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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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Process-dependent anisotropic thermal conductivity of laser powder bed fusion AlSi10Mg: impact of microstructure and aluminum-silicon interfaces

Purpose AlSi10Mg alloy is commonly used in laser powder bed fusion due to its printability, relatively high thermal conductivity, low density and good mechanical properties. However, the thermal conductivity of as-built materials as a function of processing (energy density, laser power, laser scanning speed, support structure) and build orientation, are not well explored in the literature. This study aims to elucidate the relationship between processing, microstructure, and thermal conductivity. Design/methodology/approach The thermal conductivity of laser powder bed fusion (L-PBF) AlSi10Mg samples are investigated by the flash diffusivity and frequency domain thermoreflectance (FDTR) techniques. Thermal conductivities are linked to the microstructure of L-PBF AlSi10Mg, which changes with processing conditions. The through-plane exceeded the in-plane thermal conductivity for all energy densities. A co-located thermal conductivity map by frequency domain thermoreflectance (FDTR) and crystallographic grain orientation map by electron backscattered diffraction (EBSD) was used to investigate the effect of microstructure on thermal conductivity. Findings The highest through-plane thermal conductivity (136 ± 2 W/m-K) was achieved at 59 J/mm 3 and exceeded the values reported previously. The in-plane thermal conductivity peaked at 117 ± 2 W/m-K at 50 J/mm 3 . The trend of thermal conductivity reducing with energy density at similar porosity was primarily due to the reduced grain size producing more Al-Si interfaces that pose thermal resistance. At these interfaces, thermal energy must convert from electrons in the aluminum to phonons in the silicon. The co-located thermal conductivity and crystallographic grain orientation maps confirmed that larger colonies of columnar grains have higher thermal conductivity compared to smaller columnar grains. Practical implications The thermal properties of AlSi10Mg are crucial to heat transfer applications including additively manufactured heatsinks, cold plates, vapor chambers, heat pipes, enclosures and heat exchangers. Additionally, thermal-based nondestructive testing methods require these properties for applications such as defect detection and simulation of L-PBF processes. Industrial standards for L-PBF processes and components can use the data for thermal applications. Originality/value To the best of the authors’ knowledge, this paper is the first to make coupled thermal conductivity maps that were matched to microstructure for L-PBF AlSi10Mg aluminum alloy. This was achieved by a unique in-house thermal conductivity mapping setup and relating the data to local SEM EBSD maps. This provides the first conclusive proof that larger grain sizes can achieve higher thermal conductivity for this processing method and material system. This study also shows that control of the solidification can result in higher thermal conductivity. It was also the first to find that the build substrate (with or without support) has a large effect on thermal conductivity.

Engineering↗
DOE OSTI2023

The Predictive Power of Exact Constraints and Appropriate Norms in Density Functional Theory

Ground-state Kohn-Sham density functional theory provides, in principle, the exact ground-state energy and electronic spin densities of real interacting electrons in a static external potential. In practice, the exact density functional for the exchange-correlation (xc) energy must be approximated in a computationally efficient way. About 20 mathematical properties of the exact xc functional are known. In this work, we review and discuss these known constraints on the xc energy and hole. By analyzing a sequence of increasingly sophisticated density functional approximations (DFAs), we argue that (a) the satisfaction of more exact constraints and appropriate norms makes a functional more predictive over the immense space of many-electron systems and (b) fitting to bonded systems yields an interpolative DFA that may not extrapolate well to systems unlike those in the fitting set. We discuss both how the class of well-described systems has grown along with constraint satisfaction and the possibilities for future functional development.

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

Atomistic modeling of energy band alignment in CdTe(1 0 0) and CdTe(1 1 1) surfaces

An atomic-scale perspective of energy band alignment in CdTe surfaces has not been spatially studied despite the major role surfaces play in forming interfaces within CdTe-based thin film photovoltaic devices. Atomistic modeling based on density functional theory coupled with surface Green’s function is used for calculating energy band alignment of CdTe surfaces. The CdTe(1 0 0) ((1×1) and c(2×2) reconstruction) and CdTe(1 1 1) ((1×1) and (2×2) reconstruction) facets without and with surface relaxation provide insightful band bending characteristics that influence charge carrier transport. Results show that unrelaxed (1×1) CdTe(1 0 0) and CdTe(1 1 1) surfaces bend the valence band downward with surface polarity dictating the surface potential magnitude. The reconstructed CdTe(1 0 0) c(2×2) and CdTe(1 1 1) (2×2) surfaces result in favorable surface electronic features in relation to their unreconstructed variants. In addition, the structurally relaxed CdTe(1 1 1) surfaces develop an internal energy cusp potential that may enhance hole charge transport toward the back of CdTe solar cell devices. In conclusion, energy band alignments calculated within the study lead to a detailed understanding of how CdTe surfaces may affect CdTe-based thin film photovoltaic applications.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Atomistic models of In and Ga diffusion in Cu(In,Ga)Se 2

