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DOE OSTI2023

Multiscale simulations reveal TDP-43 molecular-level interactions driving condensation

The RNA-binding protein TDP-43 is associated with mRNA processing and transport from the nucleus to the cytoplasm. TDP-43 localizes in the nucleus as well as accumulating in cytoplasmic condensates such as stress granules. Aggregation and formation of amyloid-like fibrils of cytoplasmic TDP-43 are hallmarks of numerous neurodegenerative diseases, most strikingly present in >90% of amyotrophic lateral sclerosis (ALS) patients. If excessive accumulation of cytoplasmic TDP-43 causes, or is caused by, neurodegeneration is presently not known. In this work, we use molecular dynamics simulations at multiple resolutions to explore TDP-43 self- and cross-interaction dynamics. A full-length molecular model of TDP-43, all 414 amino acids, was constructed from select structures of the protein functional domains (N-terminal domain, and two RNA recognition motifs, RRM1 and RRM2) and modeling of disordered connecting loops and the low complexity glycine-rich C-terminus domain. All-atom CHARMM36m simulations of single TDP-43 proteins served as guides to construct a coarse-grained Martini 3 model of TDP-43. The Martini model and a coarser implicit solvent Cα model, optimized for disordered proteins, were subsequently used to probe TDP-43 interactions; self-interactions from single-chain full-length TDP-43 simulations, cross-interactions from simulations with two proteins and simulations with assemblies of dozens to hundreds of proteins. Our findings illustrate the utility of different modeling scales for accessing TDP-43 molecular-level interactions and suggest that TDP-43 has numerous interaction preferences or patterns, exhibiting an overall strong, but dynamic, association and driving the formation of biomolecular condensates.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Structural basis of the activation of a metabotropic GABA receptor

Metabotropic γ-aminobutyric acid receptors (GABA B ) are involved in the modulation of synaptic responses in the central nervous system and have been implicated in neuropsychological conditions that range from addiction to psychosis. GABA B belongs to class C of the G-protein-coupled receptors, and its functional entity comprises an obligate heterodimer that is composed of the GB1 and GB2 subunits. Each subunit possesses an extracellular Venus flytrap domain, which is connected to a canonical seven-transmembrane domain. In this paper we present four cryo-electron microscopy structures of the human full-length GB1–GB2 heterodimer: one structure of its inactive apo state, two intermediate agonist-bound forms and an active form in which the heterodimer is bound to an agonist and a positive allosteric modulator. The structures reveal substantial differences, which shed light on the complex motions that underlie the unique activation mechanism of GABA B . Our results show that agonist binding leads to the closure of the Venus flytrap domain of GB1, triggering a series of transitions, first rearranging and bringing the two transmembrane domains into close contact along transmembrane helix 6 and ultimately inducing conformational rearrangements in the GB2 transmembrane domain via a lever-like mechanism to initiate downstream signalling. This active state is stabilized by a positive allosteric modulator binding at the transmembrane dimerization interface.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Artificial spin ice: Paths forward

Artificial spin ice systems are lithographically prepared arrays of interacting nanoscale magnetic moments with collective behavior resulting from the chosen array geometry. These many-body systems are unusual in that their simple constituent elements can be configured to design their interactions with exquisite control. They can then be probed experimentally over a remarkably large range of time scales and length scales, including imaging of the individual moments. The study of artificial spin ice has broadened well beyond the original focus on systems with connection to spin ice and ice models, and now the term is used in reference to many other structures that exhibit a much wider range of physical phenomena. Here in this perspective, we review progress in the field of artificial spin ice since its inception more than a decade ago. We then discuss prospects for future directions – continuing the exploration of nanomagnetism, statistical spin models, and the potential for technological devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

