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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Model representations of kerogen structures: An insight from density functional theory calculations and spectroscopic measurements

Molecular structures of kerogen control hydrocarbon production in unconventional reservoirs. Significant progress has been made in developing model representations of various kerogen structures. These models have been widely used for the prediction of gas adsorption and migration in shale matrix. However, using density functional perturbation theory (DFPT) calculations and vibrational spectroscopic measurements, we here show that a large gap may still remain between the existing model representations and actual kerogen structures, therefore calling for new model development. Using DFPT, we calculated Fourier transform infrared (FTIR) spectra for six most widely used kerogen structure models. The computed spectra were then systematically compared to the FTIR absorption spectra collected for kerogen samples isolated from Mancos, Woodford and Marcellus formations representing a wide range of kerogen origin and maturation conditions. Limited agreement between the model predictions and the measurements highlights that the existing kerogen models may still miss some key features in structural representation. A combination of DFPT calculations with spectroscopic measurements may provide a useful diagnostic tool for assessing the adequacy of a proposed structural model as well as for future model development. This approach may eventually help develop comprehensive infrared (IR)-fingerprints for tracing kerogen evolution.

03 NATURAL GAS↗
DOE OSTI2019

Understanding Active Sites in Pyrolyzed Fe–N–C Catalysts for Fuel Cell Cathodes by Bridging Density Functional Theory Calculations and 57 Fe Mössbauer Spectroscopy

Pyrolyzed Fe–N–C materials are promising platinum-group-metal-free catalysts for proton-exchange membrane fuel cell cathodes. However, the detailed structure, oxidation, and spin states of their active sites are still undetermined. As such, 57 Fe Mössbauer spectroscopy has identified FeN x moieties as the most active sites, with their fingerprint being a doublet in low-temperature Mössbauer spectra. However, the interpretation of the doublets for such materials has lacked theoretical basis. Here, we applied density functional theory to calculate the quadrupole splitting energy of doublets (Δ E QS ) for a range of FeN x structures in different oxidation and spin states. The calculated and experimental values are then compared for a reference Fe–N–C catalyst, whereas further information on the Fe oxidation and spin states was obtained from electron paramagnetic resonance, superconducting quantum interference device, and 57 Fe Mössbauer spectroscopy under external magnetic field. The combined theoretical and experimental results identify the main presence of FeN x moieties in Fe(II) low-spin and Fe(III) high-spin states, whereas a minor fraction of sites could exist in the Fe(II) S = 1 state. From the analysis of the 57 Fe Mössbauer spectrum under the external magnetic field and the comparison of calculated and measured Δ E QS values, we assign the experimental doublet D1 with a mean Δ E QS value of around 0.9 mm·s –1 to Fe(III)N 4 C 12 moieties in high-spin state and the experimental doublet D2 with a mean Δ E QS value of around 2.3 mm·s –1 to Fe(II)N 4 C 10 moieties in low and medium spin. These conclusions indicate that D1 corresponds to surface-exposed sites, whereas D2 may correspond either to bulk sites that are inaccessible to O 2 or to surface sites that bind O 2 weaker than D1.

fuel cell↗
DOE OSTI2020

Scalable implementation of polynomial filtering for density functional theory calculation in PARSEC

In this work, we present an efficient implementation of polynomial filtering methods in PARSEC, a real-space pseudopotential based Kohn–Sham density functional theory solver. The implementation described here improves upon a Chebyshev-filtered subspace iteration algorithm used in the previous version of PARSEC. We present a hybrid polynomial filtering scheme that combines Chebyshev-filtered subspace iteration and a spectrum slicing method that partitions the spectrum into several spectral slices and uses bandpass-filtered subspace iteration to compute approximate eigenpairs within each interior slice simultaneously. We describe a procedure to partition a spectrum and construct polynomial filters. We also discuss a number of practical issues such as the use of appropriate data layouts for carrying out the computation on a two-dimensional process grid and how to achieve good load balance by allocating an appropriate number of process groups to each spectral slice. Numerical examples are presented to demonstrate the effectiveness of the hybrid polynomial filtering method as well as the superior parallel scalability of spectrum slicing in comparison to that of Chebyshev-filtered subspace iteration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Density functional theory calculations of defect and fission gas properties in U-Si fuels

