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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A robust offering strategy for wind producers considering uncertainties of demand response and wind power

This paper proposes a risk-constrained decision-making approach for a wind power producer participating in the day-ahead market. In the developed model, a flexible demand response trading scheme between the wind power producer and different customers is employed. Through the proposed demand response mechanism, the wind power producer is able to trade demand response resource internally with different customers, and then trade energy externally with the market to increase the expected profit and the wind energy utilization. The uncertainties in the wind power and demand response are modeled by using the information gap decision theory approach from risk averse (robust) and risk-seeking (opportunistic) perspectives. The objective of the robust model is to maximize the robust level while satisfying the desired profit, whereas the opportunistic model aims to evaluate the possibility of achieving windfall profits with favorable uncertainties. The overall offering strategy problem is modeled as a bi-objective mixed integer nonlinear programming, which is linearized by proper techniques and solved efficiently by using the normal boundary intersection technique. In this work, simulation results show that utilizing demand response resource to mitigate wind power deviations can increase a wind power producer's profit and reduce potential risks. In addition, the results demonstrate that the proposed bi-objective optimization approach enables the wind power producer to select appropriate offering decisions with respect to uncertainties.

17 WIND ENERGY↗
DOE OSTI2024

Uncovering grain and subgrain microstructure at the scale of additive manufacturing melt tracks with a scalable cellular automaton solidification model

Metal additive manufacturing, characterized by rapid solidification, yields refined grains with a distinctive cellular subgrain microstructure that plays a pivotal role in determining material properties. Due to the significant computational expense demanded to simulate the required physics with submicron spatial resolution, their numerical simulations have been limited to proof-of-concept studies to either 2D or small subregions of a melt pool. In this study, an open-source, scalable, solidification code, muMatScale, based on the cellular automaton method, has been developed to predict the grain and the underlying subgrain microstructure over an entire melt pool. The model incorporates flexible parallelization schemes, utilizing MPI and OpenMP GPU Offloading, in addition to appropriate multi-physics specific to non-equilibrium rapid solidification in AM. The impact of nucleation parameters on grain microstructures was investigated with a focus on grain size variations and morphology transitions. With selected nucleation parameters, the simulation predicted the grain size, subgrain morphology, crystallographic orientation, and microsegregation aligned with experimental measurements. The model demonstrates that epitaxial grain growth is a dominant factor at the melt pool boundary, influencing grain size variation under different grain sizes in the build plate while maintaining consistent primary dendrite arm spacing under identical thermal conditions. Here, the highly efficient numerical model enables large-scale simulations with a spatial resolution of 100 nm or less, unveiling unprecedented insights into thermal and solutal diffusion driven grain growth, and the subgrains with microsegregation within grains in 3D across scales. muMatScale will enable the linking of submicron length-scale microstructure to part-level material behavior by investigating fundamental solidification problems at the intercellular scale in many-track and many-layer builds.

36 MATERIALS SCIENCE↗
DOE OSTI2023

DSPS: Differentiable stellar population synthesis

ABSTRACT Models of stellar population synthesis (SPS) are the fundamental tool that relates the physical properties of a galaxy to its spectral energy distribution (SED). In this paper, we present DSPS: a python package for SPS. All of the functionality in DSPS is implemented natively in the JAX library for automatic differentiation, and so our predictions for galaxy photometry are fully differentiable, and directly inherit the performance benefits of JAX, including portability onto GPUs. DSPS also implements several novel features, such as i) a flexible empirical model for stellar metallicity that incorporates correlations with stellar age, ii) support for the Diffstar model that provides a physically-motivated connection between the star formation history of a galaxy (SFH) and the mass assembly of its underlying dark matter halo. We detail a set of theoretical techniques for using autodiff to calculate gradients of predictions for galaxy SEDs with respect to SPS parameters that control a range of physical effects, including SFH, stellar metallicity, nebular emission, and dust attenuation. When forward modelling the colours of a synthetic galaxy population, we find that DSPS can provide a factor of 5 speed-up over standard SPS codes on a CPU, and a factor of 300-400 on a modern GPU. When coupled with gradient-based techniques for optimization and inference, DSPS makes it practical to conduct expansive likelihood analyses of simulation-based models of the galaxy–halo connection that fully forward model galaxy spectra and photometry.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Openpronghorn

