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DOE OSTI2021

Analytic continuation of noisy data using Adams Bashforth residual neural network

We propose a data-driven learning framework for the analytic continuation problem in numerical quantum many-body physics. Designing an accurate and efficient framework for the analytic continuation of imaginary time using computational data is a grand challenge that has hindered meaningful links with experimental data. The standard Maximum Entropy (MaxEnt)-based method is limited by the quality of the computational data and the availability of prior information. Also, the MaxEnt is not able to solve the inversion problem under high level of noise in the data. Here we introduce a novel learning model for the analytic continuation problem using a Adams-Bashforth residual neural network (AB-ResNet). Additionally, the advantage of this deep learning network is that it is model independent and, therefore, does not require prior information concerning the quantity of interest given by the spectral function. More importantly, the ResNet-based model achieves higher accuracy than MaxEnt for data with higher level of noise. Finally, numerical examples show that the developed AB-ResNet is able to recover the spectral function with accuracy comparable to MaxEnt where the noise level is relatively small.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A Knowledge Graph Approach to Analyze Systems and Assets Health

Nuclear power plants collect large amounts of equipment reliability data elements that contain information on the statuses of component, assets, and systems. All these data elements precisely record asset and system performance and health throughout the lifecycle of those assets and systems. However, several challenges have proved to be roadblocks to this process. While some of these challenges are technical in nature (i.e., data are often distributed over several physical servers or databases), others are conceptual in nature (i.e., data elements come in different formats, numeric or textual), and measured values have different scales (e.g., vibration spectra and oil temperature). This paper directly focuses on the integration of numeric and textual data elements in order to assist plant system engineers in analyzing equipment reliability data. This task begins with preprocessing the data by extracting knowledge from textual data via natural language processing methods and quantifying system, asset, and component health based on numeric data. We then employed model-based system engineering (MBSE) models of systems and assets to identify their architecture and functional (i.e., cause and effect) relations. Data elements were then associated with a single MBSE graph element, based on their nature. This bonding of MBSE models and data elements constitutes a first-of-its-kind knowledge graph of a nuclear power plants system, with data elements being organized in a structured manner that enables system engineers to identify cause-effect trends in data elements and carry out appropriate actions in response.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Pore-Scale Study on the Positive Feedback Between Stress and Porosity Caused by Pressure Solution in Porous Media

Pressure solution is an important process in the evolution of sedimentary rocks, which provide storage space for most of our petroleum resources. It directly influences the generation, migration, and storage of petroleum fluids in subsurface sedimentary rocks. Here, in this paper, we develop a pore-scale, mechanochemical model to demonstrate a possible positive feedback between the local porosity and pore surface stress, in which a higher local porosity causes a higher local pore surface stress, thus enhancing pressure solution and consequently further increasing the local porosity. Pore surface stress represents stress on a solid grain adjacent to a pore. Specifically, the pore-scale, mechanochemical model directly simulates the stress distribution over solid and pore surfaces using a finite element model. The dissolution of solids at the solid-pore interfaces under a far-from-equilibrium condition is simulated using a first-order kinetics model that accounts for the local stress distribution. The updated pore geometry, caused by pore surface dissolution, is then used in the stress simulation in the next numerical iteration. Two types of porous media, the Oriskany sandstone and an artificial porous medium with spherical pores, were tested in the mechanochemical simulation. The positive stress-porosity feedback during pressure solution was observed in both samples. In addition, the model quantitatively illustrated the distribution of local mineral dissolution rates on all pore surfaces, as well as its relation to the effective mineral dissolution rate of the entire sample. Based on the comparison between the two porous media, the local mineral dissolution was regulated by pore space distribution, geometry, and coalescence during pressure solution. This work is the first that uses direct, pore-scale numerical simulation to demonstrate the positive stress-porosity feedback during pressure solution, which has the potential to advance the understanding of the mechanical-chemical (MC) coupling in many geological processes that are relevant to subsurface energy systems, such as the recovery of petroleum hydrocarbons and geothermal energy.