POINT: Partially Observable Imitation Network for Traffic Signal Control

Smart traffic signals bring together transportation infrastructure and advance technologies to improve the mobility and efficiency of urban transportation network. Adaptive traffic signal control studies can be categorized into modeling-based approaches and learning-based approaches. In order to take advantages of these two systems, this study developed an offline-online combined Partial Observable Imitation Network for Traffic signal control (POINT). In the offline system, the traffic signal timing optimization problem was formulated as a Mixed Integer Nonlinear Programming (MINLP) given complete traffic information, i.e., second-by-second speeds and locations of all vehicles. Furthermore, the objective of MINLP is to minimize total travel delays considering individual vehicle trajectories under Connected Vehicle (CV) environment. The calculated optimal solutions under various traffic conditions were considered as the ”expert” decisions. In the online system, an imitation neural network model was developed to learn the ”expert” signal plans generated from offline system. Given partial observable traffic conditions in real time, e.g., the aggregate-level of traffic volume, the POINT model can compute the signal timing parameters in the online system. The numerical results demonstrated that the proposed method outperformed other state-of-the-art signal control method under high and unbalanced traffic demand levels in terms of reducing travel delays and queue length.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

Sources of Subseasonal-To-Seasonal Predictability of Atmospheric Rivers and Precipitation in the Western United States

Atmospheric rivers (ARs) account for a large portion of winter precipitation in the western US. To evaluate the sources of AR and precipitation predictability at subseasonal-to-seasonal timescales, we examine the relationships between two climate modes, the El Niño/Southern Oscillation (ENSO) and Madden-Julian oscillation (MJO), and winter hydroclimate in the western US. Our analysis uses a large ensemble of the Weather Research and Forecast (WRF) model simulations from 1981 to 2017, facilitating the assessment of uncertainty in climate mode-AR relationship due to climate variability and short length of observations. Over the North Pacific basin, we find ENSO-related latitudinal shifts of ARs, but ENSO has little effect on basin-wide averaged AR frequency. Over the western US, there is some uncertainty in the ENSO-AR connection due to the impacts of ENSO indices and datasets. However, extreme El Niño events defined by the ENSO longitude index are consistently linked to increased landfalling AR activity. The MJO can lead to significantly enhanced or suppressed landfalling AR activity in the large-ensembles, depending on the phase of MJO and time lag, while observations are too short in length to robustly show this signal. ENSO substantially modulates the MJO-AR relationship, triggering variegated responses of landfalling ARs and AR precipitation in La Niña and El Niño years. Our findings highlight the need to evaluate concurrent effects of different climate modes on ARs and precipitation, and may shed light on a path toward more accurate subseasonal-to-seasonal prediction of ARs and precipitation over the western US.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Mesoscopic two-point collective dynamics of glass-forming liquids

The collective density–density and hydrostatic pressure–pressure correlations of glass-forming liquids are spatiotemporally mapped out using molecular dynamics simulations. It is shown that the sharp rise of structural relaxation time below the Arrhenius temperature coincides with the emergence of slow, nonhydrodynamic collective dynamics on mesoscopic scales. The observed long-range, nonhydrodynamic mode is independent of wave numbers and closely coupled to the local structural dynamics. Below the Arrhenius temperature, it dominates the slow collective dynamics on length scales immediately beyond the first structural peak in contrast to the well-known behavior at high temperatures. Furthermore, these results highlight a key connection between the qualitative change in mesoscopic two-point collective dynamics and the dynamic crossover phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Pectic-AGP is a major form of Arabidopsis AGPs

As a key component in cell walls of numerous organisms ranging from green algae to higher plants, AGPs play principal roles in many biological processes such as cell-cell adhesion and regulating Ca 2+ signaling pathway as a Ca 2+ -capacitor. Consistently, AGP structures vary from species to species and from tissue to tissue. To understand the functions of AGPs, it is vital to know their structural differences relative to their location in the plant. Thus, AGPs were purified from different Arabidopsis tissues. Analyses of these AGPs demonstrated that the AGPs comprised covalently linked pectin and AGP, referred to as pectic-AGPs. Importantly, these pectic-AGPs were glycosylated with a remarkable variety of polysaccharides including homogalacturonan, rhamnogalacturonan-I, and type II arabinogalactan at different ratios and lengths. Furthermore, this result not only suggests that pectic-AGP is a major form of Arabidopsis AGPs, but also supports AGPs serve as crosslinkers covalently connecting pectins with structures tailored for tissue-specific functions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Medium-Range Structural Order as the Driver of Activated Dynamics and Complexity Reduction in Glass-Forming Liquids

