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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 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Interligand Coupling Drives Fast Triplet Energy Transfer Routes in PbS/Tetracene Quantum Dot Hybrids

The binding of photoactive organic ligands to inorganic quantum dots (QDs) creates a versatile hybrid architecture that allows access to photophysical processes such as efficient triplet exciton generation with near-infrared radiation. Here we report the subnanosecond generation of a hybrid triplet state with mixed ligand-QD character by replacing native oleate ligands on small PbS QDs with 5,12-tetracenepropiolic acid, a bifunctional ligand with two carboxylic acids that tends to lie face-on with the QD surface at low loadings. The face-on geometry engenders a regime of strong electronic coupling that is evident in steady-state absorption and hastens triplet energy flow by several orders of magnitude compared with more typical tetracene-based ligands exhibiting weak coupling. We further determined via Fourier transform infrared (FTIR) and supported by density functional theory (DFT)-based geometry optimizations that high ligand loading causes a shift in QD-ligand mutual disposition toward an edge-on geometry that instigates the formation of intermolecular excited states characterized by triplet excimer-like features in photoluminescence and transient absorption. Our results demonstrate the ability to control strongly coupled ligand-QD systems toward ultrafast generation of photophysically relevant species such as triplets that are valuable for photon upconversion and catalysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Design improvements for a recirculating reactor: Enhanced temperature measurement and sample-isolated reactivity in steady-state kinetic studies

Building upon a previous recirculating reactor design [S.A. Tenney, K. Xie, J.R. Monnier, A. Rodriguez, R.P. Galhenage, S. Audrey, D.A. Chen, Rev. Sci. Instrum. 84, 104101 (2013)], we present significant improvements that address key limitations in steady-state kinetic measurements for heterogeneous catalysis. The enhanced reactor design features direct sample heating with a focused IR lamp and temperature measurement in direct contact with the sample, enabling more accurate temperature control and improved kinetic analysis. A critical advancement is the isolation of sample reactivity from reactor wall contributions, ensuring that only the sample contributes to measured reaction rates. This was a limitation in earlier designs where the entire reactor contributed to the observed reactivity. The system incorporates a bypass flow cell for direct comparison with powder catalysts under identical conditions using a standard plug-flow reactor configuration. We demonstrate these capabilities through CO oxidation experiments on Pt(111) single crystals and graphene-passivated Pt(111), highlighting the system's ability to differentiate catalytic activity in model systems and directly compare them with high surface area powder catalysts. This reactor is particularly suited for thin films and low surface area catalysts that are not effectively evaluated in traditional flow reactors, especially for samples with low numbers of active sites or slow reaction rates.

36 MATERIALS SCIENCE↗
NASA NTRS1994

Stability of the Martian atmosphere: Is heterogeneous catalysis essential?

A comprehensive homogeneous gas phase photochemical model is developed to study the problem of stability of the Martian atmosphere. The one-dimensional model extends from the ground up to 220 km, passing through the homopause at 125 km. The model thus couples the lower (neutral) atmosphere to the ionosphere above which provides significant downward flux of carbon monoxide and oxygen atoms. It is concluded on the basic of currently accepted values for globally and seasonally averaged water vapor abundance, dust opacity and the middle atmospheric eddy mixing coefficient, as well as the relevant laboratory data (particularly the temperature dependence of CO2 absorption cross section and the rate constant for CO+OH reaction), that the rate of re-formation of carbon dioxide exceeds its photolytic destruction rate by about 40%. Furthermore, it is found that this result is virtually independent of the choice of eddy mixing coefficient, unless its value in the middle atmosphere exceeds 10(exp 8) sq cm/sec or is far smaller than 10(exp 5)sq cm/sec, or the dust opacity, unless it exceeds unity, or the water vapor mixing ratio at the surface, unless it is far smaller (less than or = 1 ppm) or far greater (greater than or = 500 ppm) than the average value (approximately 150 ppm). Since none of these extremes represent globally and seasonally averaged conditions on Mars, we propose that the present model requires existence of a mechanism to throttle down the recycling rate of carbon dioxide on Mars. Therefore, it is suggested that a heterogeneous process which provides a sink to the species that participate in the recycling of CO2, i.e., H2O, H2O2, OH, CO or O, in particular, may be necessary to bring about the balance between the CO2 recycling rate and its photolytic destruction rate. Aerosols of dust or ice (pure or doped water or carbon dioxide ice present in the atmosphere of Mars) can provide the appropriate adsorption sites for the above heterogeneous process. Despite our conclusion that some heterogeneous process may be needed, it is important to recognize that one-dimensional models can only provide first-order results which, most likely, represent globally and seasonally averaged conditions. However, it is only after actual temporal, latitudinal and longitudinal variations of relevant atmospheric parameters are included in the model that one can determine fuly whether the problem of atmospheric stabiltiy still continues to persist and whether some heterogeneous process is required to correct it.