OpenPronghorn is a simulation tool specifically tailored for modeling thermal-hydraulic phenomena in advanced nuclear reactors. It is built on the Multiphysics Object-Oriented Simulation Environment (MOOSE), an open-source platform that facilitates the development of high-performance scientific computing applications. OpenPronghorn solves the Navier-Stokes equations, which describe the conservation of mass, momentum, and energy in fluid flows, using the finite volume numerical method. The code supports a wide range of fluid flow conditions that are applicable to nuclear reactors, including incompressible and weakly compressible flows, as well as single-phase and multiphase flows. It is capable of modeling diverse flow regimes, including laminar and turbulent flows, using various turbulence models such as the standard k-epsilon models, the v2f model, and the mixing length model. For multiphase flows, OpenPronghorn employs a mixture a Eulerian modeling approach with mixture, drift-flux, and full Eulerian models, and includes open-sourced interfacial transfer correlations for drag, exchange, and heat transfer coming from the scientific literature. OpenPronghorn's modular design allows it to handle multiscale simulations, ranging from detailed Reynolds-Averaged Navier Stokes (RANS) simulations to coarse-mesh and lumped parameter models. This flexibility enables users to perform high-fidelity simulations of specific reactor components as well as system-level analyses of entire reactor circuits. The code can be coupled with other MOOSE-based tools using the MultiApp system, allowing for the transfer of coupling quantities such as mass flow rates, heat fluxes, and boundary conditions between different simulation scales. One of the main features of OpenPronghorn is the it includes built-in validation cases from the open-source scientific literature and supports the implementation of user-defined models and correlations through MOOSE's FunctorMaterial system. OpenPronghorn is designed to be computationally efficient, leveraging the SIMPLE projection method for large-scale problems, and can be run on high-performance computing systems to handle the extensive computational demands of detailed reactor simulations. Overall, OpenPronghorn is a versatile and robust tool that provides critical insights into the thermal-hydraulic behavior of advanced nuclear reactors, supporting the design, safety, and optimization of next-generation nuclear energy systems.

Retamales, Mauricio Eduardo Tano [Idaho National L↗
DOE OSTI2024

From Chills to Thrills: Revolutionizing Energy Efficiency and Load Flexibility in Supermarket Refrigeration

Open-vertical medium-temperature refrigerated display cases comprise nearly 50% of total case lineups in a typical supermarket, with more than 80% of their cooling load attributed to infiltration of warm and moist air from the surrounding space. The infiltration takes place across the air curtain system of the display case. While the air curtain acts as a thermal shield and as a cooling mechanism to maintain product temperature, it also entrains large amounts of heat and moisture from the adjacent space. Additionally, from food safety and quality standpoints, these fixtures are vulnerable to electric outages and traditionally cannot participate in load flexibility events. This paper describes key features of an innovative design of a self-contained, water-cooled, medium-temperature, open-vertical display case. The novel concept will eliminate the inefficient air curtain system and incorporate a hybrid radiant and low-airflow convective cooling design with a thermal-energy-storage-coupled heat exchanger integrated into the refrigeration circuit. The focus of this paper is on evaluating the thermal performance of the novel hybrid design in maintaining target product temperature. It presents thermal performance findings from thermo-fluid system modeling and robust state-of-the-art laboratory experiments used to validate those models. Load flexibility attributes from thermal energy storage are not discussed. A controlled-environment chamber at the National Renewable Energy Laboratory was leveraged to validate the thermal performance of the novel technology. Final results from bench-scale experiments indicate the proposed design maintained mean product temperatures within food safety guidelines.

commercial refrigeration↗
DOE OSTI2024

From Chills to Thrills: Revolutionizing Energy Efficiency and Load Flexibility in Supermarket Refrigeration: Preprint

