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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

NENCI-2021. I. A large benchmark database of non-equilibrium non-covalent interactions emphasizing close intermolecular contacts

In this work, we present NENCI-2021, a benchmark database of ~8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation–π and anion–π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion–π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (E int ) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The E int values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from -38.5 to +186.8 kcal/mol, with a mean (median) E int value of -1.06 kcal/mol (-2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent—these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)- based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation–π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the E int values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive E int values, and maximum errors of ±0.2–0.3 kcal/mol (i.e., ~±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

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

Thermodynamics of free and bound magnons in graphene

Symmetry-broken electronic phases support neutral collective excitations. For example, monolayer graphene in the quantum Hall regime hosts a nearly ideal ferromagnetic phase at specific filling factors that spontaneously breaks the spin-rotation symmetry. This ferromagnet has been shown to support spin-wave excitations known as magnons that can be electrically generated and detected. Although long-distance magnon propagation has been demonstrated via transport measurements, important thermodynamic properties of such magnon populations—including the magnon chemical potential and density—have not been measured. Here we present local measurements of electron compressibility under the influence of magnons, which reveal a reduction in the gap associated with the ν = 1 quantum Hall state by up to 20%. Combining these measurements with the estimates of temperature, our analysis reveals that the injected magnons bind to electrons and holes to form skyrmions, and it enables the extraction of free magnon density, magnon chemical potential and average skyrmion spin. Our methods provide a means of probing the thermodynamic properties of charge-neutral excitations that are applicable to other symmetry-broken electronic phases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2003

Structural Model for the Flip-Flop Action in Thiamin Pyrophosphate-Dependent Human Pyruvate Dehydrogenase

The derivative of vitamin B1 thiamin pyrophosphate (TPP) is a cofactor of enzymes performing catalysis in pathways of energy production, including (i) decarboxylation of alpha-keto acids followed by (ii) transketolation. These enzymes have shown a common mechanism of TPP activation by imposing an active V-conformation of this coenzyme that brings the N4 atom of the aminopyrimidine ring to the distance required for the intramolecular C-H N hydrogen-bonding with the C2- atom of the thiazolium ring. The reactive C2 atom of TPP is the nucleophile that attacks the carbonyl carbon of different substrates used by the TPP-dependent enzymes. The structure of the heterotetrameric human pyruvate dehydrogenase (Elp) recently determined in our laboratory (1) revealed the association pattern of the subunits and the specifics of two chemically equivalent cofactor binding sites. Dynamic nonequivalence of these two cofactor sites directs the flip-flop action of this enzyme, depending upon which two active sites effect each other (2). The crystal structure derived from the holo-form of Elp provided the basis for the model of the flip-flop action of Elp in which different steps of the catalytic reaction are performed in each of the two cofactor sites at any given moment, where these steps are governed by the concerted shuttle-like motion of the subunits. It is further proposed that balancing a hydrogen-bond network and related cofactor geometry determine the continuity of catalytic events.

Ciszak, Ewa↗
DOE OSTI2024

Hydrogen–Deuterium Exchange Mass Spectrometry Identifies Local and Long-Distance Interactions within the Multicomponent Radical SAM Enzyme, PqqE

Interactions among proteins and peptides are essential for many biological activities including the tailoring of peptide substrates to produce natural products. The first step in the production of the bacterial redox cofactor pyrroloquinoline quinone (PQQ) from its peptide precursor is catalyzed by a radical SAM (rSAM) enzyme, PqqE. We describe the use of hydrogen–deuterium exchange mass spectrometry (HDX-MS) to characterize the structure and conformational dynamics in the protein–protein and protein–peptide complexes necessary for PqqE function. HDX-MS-identified hotspots can be discerned in binary and ternary complex structures composed of the peptide PqqA, the peptide-binding chaperone PqqD, and PqqE. Structural conclusions are supported by size-exclusion chromatography coupled to small-angle X-ray scattering (SEC-SAXS). HDX-MS further identifies reciprocal changes upon the binding of substrate peptide and S-adenosylmethionine (SAM) to the PqqE/PqqD complex: long-range conformational alterations have been detected upon the formation of a quaternary complex composed of PqqA/PqqD/PqqE and SAM, spanning nearly 40 Å, from the PqqA binding site in PqqD to the PqqE active site Fe 4 S 4 . Interactions among the various regions are concluded to arise from both direct contact and distal communication. The described experimental approach can be readily applied to the investigation of protein conformational communication among a large family of peptide-modifying rSAM enzymes.

