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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Implementing a microphysics model in hydrodynamic simulations to study the initial plasma formation in dielectric ablator materials for direct-drive implosions

A microphysics model to describe the photoionization and impact ionization processes in dielectric ablator materials like plastic has been implemented into the 1-D hydrodynamic code LILAC for planar and spherical targets. Currently, the initial plasma formation during the early stages of a laser drive are modeled in an ad hoc manner, until the formation of a critical surface. Implementation of the physics-based models predict higher values of electron density, electron temperature, and pressure than the ad hoc model. Moreover, the numerical predictions are consistent with previous experimental observations of the shinethrough mechanism in plastic ablators. For planar targets, a decompression of the rear end of the target was observed, that is similar to recent experiments. An application of this model is to understand the laser-imprint mechanism that is caused by nonuniform laser irradiation due to single beam speckle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Impact of hydronium ions on the Pd-catalyzed furfural hydrogenation

Abstract In aqueous mediums, the chemical environment for catalytic reactions is not only comprised of water molecules but also of corresponding ionized species, i.e., hydronium ions, which can impact the mechanism and kinetics of a reaction. Here we show that in aqueous-phase hydrogenation of furfural on Pd/C, increasing the hydronium ion activities by five orders of magnitude (from pH 7 to pH 1.6) leads to an increase of less than one order of magnitude in the reaction rate. Instead of a proton-coupled electron transfer pathway, our results show that a Langmuir-Hinshelwood mechanism describes the rate-limiting hydrogen addition step, where hydrogen atom adsorbed on Pd is transferred to the carbonyl C atom of the reactant. As such, the strength of hydrogen binding on Pd, which decreases with increasing hydronium ion concentration (i.e., 2 kJ mol H2 −1 per unit pH), is a decisive factor in hydrogenation kinetics (rate constant +270%). In comparison, furfural adsorption on Pd is pH-independent, maintaining a tilted geometry that favors hydrogen attack at the carbonyl group over the furan ring.

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

Particle balance of deuterium during deuterium shattered pellet injection shutdown in DIII-D

A particle balance analysis was conducted during a deuterium (D 2 ) shattered pellet injection-induced plasma shutdown on the DIII-D tokamak to determine why less than 20% of the pellet material is assimilated into the core plasma by the mid-current quench (CQ). Initially, most of the D 2 is injected as frozen shards and ionized upon entering the vessel. During the thermal quench, ionized particles move to the divertors and subsequently to the center post (CP) walls, where they rapidly recycle and partially accumulate as neutrals without assimilating into the core plasma. In contrast, the particle flux to the outer midplane walls is negligible, despite being accompanied by hot plasma with electron temperatures exceeding 100 eV. During mid-CQ, volume recombination effects, although not large enough to impact overall particle balance, were significant enough to require accounting for accurate interpretation of fast-framing camera D-alpha signals and the estimation of the CP wall particle flux. In addition, toroidal asymmetries, observed in measurements of toroidal electron density perturbations and the phase of magnetohydrodynamic modes, are present throughout the shutdown and can account for a discrepancy in the assimilation rate for up to 50% of the observed D 2 particle inventory. These sources and sinks of particles and fluxes were identified using absolutely calibrated D-alpha brightness and Langmuir probes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Demonstration of closed shell breeding of cesium ions with an electron beam ion source

An electron beam ion source serves as a charge breeder for the Californium Rare Isotope Breeder Upgrade (CARIBU) at the Argonne Tandem Linac Accelerator System (ATLAS). The source accepts radioactive beams of 1+ or 2+ ions and raises their charge state for post-acceleration by ATLAS. The efficiency of this process impacts the length of each experiment and, hence, the type and number of experiments that can be run in each program cycle. Recent efforts to improve the charge breeding efficiency for the 80 < A < 160 species typical of CARIBU have focused on utilizing the closed shell breeding technique. Here, with this technique, the electron beam energy is manipulated to take advantage of the large gap in ionization energies at shell closures and selectively populate a single charge state. Charge breeding studies with stable cesium ions have demonstrated an absolute efficiency of 72% for Cs 27+ and a total efficiency of 93%. The Cs 27+ efficiency result represents a factor of 3 improvement over the previous best charge breeding result of 23% for Cs 27+ .

