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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Advances and Challenges of SCAN and r 2 SCAN Density Functionals in Transition‐Metal Compounds

ABSTRACT Transition‐metal compounds (TMCs) with open‐shell d ‐electrons are characterized by a complex interplay of lattice, charge, orbital, and spin degrees of freedom, giving rise to various fascinating applications. Often exhibiting exotic properties, these compounds are commonly classified as correlated systems due to strong inter‐electronic interactions called Hubbard U . This inherent complexity presents significant challenges to Kohn‐Sham density functional theory (KS‐DFT), the most widely used electronic structure method in condensed matter physics and materials science. While KS‐DFT is, in principle, exact for the ground‐state total energy, its exchange‐correlation energy must be approximated in practice. The mean‐field nature of KS implementations, combined with the limitations of current exchange‐correlation density functional approximations, has led to the perception that DFT is inadequate for correlated systems, particularly TMCs. Consequently, a common workaround involves augmenting DFT with an on‐site Hubbard‐like U correction. In recent years, the strongly constrained and appropriately normed (SCAN) density functional, along with its refined variant r 2 SCAN, has achieved remarkable progress in accurately describing the structural, energetic, electronic, magnetic, and vibrational properties of TMCs, challenging the traditional perception of DFT's limitations. This review explores the design principles of SCAN and r 2 SCAN, highlights their key advancements in studying TMCs, explains the mechanisms driving these improvements, and addresses the remaining challenges in this evolving field.

Zhang, Yubo [Minjiang Collaborative Center for The↗
DOE OSTI2023

A unified and constructive framework for the universality of neural networks

Abstract One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal approximation property. Though the past few decades have seen tremendous advances in theories of neural networks, a single constructive and elementary framework for neural network universality remains unavailable. This paper is an effort to provide a unified and constructive framework for the universality of a large class of activation functions including most of the existing ones. At the heart of the framework is the concept of neural network approximate identity (nAI). The main result is as follows: any nAI activation function is universal in the space of continuous functions on compacta. It turns out that most of the existing activation functions are nAI, and thus universal. The framework induces several advantages over the contemporary counterparts. First, it is constructive with elementary means from functional analysis, probability theory, and numerical analysis. Second, it is one of the first unified and constructive attempts that is valid for most of the existing activation functions. Third, it provides new proofs for most activation functions. Fourth, for a given activation and error tolerance, the framework provides precisely the architecture of the corresponding one-hidden neural network with a predetermined number of neurons and the values of weights/biases. Fifth, the framework allows us to abstractly present the first universal approximation with a favorable non-asymptotic rate. Sixth, our framework also provides insights into the developments, and hence providing constructive derivations, of some of the existing approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

MCML: Combining physical constraints with experimental data for a multi-purpose meta-generalized gradient approximation

The predictive power of density functional theory for materials properties can be improved without increasing the overall computational complexity by extending the generalized gradient approximation (GGA) for electronic exchange and correlation to density functionals depending on the electronic kinetic energy density in addition to the charge density and its gradient, resulting in a meta-GGA. Here, we propose an empirical meta-GGA model that is based both on physical constraints and on experimental and quantum chemistry reference data. Overall, the resulting optimized meta-GGA MCML yields improved surface and gas phase reaction energetics without sacrificing the accuracy of bulk property predictions of existing meta-GGA approaches.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Search for Higgs boson pair production in the γγ$b\overline{b} $ final state with 13 TeV pp collision data collected by the ATLAS experiment

A search is performed for resonant and non-resonant Higgs boson pair production in the γγ$b\overline{b} $ final state. The data set used corresponds to an integrated luminosity of 36.1 fb -1 of proton-proton collisions at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. No significant excess relative to the Standard Model expectation is observed. The observed limit on the non-resonant Higgs boson pair cross-section is 0.73 pb at 95% confidence level. This observed limit is equivalent to 22 times the predicted Standard Model cross-section. The Higgs boson self-coupling (κ λ = λ HHH /λ HHH SM ) is constrained at 95% confidence level to -8.2 < κ λ < 13.2. For resonant Higgs boson pair production through X→HH→γγ$b\overline{b} $, the limit is presented, using the narrow-width approximation, as a function of mX in the range 260 GeV < m X < 1000 GeV. The observed limits range from 1.1 pb to 0.12 pb over this mass range. Open image in new window