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

Dynamic Interconversion of Metal Active Site Ensembles in Zeolite Catalysis

Catalysis science is founded on understanding the structure, number, and reactivity of active sites. Kinetic models that consider active sites to be static and noninteracting entities are routinely successful in describing the behavior of heterogeneous catalysts. Yet, active site ensembles often restructure in response to their external environment and even during steady-state catalytic turnover, sometimes requiring non-mean-field kinetic treatments to describe distance-dependent interactions among sites. Such behavior is being recognized more frequently in modern catalysis research, with the advent of experimental methods to quantify turnover rates with increasing precision, an expanding arsenal of operando characterization tools, and computational descriptions of atomic structure and motion at chemical potentials and timescales increasingly relevant to reaction conditions. This review focuses on dynamic changes to metal active site ensembles on zeolite supports, which are silica-based crystalline materials substituted with Al that generate binding sites for isolated and low-nuclearity metal site ensembles. Metal sites can become solvated and mobilized during reaction, facilitating interactions among sites that change their nuclearity and function. Such intersite communication can be regulated by the zeolite support, resulting in non-single-site and potentially non-mean-field kinetic behavior arising from mechanisms of catalytic action that combine elements of those canonically associated with homogeneous and heterogeneous catalysis. Here, we discuss recent literature examples that document dynamic active site behavior in metal-zeolites and outline methodologies to identify and interpret such behavior. We conclude with our outlook on future research directions to develop this evolving branch of catalysis science and harness it for practical applications.

operando characterization↗
DOE OSTI2025

Inter-cofactor protein remodeling rewires short-circuited transmembrane electron transfer

Intraprotein electron transfer (ET) requires explicit local control of the environment of cofactors to influence their intermolecular distances, relative orientations, and redox properties. Efficient, longer-range ET often utilizes molecular orbitals of aromatic residues present in the intervening space. Here, revitalization of a vestigial ET pathway in the bacterial photosynthetic reaction center is achieved by scanning with tryptophans to uncover markedly improved routes of electron conduction in a key stabilizing step spanning 15 Å between tetrapyrrole and quinone cofactors. This ET event is maximally enhanced by pairing one or more tryptophans with a threonine to influence quinone binding and/or redox potential. Synergistic effects of these substitutions increase the yield of that ET step to ~95%. Joining these substitutions with mutant residues that improve initial ET steps dramatically enhances transmembrane charge separation via this redesigned version of a pathway that is quantitatively inactive in the native protein-cofactor complex.

Biophysical chemistry↗
NASA NTRS1992

Simulation studies for surfaces and materials strength

The progress report for the period May 1, 1992 to October 31, 1992 is presented. During this period investigations were carried out in three areas. Binding energies and high energy binding sites were calculated for carbon atoms deposited on a (2 x 1) dimerized Si(100) surface. Structure- and energy-related properties of defects formed on relaxed diamond surfaces were investigated. Tersoff-type model functions for Si were employed to investigate the energetics of the following processes: (1) neutral monovacancy and divacancy formation and migration energies; (2) neutral bond-centered, site sharing, tetrahedral, and hexagonal self-interstitial formation and migration energies; and (3) the variation of these energies with distance from a bulk site of Frenkel defect formation and from (100) and (111) surfaces. Calculations are included in the appendices.