Vondrasek, R. [Argonne National Laboratory (ANL), ↗
DOE OSTI2024

Impact of ionization and transport on pedestal density structure in DIII-D and Alcator C-Mod

Abstract This paper investigates the role of ionization on the pedestal structure using both measurements and modeling for H-mode plasmas on DIII-D and Alcator C-Mod to enhance our ability to predict pedestal behavior in future pilot plants. The impact of the neutral penetration depth on the pedestal density is investigated using dimensionally matching hydrogen and deuterium DIII-D H-mode discharges at low and high electron density. The DIII-D Lyman- α diagnostic measurements show that hydrogen neutrals penetrate deeper inside the plasma on both the high field and low field side, while the pedestal electron density structure is similar for both isotopes. However, as the opaqueness increases we observe that the pedestal density gradient becomes stiff, similar to prior observations on DIII-D and C-Mod (Mordijck 2020 Nuclear Fusion 60 082006). In addition, these results also confirm prior measured and modeled poloidal asymmetries in neutral densities, indicating that to make transport predictions, 2D neutral modeling is necessary. The first direct validation of SOLPS-ITER for the measured brightness, emissivity and neutral densities for three different confinement regimes on C-Mod is introduced. The SOLPS-ITER model shows good agreement, within the constrains of the model for all regimes. In addition, a comparison of SOLPS-ITER modeling for DIII-D and C-Mod shows that as opaqueness increases, the role of divertor fueling and thus poloidal asymmetries in the neutral density profiles decreases. Based on these experimental and modeling results we estimate the size of a potential particle pinch using typical values for the diffusion coefficient for both DIII-D and C-Mod H-mode discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Angular dependent measurement of electron-ion recombination in liquid argon for ionization calorimetry in the ICARUS liquid argon time projection chamber

This paper reports on a measurement of electron-ion recombination in liquid argon in the ICARUS liquid argon time projection chamber (LArTPC). A clear dependence of recombination on the angle of the ionizing particle track relative to the drift electric field is observed. An ellipsoid modified box (EMB) model of recombination describes the data across all measured angles. These measurements are used for the calorimetric energy scale calibration of the ICARUS TPC, which is also presented. The impact of the EMB model is studied on calorimetric particle identification, as well as muon and proton energy measurements. Accounting for the angular dependence in EMB recombination improves the accuracy and precision of these measurements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

Self-Consistent Relativistic Electron Scattering using the Sherlock Scattering Model for X-ray Diagnostics

We present on a new, self-consistent, arbitrary-temperature Romberg integration scheme for modeling electron scattering in materials in a LANL Lagrangian Shock Hydro (LSH) code. Electron beam-target interactions are fundamental to a wide range of scientific and technological applications. When high-energy electron beams hit their target, they may scatter, deposit energy, or ionize the source. These processes govern the behavior and outcomes in nanotechnology manufacturing, electron microscopy, and modern X-ray diagnostics. Simulating these interactions is essential for interpreting experimental results, predicting material responses, and designing efficient tools and experiments. At Los Alamos, this is done using a LSH code, which is a multi-dimension, multi-material, massively parallel, multi-physics code used to simulate applications from asteroid impacts to electron beam interactions. By effectively and efficiently modeling the way that electrons scatter from the beam we can bolster these simulations and more accurately predict experimental outcomes. The model currently implemented in the LSH of interest is based on work by Papp and does not self-consistently preserve momentum in the slightly relativistic regime; here we adopt a model proposed by Braams and Karney and implement a Romberg integration scheme to compute the diffusion tensor. In this paper we will provide background on the Braams-Karney diffusion tensor as well as the Romberg integration scheme we employed to numerically solve for it. We will show that our integration scheme is accurate in solving for the set of scalar potentials used to re-express the diffusion tensor in differential form, and in solving for the diffusion coefficients in the larger LSH code. By using this diffusion tensor rather than the existing Papp one, and numerically integrating it with a Romberg method, we produce much more accurate, self-consistent results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Exploring the impact of nucleotide length on lipid nanoparticle structure and properties