To improve the performance of Cu(In,Ga)Se 2 thin-film photovoltaic devices, a robust understanding of the dominant diffusion pathways of the alloy species In and Ga is needed. Here, the most probable defect complexes and mechanisms for In and Ga diffusion are identified with the aid of density functional theory. The binding energies and migration barriers for these complexes are calculated in bulk CuInSe 2 and CuGaSe 2 . Analytic models and kinetic lattice Monte Carlo simulations are employed to predict the diffusivity of In and Ga under variations in composition and temperature. Here, we find that a model based on coulombic interactions between group III antisites and vacancies on the Cu-sublattice produces results that match well with experiment.

14 SOLAR ENERGY↗
DOE OSTI2026

First-principles DFT modeling of nitrobenzene adsorption on the Ag(111) surface at varying monolayer coverages

Here, the adsorption behavior of nitrobenzene on the Ag(111) surface as a function of coverage is investigated using density functional theory. Adsorption energies and optimized geometries are analyzed together with isolated intermolecular interaction calculations and electronic structure analysis, including Bader charge partitioning and projected density of states, to disentangle the roles of adsorbate–surface bonding and through-space adsorbate–adsorbate interactions. At low and intermediate coverages (θ = 1/9 and θ = 2/9), bidentate adsorption at top sites is favored due to strong adsorbate–surface interactions, with additional stabilization at θ = 2/9 arising from favorable intermolecular separations. At higher coverage (θ = 1/3), bidentate adsorption is destabilized by strong intermolecular repulsion, and monodentate adsorption becomes energetically preferred as rotational freedom allows more favorable intermolecular spacing. Charge density differences, Bader charge, and density of states analyses show that charge transfer from the Ag surface is localized primarily on the nitro group and increases with coverage and adsorption denticity, although this increase does not directly correlate with adsorption strength at high coverage due to competing intermolecular interactions. These results demonstrate that surface coverage can induce a transition in preferred adsorption denticity driven by intermolecular interactions, highlighting the importance of adsorbate packing in organic molecule adsorption at metal interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Electronic structure of reduced CeO 2 (111) surfaces interacting with hydrogen as revealed through electron energy loss spectroscopy in comparison with theoretical investigations

Based on both, ab-initio cluster calculations as well as periodic density functional based loss function calculations, we have assigned the origins of the valence electron excitation regime in electron energy loss spectra of well-ordered ceria films in (111) orientation at various states of reduction as well as after exposing the reduced films to hydrogen from the gas phase (Li et al, Angew. Chem. Int. Ed., 58 (2019) 14686–14693). The explicit calculation of intensity distributions using the dipole approximation allow us to draw conclusions about the nature of oxygen vacancies, which occur upon reduction and how those interact with hydrogen to form hydride species. Herein, we also reports a brief discussion of vibrational excitations of hydrogen loaded ceria and corroborates previous interpretations, based on inelastic neutron scattering.

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

Controlling extrapolations of nuclear properties with feature selection

Predictions of nuclear properties far from measured data are inherently inaccurate because of uncertainties in our knowledge of nuclear forces and in our treatment of quantum many-body effects in strongly-interacting systems. While the model bias can be directly calculated when experimental data is available, only an estimate can be made in the absence of such measurements. Current approaches to compute the estimated bias quickly lose predictive power when their input variables are taken far from the training region, resulting in uncontrolled uncertainties in applications such as nucleosynthesis simulations. In this letter, we present a novel technique to identify the input variables of machine learning algorithms that can provide robust estimates of model bias. Our process is based on selecting input variables, or features, based on their probability distribution functions across the entire nuclear chart. We illustrate our approach on the problem of quantifying the model bias in nuclear binding energies calculated with Density Functional Theory (DFT). We prove that building model biases with only Z and N as features leads to highly unreliable extrapolations. Conversely, we show that proper feature selection can systematically improve theoretical predictions without increasing uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

DFT Analysis of the Binding of Rare Earth Nitrates at Internal and External Surfaces of MCM-22