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Collisional Broadening of CO{sub 2} 10{sup 0}0–00{sup 0}1 Transition Lines by O{sub 2} and N{sub 2} in the Range 300–700 K

Unsaturated absorption coefficients are measured using a tunable CO{sub 2} laser in pure CO{sub 2} and CO{sub 2}:O{sub 2} = 1:2 and CO{sub 2}:N{sub 2} = 1:2 gas mixtures at the central frequencies of the R(8), R(22), P(8), P(22), and P(36) CO{sub 2} 10{sup 0}0–00{sup 0}1 transition lines under a pressure of 100 Torr in the temperature range 300–700 K. The collisional broadening coefficients of the CO{sub 2} spectral lines by O{sub 2} and N{sub 2} are obtained. The temperature dependences of these coefficients are approximated by power functions with two different exponents.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Assessing entropy for catalytic processes at complex reactive interfaces

When chemical reactions are accelerated by a catalyst, entropy differences between reactants and their transient intermediates can be the driving force behind the promotion or inhibition of desired and parasitic chemical pathways. Understanding and controlling catalytic processes therefore requires both a fundamental and practicable understanding of entropy in addition to enthalpy. In unstructured media such as the vapor phase equilibrated with sparsely covered surfaces, entropy can be adequately accounted for by well-established approaches based on translational, rotational, and harmonic vibrational partition functions. However, these approximations become inadequate in more complex condensed phase environments, e.g., solid liquid interfaces of confined reaction spaces. In this chapter, we provide an overview of the state-of-art in the computational quantification of entropy and its known ramifications on catalysis. The fundamental roles of thermodynamics and kinetics in catalysis are covered in enough detail to appreciate and contextualize the computational methods employed to compute chemically accurate estimates of entropy. These methods are discussed in appropriate detail and range from the ubiquitous harmonic oscillator approximation where entropy unrelated to high frequency oscillations is typically underestimated, to enhanced free energy sampling with molecular dynamics where the desired accuracy must be weighed against the associated computational cost of obtaining it. The rising importance of machine learning and artificial intelligence in accelerating methodological progress in this field is touched upon, as well. Finally, applications, successes, and pitfalls of using these methods are provided to showcase past and present accomplishments while clarifying where improvements in both understanding and methodology are still needed.

Kollias, Loukas↗
DOE OSTI2021

A two-dimensional electron gas suspended above a neutralizing background

Highlights: • Two-dimensional electron gas above a neutralizing jellium background. • Analytic results for the value of the total energy. • Energy contribution originating from separation. • Added energy behaves as an effective kinetic energy term. We consider a two-dimensional electron gas system consisting of a layer of electrons suspended above its jellium neutralizing background counterpart. We investigate the energy of the system in the Hartree–Fock approximation as a function of separation distance between the layer of electrons and the background. We find that the energy of the system is influenced by the separation distance in such a way that the new energy contribution originating from such a separation behaves as an effective kinetic energy term. The increase of the overall energy with increase of the separation distance adversely affects the stability of electron liquid states at high density. The results are derived for a fully spin-polarized (spinless) system of electrons in the thermodynamic limit, but can easily be generalized to a spin unpolarized state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Uniform-in-phase-space data selection with iterative normalizing flows

Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that are routinely generated. In applications that are constrained by memory and computational intensity, excessively large datasets may hinder scientific discovery, making data reduction a critical component of data-driven methods. Datasets are growing in two directions: the number of data points and their dimensionality. Whereas dimension reduction typically aims at describing each data sample on lower-dimensional space, the focus here is on reducing the number of data points. A strategy is proposed to select data points such that they uniformly span the phase-space of the data. The algorithm proposed relies on estimating the probability map of the data and using it to construct an acceptance probability. An iterative method is used to accurately estimate the probability of the rare data points when only a small subset of the dataset is used to construct the probability map. Instead of binning the phase-space to estimate the probability map, its functional form is approximated with a normalizing flow. Therefore, the method naturally extends to high-dimensional datasets. The proposed framework is demonstrated as a viable pathway to enable data-efficient machine learning when abundant data are available.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Structural and Electronic Effects on the Properties of Fe 2 (dobdc) upon Oxidation with N 2 O