Lipid nanoparticles (LNPs) are versatile carriers for nucleic acid (NA) therapeutics, including ASOs, siRNA, mRNA, and poly-IC. While lipid composition is known to influence LNP properties, the impact of NA length on morphology and internal structure is less understood, particularly during the stages of carrier–cargo assembly. Here, we examine NA length and lipid composition immediately after mixing using high-throughput SAXS, dynamic light scattering, and cryogenic electron microscopy. All LNPs form ordered NA/lipid compartments, with longer NAs promoting inverse hexagonal (H II ) phases and larger intercompartment distances. In contrast, short NAs, especially in formulations with SM102 ionizable lipid, favor lamellar phases. SAXS peak deconvolution quantifies ordered versus disordered phases via a Robustness of Ordered Phase factor, which correlates with particle size and encapsulation efficiency. Formulations with MC3 ionizable and DOPE helper lipids exhibit the most stable H II -phase packing, highlighting the role of helper-lipid curvature in compartment stabilization. Variations in NA compartmentalization indicate differences in payload capacity, offering a framework for rational LNP design across diverse nucleic acid cargos.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Anatomy of Protein Electrospray Ionization Mass Spectra by Superconducting Tunnel Junction Mass and Energy Spectrometry

Cryogenic superconducting tunnel junction (STJ) detectors have the advantage of single-particle sensitivity, high quantum efficiency, low noise, and the ability to detect the time and relative impact energy of deposited ions. This makes them attractive for use in mass spectrometry (MS) and as a form of energy spectrometry. STJ cryodetectors have been coupled to time-offlight (TOF) mass spectrometers equipped with a matrix-assisted laser desorption ionization (MALDI) source and to an electrospray ionization (ESI) TOF mass spectrometer. Here, a lab-made linear ion trap (LIT) mass spectrometer system was coupled to an ESI source and a 16-channel Nb-STJ array with improved readout electronics. The goal was to investigate fundamentals of ESI-generated protein ions by further exploiting the advantage of resolving these ions in a third dimension of the relative energy deposited into the STJs. The proteins equine cytochrome c, bovine carbonic anhydrase, bovine serum albumin, and murine immunoglobulin G were studied using this ESI-LIT-STJ-MS instrument. Multiply charged monomers, multimers, and fragments from metastable ions were resolved from monomer peaks by differences in ion deposition energy even when these ions have the same mass-to-charge ratio as the corresponding monomer. The determination of fragment mass from metastable decomposition is accomplished without knowing the charge state of the fragment. The average charge state of the multimers is reduced with each addition of a protein which is a direct reflection of the surface area available for charging. Multiply charged in-source fragments have also been observed and distinguished in the mass spectrum of carbonic anhydrase by using the differences in the energy deposited in the STJs.

42 ENGINEERING↗
DOE OSTI2026

Impact of atomic substitution on core-hole relaxation dynamics: A study of Br 2 and IBr

Understanding inner-shell decay processes in heavy-element molecules is essential for unraveling x-ray-induced photodynamics and advancing molecular imaging techniques. Here, in this study, we investigate the influence of atomic substitution on core-hole relaxation dynamics and molecular fragmentation in Br 2 and IBr, initiated by x-ray ionization absorption at the Br K-edge. Using a combination of x-ray/ion coincidence measurements and Monte Carlo/molecular dynamics simulations, we track the charge distribution and the kinetic energy release (KER) of fragment ions with a total charge from 2+ to 8+. For both molecules, the simulated KER values show good agreement with experiment across different fragmentation channels. Our comparison reveals that substituting Br with the heavier I atom in IBr has a minimal impact on the inner-shell electronic decay process but significantly influences nuclear motion, leading to slower dissociation and thus a KER close to the Coulomb limit—an effect attributed to the atomic mass. These findings highlight the interplay between electronic and nuclear effects in molecular fragmentation, particularly in heavy-element species, and provide new insights into medical therapies, structural biology, and astrophysics.