Atreya, Sushil K.↗
DOE OSTI2025

Stimulus-Responsive Modulation of Solvation Environments in Solid Catalysts

Liquid environments play a crucial role in the biological processes occurring in living organisms as well as in many human-made processes involving electrochemistry, photo-, and thermocatalysis. In the majority of these systems, aqueous phases are ubiquitous due to water’s natural abundance. Water molecules, however, can exert large changes in the chemical environment of catalytically active sites, altering the reaction rates, selectivity, and catalyst stability. These solvation effects induced by water molecules near catalytic sites can drastically change the energy landscape and unlock unique reaction pathways with far more favorable kinetics. In nature, living organisms couple these complex interactions with detection, communication, and actuation mechanisms to induce self-regulatory behavior, ensuring stability of the system and thus long-term durability. Extrapolating this behavior to heterogeneous catalysis is desirable because the resulting “smart materials” can potentially unlock new chemical conversion processes with higher atom efficiency, rates, and stability. The combination of polymer chemistry and heterogeneous catalysis has introduced versatile approaches for creating materials that can respond to cues in the reaction medium that alter the accessibility, intrinsic activity, and selectivity of the catalyst. To achieve this, one could combine stimulus-responsive polymers, which undergo a large volumetric phase transition in response to an external stimulus, with a solid catalyst. This chemo-mechanical response has been employed to create a variety of nanoreactor vessels with stimulus-responsive character that turn on- and off- depending on the reaction conditions. In this Account, we focus on the impact of these polymer coatings on the solvation environment around the active site and the implications of these effects on the reaction energy landscape, molecular arrangement of the solvent, electric fields at the catalyst–liquid interface, binding energy, and mobility of surface reaction intermediates. These seemingly subtle changes in solvent molecules induced by the presence of polymers can have a tremendous impact on the development of bioinspired heterogeneous catalysts, reliable chemical clocks, micro/nanoreactors, and robots. The large library of polymer chemistries offers a plethora of combinations of stimulus-responsive mechanisms (e.g., temperature, pH, light, magnetic field, solvent composition), providing the possibility of creating homeostatic catalysts à la carte.

catalysts↗
DOE OSTI2022

Stabilization of Ultrasmall Platinum Nanoparticles by Nitrogen-Doped Carbon: Implications for Catalysis and Electrocatalysis