Halicioglu, Timur↗
DOE OSTI2022

Stabilization of Dinuclear Rhodium and Iridium Clusters on Layered Titanate and Niobate Supports

Atomically dispersed organometallic clusters can provide well-defined nuclearity of active sites for both fundamental studies as well as new regimes of activity and selectivity in chemical transformations. More recently, dinuclear clusters adsorbed onto solid surfaces have shown novel catalytic properties resulting from the synergistic effect of two metal centers to anchor different reactant species. Difficulty in synthesizing, stabilizing, and characterizing isolated atoms and clusters without agglomeration challenges allocating catalytic performance to atomic structure. Here, we explore the stability of dinuclear rhodium and iridium clusters adsorbed onto layered titanate and niobate supports using molecular precursors. Both systems maintain their nuclearity when Statistical analysis of HAADF-STEM images revealed that rhodium and iridium dimers had mean cluster-to-cluster distances very similar to what is expected from a random distribution of atoms over a large area, indicating that they are dispersed without aggregation. The stability of dinuclear rhodium clusters supported on titanate nanosheets was also investigated by X-ray absorption fine structure (EXAFS), DRIFTS, and first-principles calculations. Both X-ray absorption spectroscopy and HAADF-STEM simulations, guided by density functional theory (DFT)-optimized structure models, suggested that rhodium dimers adsorb onto the nanosheets in an end-on binding mode that is stable up to 100 degrees C under reducing conditions. Finally, this study highlights that crystalline nanosheets derived from layered metal oxides can be used as model supports to selectively stabilize dinuclear clusters, which could have implications for heterogeneous catalysis.

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

Comparison of Americium(III) and Neodymium(III) Monothiophosphate Complexes

Mixed-donor ligands, such as those containing a combination of O/N or O/S, have been studied extensively for the selective extraction of trivalent actinides, especially Am 3+ and Cm3+, from lanthanides during the recycling of used nuclear fuel. Oxygen/sulfur donor ligand combinations also result from the hydrolytic and/or radiolytic degradation of dithiophosphates, such as the Cyanex® class of extractants, that are initially converted to monothiophosphates. To understand potential differences between the binding of such degraded ligands to Nd 3+ and Am 3+ , the monothiophosphate complexes [M(OPS(OEt) 2 ) 5 (H 2 O) 2 ] 2- (M 3+ = Nd 3+ , Am 3+ ) were prepared and characterized by single crystal X-ray diffraction and optical spectroscopy and studied as a function of pressure up ca. 14 GPa using diamond-anvil techniques. Although Nd 3+ and Am 3+ have nearly identical eight-coordinated ionic radii, these structures reveal that while the M-O bond distances in these complexes are nearly equal that the M-S distances are statistically different. Moreover, for [Nd(OPS(OEt) 2 ) 5 (H 2 O) 2 ] 2- , the hypersensitive 4 I 9/2 → 4 G 5 / 2 transition shifts as a function of pressure by -11 cm -1 /GPa. Whereas for [Am(OPS(OEt) 2 ) 5 (H 2 O) 2 ] 2- , the 7 F 0 → 7 F 6 transition shows a slightly stronger pressure dependence with a shift of -13 cm -1 /GPa and also exhibits broadening of the 5f →5f transitions at high pressures. This data likely indicates an increased involvement of the 5f orbitals in bonding to Am 3+ relative to that of Nd 3+ in these complexes.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
NASA NTRS1984

Rotation and surface brightness in elliptical galaxies

Correlations between the mean surface brightness and level of rotational support are presented and discussed for the sample of elliptical galaxies presented by Davies et al. (1983). The importance of these distance-independent correlations lies in the ability to isolate the effects of projection, and hence to define an intrinsic, edge-on correlation. Thus the position of an elliptical galaxy in this plane contains information about its true shape. In addition, the slope of the 'edge-on' correlation can be compared cleanly with theoretical predictions. The correlation is interpreted as a manifestation of varying amounts of dissipation during the formation epoch of a galaxy, with higher surface brightness, rotating ellipticals having dissipated more binding energy.