Bhat, Nivedita [Argonne National Laboratory (ANL),↗
DOE OSTI2025

The track-length extension fitting algorithm for energy measurement of interacting particles in liquid argon TPCs and its performance with ProtoDUNE-SP data

This paper introduces a novel track-length extension fitting algorithm for measuring the kinetic energies of inelastically interacting particles in liquid argon time projection chambers (LArTPCs). The algorithm finds the most probable offset in track length for a track-like object by comparing the measured ionization density as a function of position with a theoretical prediction of the energy loss as a function of the energy, including models of electron recombination and detector response. The algorithm can be used to measure the energies of particles that interact before they stop, such as charged pions that are absorbed by argon nuclei. The algorithm's energy measurement resolutions and fractional biases are presented as functions of particle kinetic energy and number of track hits using samples of stopping secondary charged pions in data collected by the ProtoDUNE-SP detector, and also in a detailed simulation. Additional studies describe the impact of the dE/dx model on energy measurement performance. The method described in this paper to characterize the energy measurement performance can be repeated in any LArTPC experiment using stopping secondary charged pions.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Neutrons in Structural Biology: Challenges and Opportunities (Workshop Report)

Gaining a thorough understanding of biological systems requires building our knowledge about biological processes from the level of atoms and electrons, and up to whole organisms. Such comprehensive knowledge will allow for a predictive understanding of complex biological systems behavior. It will guide us in the design and development of novel therapeutics and vaccines to tackle existing health threats and to prepare for future pandemics, and it will provide information necessary to create new biomaterials and bio-inspired technologies through manipulation of biological macromolecules, their assemblies, single cells and even microorganisms. Reaching these goals will require a synergistic combination of multiple experimental techniques with molecular calculations and predictive simulations, and the design and development of new techniques and capabilities that bridge current knowledge and technology gaps. Neutron scattering provides unique information about the biomacromolecular structure and function and can play a major role in achieving these goals. A workshop was held to engage the scientific community in identifying pressing challenges in biochemistry, structural biology, enzymology and structure-guided drug design not solved with the current neutron scattering technologies or utilizing other structural biology techniques such as X-ray crystallography, NMR, and cryo-EM. The workshop brought together structural biology, biochemistry and computational experts, as well as early career researchers and students, creating a forum for discussing scientific advancement and collaboration. The workshop included a one-day satellite training workshop where graduate students and postdoctoral researchers were educated in the application of neutron crystallography and small-angle scattering in structural biology. Furthermore, the Instrument Scientific Advisory Board (ISAB) for the development of a macromolecular neutron diffractometer at ORNL’s Second Target Station was introduced at the workshop. The major outcome was that neutrons can provide atomic-level understanding of biomacromolecular structure, function and dynamics which is of paramount importance for addressing the identified challenges. Neutron crystallography, in particular, can resolve long-standing biochemical issues regarding enzyme function by delineating the underlying chemistry and can have a major impact on the design of small-molecule therapeutics, especially in combination with molecular computation (quantum chemistry and molecular dynamics simulations) and the emerging artificial intelligence (AI)-assisted drug design technologies. The unique properties of neutrons, including their high sensitivity to hydrogen and their non-destructive nature, make them ideal probes of biological matter. There is a palpable need in the scientific community to expand and enhance the impact of neutron sciences on biology. Neutron crystallography is the only structural biology method capable of determining positions of all hydrogen atoms in proteins, nucleic acids and their complexes at near-physiological temperatures and of unstable species at cryogenic temperatures. Moreover, neutron analysis is non-ionizing, non-destructive and does not perturb the structure or redox chemistry of active site metal centers and clusters in proteins, which can be invaluable for studying radiation-sensitive metalloprotein complexes. Further, neutron energies used in scattering applications are similar to atomic motions, permitting neutron spectroscopies to characterize the dynamics of biomacromolecules on the picosecond to microsecond timescales. The different sensitivities of neutrons to protium (H) and deuterium (D) isotopes of hydrogen allow enhanced visibility of specific parts of biological complexes through isotopic labeling. The impact of neutrons will be most powerful when neutron scattering is combined with complementary experimental techniques that use photons and electrons, and with high-performance computing. The interconnection and mutuality of the experimental and theoretical capabilities will drive discoveries in biological and health sciences to generate more complete picture of complex biological systems. The major limitation in the field of biological neutron crystallography has been signal-to-noise, demanding large samples that are difficult to produce for the majority of biomacromolecules and limiting the applicability of this technique in biological sciences. A neutron crystallography instrument at the Second Target Station will revolutionize biological science with neutrons by engaging a large scientific community of structural biologists, enabling successful neutron diffraction experiments from radically smaller biomacromolecular crystals, resolving unanswered biochemical questions, and meaningfully contributing to rational drug design. The meeting highlighted 10 grand challenges that will be addressed with this advanced capability over the next decade and beyond, and the recommendations required to help address them are given below.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Polarization consistent dielectric screening in polarizable continuum model calculations of solvation energies