CT scanning↗

DOE OSTI2020

Effects of Turbulence and Temperature Fluctuations on Knock Development in an Ethanol/Air Mixture

The effects of turbulence on knock development and intensity for a thermally inhomogeneous stoichiometric ethanol/air mixture at a representative end-gas autoignition condition in internal combustion engines are investigated using direct numerical simulations with a skeletal reaction mechanism. Two- and three-dimensional simulations are performed by varying the most energetic length scale of temperature, $l_T$ , and its relative ratio with the most energetic length scale of turbulence, $l_T/l_e$ , together with two different levels of the turbulent velocity fluctuation, $u'$ . It is found that $l_T$ / $l_e$ and the ratio of ignition delay time to eddy-turnover time, $\tau _{ig}/\tau _t$ , are the key parameters that control the detonation development. An increase in either $l_T$ or $l_e$ enhances the detonation propensity by allowing a longer run-up distance for the detonation development. The characteristic length scale of the temperature field, $l_T$ , is significantly modified by high turbulence intensity achieved by a large $l_e$ and $u'$ . The intense turbulence mixing effectively distributes the initial temperature field to broader scales to support the developing detonation waves, thereby increasing the likelihood of the detonation formation. On the contrary, high turbulence intensity with a short mixing time scale, achieved by a small $l_e$ and a large $u'$ , reduces the super-knock intensity attributed to the finer broken-up structures of detonation waves. Either $\tau _{ig}/\tau _t$ less than unity or $l_e = l_T$ even with a large $u'$ is found to have no significant effect on super-knock mitigation. Finally, high turbulent intensity may induce high-pressure spikes comparable to the von Neumann spike. Overall, increased temperature and pressure by combustion heating, noticeably after the peak of heat release rate, significantly enhance the collision and interaction of multiple emerging autoignition fronts near the ending combustion process, resulting in localized high-pressure spikes.

42 ENGINEERING↗

DOE OSTI2022

Extension of the PINN diffusion model to k-eigenvalue problems

This paper extends our recent work on the Physics-Informed Neural Networks (PINN) approach for the fixed source diffusion models and applies it to the diffusion theory based k-eigenvalue problems. To make the PINN equitable for the eigenvalue problems, we introduce a novel integral regularization term to the loss function in the framework, and allow the direct inference of the principal eigenvalue and the associated eigenfunction. The regularization term enforces a pre-defined value on the integration of the model predictions, and this value can be directly related to a physical property of the system. We also introduce an additional learnable parameter to approximate the principal eigenvalue. As a proof of principle, we solve the one-group two-dimensional k-eigenvalue neutron diffusion equation in this work. We then provide two numerical examples to demonstrate the applicability of the PINN approach. In each example, we solve the k-eigenvalue diffusion equation in a multi-region configuration constrained with a set of Robin boundary conditions for generality. We use a FEM solution based on the power-iteration method to verify the results of the PINN solution. The results showed relative percentage error in the predicted eigenvalue of about 0.77% and about 1.2% for example 1 and example 2, respectively. The mean absolute error in the predicted flux for example 1 is ∼ 0.002 and for example 2 is ∼ 0.0024. These results indicate some preliminary successes of the PINN application to k-eigenvalue problems. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Solar cell contacts: quantifying the impact of interfacial layers on selectivity, recombination, charge transfer, and V oc

