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At least 487 records · Page 27
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NASA NTRS2021

Reflection Modeling of the Black Hole Binary 4U 1630–47: The Disk Density and Returning Radiation

We present the analysis of X-ray observations of the black hole binary 4U 1630−47 using relativistic reflection spectroscopy. We use archival data from the Rossi X-ray Timing Explorer, Neil Gehrels Swift Observatory, and Nuclear Spectroscopic Telescope Array observatories, taken during different outbursts of the source between 1998 and 2015. Our modeling includes two relatively new advances in modern reflection codes: high-density disks, and returning thermal disk radiation. Accretion disks around stellar-mass black holes are expected to have densities well above the standard value assumed in traditional reflection models (i.e., n(e) ∼ 10^(15) per cu. cm). New high-density reflection models have important implications in the determination of disk truncation (i.e., the disk inner radius). This is because one must retain self-consistency in the irradiating flux and corresponding disk ionization state, which is a function of disk density and system geometry. We find that the disk density is n(e) ≥ 10^(20) per cu. cm across all spectral states. This density, combined with our constraints on the ionization state of the material, implies an irradiating flux impinging on the disk that is consistent with the expected theoretical estimates. Returning thermal disk radiation—the fraction of disk photons that bend back to the disk producing additional reflection components—is expected predominantly in the soft state. We show that returning radiation models indeed provide a better fit to the soft-state data, reinforcing previous results that show that in the soft state, the irradiating continuum may be blackbody emission from the disk itself.

Riley M. T. Connors↗
DOE OSTI2024

Sampling Size Optimization for Bioburden Density Estimation in Planetary Protection

Planetary protection (PP) is a discipline that focuses on minimizing the biological contamination of spacecraft to ensure compliance with international policy. Precise estimation of bioburden - the total number of microbes in or on spacecraft hardware – and the bioburden density are of utmost importance for PP. Such estimation is the way concordance with requirements is demonstrated, and it is critical for quantifying the potential risk of inadvertently contaminating other planetary bodies. Although a suite of molecular techniques have been used to thoroughly characterize and profile the microbiome of various cleanroom environments and spacecraft, the gold standard remains the physical enumeration of microbes via culturing of samples directly taken from spacecraft and associated surfaces. However, due to technical, budgetary, and programmatic constraints, only a manageable portion (around 10%) of the entire spacecraft surface is directly sampled with cotton swabs or wipes. To generate the bioburden current best estimate (CBE) for components not directly verifiable, the accepted approach is to apply a NASA-defined bioburden estimate based on the components’ manufacturing or assembly environment. This approach utilizes a prespecified bioburden density estimation that applies a maximum value across the total surface area of the specified component. For hardware components that underwent similar assembly processes, an implied bioburden is adopted for all components, based on a direct verification of a representative component within the same lot. Once all components have a CBE, the bioburden estimates are generated. In previous publication [ 1], we have shown that statistical risks quantifying the accuracy of the estimates for sampled, prespecified, and implied components can be derived and ranked. For mean squared error (MSE) function, the risks are available analytically and hence a cost function can be obtained to optimize the risks with respect to the sampling area and sampling cost. Since the sampling area and sampling cost are two complimentary variables, their sum will have a well-defined minimum. This paper presents the multivariate optimization of the integrated risk of an empirical Bayes estimator to determine the optimal sampling schedule for a given number of components. It is assumed that given a number of components, N, the bioburden density for each component can either be sampled, implied, or prespecified. The multivariate optimization searches through different options to sample, imply or prespecify the bioburden density for a component, and account for the component’s surface area and cost of sampling. The idea of the optimization is based on the observation that the statistical risk of using an estimator is a monotonically decreasing function of the sampled area. The larger the sampled area, the lower the risk of using the estimator as the estimator becomes more and more accurate as the sampling area increases. On the other hand, the cost of sampling is monotonically increasing as the sampled surface grows. This makes the risk and total cost of sampling complimentary variables which can be counterbalanced to achieve an optimal overall value with respect to the sampled surface. In this paper, the integrated risk has been used to quantify the accuracy of the estimator. This risk has been selected because it depends on neither the true value of the parameter nor on the collected data. The cost of each sample was also available to obtain the total cost of sampling of N components. The paper will present the results based on computer-simulated data as well as the data collected during the InSight mission. The computer-simulated data have N components with randomly generated total areas and each component assigned to one of the three categories according to the method of estimating of bioburden density: sampled, implied, or prespecified. The cost of sampling is also available. The cost of sampling is estimated based on a cost model provided by the planetary protection group at JPL. For this paper, the overall cost was assumed to be a linear function of exposure. The optimization process finds the allocation of the components to the three categories that minimizes the tradeoff between integrated risk and total cost. For the InSight data, a set of components is selected representing all three categories, and optimization is performed to determine if the performed allocation was optimal or if a better allocation could have been obtained. To the best of our knowledge, this work is the first attempt not only perform an accurate estimation of bioburden density but also do it in an optimal way.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Direct local parametrization of nuclear state densities using the back-shifted Bethe formula