Here, we report electronic, vibrational, and magnetic properties, together with their structural dependences, for the metal–organic framework Fe 2 (dobdc) (dobdc 4 – = 2,5-dioxido-1,4-benzenedicarboxylate) and its derivatives, Fe 2 (O) 2 (dobdc) and Fe 2 (OH) 2 (dobdc)—species arising in the previously proposed mechanism for the oxidation of ethane to ethanol using N 2 O as an oxidant. Magnetic susceptibility measurements reported for Fe 2 (dobdc) in an earlier study and reported in the current study for Fe II 0.26 [Fe III (OH)] 1.74 (dobdc)(DMF) 0.15 (THF) 0.22 , which is more simply referred to as Fe 2 (OH) 2 (dobdc), were used to confirm the computational results. Theory was also compared to experiment for infrared spectra and X-ray powder diffraction structures. Structural and magnetic properties were computed by using Kohn-Sham density functional theory both with periodic boundary conditions and with cluster models. In addition, we studied the effects of different treatments of the exchange interactions on the magnetic coupling parameters by comparing several approaches to the exchange-correlation functional: generalized gradient approximation (GGA), GGA with empirical Coulomb and exchange integrals for 3d electrons (the GGA+U method), nonseparable gradient approximation with empirical Coulomb and exchange integrals for 3d electrons (GAM+U), hybrid GGA, meta-GGA, and hybrid meta- GGA. We found the coupling between the metal centers to be ferromagnetic in the case of Fe 2 (dobdc) and antiferromagnetic in the cases of Fe 2 (O) 2 (dobdc) and Fe 2 (OH) 2 (dobdc). The shift in magnetic coupling behavior correlates with the changing electronic structure of the framework, which derives from both structural and electronic changes that occur upon metal oxidation and addition of the charge-balancing oxo and hydroxo ligands.

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

Predicting Bond Dissociation Energies and Bond Lengths of Coordinatively Unsaturated Vanadium–Ligand Bonds

Understanding the electronic structure of coordinatively unsaturated transition-metal compounds and predicting their physical properties are of great importance for catalyst design. Bond dissociation energy D e and bond length r e are two of the fundamental quantities for which good predictions are important for a successful design strategy. In the present work, recent experimentally measured bond energies and bond lengths of VX diatomic molecules (X = C, N, S) are used as a gauge to consider the utility of a number of electronic structure methods. Single-reference methods are one focus because of their efficiency and utility in practical calculations, and multireference configuration interaction (MRCISD) methods and a composite coupled cluster (CCC) method are a second focus because of their potential high accuracy. The comparison is especially challenging because of the large multireference M diagnostics of these molecules, in the range 0.15–0.19. For the single-reference methods, Kohn–Sham density functional theory (KS-DFT) has been tested with a variety of approximate exchange-correlation functionals. Of these, MOHLYP provides the bond dissociation energies in best agreement with experiments, and BLYP provides the bond lengths that are in best agreement with experiments; but by requiring good performance for both the D e and r e of the vanadium compounds, MOHLYP, MN12-L, MGGA_MS1, MGGA_MS0, O3LYP, and M06-L are the most highly recommended functionals. The CCC calculations include up to connected pentuple excitations for the valence electrons and up to connected quadruple excitations for the core–valence terms; this results in highly accurate dissociation energies and good bond lengths. In conclusion, averaged over the three molecules, the mean unsigned deviation of CCC bond energies from experimental ones is only 0.4 kcal/mol, demonstrating excellent convergence of theory and experiments.