Open-vertical medium-temperature refrigerated display cases comprise nearly 50% of total case lineups in a typical supermarket, with more than 80% of their cooling load attributed to infiltration of warm and moist air from the surrounding space. The infiltration takes place across the air curtain system of the display case. While the air curtain acts as a thermal shield and as a cooling mechanism to maintain product temperature, it also entrains large amounts of heat and moisture from the adjacent space. Additionally, from food safety and quality standpoints, these fixtures are vulnerable to electric outages and traditionally cannot participate in load flexibility events. This paper describes key features of an innovative design of a self-contained, water-cooled, medium-temperature, open-vertical display case. The novel concept will eliminate the inefficient air curtain system and incorporate a hybrid radiant and low-airflow convective cooling design with a thermal-energy-storage-coupled heat exchanger integrated into the refrigeration circuit. The focus of this paper is on evaluating the thermal performance of the novel hybrid design in maintaining target product temperature. It presents thermal performance findings from thermo-fluid system modeling and robust state-of-the-art laboratory experiments used to validate those models. Load flexibility attributes from thermal energy storage are not discussed. A controlled-environment chamber at the National Renewable Energy Laboratory was leveraged to validate the thermal performance of the novel technology. Final results from bench-scale experiments indicate the proposed design maintained mean product temperatures within food safety guidelines.

commercial refrigeration↗
DOE OSTI2024

Grid Interactive Micro-Distributed Refrigerated Display Case

Open-vertical medium-temperature refrigerated display cases comprise nearly 50% of total case lineups in a typical supermarket, with more than 80% of their cooling load attributed to infiltration of warm and moist air from the surrounding space. The infiltration takes place across the air curtain system of the display case. While the air curtain acts as a thermal shield and as a cooling mechanism to maintain product temperature, it also entrains large amounts of heat and moisture from the adjacent space. Additionally, from food safety and quality standpoints, these fixtures are vulnerable to electric outages and traditionally cannot participate in load flexibility events. This paper describes key features of an innovative design of a self-contained, water-cooled, medium-temperature, open-vertical display case. The novel concept will eliminate the inefficient air curtain system and incorporate a hybrid radiant and low-airflow convective cooling design with a thermal-energy-storage-coupled heat exchanger integrated into the refrigeration circuit. The focus of this paper is on evaluating the thermal performance of the novel hybrid design in maintaining target product temperature. It presents thermal performance findings from thermo-fluid system modeling and robust state-of-the-art laboratory experiments used to validate those models. Load flexibility attributes from thermal energy storage are not discussed. A controlled-environment chamber at the National Renewable Energy Laboratory was leveraged to validate the thermal performance of the novel technology. Final results from bench-scale experiments indicate the proposed design maintained mean product temperatures within food safety guidelines.

commercial refrigeration↗
DOE OSTI2020

Scale bridging damage model for quasi-brittle metals informed with crack evolution statistics

Computationally efficient methods for bridging length scales, from highly resolved micro/meso-scale models that can explicitly model crack growth, to macro-scale continuum models that are more suitable for modeling large parts, have been of interest to researchers for decades. In this work, an improved brittle damage model is presented for the simulation of dynamic fracture in continuum scale quasi-brittle metal components. Crack evolution statistics, including the number, length, and orientation of individual cracks, are extracted from high-fidelity, finite discrete element method (FDEM) simulations and used to generate effective material moduli that reflect the material’s damaged state over time. This strategy allows for the retention of small-scale physical behaviors such as crack growth and coalescence in continuum scale hydrodynamic simulations. However, the high-fidelity simulations required to generate the crack statistics are computationally expensive. Thus, steps were taken to produce a flexible constitutive model to reduce the number of costly high-fidelity simulations needed to produce accurate results. A new stress based degradation criterion is introduced for the degradation of individual material zones. This allows for the development of a heterogeneous damage distribution within the bulk material. Then a flow stress model is added to the hydrodynamic simulation to account for plasticity in quasi-brittle materials. As a result, the effective moduli model can be applied to a larger range of materials. The effective moduli constitutive model is used to simulate beryllium flyer plate experiments. The results from the continuum scale simulations using statistics from a single high-fidelity simulation are found to be in excellent agreement with numerical and experimental velocity interferometer data. The same set of crack statistics are used to extrapolate the results of a higher rate flyer plate case using the effective moduli model. In conclusion, the extension of this model to higher rate cases shows promise for further reducing the number of costly high-fidelity simulations needed to generate crack statistics.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Alginate–Amorphous Calcium Carbonate Hydrogels for Controlled Therapeutic Release