A polarization consistent framework, where dielectric screening is affected consistently in polarizable continuum model (PCM) calculations, is employed for the study of solvation energies. The computational framework combines a screened range-separated-hybrid functional (SRSH) with PCM calculations, SRSH-PCM, where dielectric screening is imposed in both PCM self-consistent reaction field (SCRF) iterations and the electronic structure Hamiltonian. We begin by demonstrating the impact of modifying the Hamiltonian to include such dielectric screening in SCRF iterations by considering the solutions of electrostatically embedded Hartree–Fock (HF) exact exchange equations. Long-range screened HF-PCM calculations are shown to capture properly the linear dependence of gap energy of frontier orbitals on the inverse of the dielectric constant, whereas unscreened HF-PCM orbital energies are fallaciously semi-constant with respect to the dielectric constant and, therefore, inconsistent with the ionization energy gaps. Similar trends affect density functional theory (DFT) calculations that aim to achieve predictive quality. Importantly, the dielectric screened calculations are shown to significantly affect DFT- and HF PCM-based solvation energies, where screened solvation energies are smaller compared to the unscreened values. Importantly, SRSH-PCM, therefore, appears to reduce the tendency of DFT-PCM to overestimate solvation energies, where we find the effect to increase with the dielectric constant and the polarity of the molecular solute, trends that enhance the quality of DFT-PCM calculations of solvation energy. Understanding the relationship of dielectric screening in the Hamiltonian and DFT-PCM calculations can ultimately benefit on-going efforts for the design of predictive and parameter free descriptions of solvation energies.

Chemistry↗
DOE OSTI2022

Uncertainties in Atomic Data for Modeling Astrophysical Charge Exchange Plasmas

Relevant uncertainties of theoretical atomic data are vital to determining the accuracy of plasma diagnostics in a number of areas, including, in particular, the astrophysical study. We present a new calculation of the uncertainties on the present theoretical ion-impact charge exchange atomic data and X-ray spectra, based on a set of comparisons with the existing laboratory data obtained in historical merged-beam, cold-target recoil-ion momentum spectroscopy, and electron beam ion traps experiments. The average systematic uncertainties are found to be 35–88% on the total cross sections, and 57–75% on the characteristic line ratios. The model deviation increases as the collision energy decreases. The errors on total cross sections further induce a significant uncertainty to the calculation of ionization balance for low-temperature collisional plasmas. Substantial improvements of the atomic database and dedicated laboratory measurements are needed to obtain the current models, ready for the X-ray spectra from the next X-ray spectroscopic mission.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