Wyse, R. F. G.↗
DOE OSTI2022

A comparative analysis of different van der Waals treatments for molecular adsorption on the basal plane of 2H-MoS 2

The binding energy of hydrogen sulfide, ammonia, ethane, ethylene, butadiene, benzene, toluene, pyridine, pyrrole, and thiophene on the basal plane of the semi-conducting 2H-molybdenum sulfide (MoS 2 ) was calculated with the following flavors of Density Functional Theory (DFT): GGA-PW91, PBE-D3, vdW-DF, optPBE, optB86b, optB88, vdW-TS, and BEEF-vdW. The GGA-PW91 binding energies are negligible (<0.07 eV in magnitude) in all cases. The predictions with vdW-DF and PBE-D3 are the closest (error <0.05 eV) to the isosteric heats of adsorption calculated from reported temperature programmed desorption data for thiophene and butadiene. For all dispersion flavors examined here, the magnitude of the dispersion contribution to the binding energy increases linearly with the number of heavy atoms in the adsorbate, with each atom contributing 0.05 eV (BEEF-vdW) – 0.09 eV (optB88-vdW). Further, this implies that the calculated adsorption constants of molecules larger than acridine (i.e., comprising > 14 non-heavy atoms) can vary by more than four orders of magnitude at industrial conditions depending on the chosen method of dispersion correction. Further, dispersion effects fall off rapidly (>0.03 eV/ non-hydrogen atom/Å) as the adsorbate-surface distance increases.

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

Single photon emitters in van der Waals solids for quantum photonics: materials, theory and molecular-scale characterization probes

Strong light–matter interactions in two-dimensional layered materials (2D materials) have attracted the interest of researchers from interdisciplinary fields for more than a decade now. A unique phenomenon in some 2D materials is their large exciton binding energies (BEs), increasing the likelihood of exciton survival at room temperature. It is this large BE that mediates the intense light–matter interactions of many of the 2D materials, particularly in their monolayer limit, where the interplay of excitonic phenomena poses a wealth of opportunities for high-performance optoelectronics and quantum photonics. Within quantum photonics, quantum information science (QIS) is growing rapidly, where photons are a promising platform for information processing due to their low-noise properties, excellent modal control, and long-distance propagation. A central element for QIS applications is a single photon emitter (SPE) source, where an ideal on-demand SPE emits exactly one photon at a time into a given spatiotemporal mode. Recently, 2D materials have shown practical appeal for QIS which is directly driven from their unique layered crystalline structure. This structural attribute of 2D materials facilitates their integration with optical elements more easily than the SPEs in conventional three-dimensional solid state materials, such as diamond and SiC. In this review article, we will discuss recent advances made with 2D materials towards their use as quantum emitters, where the SPE emission properties maybe modulated deterministically. Here, the use of unique scanning tunneling microscopy tools for the in-situ generation and characterization of defects is presented, along with theoretical first-principles frameworks and machine learning approaches to model the structure-property relationship of exciton–defect interactions within the lattice towards SPEs. Given the rapid progress made in this area, the SPEs in 2D materials are emerging as promising sources of nonclassical light emitters, well-poised to advance quantum photonics in the future.

2D layered materials↗
NASA NTRS1991

Functional characteristics of the calcium modulated proteins seen from an evolutionary perspective

We have constructed dendrograms relating 173 EF-hand proteins of known amino acid sequence. We aligned all of these proteins by their EF-hand domains, omitting interdomain regions. Initial dendrograms were computed by minimum mutation distance methods. Using these as starting points, we determined the best dendrogram by the method of maximum parsimony, scored by minimum mutation distance. We identified 14 distinct subfamilies as well as 6 unique proteins that are perhaps the sole representatives of other subfamilies. This information is given in tabular form. Within subfamilies one can easily align interdomain regions. The resulting dendrograms are very similar to those computed using domains only. Dendrograms constructed using pairs of domains show general congruence. However, there are enough exceptions to caution against an overly simple scheme in which one pair of gene duplications leads from one domain precurser to a four domain prototype from which all other forms evolved. The ability to bind calcium was lost and acquired several times during evolution. The distribution of introns does not conform to the dendrogram based on amino acid sequences. The rates of evolution appear to be much slower within subfamilies, especially within calmodulin, than those prior to the definition of subfamily.