Accident tolerant fuels (ATF) are being developed in response to the Fukushima Daiichi accident in Japan. One of the options being pursued is U-Si fuels, such as the U 3 Si 2 and U 3 Si 5 compounds, which benefit from high thermal conductivity (metallic) compared to the UO 2 fuel (insulator or semi-conductor) used in current Light Water Reactors (LWRs). The U-Si fuels also have higher fissile density. In order to perform meaningful engineering scale nuclear fuel performance simulations, the material properties of the fuel, including the response to irradiation environments, must be known. Unfortunately, the data available for U-Si fuels are rather limited, in particular for the temperature range where LWRs would operate. The ATF HIP is using multi-scale modeling and simulations to address this knowledge gap. The present study investigates point defect and fission gas properties in U 3 Si 2 , which is one of the main fuel candidates, using density functional theory (DFT) calculations. Based on a few assumption regarding entropy contributions, defect and fission diffusivities are predicted. Even though uranium silicides have been shown to amorphize easily at low temperature, we assume that U 3 Si 2 remains crystalline under the conditions expected in Light Water Reactors (LWRs). The temperature and dose where amorphization occurs has not yet been well established.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2016

Cellulose Structural Polymorphism in Plant Primary Cell Walls Investigated by High-Field 2D Solid-State NMR Spectroscopy and Density Functional Theory Calculations

The native cellulose of bacterial, algal, and animal origins has been well studied structurally using X-ray and neutron diffraction and solid-state NMR spectroscopy, and is known to consist of varying proportions of two allomorphs, Iα and Iβ, which differ in hydrogen bonding, chain packing, and local conformation. In comparison, cellulose structure in plant primary cell walls is much less understood because plant cellulose has lower crystallinity and extensive interactions with matrix polysaccharides. Here we have combined two-dimensional magic-angle-spinning (MAS) solid-state nuclear magnetic resonance (solid-state NMR) spectroscopy at high magnetic fields with density functional theory (DFT) calculations to obtain detailed information about the structural polymorphism and spatial distributions of plant primary-wall cellulose. 2D 13 C– 13 C correlation spectra of uniformly 13 C-labeled cell walls of several model plants resolved seven sets of cellulose chemical shifts. Among these, five sets (denoted a–e) belong to cellulose in the interior of the microfibril while two sets (f and g) can be assigned to surface cellulose. Importantly, most of the interior cellulose 13 C chemical shifts differ significantly from the 13 C chemical shifts of the Iα and Iβ allomorphs, indicating that plant primary-wall cellulose has different conformations, packing, and hydrogen bonding from celluloses of other organisms. 2D 13 C– 13 C correlation experiments with long mixing times and with water polarization transfer revealed the spatial distributions and matrix-polysaccharide interactions of these cellulose structures. Celluloses f and g are well mixed chains on the microfibril surface, celluloses a and b are interior chains that are in molecular contact with the surface chains, while cellulose c resides in the core of the microfibril, outside spin diffusion contact with the surface. Interestingly, cellulose d, whose chemical shifts differ most significantly from those of bacterial, algal, and animal cellulose, interacts with hemicellulose, is poorly hydrated, and is targeted by the protein expansin during wall loosening. To obtain information about the C6 hydroxymethyl conformation of these plant celluloses, we carried out DFT calculations of 13 C chemical shifts, using the Iα and Iβ crystal structures as templates and varying the C5–C6 torsion angle. Comparison with the experimental chemical shifts suggests that all interior cellulose favor the tg conformation, but cellulose d also has a similar propensity to adopt the gt conformation. In conclusion, these results indicate that cellulose in plant primary cell walls, due to their interactions with matrix polysaccharides, and has polymorphic structures that are not a simple superposition of the Iα and Iβ allomorphs, thus distinguishing them from bacterial and animal celluloses.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Time-dependent density-functional-theory calculations of the nonlocal electron stopping range for inertial confinement fusion applications