MCM-22-type zeolites constitute a well-characterized tunable class of aluminosilicates suitable for elucidating the fundamental aspects of the binding of rare earth elements (REEs) in layered materials. Starting from the pure silica version ITQ-1 with a unit cell of Si 72 O 144 , a model for periodic bulk crystalline MCM-22 with a finite Al concentration is provided by replacing a Si atom with an Al atom in the unit cell at suitable tetrahedral sites near an internal pore surface. Then, a H atom is added to an O atom bridging Si and Al atoms to create a Brønsted acid site (BAS). There are no internal silanol groups in this bulk model. To generate a model for an external surface, we adopt the fully hydroxylated surface structure of a layer within the ITQ-1 precursor with two silanols per lateral unit cell. A BAS on the external surface can be generated by replacing a near-surface Si atom with an Al atom and adding a H atom, as above. The strength of binding at a BAS of REE, X, taken to be present in the solution phase as nitrates, is determined from the energy change in the reaction X(NO 3 ) 3 + ≡Si–{OH}–Al≡ → ≡Si–{OX(NO 3 ) 2 }–Al≡+ HNO 3 . The strength of binding at the silanols is determined similarly. Binding energies are determined from two approaches. The first performs periodic plane-wave density functional theory (DFT) total energy analysis for an entire unit cell of MCM-22. The second utilizes cluster models capturing the local environment of REE binding sites and performs DFT analysis with localized basis sets. The two approaches yield consistent results for Nd, revealing similarly strong binding at either an external or internal BAS, but much weaker binding at a silanol site. This is consistent with the picture deduced from recent experiments. Here, we also comment on binding at Al-bridged siloxane sites, which have been suggested as alternative binding sites to BAS.

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

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based Ab Initio Molecular Dynamics. 1. Theory, Algorithm, and Performance

By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal density functional theory (DFT) and thereby furnish a more accurate and reliable description of the underlying electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we describe a linear-scaling approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions (MLWFs)) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems of interest at the hybrid DFT level. We focus our theoretical discussion on the integration of this approach into the framework of Car–Parrinello AIMD, and highlight the central role played by the MLWF-product potential (i.e., the solution of Poisson’s equation for each corresponding MLWF-product density) in the evaluation of the EXX energy and wave function forces. We then provide a comprehensive description of the exx algorithm implemented in the open-source Quantum ESPRESSO program, which employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the high-performance computing (HPC) resources available on current- and next-generation supercomputer architectures. Furthermore, this is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when AIMD simulations of liquid water are performed in the canonical (NVT) ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT-based AIMD simulations of condensed-phase systems containing 500–1000 atoms (e.g., (H₂O)₂₅₆) with a wall time cost that is comparable to that of semilocal DFT. In doing so, exx takes us one step closer to routinely performing AIMD simulations of complex and large-scale condensed-phase systems for sufficiently long time scales at the hybrid DFT level of theory.

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

DeePKS: A Comprehensive Data-Driven Approach toward Chemically Accurate Density Functional Theory

We propose a general machine learning-based framework for building an accurate and widely applicable energy functional within the framework of generalized Kohn–Sham density functional theory. To this end, we develop a way of training self-consistent models that are capable of taking large datasets from different systems and different kinds of labels. Here, we demonstrate that the functional that results from this training procedure gives chemically accurate predictions on energy, force, dipole, and electron density for a large class of molecules. It can be continuously improved when more and more data are available.

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

Redox Defect Thermochemistry of FeAl 2 O 4 Hercynite in Water Splitting from First-Principles Methods

Solar thermochemical hydrogen (STCH) production is a promising route to produce fuels from sunlight via high-temperature water splitting. However, efficient and technologically viable implementations of this process only allow a narrow window of thermodynamic boundary conditions that can be used to cycle the system, thus limiting the design space for suitable metal oxide redox mediators. An oxygen defect redox mechanism can contribute a favorable reduction entropy to expand this window, and computational evaluation of materials with high oxygen defect entropies could play a pivotal role in guiding the discovery and design of suitable oxides. This study employs first-principles calculations to investigate the redox mediating defect mechanism of the STCH candidate material, hercynite (FeAl 2 O 4 ). We compare the results of total energy calculations from density functional theory (DFT) with beyond-DFT approaches, including hybrid functionals and the random phase approximation, which are among the most advanced methods currently feasible for supercell defect calculations. Using the predicted formation energies, we perform thermodynamic modeling of FeAl2O4 reduction and oxidation via free energy minimization that incorporates ideal gas, configurational, and vibrational entropy contributions evaluated within the quasi-harmonic approximation. Special attention is devoted to understanding interactions among co-existing defects, such as the association of pairs and complexes of O vacancies and cation antisite defects, and the effect of mutually compensating defect charges. Our results corroborate the notion that the details of defect interactions can be decisive for the viability of hydrogen production within the desirable STCH process window.

