show that the van der Waals (vdW)-corrected density functional (vdW-DF-optB86b) provides structural parameters that are much closer to experimental values than the standard generalized gradient approximation, with volume predictions that fall within the experimentally observed range. Phonon band structure analysis shows that the inclusion of vdW interactions stabilizes soft phonon modes, highlighting the importance of dispersion corrections for accurate predictions of lattice dynamics. Experimental measurements of the phonon density of states for OsO 4 , obtained via inelastic neutron scattering, demonstrate good agreement with our vdW-DF-optB86b calculations. These results validate OsO 4 and RuO 4 as valuable benchmarks for structural and vibrational calculations via vdW-corrected DFT methods and offer insights for studying the broader class of sparse molecular materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Comparative Density Functional Theory Study of Magnetic Exchange Couplings in Dinuclear Transition-Metal Complexes

Multicenter transition-metal complexes (MCTMs) with magnetically interacting ions have been proposed as components for information-processing devices and storage units. For any practical application of MCTMs as magnetic units, it is crucial to characterize their magnetic behavior, and in particular, the isotropic magnetic exchange coupling, J, between its magnetic centers. Due to the large size of typical MCTMs, density functional theory is the only practical electronic structure method for evaluating the J coupling. Here, we assess the accuracy of different density functional approximations for predicting the magnetic couplings of eight dinuclear transition-metal complexes, including five dimanganese, two dicopper, and one divanadium with known reliable experimental J couplings spanning from ferromagnetic to strong antiferromagnetic. The density functionals considered include global hybrid functionals which mix semilocal density functional approximations and exact exchange with a fixed admixing parameter, six local hybrid functionals where the admixing parameters are extended to be spatially dependent, the SCAN and r 2 SCAN meta-generalized gradient approximations (GGAs), and two widely used GGAs. We found that global hybrids tested in this work have a tendency to over-correct the error in magnetic coupling parameters from the Perdew–Burke–Ernzerhof (PBE) GGA as seen for manganese complexes. The performance of local hybrid density functionals shows no improvement in terms of bias and is scattered without a clear trend, suggesting that more efforts are needed for the extension from global to local hybrid density functionals for this particular property. The SCAN and r 2 SCAN meta-GGAs are found to perform as well as benchmark global hybrids on most tested complexes. We further analyze the charge density redistribution of meta-GGAs as well as global and local hybrid density functionals with respect to that of PBE, in connection to the self-interaction error or delocalization error.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Formation energy puzzle in intermetallic alloys: Random phase approximation fails to predict accurate formation energies

We performed density functional calculations to estimate the formation energies of intermetallic alloys. We used two semilocal approximations, the generalized gradient approximation (GGA) by Perdew-Burke- Ernzerhof (PBE) and the strongly constrained and appropriately normed (SCAN) meta-GGA. In addition, we utilized two nonlocal DFT functionals, the hybrid HSE06, and the state-of-the-art random phase approximation (RPA). The nonlocal functionals such as HSE06 and RPA yield accurate formation energies of binary alloys with completely-filled d-band metals, where semilocal functionals underperform. The accuracy at the nonlocal functionals is greatly reduced when a partially-filled d-band metal is present in an alloy, while PBE-GGA outperforms in these cases. We show that the accurate prediction of formation energies by any DFT method depends on its ability to predict the accurate electronic properties, e.g., valence d-band contribution to the density of states (DOS). The SCAN meta-GGA often corrects the PBE-DOS, however, it does not provide accurate formation energies compared to PBE. This is assumed to be due to the lack of proper error cancellation that should be expected due to the similar bulk nature of both alloys and their constituents, which may improve with the modification of meta-GGA ingredients. RPA yields too negative formation energies of alloys with partially-filled d-band metals. RPA results can be corrected by restoring the exchange-correlation kernel, thereby improving the short-range electron-electron correlation in metallic densities.

36 MATERIALS SCIENCE↗

Re-examining the silicon self-interstitial charge states and defect levels: A density functional theory and bounds analysis study

The self-interstitial atom (SIA) is one of two fundamental point defects in bulk Si. Isolated Si SIAs are extremely difficult to observe experimentally. Even at very low temperatures, they anneal before typical experiments can be performed. Given the challenges associated with experimental characterization, accurate theoretical calculations provide valuable information necessary to elucidate the properties of these defects. Previous studies have applied Kohn–Sham density functional theory (DFT) to the Si SIA, using either the local density approximation or the generalized gradient approximation to the exchange-correlation (XC) energy. The consensus of these studies indicates that a Si SIA may exist in five charge states ranging from -2 to +2 with the defect structure being dependent on the charge state. This study aims to re-examine the existence of these charge states in light of recently derived “approximate bounds” on the defect levels obtained from finite-size supercell calculations and new DFT calculations using both semi-local and hybrid XC approximations. We conclude that only the neutral and +2 charge states are directly supported by DFT as localized charge states of the Si SIA. Within the current accuracy of DFT, our results indicate that the +1 charge state likely consists of an electron in a conduction-band-like state that is coulombically bound to a +2 SIA. Furthermore, the -1 and -2 charge states likely consist of a neutral SIA with one and two additional electrons in the conduction band, respectively.

36 MATERIALS SCIENCE↗

Bending as a control knob for the electronic and optical properties of phosphorene nanoribbons

We have assessed mechanical bending as a powerful controlling tool for the electronic structure and optical properties of phosphorene nanoribbons. We use state-of-the-art density functional approximations in our work. The overall performance of the recently developed meta-generalized gradient approximation (meta-GGA) mTASK [Phys. Rev. Materials 5, 063803 (2021)] functional establishes the method as a useful alternative to the screened hybrid HSE06 for better band gaps of phosphorene nanoribbons. We present a detailed analysis to interpret the optical absorption of bent phosphorene nanoribbons using the GW-Bethe-Salpeter approximation. Finally, we demonstrate the important role of the unoccupied in-gap state and conclude that this in-gap state in armchair nanoribbons introduced by bending can significantly affect the properties of low-energy excitons and add some useful opportunities for applications in optoelectronic devices.

36 MATERIALS SCIENCE↗

Hydrogen-induced degradation dynamics in silicon heterojunction solar cells via machine learning

Abstract Among silicon-based solar cells, heterojunction cells hold the world efficiency record. However, their market acceptance is hindered by an initial 0.5% per year degradation of their open circuit voltage which doubles the overall cell degradation rate. Here, we study the performance degradation of crystalline-Si/amorphous-Si:H heterojunction stacks. First, we experimentally measure the interface defect density over a year, the primary driver of the degradation. Second, we develop SolDeg, a multiscale, hierarchical simulator to analyze this degradation by combining Machine Learning, Molecular Dynamics, Density Functional Theory, and Nudged Elastic Band methods with analytical modeling. We discover that the chemical potential for mobile hydrogen develops a gradient, forcing the hydrogen to drift from the interface, leaving behind recombination-active defects. We find quantitative correspondence between the calculated and experimentally determined defect generation dynamics. Finally, we propose a reversed Si-density gradient architecture for the amorphous-Si:H layer that promises to reduce the initial open circuit voltage degradation from 0.5% per year to 0.1% per year.

14 SOLAR ENERGY↗

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