Alginate hydrogels are widely explored as biocompatible matrices for transdermal delivery of therapeutic compounds but burst release and mechanical stability remain persistent challenges in drug delivery systems. This experimental study investigated alginate–amorphous calcium carbonate (ACC) hydrogel composites designed to regulate release of model anti-inflammatory compound, ibuprofen. Hydrogels containing 1.6–2.0 wt% sodium alginate were crosslinked with CaCl₂ and combined with ACC through two incorporation pathways: (i) separate addition of ACC and ibuprofen or (ii) co-precipitation of ACC onto ibuprofen prior to hydrogel incorporation. Hydrogels without ACC served as Control. Biocomposite structure and properties were characterized and release profiles quantified using Korsmeyer–Peppas (KP) model.Burst release was curbed as crosslinking time increased, highlighting importance of network density in diffusion control. Co-precipitating ACC with ibuprofen prior to incorporating into the hydrogel suppressed burst release and sustained release for > ~72 h. Rheological measurements indicate ACC reinforces hydrogel network, increasing storage modulus while maintaining hydration and flexibility. KP model indicates release is diffusion-controlled, with deviations reflecting contributions from diffusion barriers and morphologic/structural changes near the ACC coated ibuprofen. ACC within alginate hydrogels provides a strategy for tuning drug release while preserving mechanical properties relevant to transdermal applications.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Small-scale clumping at recombination and the Hubble tension

Despite the success of the standard ΛCDM model of cosmology, recent data improvements have made tensions emerge between low- and high-redshift observables, most importantly in determinations of the Hubble constant H 0 and the (rescaled) clustering amplitude S 8 . The high-redshift data, from the cosmic microwave background (CMB), crucially relies on recombination physics for its interpretation. In this work, we study how small-scale baryon inhomogeneities (i.e., clumping) can affect recombination and consider whether they can relieve both the H 0 and S 8 tensions. Such small-scale clumping, which may be caused by primordial magnetic fields or baryon isocurvature below kpc scales, enhances the recombination rate even when averaged over larger scales, shifting recombination to earlier times. We introduce a flexible clumping model, parametrized via three spatial zones with free densities and volume fractions, and use it to study the impact of clumping on CMB observables. We find that increasing H 0 decreases both Ω m and S 8 , which alleviates the S 8 tension. On the other hand, the shift in Ω m is disfavored by the low-z baryon-acoustic-oscillations measurements. We find that the clumping parameters that can change the CMB sound horizon enough to explain the H 0 tension also alter the damping tail, so they are disfavored by current Planck 2018 data. We test how the CMB damping-tail information rules out changes to recombination by first removing ℓ > 1000 multipoles in Planck data, where we find that clumping could resolve the H 0 tension. Furthermore, we make predictions for future CMB experiments, as their improved damping-tail precision can better constrain departures from standard recombination. Both the Simons Observatory and CMB-S4 will provide decisive evidence for or against clumping as a resolution to the H 0 tension.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