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

Extremely Slow Trap-Mediated Hole Relaxation in Room-Temperature InP/ZnSe/ZnS Quantum Dots

Time-resolved photoluminescence (PL) and transient absorption (TA) spectroscopy have been used to elucidate the hole relaxation dynamics in high-quality InP/ZnSe/ZnS quantum dots (QDs) at room temperature. In QDs having an In/P ratio close to 1:1, hole cooling is fast compared to the ~40 ps time-correlated photon-counting instrument response. However, in QDs that luminesce at wavelengths greater than around 600 nm and have excess indium, a significant fraction of the PL exhibits a slower rise time. In this case, the PL rises over a range of timescales varying from close to the instrument response to approximately 300–400 ps. The time constant of the slowest component increases with increasing InP core size and the fraction of the PL that has the slow rise time increases with excess indium in the particle. In all cases, a slow rise time and any spectral evolution on that timescale are absent in the TA results, indicating that the slow dynamics may be assigned to relaxation in the valence band. QDs emitting at wavelengths below 560 nm show very different dynamics, exhibiting a barely detectable <50 ps rise time. Based on these results and measured elemental compositions, the slow hole relaxation is assigned to the transient population of indium-based traps in the ZnSe shell that are above the valence band edge only for the larger, red-emitting QDs. Here, the relative trap to band edge relaxation rates can be understood in terms of effective mass approximation hole wave function calculations, which show that the relaxation rate is largely determined by the extent to which the hole wave function in the lowest exciton penetrates into the ZnSe shell, overlapping the trapped-hole wave functions.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2019

Stable Surfaces That Bind Too Tightly: Can Range-Separated Hybrids or DFT+U Improve Paradoxical Descriptions of Surface Chemistry?

Approximate, semilocal density functional theory (DFT) suffers from delocalization error that can lead to a paradoxical model of catalytic surfaces that both overbind adsorbates yet are also too stable. We investigate the effect of two widely applied approaches for delocalization error correction, (i) affordable DFT+U (i.e., semilocal DFT augmented with a Hubbard U) and (ii) hybrid functionals with an admixture of Hartree–Fock (HF) exchange, on surface and adsorbate energies across a range of rutile transition metal oxides widely studied for their promise as water-splitting catalysts. We observe strongly row- and period-dependent trends with DFT+U, which increases surface formation energies only in early transition metals (e.g., Ti and V) and decreases adsorbate energies only in later transition metals (e.g., Ir and Pt). Both global and local hybrids destabilize surfaces and reduce adsorbate binding across the periodic table, in agreement with higher-level reference calculations. Density analysis reveals why hybrid functionals correct both quantities, whereas DFT+U does not. We recommend local, range-separated hybrids for the accurate modeling of catalysis in transition metal oxides at only a modest increase in computational cost over semilocal DFT.

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

Descriptors for Electrolyte-Renormalized Oxidative Stability of Solvents in Lithium-Ion Batteries

Electrolyte stability against oxidation is an important factor limiting the development of high energy density batteries. The highest occupied molecular orbital (HOMO) level of solvent molecules has been traditionally used for understanding trends in their oxidative stability, but this assumes a noninteracting environment. However, solvent HOMO levels are renormalized because of molecules in their solvation shells. In this work, we first demonstrate an inexpensive and accurate method to determine the HOMO level of the solvent followed by simple descriptors for renormalization of the HOMO level due to different electrolyte components. The descriptors are based on Gutmann donor and acceptor numbers of the solvent and other components. The method uses fast generalized gradient approximation-level density functional theory calculations compared to previously used expensive, experimental data-dependent methods. This method can be used to screen for unexplored stable solvents among the large number of known organic compounds to design novel high-voltage stable electrolytes.

25 ENERGY STORAGE↗
DOE OSTI2025

Dynamic Metal–Support Interaction Dictates Cu Nanoparticle Sintering on Al 2 O 3 Surfaces