Nonlocal electron transport is important for understanding laser-target coupling for laser-direct-drive (LDD) inertial confinement fusion (ICF) simulations. Current models for the nonlocal electron mean free path in radiation-hydrodynamic codes are based on plasma-physics models developed decades ago; improvements are needed to accurately predict the electron conduction in LDD simulations of ICF target implosions. Here we utilized time-dependent density functional theory (TD-DFT) to calculate the electron stopping power (SP) in the so-called conduction-zone plasmas of polystyrene in a wide range of densities and temperatures relevant to LDD. Compared with the modified Lee-More model, the TD-DFT calculations indicated a lower SP and a higher stopping range for nonlocal electrons. We fit these electron SP calculations to obtain a global analytical model for the electron stopping range as a function of plasma conditions and the nonlocal electron kinetic energy. This model was implemented in the one-dimensional radiation-hydrodynamic code LILAC to perform simulations of LDD ICF implosions, which are further compared with simulations by the standard modified Lee-More model. In conclusion, results from these integrated simulations are discussed in terms of the implications of this TD-DFT-based mean-free-path model to ICF simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Terahertz spectroscopy and solid-state density functional theory calculation of anthracene: Effect of dispersion force on the vibrational modes

The phonon modes of molecular crystals in the terahertz frequency region often feature delicately coupled inter- and intra-molecular vibrations. Recent advances in density functional theory such as DFT-D{sup *} have enabled accurate frequency calculation. However, the nature of normal modes has not been quantitatively discussed against experimental criteria such as isotope shift (IS) and correlation field splitting (CFS). Here, we report an analytical mode-decoupling method that allows for the decomposition of a normal mode of interest into intermolecular translation, libration, and intramolecular vibrational motions. We show an application of this method using the crystalline anthracene system as an example. The relationship between the experimentally obtained IS and the IS obtained by PBE-D{sup *} simulation indicates that two distinctive regions exist. Region I is associated with a pure intermolecular translation, whereas region II features coupled intramolecular vibrations that are further coupled by a weak intermolecular translation. We find that the PBE-D{sup *} data show excellent agreement with the experimental data in terms of IS and CFS in region II; however, PBE-D{sup *} produces significant deviations in IS in region I where strong coupling between inter- and intra-molecular vibrations contributes to normal modes. The result of this analysis is expected to facilitate future improvement of DFT-D{sup *}.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Assessment of amide I spectroscopic maps for a gas-phase peptide using IR-UV double-resonance spectroscopy and density functional theory calculations

The spectroscopy of amide I vibrations has become a powerful tool for exploring protein structure and dynamics. To help with spectral interpretation, it is often useful to perform molecular dynamics (MD) simulations. To connect spectroscopic experiments to simulations in an efficient manner, several researchers have proposed “maps,” which relate observables in classical MD simulations to quantum spectroscopic variables. It can be difficult to discern whether errors in the theoretical results (compared to experiment) arise from inaccuracies in the MD trajectories or in the maps themselves. In this work, we evaluate spectroscopic maps independently from MD simulations by comparing experimental and theoretical spectra for a single conformation of the α-helical model peptide Ac-Phe-(Ala){sub 5}-Lys-H{sup +} in the gas phase. Conformation-specific experimental spectra are obtained for the unlabeled peptide and for several singly and doubly {sup 13}C-labeled variants using infrared-ultraviolet double-resonance spectroscopy, and these spectra are found to be well-modeled by density functional theory (DFT) calculations at the B3LYP/6-31G** level. We then compare DFT results for the deuterated and {sup 13}C{sup 18}O-labeled peptide with those from spectroscopic maps developed and used previously by the Skinner group. We find that the maps are typically accurate to within a few cm{sup −1} for both frequencies and couplings, having larger errors only for the frequencies of terminal amides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