3-D Radiological Data Acquisition, Visualization and Modeling - 20211

The U.S. Army Corps of Engineers (USACE) was tasked to investigate and remediate low activity radiological contamination from research and production of the nation's first nuclear weapons at the former DuPont Chambers Works Formerly Utilized Sites Remedial Action Program (FUSRAP) site (DuPont). The DuPont site had several buildings used for the Manhattan project that were demolished in the 1940's and 1950's apparently using heavy earthmoving equipment. Some of the contaminated rubble from the demolition appears to have been spread out by this equipment resulting in somewhat random scattering of radiologically contaminated soil and debris along with aqueous spills. Traditional investigative methods such as soil borings, test pits and 2-dimensional gamma walkovers were only partially successful in delineating the radiological contamination at the site. It was feared that even 'chasing' the contamination during remediation would miss contamination if the demolition resulted in discontinuous trails of radiologically contaminated soils. In evaluating the data generated over the interceding decades, the USACE determined that a better method to collect and process the remedial action radiological data was needed to enable the project team to optimize predictive planning and meet documentation expectations. The purpose of this paper is to provide an overview of the effort and progress to combine and organize radiological survey methods into a highly flexible sampling, modeling, and decision analysis approach that emphasizes the quality of decision-making during remediation. This innovative system blends multiple tools to develop a methodology that can extend MARRSIM [1] into the subsurface and provide tools that can be applied to other sites. (authors)

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

Practical choices for space-filling designs

Space-filling designs are now commonly used as a flexible model-free strategy for providing good coverage throughout an input space of interest for a variety of computer and physical experiment design scenarios. Some of the preliminary choices about how to frame the problem and which type of design to use can have a substantial impact on the success or failure of the experiment, and yet how to make these critical choices is often under-emphasized in the literature. In this paper, we explore several of the practical choices required by the experimenter and describe a sequence of steps to help create an ideal design that matches the goals and constraints of the experiment. These choices include the specification of the input space, the scaling of the variables, the degree of uniformity of the design points across the input space, and the space-filling characteristics. In addition, some new tools for defining the weights to implement non-uniform space-filling designs are provided. Finally, the methods are demonstrated with several illustrative examples and a real-world chemical engineering experiment for carbon capture.

42 ENGINEERING↗
DOE OSTI2024

Denoising diffusion probabilistic models for generative alloy design

Inverse material design is an extremely challenging optimization task made difficult by, in part, the highly nonlinear relationship linking performance with composition. Quantitative approaches have improved significantly owing to advances in high throughput experimentation and computational thermodynamics. However, existing physics-based tools are mostly forward models; input a chemistry and obtain a prediction. More recently the materials community has leveraged advances in the machine learning community to establish novel inverse design frameworks. Very recently denoising diffusion probabilistic models have been shown to be extremely powerful generators producing synthetic data of various modalities e.g. images, text, audio, tables, etc.. In this work a novel framework for alloy design and optimization is proposed leveraging these class of models. Five key generative tasks are demonstrated (1) unconditional generation (2) composition conditioned generation (3) property conditioned generation (4) multi-feedstock conditioned generation and (5) generative optimization. These methods were tested on three case studies: high entropy alloy design, superalloy binder jet additive manufacturing, and in-situ dual-feedstock wire-arc additive manufacturing. Results indicate that the established models are extremely flexible, expressive, and robust. The architecture’s flexibility and training procedure empower the model to learn complex intra-compositional and composition-property relationships. Furthermore, the probabilistic nature of these models makes them well suited for addressing solution non-uniqueness and tackling uncertainty quantification tasks. While the fidelity and quantity of the underlying training data is paramount, we envision that future alloy design frameworks will make extensive use of these kinds of machine learning models as “search” tools bolstering the utility of experimental and computational approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Typological representation of the offshore oceanographic environment along the Alaskan North Slope