Level densities are often parametrized using the back-shifted Bethe formula (BBF) for nuclei that possess experimental data for s-wave neutron resonance average spacings and a complete discrete level sequence at low excitation energies. However, these parametrizations require the additional modeling of the dependence of the spin-cutoff parameter on excitation energy. Here, in this work, we avoid the need to model the spin distribution of level densities by using the experimental data to parametrize directly the state densities, for which the BBF does not depend on the spin-cutoff parameter. This approach allows for a local parameterization of state densities that is independent of the spin-cutoff parameter. We provide these parameters in a tabulated form for applications in nuclear reaction calculations and for testing microscopic approaches to state densities.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

High-Sensitivity Low-Energy Ion Spectroscopy with Sub-Nanometer Depth Resolution Reveals Oxidation Resistance of MoS 2 Increases with Film Density and Shear-Induced Nanostructural Modifications of the Surface

For decades, density has been attributed as a critical aspect of the structure of sputter-deposited nanocrystalline molybdenum disulfide (MoS 2 ) coatings impacting oxidation resistance and wear resistance. Despite its importance, there are few examples in the literature that explicitly investigate the relationship between the density and oxidation behaviors of MoS 2 coatings. Aging and oxidation are primary considerations for the use of MoS 2 coatings in aerospace applications as they inevitably experience prolonged storage in water and oxygen-rich environments prior to use. Oxidation that is either limited to the first few nanometers or through the bulk of the coating can result in seizure due to high initial coefficients of friction or component failure from excessive wear. High-sensitivity low-energy ion spectroscopy (HS-LEIS) and Rutherford backscattering spectrometry (RBS) are both used to understand the extent of oxidation throughout the first ~10 nanometers of the surface of pure sputtered nanocrystalline MoS 2 coatings after high-temperature aging and how it is impacted by the density of coatings as measured by RBS. Results show that low-density coatings (ρ = 3.55 g/cm 3 ) exhibit a more columnar microstructure and voiding, which act as pathways for oxidative species to penetrate and interact with edge sites, causing severe surface and subsurface oxidation. Furthermore, HS-LEIS of surfaces sheared prior to oxidation reveals that the oxidation resistance of low-density MoS 2 coatings can be significantly improved by shear-induced reorientation of the surface microstructure to a basal orientation and elimination of pathways for oxygen into the bulk through compaction of surface and subsurface voids.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study

Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew–Burke–Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew–Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. Finally, the quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Assessing the source of error in the Thomas–Fermi–von Weizsäcker density functional

We investigate the source of error in the Thomas–Fermi–von Weizsäcker (TFW) density functional relative to Kohn–Sham density functional theory (DFT). In particular, through numerical studies on a range of materials, for a variety of crystal structures subject to strain and atomic displacements, we find that while the ground state electron density in TFW orbital-free DFT is close to the Kohn–Sham density, the corresponding energy deviates significantly from the Kohn–Sham value. Here, we show that these differences are a consequence of the poor representation of the linear response within the TFW approximation for the electronic kinetic energy, confirming conjectures in the literature. In so doing, we find that the energy computed from a non-self-consistent Kohn–Sham calculation using the TFW electronic ground state density is in very good agreement with that obtained from the fully self-consistent Kohn–Sham solution.

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

Highly accurate and constrained density functional obtained with differentiable programming

Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain a highly accurate neural network–based exchange and correlation (XC) functional of the electronic density. The functional is optimized using information on both energy and density while exact constraints are enforced through an appropriate neural network architecture. Here we evaluate our model against different families of XC approximations and show that at the meta-GGA level our functional exhibits unprecedented accuracy for both energy and density predictions. For nonempirical functionals, there is a strong linear correlation between energy and density errors. We use this correlation to define an XC functional quality metric that includes both energy and density errors, leading to an improved way to rank different approximations.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Spectral-partitioned Kohn-Sham density functional theory

Here we introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A Flexible, Redox-Active, Aqueous Electrolyte-Based Asymmetric Supercapacitor with High Energy Density Based on Keratin-Derived Renewable Carbon