Here, we analyze in depth the Elastically Collective Nonlinear Langevin Equation theory of activated dynamics in metastable liquids to establish that the predicted inter-relationships between the alpha relaxation time, local cage and collective elastic barriers, dynamic localization length, and shear modulus are causally related within the theory to the medium range order (MRO) static correlation length. The latter grows exponentially with density for metastable hard sphere fluids and as a nonuniversal inverse power law with temperature for supercooled liquids under isobaric conditions. The physical origin of predicted connections between the alpha time and other metrics of cage order and the thermodynamic inverse dimensionless compressibility is fully established. It is discovered that although kinetic constraints from the real space first coordination shell are important for the alpha time, they are of secondary importance compared to the consequences of the more universal MRO correlations in both the modestly and deeply metastable regimes. This understanding sheds new light on the theoretical basis for, and prior successes of, the predictive mapping of chemically complex thermal liquids to effective hard sphere fluids based on matching their dimensionless compressibilities, a scheme we call “complexity reduction”. In essence, the latter is equivalent to the physical requirement that the thermal liquid MRO correlation equals that of its effective hard sphere analog. The mapping alone is shown to provide a remarkable level of quantitative predictive power for the glass transition temperature T g of 21 molecular and polymer liquids. Predictions for the chemically specific absolute magnitude and growth with cooling of the MRO correlation length are obtained and lie in the window of 2–6 nm at T g . Dynamic heterogeneity, elastic facilitation, and beyond pair structure issues are briefly discussed. Future opportunities to theoretically analyze the equilibrated deep glass regime are outlined.

cancer↗

DOE OSTI2020

Robust late twenty-first century shift in the regional monsoons in RegCM-CORDEX simulations

Abstract We use an unprecedented ensemble of regional climate model (RCM) projections over seven regional CORDEX domains to provide, for the first time, an RCM-based global view of monsoon changes at various levels of increased greenhouse gas (GHG) forcing. All regional simulations are conducted using RegCM4 at a 25 km horizontal grid spacing using lateral and lower boundary forcing from three General Circulation Models (GCMs), which are part of the fifth phase of the Coupled Model Inter-comparison Project (CMIP5). Each simulation covers the period from 1970 through 2100 under two Representative Concentration Pathways (RCP2.6 and RCP8.5). Regional climate simulations exhibit high fidelity in capturing key characteristics of precipitation and atmospheric dynamics across monsoon regions in the historical period. In the future period, regional monsoons exhibit a spatially robust delay in the monsoon onset, an increase in seasonality, and a reduction in the rainy season length at higher levels of radiative forcing. All regions with substantial delays in the monsoon onset exhibit a decrease in pre-monsoon precipitation, indicating a strong connection between pre-monsoon drying and a shift in the monsoon onset. The weakening of latent heat driven atmospheric warming during the pre-monsoon period delays the overturning of atmospheric subsidence in the monsoon regions, which defers their transitioning into deep convective states. Monsoon changes under the RCP2.6 scenario are mostly within the baseline variability.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Synchrotron X-ray microtomography and multifractal analysis for the characterization of pore structure and distribution in softwood pellet biochar

Biochar pores in the micrometer range (1–100 µm) derive from cellular structures of the plant biomass subjected to pyrolysis or can be the result of mechanical processing, such as pelleting. In this study, synchrotron X-ray microtomography was used to investigate the internal pore structure of softwood pellet biochar produced by slow pyrolysis at 550 and 700 °C. The microtomographic data sets consisted of 2025 images of 2560 × 2560 voxels with a voxel side length of 0.87 µm. The three-dimensional reconstructions revealed that pelleting and pyrolysis significantly altered the pore structures of the wood feedstock, creating a network of connected pores between fragments that resembled the wood morphology. While higher pyrolysis temperature increased the specific surface area (as determined by BET nitrogen adsorption), it did not affect the total observed porosity. Multifractal analysis was applied to assess the characteristics of the frequency distribution of pores along each of the three dimensions of reconstructed images of five softwood pellet biochar samples. The resulting singularity and Rényi spectra (generalized dimensions) indicated that the distribution of porosity had monofractal scaling behavior, was homogeneous within the analyzed volumes and consistent between replicate samples. Moreover, the pore distributions were isotropic (direction-independent), which is in strong contrast with the anisotropic pore structure of wood. As pores at the scale analyzed in this study are relevant, for example, for the supply of plant accessible water and habitable space for microorganisms, our findings combined with the ability to reproduce biochar with such pore distribution offer substantial advantages in various biochar applications.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Global analysis of SBP gene family in Brachypodium distachyon reveals its association with spike development