Erosion and flooding impacts to Arctic coastal environments are intensifying with nearshore oceanographic conditions acting as a key environmental driver. Robust and comprehensive assessment of the nearshore oceanographic conditions require knowledge of the following boundary conditions: incident wave energy, water level, incident wind energy, ocean temperature and salinity, bathymetry, and shoreline orientation. The number of offshore oceanographic boundary conditions can be large, requiring a significant computational investment to reproduce nearshore conditions. This present study develops location-independent typologies to reduce the number of boundary conditions needed to assess nearshore oceanographic environments in both a Historical (2007–2019) and Future (2020–2040) timespan along the Alaskan North Slope. We used WAVEWATCH III® and Delft3D Flexible Mesh model output from six oceanographic sites located along a constant ~50 m bathymetric line spanning the Chukchi to Beaufort Seas. K-means clustering was applied to the energy-weighted joint-probability distribution of significant wave height (H s ) and peak period (T p ). Distributions of wave and wind direction, wind speed, and water level associated with location-independent centroids were assigned single values to describe a reduced order, typological rendition of offshore oceanographic conditions. Reanalysis data (e.g., ASRv2, ERA5, and GOFS) grounded the historical simulations while projected conditions were obtained from downscaled GFDL-CM3 forced under RCP8.5 conditions. Location-dependence for each site is established through the occurrence joint-probability distribution in the form of unique scaling factors representing the fraction of time that the typology would occupy over a representative year. As anticipated, these typologies show increasingly energetic ocean conditions in the future. They also enable computationally efficient simulation of the nearshore oceanographic environment along the North Slope of Alaska for better characterization of coastal processes (e.g., erosion, flooding, or sediment transport).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Water–Hydrocarbon Interactions in Anionic Pyrene Monohydrate

Interactions between water and polycyclic aromatic hydrocarbons are essential in many aspects of chemistry, from interstellar and atmospheric processes to interfacial hydrophobicity and wetting phenomena. Despite their growing importance, the intermolecular potentials of the water-hydrocarbon interactions are underdeveloped compared to water-water potentials, and there are similarly few experimental probes that are sensitive to the details of the water-hydrocarbon potential. We present a combined experimental and computational study of anionic pyrene monohydrate, one of the simplest water/hydrocarbon clusters. The action spectrum in the OH region of the mass-selected cluster ion provides a rigorous benchmark for intermolecular potentials and computational methodologies. We identify missing intermolecular interactions and shortcomings in conventional dynamics calculations by comparing experimental data to density functional theory and classical molecular dynamics calculations. Kinetic trapping is prevalent, even for one water molecule and one pyrene molecule, leading to slow equilibration in conventional molecular dynamics calculations, even on nanosecond timescales and at low temperatures (50 K). At constant energy, temperature fluctuations for the pair of molecules are substantial. Immersing the system in a bath of soft spheres and employing parallel tempering alleviates kinetic trapping and dampens temperature fluctuations, bringing the system closer to the thermodynamic limit. With such augmented sampling, a simple, flexible water model reproduces the linewidth and the asymmetric broadening of the symmetric OH stretching mode, which we assign to spectral diffusion. In the OH stretching region, dynamics calculations predict a more intense antisymmetric peak than experiments observe but do not predict the bimodal split symmetric peak that the experiments show. Furthermore, our work suggests that electronic polarization, missing in the empirical force field, is responsible for the first discrepancy and that quantum nuclear effects, captured neither in density functional theory nor in classical dynamics, may be responsible for the second.

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

An artificial intelligence accelerated virtual screening platform for drug discovery

Abstract Structure-based virtual screening is a key tool in early drug discovery, with growing interest in the screening of multi-billion chemical compound libraries. However, the success of virtual screening crucially depends on the accuracy of the binding pose and binding affinity predicted by computational docking. Here we develop a highly accurate structure-based virtual screen method, RosettaVS, for predicting docking poses and binding affinities. Our approach outperforms other state-of-the-art methods on a wide range of benchmarks, partially due to our ability to model receptor flexibility. We incorporate this into a new open-source artificial intelligence accelerated virtual screening platform for drug discovery. Using this platform, we screen multi-billion compound libraries against two unrelated targets, a ubiquitin ligase target KLHDC2 and the human voltage-gated sodium channel Na V 1.7. For both targets, we discover hit compounds, including seven hits (14% hit rate) to KLHDC2 and four hits (44% hit rate) to Na V 1.7, all with single digit micromolar binding affinities. Screening in both cases is completed in less than seven days. Finally, a high resolution X-ray crystallographic structure validates the predicted docking pose for the KLHDC2 ligand complex, demonstrating the effectiveness of our method in lead discovery.

Science & Technology - Other Topics↗
DOE OSTI2023

Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