Interfacial layers (IFLs) are ubiquitous in solar cells, but their precise impact on carrier transfer rates and the relation of these rates to performance metrics and the concepts of selectivity and recombination is lacking. We report the use of a well-defined interdigitated back-contact (IBC) silicon solar cell to determine the precise role of such IFLs. We characterize the action of the common IFL spiro-OMeTAD by making it a third contact to the IBC cell. This architecture creates three solar cells within a single structure that, with numerical simulation, provide the exchange current densities (i.e., charge transfer rates) for electrons ( J 0n ) and holes ( J 0p ) and the quasi Fermi-level splitting in the absorber, which measures the balance of generation and recombination. Further, we describe the relation of V oc to contact recombination, the asymmetry in electron/hole collection rates at a single contact (contact selectivity), and the asymmetry in collection rates of the same carrier at separate contacts (carrier selectivity). Relative to bare gold, neat spiro-OMeTAD reduces J 0n and J 0p (their geometric mean ( J 0n J 0p ) 0.5 decreases by 10 4 ), decreasing contact recombination. Addition of the common dopant Li-TFSI and air increase J 0p / J 0n by 10 6 with little effect on ( J 0n J 0p ) 0.5 , increasing contact hole selectivity. The significant increase in V oc observed by introducing spiro-OMeTAD/Li-TFSI IFLs into the cells studied, however, is due to an increase in the carrier selectivity rather than the contact selectivity or recombination of the spiro-OMeTAD-modified contact. Operando measurements further show voltage-dependent changes in the J 0 s, demonstrating that spiro-OMeTAD contributes to hysteresis. Broader context : Solar cells operate by photogenerating excess charge carriers in an absorber material and, in competition with recombination, asymmetrically extracting them at so-called carrier-selective contacts, one that ideally collects only electrons and the other, only holes. Particularly in emerging photovoltaics such as perovskites, thin layers of organic semiconductors or related materials are introduced between the absorber and contact to improve power conversion efficiency. In terms of interfacial charge transfer, a prevailing view is that such interfacial layers improve performance by helping block the collection of the undesired carrier, considered a form of recombination. We use a novel platform to study the simultaneous impact of spiro-OMeTAD, a common interfacial layer, on the collection of electrons, the collection of holes, and on the recombination of electrons and holes. We quantitatively demonstrate that spiro-OMeTAD layers indeed passivate the contact toward recombination, but that larger improvements in the open-circuit voltage, a key cell metric, can come not only from this but also from increasing the asymmetry of the collection of electrons in the system. Further, operando measurements show transient changes in the properties of spiro-OMeTAD which suggest that it contributes to hysteresis phenomena commonly observed in perovskite and other solar cells.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Experimental and theoretical study of energy transfer in a chromophore triad: What makes modeling dynamics successful?

Simulation of electronic dynamics in realistically large molecular systems is a demanding task that has not yet achieved the same level of quantitative prediction already realized for its static counterpart. This is particularly true for processes occurring beyond the Born–Oppenheimer regime. Non-adiabatic molecular dynamics (NAMD) simulations suffer from two convoluted sources of error: numerical algorithms for dynamics and electronic structure calculations. While the former has gained increasing attention, particularly addressing the validity of ad hoc methodologies, the effect of the latter remains relatively unexplored. Indeed, the required accuracy for electronic structure calculations to reach quantitative agreement with experiment in dynamics may be even more strict than that required for static simulations. In this study, we address this issue by modeling the electronic energy transfer in a donor–acceptor–donor (D–A–D) molecular light harvesting system using fewest switches surface hopping NAMD simulations. In the studied system, time-resolved experimental measurements deliver complete information on spectra and energy transfer rates. Subsequent modeling shows that the calculated electronic transition energies are “sufficiently good” to reproduce experimental spectra but produce over an order of magnitude error in simulated dynamical rates. We further perform simulations using artificially shifted energy gaps to investigate the complex relationship between transition energies and modeled dynamics to understand factors affecting non-radiative relaxation and energy transfer rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Mesoscale shock structure in particulate composites