SQUAMOSA-promoter binding like proteins (SBPs/SPLs) are plant specific transcription factors targeted by miR156 and involved in various biological pathways, playing multi-faceted developmental roles. This gene family is not well characterized in Brachypodium. We identified a total of 18 SBP genes in B. distachyon genome. Phylogenetic analysis revealed that SBP gene family in Brachypodium expanded through large scale duplication. A total of 10 BdSBP genes were identified as targets of miR156. Transcript cleavage analysis of selected BdSBPs by miR156 confirmed their antagonistic connection. Alternative splicing was observed playing an important role in BdSBPs and miR156 interaction. Characterization of T-DNA Bdsbp9 mutant showed reduced plant growth and spike length, reflecting its involvement in the spike development. Expression of a majority of BdSBPs elevated during spikelet initiation. Specifically, BdSBP1 and BdSBP3 differentially expressed in response to vernalization. Differential transcript abundance of BdSBP1, BdSBP3, BdSBP8, BdSBP9, BdSBP14, BdSBP18 and BdSBP23 genes was observed during the spike development under high temperature. Co-expression network, protein–protein interaction and biological pathway analysis indicate that BdSBP genes mainly regulate transcription, hormone, RNA and transport pathways. Our work reveals the multi-layered control of SBP genes and demonstrates their association with spike development and temperature sensitivity in Brachypodium.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

FeederGAN: Synthetic Feeder Generation via Deep Graph Adversarial Nets

This paper presents a novel, automated, generative adversarial networks (GAN) based synthetic feeder generation mechanism, abbreviated as FeederGAN. FeederGAN digests real feeder models represented by directed graphs via a deep learning framework powered by GAN and graph convolutional networks (GCN). Information of a distribution feeder circuit is extracted from its model input files so that the device connectivity is mapped onto the adjacency matrix and the device characteristics, such as circuit types (i.e., 3-phase, 2-phase, and 1-phase) and component attributes (e.g., length and current ratings), are mapped onto the attribute matrix. Then, Wasserstein distance is used to optimize the GAN and GCN is used to discriminate the generated graphs from the actual ones. A greedy method based on graph theory is developed to reconstruct the feeder using the generated adjacency and attribute matrices. Furthermore, our results show that the GAN generated feeders resemble the actual feeder in both topology and attributes verified by visual inspection and by empirical statistics obtained from actual distribution feeders.

42 ENGINEERING↗

DOE OSTI2021

Spatiotemporal Crossover between Low- and High-Temperature Dynamical Regimes in the Quantum Heisenberg Magnet

The stranglehold of low temperatures on fascinating quantum phenomena in one-dimensional quantum magnets has been challenged recently by the discovery of anomalous spin transport at high temperatures. Whereas both regimes have been investigated separately, no study has attempted to reconcile them. For instance, the paradigmatic quantum Heisenberg spin-$1/2$ chain falls at low-temperature within the Tomonaga-Luttinger liquid framework, while its high-temperature dynamics is superdiffusive and relates to the Kardar-Parisi-Zhang universality class in $1+1$ dimensions. This work aims at reconciling the two regimes. Building on large-scale matrix product state simulations, we find that they are connected by a temperature-dependent spatiotemporal crossover. In this work, as the temperature $T$ is reduced, we show that the onset of superdiffusion takes place at longer length and time scales $\propto 1/T$. This prediction has direct consequences for experiments including nuclear magnetic resonance: it is consistent with earlier measurements on the nearly ideal Heisenberg $S=1/2$ chain compound Sr$_2$CuO$_3$ yet calls for new and dedicated experiments.