Does Chirality Influence the Stability of Amino Acid –Cu Complexes in the Salt-Induced Peptide Formation Reaction? Insights from Density Functional Theory Calculations

The polymerization of amino acids into peptides and ultimately proteins is critical to evolution of life. Ribosomally-synthesized proteins are homochiral, composed entirely of L-amino acids. Abiotic syntheses of amino acids, however, produce racemic mixtures(equal amounts of L and D enantiomers), meaning that the pool of monomers available for abiotic protein synthesis would be racemic or nearly so. There are no prebiotically plausible mechanisms known to yield homochiral peptides from racemic pools of amino acids. While some mechanisms capable of producing or amplifying enantiomeric excesses have been observed, these excesses are small or not applicable to all biologically relevant amino acids. As a result, a prebiotically-feasible mechanism to create enantiopure pools of amino acids has not been identified. However, it is not clear that these enantio-enriched or enantiopure pools are necessary to produce homochiral peptides. Steric and electronic effects, or a combination of both, may influence how different enantiomers interact with each other, potentially leading to homochiral peptides from racemic mixtures. Here, we use density functional theory (DFT) calculations to assess the stability of homochiral and heterochiral reactive complexes produced during polymerization via the salt-induced peptide formation (SIPF) reaction. Experimental studies of the SIPF reaction have shown that it enables the formation of peptides under diverse environmental conditions, making it a plausible pathway to peptide formation on early Earth. In the SIPF reaction, NaCl acts as a condensation reagent while a divalent metal cation, primarily Cu2+, facilitates polymerization by complexing and activating amino acids forming a monochlorocuprate complex. To assess if hetero-or homochiral monochlorocuprate complexes were energetically favored, we compared the stability of LL, DD, and LD enantiomers of Cu2+–(alanine)2and Cu2+–(valine) 2 complexes. Gaussian 09 density DFT energy-minimization calculations were made for each Cu –amino acid complex in the cis and trans configuration. Models were energy minimized using the BH and HLYP/6-31++G(d,p) level of theory and free energies were compared to determine the most stable configuration.

A C Fox↗
DOE OSTI2016

RDX Compression, α→ γ Phase Transition, and Shock Hugoniot Calculations from Density-Functional-Theory-Based Molecular Dynamics Simulations

Prediction of the density and lattice compression properties of the α and γ phases of the hexahydro-1,3,5-trinitro-1,3,5-s-triazine (RDX) crystal and of the low-pressure α → γ phase transition upon pressure increase are general tests used to assess the accuracy of density-functional-theory- (DFT-) based computational methods and to identify the essential parameters that govern the behavior of this high-energy-density material under extreme conditions. The majority of previous DFT studies have analyzed such issues under static optimization conditions by neglecting the corresponding temperature effects. In this paper, we extend previous investigations and analyze the performance of dispersion-corrected density functional theory to predict the compression of RDX in the pressure range of 0–9 GPa and the corresponding α → γ phase transition under realistic temperature and pressure conditions. We demonstrate that, by using static dispersion-corrected density functional theory calculations, direct interconversion between the α and γ phases upon compression is not observed. This limitation can be addressed by using isobaric–isothermal molecular dynamic simulations in conjunction with DFT-D2-calculated potentials, an approach that is shown to provide an accurate description of both the crystallographic RDX lattice parameters and the dynamical effects associated with the α→ γ phase transformation. An even more comprehensive and demanding analysis was done by predicting the corresponding shock Hugoniot curve of RDX in the pressure range of 0–9 GPa. It was found that the theoretical results reproduce reasonably well the available experimental Hugoniot shock data for both the α and γ phases. Finally, the results obtained demonstrate that a satisfactory prediction of the shock properties in high-energy-density materials undergoing crystallographic and configurational transformations is possible through the combined use of molecular dynamics simulations in the isobaric–isothermal ensemble with dispersion-corrected density functional theory methods.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Predicting the potentials, solubilities and stabilities of metal-acetylacetonates for non-aqueous redox flow batteries using density functional theory calculations