Kretsinger, R. H.↗
DOE OSTI2022

Complexation of Astatine(III) with Ketones: Roles of NO 3 – Counterion and Exploration of Possible Binding Modes

Ketones have been proven effective in extracting astatine(III) from aqueous solvents. Previous theoretical studies suggested a mechanism where the “sp 2 ” lone pair on the carbonyl oxygen donates electron density into the π system of the AtO + molecular cation to form a dative-type bond. In this study, co-extraction of NO 3 – as AtO(NO 3 )·(O=CR 1 R 2 ) species into the organic phase appears to be a key factor. Adjusting the electronic properties of the ketone, by having an aryl group instead of an alkyl group in the alpha position of the ketone, increased the electron density on C=O, increased the bond strength between the ketone and AtO + , and in turn increased the extraction of 211 At into the organic phase. Extraction with diketones shows dependence on the bridging distance between the two carbonyl moieties, where a C 3 or longer bridge results in a 10-fold increase in extraction into the organic phase. Furthermore, DFT calculations show the longer bridge allows for the chelation of AtO(NO 3 ) by either the second carbonyl or the phenyl ring.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

Severe new limits on extragalactic models of gamma-ray bursts

A new and much more restrictive limit is imposed here on the distance of gamma ray bursts (GRBs) in extragalactic models of the bursts. This limit is based on the fact that deep optical and infrared surveys do not find any host galaxies in many GRB error boxes. It is shown that 10 of the brighter GRB sources must be farther than 1 gigaparsec and that eight of these must emit more than 10 exp 13 ergs during a burst. This result is about four orders of magnitude stricter in energy than the previous limit. Five of the sources have limits in that the energy must be greater than the binding energy of a neutron star.

Schaefer, Bradley E.↗
DOE OSTI2023

Combining Force Fields and Neural Networks for an Accurate Representation of Chemically Diverse Molecular Interactions

A key goal of molecular modeling is the accurate reproduction of the true quantum mechanical potential energy of arbitrary molecular ensembles with a tractable classical approximation. The challenges are that analytical expressions found in general purpose force fields struggle to faithfully represent the intermolecular quantum potential energy surface at close distances and in strong interaction regimes; that the more accurate neural network approximations do not capture crucial physics concepts, e.g., nonadditive inductive contributions and application of electric fields; and that the ultra-accurate narrowly targeted models have difficulty generalizing to the entire chemical space. We therefore designed a hybrid wide-coverage intermolecular interaction model consisting of an analytically polarizable force field combined with a short-range neural network correction for the total intermolecular interaction energy. Here, we describe the methodology and apply the model to accurately determine the properties of water, the free energy of solvation of neutral and charged molecules, and the binding free energy of ligands to proteins. The correction is subtyped for distinct chemical species to match the underlying force field, to segment and reduce the amount of quantum training data, and to increase accuracy and computational speed. For the systems considered, the hybrid ab initio parametrized Hamiltonian reproduces the two-body dimer quantum mechanics (QM) energies to within 0.03 kcal/mol and the nonadditive many-molecule contributions to within 2%. Simulations of molecular systems using this interaction model run at speeds of several nanoseconds per day.

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

Quantum Monte Carlo Approaches to Na Intercalation on Bilayer Graphene

We have performed Quantum Monte Carlo (QMC) simulations on Na-intercalated bilayer graphene to study the evolution of electronic and optical properties upon Na intercalation into hard carbon layers. The objective was to model the optimal configuration of Na intercalation into a hard carbon matrix containing graphene regions. Our study showed that Na intercalation can be energetically stabilized at large interlayer distances (over 6 Å) in both AA- and AB-stacked bilayer graphene. In the QMC results, we found a significant band gap opening at the equilibrium interlayer distance of Na-intercalated bilayer graphene, while corresponding density functional theory (DFT) results showed no gap. This difference between DFT and QMC results indicates that the gap opening induced by Na intercalation into a hard carbon is underestimated within the DFT framework. In addition, a zigzag configuration of Na atoms was found to be energetically stable at interlayer distances up to 10 Å, leading us to predict the existence of a local minimum of Na intercalation at large interlayer distance. These computation and modeling results can provide guidance on how to synthesize and optimize hard carbon with bilayer graphene regions that permit a zigzag intercalation configuration that will maximize and stabilize sodium hosting.

Binding energy↗