1-dimensional spin chains↗

DOE OSTI2021

Nanosecond Gated CMOS Camera (NSGCC) ICD (Rev. 2.1)

The Ultra-Fast X-ray Imager (UXI) program is an ongoing effort at Sandia National Laboratories to create high speed, multi-frame, time-gated Read Out Integrated Circuits (ROICs), and a corresponding suite of photodetectors to image a wide variety of High Energy Density (HED) physics experiments on both Sandia’s Z-Machine and LLNL’s National Ignition Facility (NIF). Several cameras have been designed over the length of the program; one of the most recent is the Icarus, which is an improvement on past imagers (Furi and Hippogriff). A second sensor that can be connected is the Daedalus sensor. The Icarus is a 1024 × 512-pixel array with either 25 μm or 8 µm spatial resolution containing four frames of storage per pixel and has improved timing generation and distribution components while achieved 2 ns time gating. The Daedalus sensor is also a 1024 x 512-pixel array with 25 µm special resolution containing three frames of storage per pixel and has an increased set of features for a wider variety of applications from interlacing of rows in each frame to configurability of all shutters. See Section 14 for details regarding the Icarus implementation of the firmware and Section 15 for details regarding the Daedalus implementation. Due to the unique test environments UXI sensors are targeted for, full custom hardware was required to physically mount an Icarus or Daedalus sensor, manage its various functions, and read out pixel data for transfer to a host computer. Beyond experimental functionality, the hardware also needed to accommodate sensor characterization requirements. Lawrence Livermore National Laboratory’s ‘Version 4.0 Board’ was the result of these efforts. It mounts all the components required to fully utilize the Icarus and Daedalus sensors including analog to digital converters to convert pixel data and various system voltages to digital form for readout and analysis, DAC channels for remote configuration of critical bias voltages, static random-access memories to buffer pixel data, RS422 and Gigabit Ethernet communications for remote access, and an FPGA to tie these components together. This document describes the FPGA electrical interfaces in detail to allow the reader a greater understanding of the device, and to facilitate implementation of custom software to control and manage it. The Version 4.0 Board is a continuation of the Nano-second Gated CMOS hardware design that retains much of the functionality of the Version 1.0 Board while adding features including a DAC instead of digital potentiometers, as well as sensors for pressure and radiation. The Version 4.0 board is intended for applications requiring tight form-factor enclosures. It is composed of two stacking boards; one holds the FPGA and regulators to power the various components of the board while the other contains the mating connector to the sensor, image-readoff ADCs, the DAC, and other components.

42 ENGINEERING↗

DOE OSTI2022

Update on the Investigation of Commercial Drying Cycles Using the Advanced Drying Cycle Simulator

The purpose of this report is to document updates on the apparatus to simulate commercial vacuum drying procedures at the Nuclear Energy Work Complex at Sandia National Laboratories. Validation of the extent of water removal in a dry spent nuclear fuel storage system based on drying procedures used at nuclear power plants is needed to close existing technical gaps. Operational conditions leading to incomplete drying may have potential impacts on the fuel, cladding, and other components in the system during subsequent storage and disposal. A general lack of data suitable for model validation of commercial nuclear canister drying processes necessitates well-designed investigations of drying process efficacy and water retention. Scaled tests that incorporate relevant physics and well-controlled boundary conditions are essential to provide insight and guidance to the simulation of prototypic systems undergoing drying processes. This report documents a new test apparatus, the Advanced Drying Cycle Simulator (ADCS). This apparatus was built to simulate commercial drying procedures and quantify the amount of residual water remaining in a pressurized water reactor (PWR) fuel assembly after drying. The ADCS was constructed with a prototypic 17×17 PWR fuel skeleton and waterproof heater rods to simulate decay heat. These waterproof heaters are the next generation design to heater rods developed and tested at Sandia National Laboratories in FY20. This report describes the ADCS vessel build that was completed late in FY22, including the receipt of the prototypic length waterproof heater rods and construction of the fuel basket and the pressure vessel components. In addition, installations of thermocouples, emissivity coupons, pressure and vacuum lines, pressure transducers, and electrical connections were completed. Preliminary power functionality testing was conducted to demonstrate the capabilities of the ADCS. In FY23, a test plan for the ADCS will be developed to implement a drying procedure based on measurements from the process used for the High Burnup Demonstration Project. While applying power to the simulated fuel rods, this procedure is expected to consist of filling the ADCS vessel with water, draining the water with applied pressure and multiple helium blowdowns, evacuating additional water with a vacuum drying sequence at successively lower pressures, and backfilling the vessel with helium. Additional investigations are expected to feature failed fuel rod simulators with engineered cladding defects and guide tubes with obstructed dashpots to challenge the drying system with multiple water retention sites.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Computational approaches to model X-ray photon correlation spectroscopy from molecular dynamics