Multiscale experiments in heterogeneous materials and the knowledge of their physics under shock compression are limited. Here, this study examines the multiscale shock response of particulate composites comprised of soda-lime glass particles in a PMMA matrix using full-field high speed digital image correlation (DIC) for the first time. Normal plate impact experiments, and complementary numerical simulations, are conducted at stresses ranging from 1.1 - 3.1 GPa to elucidate the mesoscale mechanisms responsible for the distinct shock structure observed in particulate composites. The particle velocity from the macroscopic measurement at continuum scale shows a relatively smooth velocity profile, with shock thickness decreasing with an increase in shock stress, and the composite exhibits strain rate scaling as the second power of the shock stress. In contrast, the mesoscopic response was highly heterogeneous, which led to a rough shock front and the formation of a train of weak shocks traveling at different velocities. Additionally, the normal shock was seen to diffuse the momentum in the transverse direction, affecting the shock rise and the rounding-off observed at the continuum scale measurements. The numerical simulations indicate that the reflections at the interfaces, wave scattering, and interference of these reflected waves are the primary mechanisms for the observed rough shock fronts.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A Machine Learns to Predict the Stability of Highly Diverse Multi-planetary Systems

Machine learning has proven to be an invaluable tool for characterizing the stability of planets in simplified planetary systems. In this work, we investigate the performance of a machine learning classifier on tightlypacked systems containing a rich diversity of planets, from Earths to Jupiters. Using information derived from short numerical simulations about a planet’s early orbital evolution and its relationship with the most massive planets in the system, we train a random forest classifier to predict instability with a > 88 percent accuracy. Our classifier relies on relative planet masses and the standard deviation of eccentricity for much of its predictive power. Most misclassified planets lie along a multi-dimensional boundary between stable and unstable planets, indicating that their early orbital evolution is ambiguous. The major reason for misclassification in this work is timescale: because our classifier uses information from only the first 137 years of simulation data, it is blind to late time interactions that cause or prevent instability. Machine learning methods like those utilized in this work provide powerful tools to complement numerical simulations across a wide range of planetary architectures.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space

We propose a spectral method for the 1D-1V Vlasov–Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling α and shifting u of the velocity variable. Specifically, at each time instant an adaptivity criterion selects new values of α and u based on the numerical solution of the discrete Vlasov–Poisson system obtained at that time step. Once the new values of the Hermite parameters α and u are fixed, the Hermite expansion is updated and the discrete system is further evolved for the next time step. The procedure is applied iteratively over the desired temporal interval. The key aspects of the adaptive algorithm are: the map between approximation spaces associated with different values of the Hermite parameters that preserves total mass, momentum and energy; and the adaptivity criterion to update α and u based on physics considerations relating the Hermite parameters to the average velocity and temperature of each plasma species. For the discretization of the spatial coordinate, we rely on Fourier functions and use the implicit midpoint rule for time stepping. The resulting numerical method possesses intrinsically the property of fluid-kinetic coupling, where the low-order terms of the expansion are akin to the fluid moments of a macroscopic description of the plasma, while kinetic physics is retained by adding more spectral terms. Moreover, the scheme features conservation of total mass, momentum and energy associated in the discrete, for periodic boundary conditions. A set of numerical experiments confirms that the adaptive method outperforms the non-adaptive one in terms of accuracy and stability of the numerical solution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Relating flow resistance to equivalent roughness

Describing flow resistance using the physical properties of an underlying surface is a recalcitrant problem in overland flow models. If discharge measurements are available, an equivalent roughness (e.g., Manning’s n) can be calibrated to represent the effects of surface properties within the domain with a single numerical value. Alternatively, the flow resistance can be estimated from discharge and velocity measured at a point, typically a runoff plot outlet. However, such experimental estimates are often inconsistent with the equivalent roughness determined from calibration to discharge, even if both derive from the same dataset. For example, if Manning’s equation is used to parameterize flow resistance, the Manning’s n obtained by calibrating a model to discharge differs from the value of n calculated from measured flow and velocity at the hillslope outlet. Here, this discrepancy is resolved by deriving a correction factor relating experimentally-determined flow resistance to the equivalent roughness. The derived correction factor is tested for four commonly-used resistance formulations using 129 rainfall simulator experiments. The correction factor is necessary to reproduce measured velocities, and yields minor improvements in discharge prediction. Plain Language Summary: Accurate runoff prediction is needed for land and water management in dryland regions, where sporadic and limited rainfall necessitate efficient water use and drought mitigation strategies. The skill of runoff models is known to be hindered by out ability to estimate flow resistance, which is the quantity that describes how energy is lost from flowing water to the underlying surface. Typically, models represent flow resistance with an equivalent roughness, e.g., Manning’s n, that is adjusted until the model can reproduce available discharge observations at watershed scale. However, the flow resistance measured in plot-scale experiments (1–10 m) often exceeds equivalent roughness coefficients by a factor of 10. This means that the direct use of plot-scale experimental data to parameterize runoff models could cause errors in discharge and runoff velocity predictions. Here, we resolve these differences by deriving an analytic correction factor that relates flow resistance to the equivalent roughness required for models to reproduce experimental velocity and discharge data. This correction factor is tested using rainfall simulator data from 129 experiments performed in the US Southwest covering a wide range of precipitation intensities, soil textures and vegetation types. Use of the correction factor substantially improves model prediction of flow velocity, which is needed for reproducing the timing of flood events and the estimation of erosion.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Understanding aerosol–cloud interactions using a single-column model for a cold-air outbreak case during the ACTIVATE campaign