This work exploits the advantage of asymmetric configuration over symmetric supercapacitor in designing high energy density flexible devices from two active electrode materials–keratin-based renewable-resource hierarchically porous carbon and hydrous ruthenium oxide (RuO 2 ). Here, the asymmetric device exhibits significantly high capacitance. Conventional estimation of energy storage parameters, however, cannot be applied for devices with a Faradaic energy storage contribution via redox charge transfer mechanism. Therefore, this work applies a precise measurement of pseudocapacitance contribution at various scan rates to correct the device data that reveals effective capacitance of 120 F g –1 with the energy density of 37 W h kg –1 at 776 W kg –1 . It also retains excellent rate capability, >74% at high current density 25 A g –1 . The charge storage activity and device stability can be further enhanced by introducing redox-active electrolytes that improve specific capacitance, but the rate capabilities deteriorate at high current densities. Further, the principle of asymmetric electrode design is applied to fabricate a bending-tolerant, flexible device by depositing active electrode material on wire-shaped current collector followed by coupling those separated with polyvinyl alcohol gel containing redox electrolyte; it yields 36.8 mF cm –1 specific capacitance at a 0.2 mA cm –1 current density.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Nutrients strengthen density dependence of per-capita growth and mortality rates in the soil bacterial community

Density dependence in an ecological community has been observed in many macro-organismal ecosystems and is hypothesized to maintain biodiversity but is poorly understood in microbial ecosystems. Here, in this study, we analyze data from an experiment using quantitative stable isotope probing (qSIP) to estimate per-capita growth and mortality rates of bacterial populations in soils from several ecosystems along an elevation gradient which were subject to nutrient addition of either carbon alone (glucose; C) or carbon with nitrogen (glucose + ammonium-sulfate; C + N). Across all ecosystems, we found that higher population densities, quantified by the abundance of genomes per gram of soil, had lower per-capita growth rates in C + N-amended soils. Similarly, bacterial mortality rates in C + N-amended soils increased at a significantly higher rate with increasing population size than mortality rates in control and C-amended soils. In contrast to the hypothesis that density dependence would promote or maintain diversity, we observed significantly lower bacterial diversity in soils with stronger negative density-dependent growth. Here, density dependence was significantly but weakly responsive to nutrients and was not associated with higher bacterial diversity.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Volumetric Density-Equalizing Reference Map with Applications

The density-equalizing map, a technique developed for cartogram creation, has been widely applied to data visualization but only for 2D applications. Here, we propose a novel method called the volumetric density-equalizing reference map (VDERM) for computing density-equalizing map for volumetric domains. Given a prescribed density distribution in a volumetric domain in $\mathbb{R}^3$, the proposed method continuously deforms the domain, with different volume elements enlarged or shrunk according to the density distribution. With the aid of the proposed method, medical and sociological data can be visualized via deformations of 3D objects. The method can also be applied to adaptive remeshing and shape modeling. Furthermore, by exploiting the time-dependent nature of the proposed method, applications to shape morphing can be easily achieved. Experimental results are presented to demonstrate the effectiveness of the proposed method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Improved thermoelectric performance of α- and β- Cu 2 Se through suppression of hole density using extrinsic copper vacancies

Modulating Cu + ion disorder in Cu 2 Se can enable control over the polymorphism and the carrier density leading to enhanced thermoelectric properties for both α- and β-Cu 2 Se. Here we report that the incorporation of Cr 3+ into the Cu 2 Se crystal lattice facilitates the stabilization of α-Cu 2 Se at 300 K leading to a large (~140%) reduction in the carrier density both below and above the phase transition. This is attributed to the reduction in the density of intrinsic copper interstitials (Cu$^{•}_{i}$) within the Cu (2-δ-λ) (Cr$^{··}_{Cu}$)λ(V$^{'}_{Cu}$)δ(Cu$^{π}_{i}$) δ-2λ (h • ) δ-2λ Se crystal lattice. Such optimization of the carrier density led to a large (63%) increase in the thermopower and a drastic (46%) reduction in the total thermal conductivity for both α- and β-Cu 2 Se matrices. Consequently, a significant enhancement of the thermoelectric performance is observed in the entire temperature range from 300 K to 773 K. This results in high average ZT values for both α-Cu 2 Se (ZT ave = 0.60) and β-Cu 2 Se (ZT ave = 0.97), which paves the way for both near room temperature and high temperatures applications. Furthermore, this work provides a new approach to optimize the thermoelectric performance of Cu 2 Se-based materials by leveraging the interaction between mobile intrinsic Cu$^{·}_{i}$ and extrinsic V$^{'}_{Cu}$ to suppress the hole density.