X-ray photon correlation spectroscopy (XPCS) allows for the resolution of dynamic processes within a material across a wide range of length and time scales. X-ray speckle visibility spectroscopy (XSVS) is a related method that uses a single diffraction pattern to probe ultrafast dynamics. Interpretation of the XPCS and XSVS data in terms of underlying physical processes is necessary to establish the connection between the macroscopic responses and the microstructural dynamics. To aid the interpretation of the XPCS and XSVS data, we present a computational framework to model these experiments by computing the X-ray scattering intensity directly from the atomic positions obtained from molecular dynamics simulations. We compare the efficiency and accuracy of two alternative computational methods: the direct method computing the intensity at each diffraction vector separately, and a method based on fast Fourier transform that computes the intensities at all diffraction vectors at once. Furthermore, the computed X-ray speckle patterns capture the density fluctuations over a range of length and time scales and are shown to reproduce the known properties and relations of experimental XPCS and XSVS for liquids.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Superposition principle and nonlinear response in spin glasses

The extended principle of superposition has been a touchstone of spin-glass dynamics for almost 30 years. Here the Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields H up to 10 Oe at the reduced temperature T r = T/T g = 0.95, where T g is the spin-glass condensation temperature. For H > 10 Oe, they observe a departure from linear response which they ascribe to the development of nonlinear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin-glass correlation length, ξ(t, t w ; H). Here, t is the time after H changes, and t w is the time from the quench for T > T g to the working temperature T until H changes. We connect the growth of ξ(t, t w ; H) to the barrier heights Δ(t w ) that set the dynamics. The effect of H on the magnitude of Δ (t w ) is responsible for affecting differently the two dynamical protocols associated with turning H off (TRM, or thermoremanent magnetization) or on (ZFC, or zero-field-cooled magnetization). This difference is a consequence of nonlinearity based on the effect of H on Δ (t w ). Superposition is preserved if Δ(t w ) is linear in the Hamming distance Hd (proportional to the difference between the self-overlap q EA and the overlap q[Δ(t w )]). However, superposition is violated if Δ(t w ) increases faster than linear in Hd. We have previously shown, through experiment and simulation, that the barriers Δ(t w ) do increase more rapidly than linearly with Hd through the observation that the growth of ξ(t,t w ;H) slows down as ξ(t,t w ; H) increases. In this paper, we display the difference between the zero-field-cooled ξ ZFC (t, t w ; H) and the thermoremanent magnetization ξ TRM (t, t w ; H) correlation lengths as H increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Calculation and interpretation of classical turning surfaces in solids

Abstract Classical turning surfaces of Kohn–Sham potentials separate classically allowed regions (CARs) from classically forbidden regions (CFRs). They are useful for understanding many chemical properties of molecules but need not exist in solids, where the density never decays to zero. At equilibrium geometries, we find that CFRs are absent in perfect metals, rare in covalent semiconductors at equilibrium, but common in ionic and molecular crystals. In all materials, CFRs appear or grow as the internuclear distances are uniformly expanded. They can also appear at a monovacancy in a metal. Calculations with several approximate density functionals and codes confirm these behaviors. A classical picture of conduction suggests that CARs should be connected in metals, and disconnected in wide-gap insulators, and is confirmed in the limits of extreme compression and expansion. Surprisingly, many semiconductors have no CFR at equilibrium, a key finding for density functional construction. Nonetheless, a strong correlation with insulating behavior can still be inferred. Moreover, equilibrium bond lengths for all cases can be estimated from the bond type and the sum of the classical turning radii of the free atoms or ions.

Chemistry↗