Marine boundary layer clouds play a critical role in Earth's energy balance. Their microphysical and radiative properties are highly impacted by ambient aerosols and dynamic forcings. In this study, we evaluate the representation of these clouds and related aerosol–cloud interaction processes in the single-column version of the E3SM climate model (SCM) against field measurements collected during the NASA ACTIVATE campaign over the western North Atlantic, as well as intercompare results with high-resolution process level models. We show that E3SM SCM reproduces the macrophysical properties of post-frontal boundary layer clouds in a cold-air outbreak (CAO) case well. However, it generates fewer but larger cloud droplets compared to aircraft measurements. Further sensitivity tests show that the underestimation of both aerosol number concentration and vertical velocity variance contributes to this bias. Aerosol–cloud interactions are examined by perturbing prescribed aerosol properties in E3SM SCM with fixed dynamics. Higher aerosol number concentration or hygroscopicity leads to more numerous but smaller cloud droplets, resulting in a stronger cooling via shortwave cloud forcing. This apparent Twomey effect is consistent with prior climate model studies. The cloud liquid water path shows a weakly positive relation with cloud droplet number concentration due to precipitation suppression. This weak aerosol effect on cloud macrophysics may be attributed to the dominant impact of strong dynamical forcing associated with the CAO. Our findings indicate that the SCM framework is a key tool to bridge the gap between climate models, process level models, and field observations to facilitate process level understanding.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Physically rigorous reduced-order flow models of fractured subsurface environments without explosive computational cost

Fractured media models comprise discontinuities of multiple lengths (e.g. fracture lengths and apertures, wellbore area) that fall into the relatively insignificant length scales spanning millimeter-scale fractures to centimeter-scale wellbores in comparison to the extensions of the field of interest, and challenge the conventional discretization methods imposing highly-fine meshing and formidably large numerical cost. By utilizing the recent developments in the finite element analysis of electromagnetics that allow to represent material properties on a hierarchical geometry, this project develops computational capabilities to model fluid flow, heat conduction, transport and induced polarization in large-scale geologic environments that possess geometrically-complex fractures and man-made infrastructures without explosive computational cost. The computational efficiency and robustness of this multi-physics modeling tool are demonstrated by considering various highly-realistic complex geologic environments that are common in many energy and national security related engineering problems.

42 ENGINEERING↗

DOE OSTI2020

Impact of isolation and fiducial cuts on qT and N-jettiness subtractions

Kinematic selection cuts and isolation requirements are a necessity in experimental measurements for identifying prompt leptons and photons that originate from the hard-interaction process of interest. We analyze how such cuts affect the application of the q T and N-jettiness subtraction methods for fixed-order calculations. We consider both fixed-cone and smooth-cone isolation methods. We find that kinematic selection and isolation cuts both induce parametrically enhanced power corrections with considerably slower convergence compared to the standard power corrections that are already present in inclusive cross sections without additional cuts. Using analytic arguments at next-to-leading order we derive their general scaling behavior as a function of the subtraction cutoff. We also study their numerical impact for the case of gluon-fusion Higgs production in the H → γγdecay mode and for pp → γγ direct diphoton production. We find that the relative enhancement of the additional cut-induced power corrections tends to be more severe forq T , where it can reach an order of magnitude or more, depending on the choice of parameters and subtraction cutoffs. We discuss how all such cuts can be incorporated without causing additional power corrections by implementing the subtractions differentially rather than through a global slicing method. We also highlight the close relation of this formulation of the subtractions to the projection-to-Born method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Disentangling observable dependence in SCET I and SCET II anomalous dimensions: angularities at two loops