Heterogeneous materials comprising platinum nanoparticles on carbon supports have numerous applications including fuel cell electrodes and heterogeneous catalysts. The effective application of these materials for fuel cells and catalysis will be greatly advanced by the ability to control the oxidation and sintering of the nanoparticles by modifications of the carbon support. One attempt of such control has been doping carbon supports with nitrogen. Here, in this work, a cutting-edge, high-sensitivity, in situ XRD instrument, which allows observation of ultrasmall Pt nanoparticles, has been combined with in situ XPS to provide unprecedented clarity in the characterization of supported Pt nanoparticles in oxidizing and high-temperature environments. On a nitrogen-doped carbon support derived from poly-phenylporphyrin, Pt nanoparticles show increased stability to oxidation and thermal sintering. The enhanced Pt–support interaction arising from the N dopant versus the N-free carbon is manifested by (1) decreased initial Pt particle sizes, (2) small particle size at higher surface densities, (3) increased resistance of Pt nanoparticles to oxidation, (4) increased electron binding energy of Pt0, and (5) increased resistance of Pt nanoparticles to sintering. It is expected that the higher stability of Pt on NC will be manifested in higher activity in fuel cells and high-temperature catalytic reactions.

catalytic reactions↗
DOE OSTI2020

Ion irradiation induced phase transformation in gold nanocrystalline films

Gold is a noble metal typically stable as a solid in a face-centered cubic (FCC) structure under ambient conditions; however, under particular circumstances aberrant allotropes have been synthesized. In this work, we document the phase transformation of 25 nm thick nanocrystalline (NC) free-standing gold thin-film via in situ ion irradiation studied using atomic-resolution transmission electron microscopy (TEM). Utilizing precession electron diffraction (PED) techniques, crystallographic orientation and the radiation-induced relative strains were measured and furthermore used to determine that a combination of surface and radiation-induced strains lead to an FCC to hexagonal close packed (HCP) crystallographic phase transformation upon a 10 dpa radiation dose of Au 4+ ions. Contrary to previous studies, HCP phase in nanostructures of gold was stabilized and did not transform back to FCC due to a combination of size effects and defects imparted by damage cascades.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Catalytic upcycling of high-density polyethylene via a processive mechanism

The overconsumption of single-use plastics is creating a global waste catastrophe, with widespread environmental, economic and health-related consequences. In this work we show that the benefits of processive enzyme-catalysed conversions of biomacromolecules can be leveraged to affect the selective hydrogenolysis of high-density polyethylene into a narrow distribution of diesel and lubricant-range alkanes using an ordered, mesoporous shell/active site/core catalyst architecture that incorporates catalytic platinum sites at the base of the mesopores. Solid-state nuclear magnetic resonance revealed that long hydrocarbon macromolecules readily move within the pores of this catalyst, with a subsequent escape being inhibited by polymer–surface interactions, a behaviour that resembles the binding and translocation of macromolecules in the catalytic cleft of processive enzymes. Accordingly, the hydrogenolysis of polyethylene with this catalyst proceeds processively to yield a reliable, narrow and tunable stream of alkane products.

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

Solvent Reorganization and Surface–Species Interactions Control Transfer Hydrogenation Rates in Sn-Beta Zeolites

Reorganization of confined alcohol networks reshapes adsorption and activation thermodynamics in Lewis acid zeolites, yet the roles of adsorbate sterics and non-H-bonding cosolvents remain unclear. Here, we investigate transfer hydrogenation of methyl- (mCH) and tert-butylcyclohexanone (tbCH) with 2-butanol over hydrophobic Sn-Beta. First-order rates per defect-open Sn site are 2–5× higher for mCH than tbCH, but converge in the zero-order regime (333–393 K), indicating that solvent reorganization entropically drives adsorption, while bond activation is insensitive to ketone structure. Reactions in toluene or acetonitrile (with 1 M 2-butanol) show that intraporous solvent organization governs transition-state stabilization: on hydrophobic Sn-Beta, apparent enthalpies and entropies rise with decreasing solvent polarity, whereas hydrophilic zeolites display nearly constant barriers across solvents. Liquid-phase IR spectroscopy corroborates these trends, showing that hydrophilic pores enforce 2-butanol-like solvation environments even in toluene. Together, these results reveal how zeolite pores regulate the intraporous solvent structure, whose reorganization upon adsorption reshapes the thermodynamic landscape of Lewis acid catalysis