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

Fission Fragment Intrinsic Spins and Their Correlations

The intrinsic spins and their correlations are the least understood characteristics of fission fragments from both theoretical and experimental points of view. In many nuclear reactions, the emerging fragments are typically excited and acquire an intrinsic excitation energy and an intrinsic spin depending on the type of the reactions and interaction mechanism. Both the intrinsic excitation energies and the fragments’ intrinsic spins and parities are controlled by the interaction mechanism and conservations laws, which lead to their correlations and determines the character of their deexcitation mechanism. We outline here a framework for the theoretical extraction of the intrinsic spin distributions of the fragments and their correlations within the fully microscopic real-time density-functional theory formalism and illustrate it on the example of induced fission of 236 U and 240 Pu, using two nuclear energy density functionals. Here, these fission fragment intrinsic spin distributions display new qualitative features previously not discussed in literature. Within this fully microscopic framework, we extract for the first time the intrinsic spin distributions of fission fragments of 236 U and 240 Pu as well as the correlations of their intrinsic spins, which have been debated in literature for more than six decades with no definite conclusions so far.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Unveiling the Electrocatalytic Hydrogen Evolution Reaction Pathway on RuP 2 through Ab Initio Grand Canonical Monte Carlo

In this study, the high catalytic reactivity of ruthenium phosphide (RuP 2 ) has been identified by first-principles density functional theory (DFT) calculations for the electrocatalytic hydrogen evolution reaction (HER). Complex surface reconstructions are considered by applying the ab initio grand canonical Monte Carlo (ai-GCMC) algorithm, efficiently providing a sufficient phase-space exploration of possible surfaces. Combined with surface-phase Pourbaix diagrams, we are able to identify the actual surfaces that obtained under specific experimental environments, thus leading to a more accurate understanding of the nature of the active sites and the binding strength of adsorbates. Specifically, through hundreds of surface reconstructions and hydrogenation states generated with ai-GCMC, we identify the most favorable surface phases of RuP 2 under aqueous acidic conditions. We discover that the HER activity is determined by multiple surfaces with different stoichiometries within a narrow electrode potential window. Low HER overpotential (η) has been found for each of the identified surfaces, as low as 0.04 V. High H-coverage reconstructed surfaces have been discovered under acidic conditions, and the surface Ru sites introduced by additional Ru adatoms or exposed by P-vacancies serve as the active sites for HER based on their nearly reversible H binding. Furthermore, this work provides atomistic insights into the origin of high HER activity on RuP 2 by exploring the dynamic surface phases of electrocatalysts and features a generalizable method to explore the reconstructed/hydrogenated surface space as a function of experimental conditions.

25 ENERGY STORAGE↗
DOE OSTI2020

Mechanism of the Accelerated Water Formation Reaction under Interfacial Confinement

Subnanoscale spaces at the interface between weakly coupled thin films and their metal supports offer exciting opportunities for studying chemical reactions under confinement. Here, we investigated the kinetics of water formation (from hydrogen and chemisorbed oxygen) in the confined space at the interface between bilayer (BL) silica and a Ru(0001) support, compared to the reaction on the bare Ru(0001) surface. Ambient pressure X-ray photoelectron spectroscopy (AP-XPS) experiments were carried out at different temperatures at elevated pressures of H 2 to follow the reaction kinetics. The apparent activation energy at the BL-silica/Ru(0001) interface was found to be 0.38 eV lower than that on bare Ru(0001), consistent with a recent report by Prieto et al. (Angew. Chem., Int. Ed.2018, 57(28), 8749–8753) carried out at lower H 2 pressures using low-energy electron microscopy. Density functional theory calculations revealed that the rate-limiting step in the direct hydrogenation pathway on the Ru(0001) surface is the first hydrogen addition step (*H + *O ↔ *OH). The confinement at the BL-silica/Ru(0001) interface only marginally affects the energy barrier of the first hydrogen addition. Instead, it activates an alternative disproportionation reaction pathway (*H 2 O + *O ↔ 2*OH). On the bare Ru(0001) surface, the disproportionation pathway can only occur at cryogenic temperatures or under high water vapor pressures. However, the presence of the BL-silica increases the desorption barrier for water molecules at the interface. The increased residence time allows trapped water molecules to react with chemisorbed oxygen to produce two *OH per H 2 O with an activation energy 0.25 eV lower than that of the first hydrogen addition step. Finally, this work reveals the origin of the observed accelerated water formation reaction at the BL-silica/Ru(0001) interface in the low-temperature regime (T < 350 K) and points to a route to engineer chemical reaction pathways by leveraging subnanoscale confined spaces at metal–oxide interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Elastic Bayesian Model Calibration

Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have resulted in tools for emulation, sensitivity analysis, and calibration that are widely used. However, many of these tools do not perform well when the computer model’s parameters control both the amplitude variation of the functional output and its alignment (or phase variation). This paper introduces a framework for Bayesian model calibration when the model responses are misaligned functional data. The approach generates two types of data out of the misaligned functional responses: (1) aligned functions so that the amplitude variation is isolated and (2) warping functions that isolate the phase variation. These two types of data are created for the computer simulation data (both of which may be emulated) and the experimental data. The calibration approach uses both types so that it seeks to match both the amplitude and phase of the experimental data. The framework is careful to respect constraints that arise, especially when modeling phase variation, and is framed in a way that it can be done with readily available calibration software. In conclusion, we demonstrate the techniques on two simulated data examples and on two dynamic material science problems: a strength model calibration using flyer plate experiments and an equation of state model calibration using experiments performed on the Sandia National Laboratories’ Z-machine.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Finite-range pairing in nuclear density functional theory

Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Many pairing functionals currently used can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational schemes diverge as the single-particle space increases, and the results depend on how marginally occupied states are incorporated. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this study, this is done by folding the pair density with Gaussians. Here, we show that a folding radius of about 1 fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications.

Nuclear density functional theory↗
DOE OSTI2020

High-throughput experimentation for microstructural design in additively manufactured 316L stainless steel

In the present study, a combination of high-throughput (HT) and low-throughput (LT) techniques was used to rapidly determine the processing window and generate processing maps for Selective Laser Melting (SLM) of 316L stainless steel. The HT method includes the fabrication of hundreds of hex nut-shaped specimens, each processed with a unique combination of laser power, scanning speed, and hatch spacing. An easily removable scaffolding permitted rapid sample extraction from the base plate, thus saving machining cost and time. Hardness and immersion density measurements were used for HT characterization to identify a processing window for maximum strength and density. Within the defined processing window, a low-throughput (LT) microstructural interrogation of specimens were performed. The microstructural analysis included quantification at various length scales (i.e., grains size and morphology, texture, primary dendrite arm spacing, and melt pool geometry analysis). Microstructure-based processing maps as a function of volumetric energy density were generated. The combination of HT and LT methods produced a predictive relationship between hardness and primary dendrite arm spacing using a Hall-Petch relationship. A model is proposed to explain the dependence of microstructure on the melt pool geometry. Here, the HT method can be applied for the microstructural design of SLM-fabricated components in other alloys.

316L stainless steel↗
DOE OSTI2022

Importance of imposing gauge invariance in time-dependent density functional theory calculations with meta-generalized gradient approximations

It has been known for more than a decade that the gauge variance of the kinetic energy density τ leads to additional terms in the magnetic orbital rotation Hessian used in linear-response time-dependent density functional theory (TDDFT), affecting excitation energies obtained with τ-dependent exchange–correlation functionals. While previous investigations found that a correction scheme based on the paramagnetic current density has a small effect on benchmark results, we report more pronounced effects here, in particular, for the popular M06-2X functional and for some other meta-generalized gradient approximations (mGGAs). In the first part of this communication, this is shown by a reassessment of a set of five Ni(II) complexes for which a previous benchmark study that did not impose gauge invariance has found surprisingly large errors for excitation energies obtained with M06-2X. These errors are more than halved by restoring gauge invariance. The variable importance of imposing gauge invariance for different mGGA-based functionals can be rationalized by the derivative of the mGGA exchange energy integrand with respect to τ. In the second part, a large set of valence excitations in small main-group molecules is analyzed. For M06-2X, several selected n → π* and π→π$^{*}_{⊥}$ excitations are heavily gauge-dependent with average changes of –0.17 and –0.28 eV, respectively, while π→π$^{*}_{∥}$ excitations are marginally affected (–0.04 eV). Similar patterns, but of the opposite signs, are found for SCAN0. Here, the results suggest that reevaluation of previous gauge variant TDDFT results based on M06-2X and other mGGA functionals is warranted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