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

Interpretable, extensible linear and symbolic regression models for charge density prediction using a hierarchy of many-body correlation descriptors

Here, density functional theory (DFT) is routinely used to make electronic structure predictions for high-throughput screening of materials and molecules for technologically relevant areas, like the identification of better catalysts, electronic materials, and drug discovery. However, the DFT formalism is limited by (a) its poor (quadratic-to-quartic) scaling, and (b) the need to perform repeated eigenvalue computations of the electronic Hamiltonian as part of its self-consistent field (SCF) iteration procedure to obtain the converged ground state electron density, ρ (r). Approaches that directly predict ρ (r) of a structure with high accuracy can accelerate conventional SCF calculations and can also be used in linearly scaling methods such as orbital-free DFT. To this end, we present a procedure to predict the ground state electron density of molecular and periodic three-dimensional systems directly from the atomic structure with a particular emphasis on physical interpretability. In our framework, ρ (r) is modeled using many-body correlation descriptors that accurately capture the effects of local atomic arrangements in the neighborhood of a grid point. Our use of a linear regression scheme to fit to charge density data enables transparent analysis of the relative contributions of various types of local atomic correlations. By systematically including increasingly complex correlations, our model is shown to accurately predict ρ (r) for a variety of chemically and electronically diverse systems — amorphous Ge, Al(001) slab, crystalline Ga 2 O 3 , molecular benzene, and polyethylene. We then demonstrate a symbolic regression-based protocol to construct easily computable, interpretable features from lower-order correlations that significantly improves our electron density predictions with effectively no increase in the computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Pressure-driven density match nucleates metastable r8 phases from amorphous Si and Ge

The pressure–temperature phase behavior of covalent disordered solids such as amorphous silicon and germanium is complex. Questions remain on possible glass transitions, on polyamorphism via amorphous–amorphous transitions, on connections with liquid–liquid transitions, on structure-behavior relationships, and on their potential as precursor for novel methods for material discovery. Here we demonstrate experimentally the nucleation of a metastable, four-fold coordinated rhombohedral r8 phase from pure amorphous silicon and germanium upon room temperature compression at pressures below 10 GPa. Accompanying theory reveals a strong pressure-driven distortion of the bond angle transforming the starting tetrahedral low-density amorphous network to a distorted four-fold coordinated medium-density state. This state is of lower density than metallic high-density networks, resembles the crystalline r8 phase and initiates its nucleation. Our finding shows that polyamorphism is not the only possible transformation mode for these amorphous solids and that instead nucleation of interesting functional phases at potentially useful pressures is possible. Such novel access modes to metastable structures are critical for future exploitability and could be useful for other tetrahedral materials including carbon, where the related (bc8) post-diamond phase remains elusive. Our observed density match between an amorphous and a metastable crystalline phase clearly allows for a new phase transition pathway, while corresponding theory demonstrates how carefully validated atomistic simulations can guide prediction, discovery and synthesis of novel material structures.

Materials discovery↗
DOE OSTI2023

The need for ion-exchange membranes with high charge densities

Ion-exchange membranes (IEMs) are essential for controlling ion transport in electrochemical membrane-based technologies for water purification, energy generation, and energy storage. In general, IEMs must exhibit high ionic conductivity and selectivity, both of which are significantly influenced by the charge and water content of the hydrated membrane. In this perspective, we compiled the charge and water contents of approximately 1,000 IEMs reported over the past several decades to assess their range and variability, as well as to reveal gaps and set clear targets for future membrane design. We compared the charge and water content of negatively and positively charged membranes, as well as membranes developed for desalination and energy applications. The majority of IEMs, regardless of structure or intended application, have volumetric charge densities below 3 mol/L[membrane]. This narrow range of charge densities limits the performance of IEMs and contributes to the observed tradeoff between ion throughput and selectivity. It is critical to develop IEMs with higher charge densities to overcome this performance limitation. Further, we highlighted several design strategies that yielded IEMs with fixed charge densities higher than 3 mol/L[membrane]. These strategies provide valuable insights and can guide the design of next-generation IEMs with high charge densities.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Durability enhancement of all-solid-state electrochromic devices by adjusting the charge density ratio between electrochromic and counter electrode layers