Adsorption↗
DOE OSTI2025

Unraveling Adsorbate-Induced Structural Evolution of Iron Carbide Nanoparticles

Iron carbide (Fe x C y ) nanoparticles (NPs) are promising candidates for replacing platinum group metals in industrial applications, such as high-temperature Fischer–Tropsch synthesis. However, due to their amorphous nature, characterization of the active sites has been challenging experimentally and computationally. Here, using a combined density functional theory (DFT), neural network interatomic potential-assisted global optimization, and ensemble learning study, we evaluate dynamic surface changes associated with syngas (H and CO) interactions. For this purpose, we have developed a general procedure that we use to model an experimentally relevant 270-atom Fe 182 C 88 NP using the neural network-assisted stochastic surface walk global optimization algorithm (SSW-NN). Once generated, the Fe 182 C 88 NP active sites and particle morphology are thoroughly characterized before the effects of syngas adsorbate interactions are explored by using DFT and molecular dynamics simulations. Lastly, we explore correlations between geometric and electronic features of the active sites and the adsorption of H (H ads ), using a regularized random forest machine learning algorithm. In doing so, we identified the Fe–C coordination number and p orbital occupancy as the most important descriptors affecting H ads . Furthermore, using a combined ML and quantum chemistry approach, our work demonstrates a general and efficient procedure for generating and probing complex surface phenomena on binary nanoparticles.

Adsorption↗
DOE OSTI2022

Plasma-Catalyst Reactivity Control of Surface Nitrogen Species through Plasma-Temperature-Programmed Hydrogenation to Ammonia

Nonthermal plasma activation of N 2 can facilitate nitrogen adsorption on metal catalysts at low bulk temperatures and atmospheric pressure. Here, we apply a plasma-assisted temperature-programmed reaction (plasma-TPRxn) for ammonia (NH 3 ) synthesis using sequential exposure of a silica-supported metal catalyst to N 2 plasma followed by thermal hydrogen treatment while ramping the temperature to decouple the plasma activation of N 2 from surface catalyzed hydrogenation steps. This approach eliminates the effects from bulk plasma phase reactions, thereby allowing for direct interrogation of plasma activated nitrogen on the active metal surfaces. We confirm previously reported spectroscopic observations that show plasma-generated surface nitrogen can be converted to NH 3 through surface catalyzed pathways. Further, we demonstrate that the ammonia desorption peak temperature is sensitive to metal, with Pt desorbing NH 3 at the lowest temperature. Unsteady state microkinetic models of desorption kinetics as a function of initial N coverage and metal recover observed trends in NH 3 desorption temperatures and confirm that observed results reflect hydrogenation of plasma-induced N accommodation at each surface. In total, we show that the hydrogenation ability of the catalyst after plasma activation of N 2 is responsible for the reactivity trends observed in plasma-assisted NH 3 synthesis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Automated calculation and convergence of defect transport tensors

Defect diffusion is a key process in materials science and catalysis, but as migration mechanisms are often too complex to enumerate a priori, calculation of transport tensors typically have no measure of convergence and require significant end-user intervention. These two bottlenecks prevent high-throughput implementations essential to propagate model-form uncertainty from interatomic interactions to predictive simulations. In order to address these issues, we extend a massively parallel accelerated sampling scheme, autonomously controlled by Bayesian estimators of statewide sampling completeness, to build atomistic kinetic Monte Carlo models on a state-space irreducible under exchange and space group symmetries. Focusing on isolated defects, we derive analytic expressions for drift and diffusion coefficients, providing a convergence metric by calculating the Kullback–Leibler divergence across the ensemble of diffusion processes consistent with the sampling uncertainty. The autonomy and efficacy of the method is demonstrated on surface trimers in tungsten and Hexa-interstitials in magnesium oxide, both of which exhibit complex, correlated migration mechanisms.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Development, characterization, and modeling of a high-performance Ru/B2CA catalyst for ammonia synthesis