New active materials are needed to improve the performance and reduce the cost of non-aqueous redox flow batteries (RFBs) for grid-scale energy storage applications. Efforts to develop better performing materials, which have largely been empirical, would benefit from a better understanding of relationships between structural, electronic and RFB-relevant functional properties. This paper focuses on metal-acetylacetonates, a class of metal coordination complexes that has shown promise for use in RFBs, and describes correlations between their experimentally measured standard potentials, solubilities, and stabilities (cycle lifes), and selected chemical, structural and electronic properties determined from Density Functional Theory (DFT) calculations. The training set consisted of 16 complexes including 5 different metals and 11 different substituents on the acetylacetonate ligand. Standard potentials for those compounds were calculated and are in good agreement with experimentally measured results. A predictive equation based on the solvation energies and dipole moments, two easily computed properties, reasonably modeled the experimentally determined solubilities. Importantly, we were able to identify a descriptor for the stability of acetylacetonates. The experimentally determined stability, quantified as the cycle life to a given degree of degradation, correlated with the percentage of the highest occupied (HOMO) or lowest unoccupied molecular orbital (LUMO) on the metal of the complex. This percentage is influenced by the degree of ligand innocence (irreducibility), and complexes with the most innocent ligands yielded the most stable redox reactions. To this end, VO(acetylacetonate)(2) and Fe(acetylacetonate)(3), with nearly 80% of the HOMO and LUMO on the metal, possessed the most stable oxidation and reduction half-reactions, respectively. The structure-function relationships and correlations presented in this paper could be used to predict new, highly soluble and stable complexes for RFB applications.

Kucharyson, J. F.↗
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↗
DOE OSTI2019

The effect of self-interaction error on electrostatic dipoles calculated using density functional theory

Spurious electron self-interaction in density functional approximations (DFAs) can lead to inaccurate predictions of charge transfer in heteronuclear molecules that manifest as errors in calculated electrostatic dipoles. Here we show the magnitude of these errors on dipoles computed for a diverse set of 47 molecules taken from the recent benchmark study of Hait and Head-Gordon. We compare results of Perdew-Wang local spin density approximation (PW92), Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and strongly constrained and appropriatedly normed (SCAN) meta-GGA dipole calculations, along with those of their respective self-interaction-corrected (SIC) counterparts, to reference values from accurate wave function-based methods. The SIC calculations were carried out using the Fermi-Löwdin orbital (FLO-SIC) approach. We find that correcting for self-interaction generally increases the degree of charge transfer, thereby increasing the size of calculated dipole moments. The FLO-SIC-PW92 and FLO-SIC-PBE dipoles are in better agreement with reference values than their uncorrected DFA counterparts, particularly for strongly ionic molecules where significant improvement is seen. Applying FLO-SIC to SCAN does not improve dipole values overall. In addition, we show that removing self-interaction improves the description of the dipole for stretched-bond geometries and recovers the physically correct separated atom limit of zero dipole. Finally, we find that the best agreement between the FLO-SIC-DFA and reference dipoles occurs when the molecular geometries are optimized using the FLO-SIC-DFA.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Self-consistent self-interaction corrected density functional theory calculations for atoms using Fermi-Löwdin orbitals: Optimized Fermi-orbital descriptors for Li–Kr