Here, owing to an increase in global warming, smart-window devices based on charge-balanced electrochromic devices (ECDs), which exhibit high potential to increase the thermal efficiency of buildings, have gained prominence. However, studies on the fabrication and cycling stability of charge-balanced ECDs are scarce. In this study, WO 3 and NiO x films were deposited on indium-tin-oxide (ITO)-coated glass substrates by reactive direct-current magnetron sputtering, and the deposition time was varied to control the thickness and charge density of the thin films. Subsequently, the NiO x /ITO/glass and WO 3 /ITO/glass substrates were laminated with a Li-based polymeric electrolyte to fabricate all-solid-state ECDs comprising electrochromic (EC) and counter-electrode (CE) layers in charge-density ratios of 12.6, 6.4, 2.3, and 1.1. Changes in the electrochromic properties, device-layer microstructure, crystal structure, and elemental composition of the as-constructed ECDs before and after degradation were investigated to understand the influence of the charge-density ratio of the EC and CE layers on the long-term durability of ECDs. Increasing the charge-density ratio decreased the cycling stability of the device owing to changes in the microstructure and crystal structure of the NiO x layer in the microstructural deep-trap sites. Among all the ECDs, those comprising EC and CE layers with similar charge densities showed the most stable optical modulation and highest long-term durability. Finally, based on the aforementioned results, a degradation mechanism for charge-imbalanced all-solid-state ECDs was proposed. This study is expected to open new frontiers in designing optimal-performance electrochemical devices with a wide variety of potential applications.

14 SOLAR ENERGY↗
DOE OSTI2020

Comparing the performance of density functionals in describing the adsorption of atoms and small molecules on Ni(111)

Reaction networks calculated using density functional theory (DFT) play a crucial role in understanding and predicting heterogeneous catalyst performance. However, results obtained using different density functionals can vary significantly. Accordingly, it is important to assess the accuracy of available functionals in capturing adsorption energetics derived from single-crystal adsorption microcalorimetry experiments. Here, we evaluate how different density functionals describe the molecular and dissociative adsorption of CH 3 I, the adsorption of CH 3 , I, and H, and the dissociative adsorption of CH 4 on Ni(111). First, we identify energetically-preferred adsorbed states for each adsorbate at three surface coverages and calculate the corresponding enthalpies of adsorption at 160 K. Then, we compare the results to experimental measurements published in the literature. For each adsorption process we find at least one functional that is quantitatively accurate within experimental error, but no functional is accurate (within experimental error) for all adsorption processes studied. Even when assuming an additional DFT error of ±20 kJ/mol on top of the experimental error, only the PBE-D3 and RPBE-D3 functionals are accurate for all considered adsorption systems. Overall, these results indicate that quantitative agreement between density functional theory calculations and experimental measurements is both system- and functional-dependent. Importantly, single-crystal adsorption microcalorimetry experiments will continue to play an important role for benchmarking density functionals.

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

Accelerating Embedding Potential Optimization by Reconstructing the Pseudo-Valence Electron Density

Density functional embedding theory (DFET) enables use of electronic structure methods with higher accuracy than density functional theory in a local region, with applications thus far ranging from (photo/electro)catalysis to reactions in solution. DFET partitions a large collection of atoms into smaller groups that interact via a shared embedding (interaction) potential V emb , determined via functional optimization. The optimized effective potential (OEP) process used to optimize V emb is time-consuming and becomes a computational bottleneck due to sharp, oscillating features of V emb near nuclei. Here, similar to pseudopotential theory, by reconstructing electron densities used in the OEP process from smoother pseudo-valence-only (PVO) electron densities as proxies for total densities of the full system and subsystems, we can retain accuracy in the embedded electronic structure calculations while potentially reducing the overhead of V emb construction, within the projector augmented-wave (PAW) formalism. We explore three different chemical reactions as exemplars to test PVO–DFET, namely, H 2 dissociative adsorption on a Cu(111) surface, H 2 O adsorption on a Pt(111) surface, and aqueous [Ca 2+ –SO 4 2– ] ion-pair formation. The PVO approximation works well for all three systems with minimal loss of accuracy (∼10–70 meV error relative to the original exact-derivative (ED) approach) while accelerating V emb generation for the Cu and Pt systems respectively by 20× and 5×. Given proper numerical convergence parameters, the spatial distributions of differences between PVO- and ED-based V emb outside the core regions are small, explaining the exceptional agreement between the two approaches. Finally, we anticipate that this more efficient PVO–DFET approximation will be useful whenever computation of V emb is much more expensive than subsequent embedded high-level electron correlation calculations.

approximation↗