This paper documents the development and performance of a nano-phase Ru catalyst on a (BaO) x (CaO) y (Al 2 O 3 ) support. Extensive screening of the support’s ternary composition shows the best stoichiometry is (BaO) 2 (CaO)(Al 2 O 3 ), denoted B2CA. The paper first describes catalyst preparation and characterization. The paper reports a detailed 12-step reaction mechanism that represents ammonia synthesis over wide ranges of temperature, pressure, space velocity, and feed composition. Additionally, the mechanism is developed and validated using results of packed-bed experiments. The elementary reaction pathways consider surface adsorbates, including catalyst-poisoning behaviors. The rate expressions include important coverage-dependent activation barriers. Machine learning models assist interpretation of the catalyst-support interactions. The detailed chemistry is much more predictive than is possible with global representations (N 2 + 3H 2 ⇌ 2NH 3 ). The validated models can be applied to assist optimizing reactor design and operating conditions.

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

Adsorbate-induced adatom formation on Au-Cu bimetallic alloys and its possible consequences for CO 2 electroreduction

The adsorbate-induced formation of sub-nanometer clusters on transition-metal single crystals observed in previous high-pressure microscopic studies hinted at the in-situ formation of unique active sites even on large nanoparticle catalysts. We propose that the adatom formation energy can be used as an energetic descriptor for the initial step toward the adsorbate-induced metal-cluster formation process. This descriptor can be efficiently computed using density functional theory (DFT) calculations and applied for screening and identification of metal catalysts where this phenomenon may play an important role in generating active sites in-situ. As a proof of concept, here, we construct an adatom formation energy database for three Au x Cu y alloys (x:y = 3:1, 1:1, or 1:3) and eighteen adsorbates (H, C, N, O, F, S, Cl, Br, I, CH x , NH x (x = 1 – 3), CO, NO, and OH) commonly involved in catalytic reactions. The energetics of adatom formation were examined in all cases where the (111) terrace, (211) step-edge, and (874) kink were the sources of the adatom. We demonstrate that the presence of an adsorbate could alter not only the energetics for adatom formation but also the elemental nature of the preferred adatom being formed. Using our database, we identified promising systems which favor adsorbate-induced adatom formation under near-ambient conditions. Specifically, CO-induced adatom formation on all three Au-Cu alloy surfaces could occur under CO 2 electroreduction (CO 2 RR) conditions. This phenomenon offers a qualitative explanation for the experimentally observed CO 2 RR activity on Au-Cu alloy catalysts. As a result, our methodology offers an easily expandable and efficient approach for large-scale catalyst screening with regards to adatom/cluster formation under reaction conditions and provides insight into the possible nature of active sites on alloy catalysts from a novel perspective.

Active site↗
DOE OSTI2024

Dynamic Activation of Single-Atom Catalysts by Reaction Intermediates: Conversion of Formic Acid on Rh/Fe 3 O 4 (001)

The stability and activity of supported single-atom catalysts (SACs) represent critical yet opposing factors limiting our ability to explore and exploit their unique properties. Here, this study demonstrates the operation of a switchable catalyst that is activated in the presence of surface intermediates and reverts back to a stable but inactive form when the reaction is completed. We employ atomically defined Rh-Fe 3 O 4 (001) catalysts to demonstrate how structurally stable Rh, bound in surface octahedral Fe sites, gets destabilized to form highly active Rh adatoms and small clusters. Conversion of formic acid, leading initially to surface formate and hydroxyl species, is employed as a model reaction to probe the dynamics of such processes. We find that surface hydroxyl recombination to water through the Mars van Krevelen mechanism reduces Rh coordination, triggering its conversion to active Rh adatoms. Since such lattice oxygen exchange is observed in many acid-base and redox chemistries, the process can be broadly applicable to controlling the activation of the range of SACs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Deactivation of Cu-Exchanged Automotive-Emission NH 3 -SCR Catalysts Elucidated with Nanoscale Resolution Using Scanning Transmission X-ray Microscopy