In the Fermi-Löwdin orbital method for implementing self-interaction corrections (FLO-SIC) in density functional theory (DFT), the local orbitals used to make the corrections are generated in a unitary-invariant scheme via the choice of the Fermi orbital descriptors (FODs). These are M positions in 3-d space (for an M-electron system) that can be loosely thought of as classical electron positions. The orbitals that minimize the DFT energy including the SIC are obtained by finding optimal positions for the FODs. In this paper, we present optimized FODs for the atoms from Li–Kr obtained using an unbiased search method and self-consistent FLO-SIC calculations. The FOD arrangements display a clear shell structure that reflects the principal quantum numbers of the orbitals. We describe trends in the FOD arrangements as a function of atomic number. FLO-SIC total energies for the atoms are presented and are shown to be in close agreement with the results of previous SIC calculations that imposed explicit constraints to determine the optimal local orbitals, suggesting that FLO-SIC yields the same solutions for atoms as these computationally demanding earlier methods, without invoking the constraints

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Development of an ab initio learned model of electron deposition range in deuterium-tritium plasmas through time-dependent density functional theory calculations and machine learning

Accurate hydrodynamic modeling for laser-direct-drive (LDD) inertial-confinement-fusion (ICF) relies on precise calculations of the electron thermal conduction in all target materials. The nonlocal stopping range of electrons in ICF plasmas directly influences thermal conduction; yet, no first principles model exists for the electron mean free path in the conduction-zone regime. This work utilized time-dependent stochastic density-functional theory (TD-sDFT) to calculate the electron stopping power in deuterium-tritium (DT) plasmas at (ρ, T) conditions relevant to the conduction zone and the compressed shell in ICF. Using a combination of our TD-sDFT data and already established analytical models, we developed and trained an artificial neural network to create a global model for the nonlocal electron deposition range, λ E . We compared our machine-learning (ML) based model for λ E to the currently-used modified-Lee-More model in LDD radiation-hydrodynamic codes, such as lilac, and saw an overall decrease in the deposition range. To understand the effects of λ E on LDD ICF implosion dynamics, we implemented the ML-based model into lilac; specifically, we looked at designs consistent with a current experiment on the OMEGA laser and for a newly designed LDD-ICF target for the future OMEGA-Next facility. In both cases, we saw an overall drop in predicted ablation pressure, peak areal density, and neutron yield due to the reduced thermal conduction (smaller λ E ) in DT plasmas. Comparisons with the experiment on OMEGA are also made.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Towards efficient density functional theory calculations without self-interaction: The Fermi-Löwdin orbital self-interaction correction

The Fermi-Löwdin orbital (FLO) approach to the Perdew-Zunger self-interaction correction (PZ-SIC) to density functional theory (DFT) is described and an improved approach to the problem of optimizing the Fermi-orbitals in order to minimize the DFT-SIC total energy is introduced. To illustrate the use of the FLO-SIC method, results are given for several applications involving problems where self-interaction errors are pronounced.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Precision Determination of the Neutral Weak Form Factor of Ca 48

In this work, we report a precise measurement of the parity-violating asymmetry $A_{\rm PV}$ in the elastic scattering of longitudinally polarized electrons from $^{48}{\rm Ca}$. We measure $A_{\rm PV} =2668\pm 106\ {\rm (stat)}\pm 40\ {\rm (syst)}$ parts per billion, leading to an extraction of the neutral weak form factor $F_{\rm W} (q=0.8733$ fm$^{-1}) = 0.1304 \pm 0.0052 \ {\rm (stat)}\pm 0.0020\ {\rm (syst)}$ and the charge minus the weak form factor $F_{\rm ch} - F_{\rm W} = 0.0277\pm 0.0055$. The resulting neutron skin thickness $R_n-R_p=0.121 \pm 0.026\ {\rm (exp)} \pm 0.024\ {\rm (model)}$~fm is relatively thin yet consistent with many model calculations. The combined CREX and PREX results will have implications for future energy density functional calculations and on the density dependence of the symmetry energy of nuclear matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