The resummation of radiative corrections to collider jet observables using soft collinear effective theory is encoded in differential renormalization group equations (RGEs), with anomalous dimensions depending on the observable under consideration. This observable dependence arises from the ultraviolet (UV) singular structure of real phase space integrals in the effective field theory. We show that the observable dependence of anomalous dimensions in SCET I problems can be disentangled by introducing a suitable UV regulator in real radiation integrals. Resummation in the presence of the new regulator can be performed by solving a two-dimensional system of RGEs in the collinear and soft sectors, and resembles many features of resummation in SCET II theories by means of the rapidity renormalization group. We study the properties of SCET I with the additional regulator and explore the connection with the system of RGEs in SCET II theories, highlighting some universal patterns that can be exploited in perturbative calculations. As an application, we compute the two-loop soft and jet anomalous dimensions for a family of recoil-free angularities and give new analytic results. This allows us to study the relations between the SCET I and SCET II limits for these observables. We also discuss how the extra UV regulator can be exploited to calculate anomalous dimensions numerically, and the prospects for numerical resummation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Flow maldistribution in plate heat exchangers – Impact, analysis, and solutions

Plate heat exchangers are commonly used in various industrial applications, such as refrigeration, air conditioning, heat pumps, powerplants, and chemical industries. Plate heat exchangers are well known for their superior heat transfer performance, compactness, and low refrigerant charge. Despite offering several advantages, they suffer from flow maldistribution issues. The flow maldistribution can deteriorate both the heat transfer and pressure drop performance, ultimately resulting in a lower system efficiency where plate heat exchangers are deployed. The flow maldistribution issues become more pronounced when the heat exchanger size is relatively large and the number of plates is higher, limiting the deployment of plate heat exchangers in larger industrial systems. Consequently, analyzing and understanding the flow maldistribution behavior in plate heat exchangers and finding ways to mitigate flow maldistribution related issues become essential topics of interest. Further, this review aims to address the effect of flow maldistribution on plate heat exchanger characteristics. First, the experimental and numerical works on flow maldistribution under single-phase and two-phase conditions are detailed. Subsequently, the end-channel and end-plate effects are discussed. Then, the methods to mitigate flow maldistribution in plate heat exchangers are outlined. Finally, based on a thorough literature survey and industrial requirements, future research directions are recommended.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Scaling of magnetic dissipation and particle acceleration in ABC fields

Using particle-in-cell numerical simulations with electron–positron pair plasma, we study how the efficiencies of magnetic dissipation and particle acceleration scale with the initial coherence length λ 0 in relation to the system size L of the two-dimensional ‘Arnold–Beltrami–Childress’ (ABC) magnetic field configurations. Topological constraints on the distribution of magnetic helicity in two-dimensional systems, identified earlier in relativistic force-free simulations, that prevent the high-(L/λ 0 ) configurations from reaching the Taylor state, limit the magnetic dissipation efficiency to about ϵ diss ≃60% . Here we find that the peak growth time scale of the electric energy τ E,peak scales with the characteristic value of initial Alfvén velocity β A,ini like τ E,peak ∝(λ 0 /L)β$^{–3}_{A,ini}$ . The particle energy change is decomposed into non-thermal and thermal parts, with non-thermal energy gain dominant only for high initial magnetisation. The most robust description of the non-thermal high-energy part of the particle distribution is that the power-law index is a linear function of the initial magnetic energy fraction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