TRANSLATE - a Monte Carlo simulation of electron transport in liquid argon

Here, the microphysics of electron and photon propagation in liquid argon is a key component of detector design and calibrations needed to construct and perform measurements within a wide range of particle physics experiments. As experiments grow in scale and complexity, and as the precision of their intended measurements increases, the development of tools to investigate important microphysics effects impacting such detectors becomes necessary. In this paper we present a new time-domain Monte Carlo simulation of electron transport in liquid argon. The simulation models the TRANSport in Liquid Argon of near-Thermal Electrons (TRANSLATE) with the aim of providing a multi-purpose software package for the study and optimization of detector environments, with a particular focus on ongoing and next generation liquid argon neutrino experiments utilizing the time projection chamber technology. TRANSLATE builds on previous work of Wojcik and Tachiya, amongst others, introducing additional processes, including ionization, thus modeling the full range of drift electron scattering interactions. The simulation is validated by benchmarking its performance with swarm parameters from data collected in experimental setups operating in gas and liquid.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Mitigation of nitrogen vacancy photoluminescence quenching from material integration for quantum sensing

The nitrogen-vacancy (NV) color center in diamond has demonstrated great promise in a wide range of quantum sensing. Recently, there have been a series of proposals and experiments using NV centers to detect spin noise of quantum materials near the diamond surface. This is a rich complex area of study with novel nano-magnetism and electronic behavior, that the NV center would be ideal for sensing. However, due to the electronic properties of the NV itself and its host material, getting high quality NV centers within nanometers of such systems is challenging. Band bending caused by space charges formed at the metal-semiconductor interface force the NV center into its insensitive charge states. Here, we investigate optimizing this interface by depositing thin metal films and thin insulating layers on a series of NV ensembles at different depths to characterize the impact of metal films on different ensemble depths. We find an improvement of coherence and dephasing times we attribute to ionization of other paramagnetic defects. The insulating layer of alumina between the metal and diamond provide improved photoluminescence and higher sensitivity in all modes of sensing as compared to direct contact with the metal, providing as much as a factor of 2 increase in sensitivity, decrease of integration time by a factor of 4, for NV T 1 relaxometry measurements.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Spectroscopic and Computational Studies of Spin-Orbit Coupling of Lanthanide Oxides

Spin-orbit (SO) coupling makes it possible for spin forbidden transitions or reactions within non-relativistic quantum theory feasible. Thus, quantification of such interactions has important implications in photophysics and chemical catalysis. This work aims to quantify SO interactions using lanthanide (Ln) oxides as target molecular systems. Through these systems, we examine the impact on the SO coupling by electron configurations and 4f orbital occupancies of Ln elements and sizes of the metal oxides. By examining these factors, we explore how SO coupling is affected by the number of Ln 4f electrons for a given size of molecules and if the Ln 4f orbitals remain atomic in nature in these small clusters. Ln oxides are produced in laser ablation molecular beams, identified with time-of-fight mass spectrometry, and characterized with laser spectroscopy and relativistic quantum chemical computations. Spectroscopic measurements include mass-analyzed threshold ionization (MATI), zero electron kinetic energy, and slow electron velocity-map imaging spectroscopies. Relativistic computations treat scalar relativistic corrections, electron correlations, and SO interactions. The main results are SO terms and energies of the neutral molecules and singly charged cations, ionization energies of the neutral species, metal-metal and metal-oxygen vibrational frequencies of the ions and, in some cases, neutrals as well, and charge effects on the bonding and structures.

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

Cohesion and excitations of diamond-structure silicon by quantum Monte Carlo: Benchmarks and control of systematic biases

We have carried out quantum Monte Carlo (QMC) calculations of silicon crystal focusing on the accuracy and systematic biases that affect the electronic structure characteristics. The results show that 64 and 216 atom supercells provide an excellent consistency for extrapolated energies per atom in the thermodynamic limit for ground, excited, and ionized states. We have calculated the ground state cohesion energy with both systematic and statistical errors below ≈ 0.05 eV. The ground state exhibits a fixed-node error of only 1.3(2)% of the correlation energy, suggesting an unusually high accuracy of the corresponding single-reference trial wave function. We obtain a very good agreement between optical and quasiparticle gaps that affirms the marginal impact of excitonic effects. Our most accurate results for band gaps differ from the experiments by about 0.2 eV. This difference is assigned to a combination of residual finite-size and fixed-node errors. In conclusion, we have estimated the crystal Fermi level referenced to vacuum that enabled us to calculate the edges of valence and conduction bands in agreement with experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