To gain insight into the underlying mechanisms of catalyst durability for the selective catalytic reduction (SCR) of NO x with an ammonia reductant, we employed scanning transmission X-ray microscopy (STXM) to study Cu-exchanged zeolites with the CHA and MFI framework structures before and after simulated 135 000-mile aging. X-ray absorption near-edge structure (XANES) measurements were performed at the Al K- and Cu L-edges. The local environment of framework Al, the oxidation state of Cu, and geometric changes were analyzed, showing a multi-factor-induced catalytic deactivation. In Cu-exchanged MFI, a transformation of Cu II to Cu I and Cu x O y was observed. We also found a spatial correlation between extra-framework Al and deactivated Cu species near the surface of the zeolite as well as a weak positive correlation between the amount of CuI and tri-coordinated Al. By inspecting both Al and Cu in fresh and aged Cu-exchanged zeolites, we conclude that the importance of the preservation of isolated Cu II sites trumps that of Brønsted acid sites for NH 3 -SCR activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2004

Gas-phase production of single-walled carbon nanotubes from carbon monoxide: a review of the hipco process

The latest process for producing large quantities of single-walled carbon nanotubes (SWNTs) to emerge from the Rice University, dubbed HiPco, is living up to its promise. The current production rates approach 450 mg/h (or 10 g/day), and nanotubes typically have no more than 7 mol % of iron impurities. Second-generation HiPco apparatus can run continuously for 7-10 days at a time. In the HiPco process nanotubes grow in high-pressure, high-temperature flowing CO on catalytic clusters of iron. Catalyst is formed in situ by thermal decomposition of iron pentacarbonyl, which is delivered intact within a cold CO flow and then rapidly mixed with hot CO in the reaction zone. Upon heating, the Fe(CO)5 decomposes into atoms that condense into larger clusters. SWNTs nucleate and grow on these particles in the gas phase via CO disproportionation: CO + CO --> CO2 + C (SWNT), catalyzed by the Fe surface. The concentration of CO2 produced in this reaction is equal to that of carbon and can therefore serve as a useful real-time feedback parameter. It was used to study and optimize SWNT production as a function of temperature, pressure, and Fe(CO)5 concentration. The results of the parametric study are in agreement with current understanding of the nanotube formation mechanism.

Review↗
DOE OSTI2025

The Chemistry, Formation and Passivation of Solid-Electrolyte Interphase (SEI) from FSI- Breakdown at Li-metal Potential

LiFSI-based liquid electrolytes are promising for realizing high Coulombic efficiency (CE) and long cycle life of next-generation high-energy Li metal battery. Nevertheless, the fundamentals of both the chemistry and formation of solid-electrolyte interphase (SEI) in these electrolytes have remained elusive. Herein, we extensively combine electrochemistry and X-ray photoelectron spectroscopy (XPS) to illustrate the reaction pathways of electrolyte decomposition, especially FSI- breakdown, as well as the dissolution trend of various inorganic SEI components. The SEI-forming reactions at Cu/electrolyte interface manifest a potential (E) dependence, driven by direct electron-transfer (ET) and Li underpotential-deposition (Li UPD) at high and low E regions, respectively. By closely correlating the XPS data obtained with and without solvent washing, we demonstrate that not all the products derived from SEI reactions are incorporated into forming a passivating surface layer, with a notable portion dissolving into liquid electrolyte instead. Importantly, high-CE electrolyte dictated by the chemical identity of solvent, is found to exhibit minimized interfacial reactivity of SEI formation enabling more effective interphasial passivation, via preferential integration of passivating ingredients such as LiF. Overall, this work formulates a systematic understating of bridging the SEI chemistry, formation and passivation while identifying key characteristics of high-performance electrolyte for guiding future design.

Bao, Zhenan [SLAC National Accelerator Laboratory ↗
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↗