Nanoparticle sintering remains a critical challenge in heterogeneous catalysis. In this work, we present a unified deep potential (DP) model based on the Perdew–Burke–Ernzerhof approximation of density functional theory for Cu nanoparticles on three Al 2 O 3 surfaces (γ-Al 2 O 3 (100), γ-Al 2 O 3 (110), and α-Al 2 O 3 (0001)). Using DP-accelerated simulations, we reveal that the nanoparticle size-mobility relationship strongly depends on the supporting surface. The diffusion of nanoparticles on the two γ-Al 2 O 3 surfaces is almost independent of the size of the nanoparticle, while the diffusion on α-Al 2 O 3 (0001) decreases rapidly with increasing size. Interestingly, nanoparticles with fewer than 55 atoms diffuse several times faster on α-Al 2 O 3 (0001) than on γ-Al 2 O 3 (100) at 800 K while expected to be more sluggish based on their larger binding energy at 0 K. The diffusion on α-Al 2 O 3 (0001) is facilitated by dynamic metal–support interaction (MSI), where Al atoms move out of the surface plane to optimize contact with the nanoparticle and relax back to the plane as the nanoparticle moves away. In contrast, the MSI on γ-Al 2 O 3 (100) and on γ-Al 2 O 3 (110) is dominated by more stable and directional Cu–O bonds, consistent with the limited diffusion observed on these surfaces. Our extended MD simulations provide insight into the sintering processes, showing that the dispersity of the nanoparticles strongly influences the coalescence driven by nanoparticle diffusion. We observed that the coalescence of Cu 13 nanoparticles on α-Al 2 O 3 (0001) can occur in a short time (10 ns) at 800 K even with an initial internanoparticle distance increased to 3 nm, while the coalescence on the two γ-Al 2 O 3 surfaces are inhibited significantly by increasing the initial internanoparticle distance. These findings demonstrate that the dynamics of the supporting surface is crucial to understanding the sintering mechanism and offer guidance for designing sinter-resistant catalysts by engineering the support morphology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

First-principles calculation of intrinsic defect chemistry and self-doping in PbTe

Semiconductor dopability is inherently limited by intrinsic defect chemistry. In many thermoelectric materials, narrow band gaps due to strong spin-orbit interactions make accurate atomic level predictions of intrinsic defect chemistry and self-doping computationally challenging. For this study, we use different levels of theory to model point defects in PbTe, and compare and contrast the results against each other and a large body of experimental data. We find that to accurately reproduce the intrinsic defect chemistry and known self-doping behavior of PbTe, it is essential to (a) go beyond the semi-local GGA approximation to density functional theory, (b) include spin-orbit coupling, and (c) utilize many-body GW theory to describe the positions of individual band edges. The hybrid HSE functional with spin-orbit coupling included, in combination with the band edge shifts from G0W0 is the only approach that accurately captures both the intrinsic conductivity type of PbTe as function of synthesis conditions as well as the measured charge carrier concentrations, without the need for experimental inputs. Our results reaffirm the critical role of the position of individual band edges in defect calculations, and demonstrate that dopability can be accurately predicted in such challenging narrow band gap materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Learning continuous models for continuous physics

Abstract Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Structural and electronic properties of GaAs and GaP semiconductors

The Structural and Electronic properties of Zinc Blende phase of GaAs and GaP compounds are studied using self consistent SIESTA-code, pseudopotentials and Density Functional Theory (DFT) in Local Density Approximation (LDA). The Lattice Constant, Equillibrium Volume, Cohesive Energy per pair, Compressibility and Band Gap are calculated. The band gaps calcultated with DFT using LDA is smaller than the experimental values. The P-V data fitted to third order Birch Murnaghan equation of state provide the Bulk Modulus and its pressure derivatives. Our Structural and Electronic properties estimations are in agreement with available experimental and theoretical data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Ultra-sensitive pressure dependence of bandgap of rutile-GeO{sub 2} revealed by many body perturbation theory

The reported values of bandgap of rutile GeO{sub 2} calculated by the standard density functional theory within local-density approximation (LDA)/generalized gradient approximation (GGA) show a wide variation (∼2 eV), whose origin remains unresolved. Here, we investigate the reasons for this variation by studying the electronic structure of rutile-GeO{sub 2} using many-body perturbation theory within the GW framework. The bandgap as well as valence bandwidth at Γ-point of rutile phase shows a strong dependence on volume change, which is independent of bandgap underestimation problem of LDA/GGA. This strong dependence originates from a change in hybridization among O-p and Ge-(s and p) orbitals. Furthermore, the parabolic nature of first conduction band along X-Γ-M direction changes towards a linear dispersion with volume expansion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