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DOE OSTI2026

Thermal exchange-correlation functionals: Capturing quantum electron behavior in warm, dense plasmas

We summarize and give perspective upon recent progress in developing non-empirical constraint-based thermal (i.e., free energy) exchange-correlation (XC) density functionals essential for accurate description of the quantum behavior of electrons in warm, dense plasmas. After delineating the critical role of ground-state functionals for zero-temperature, time-dependent DFT, we outline the underpinnings of local density approximation, generalized gradient approximation (GGA), and meta-GGA XC free-energy functionals. Two basic thermalization principles for upgrading ground-state XC functionals to successful thermal ones are emphasized. Then, we turn to a long-standing challenge, assessment of the accuracy of well-founded functionals. Unlike the ground state, there are a few exact results for large T and P. An exception is path integral Monte Carlo (PIMC) data for dense H/D and He plasmas. For those, we did ab initio molecular dynamics simulations under selected thermodynamic conditions employing five thermal XC functionals: two approximate thermal GGAs, fully thermal GGA, an approximate meta-GGA, and fully thermal meta-GGA. Comparisons with the PIMC data show that functionals thermalized by augmenting a non-thermal functional with a lower-level thermal contribution are inferior to functionals with thermal XC and spatial inhomogeneity effects taken into account at the same level of refinement. We believe this and similar evidence should be convincing to the high-energy density physics community of the necessity of use of proper thermal XC functionals in simulation studies of finite-temperature quantum effects in warm, dense plasmas.

Ab-initio molecular dynamics↗

DOE OSTI2025

Fully thermal meta-GGA exchange correlation free-energy density functional

The application of density functional theory to materials in the warm dense matter regime has motivated the development of exchange-correlation functionals which incorporate proper, explicit temperature dependence. Previous work has yielded fully-thermal exchange-correlation free energy functionals at the local density approximation (LDA) and generalized gradient approximation (GGA) levels of refinement. Recently an additive thermal correction scheme was utilized to construct a meta-GGA exchange-correlation (XC) functional in which thermal effects are treated at the GGA level. Here, the f TSCAN free-energy XC functional presented here includes thermal effects through the meta-GGA level in the context of the SCAN (strongly constrained and appropriately normed) ground-state functional. The f TSCAN functional provides generality while achieving similar performance to a thermal GGA functional at high temperatures, e.g. pressures within 1% of path integral Monte Carlo simulations of warm dense hydrogen, and a significant improvement over ground-state functionals. At low temperatures, f TSCAN demonstrates improvements in accuracy relative to lower-level and deorbitalized functionals, indicating that calculations using f TSCAN may be expected to perform well across experimentally relevant densities and pressures.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A compendium of human gene functions derived from evolutionary modelling

A comprehensive, computable representation of the functional repertoire of all macromolecules encoded within the human genome is a foundational resource for biology and biomedical research. The Gene Ontology Consortium has been working towards this goal by generating a structured body of information about gene functions, which now includes experimental findings reported in more than 175,000 publications for human genes and genes in experimentally tractable model organisms 1,2 . Here, we describe the results of a large, international effort to integrate all of these findings to create a representation of human gene functions that is as complete and accurate as possible. Specifically, we apply an expert-curated, explicit evolutionary modelling approach to all human protein-coding genes. This approach integrates available experimental information across families of related genes into models that reconstruct the gain and loss of functional characteristics over evolutionary time. The models and the resulting set of 68,667 integrated gene functions cover approximately 82% of human protein-coding genes. The functional repertoire reveals a marked preponderance of molecular regulatory functions, and the models provide insights into the evolutionary origins of human gene functions. We show that our set of descriptions of functions can improve the widely used genomic technique of Gene Ontology enrichment analysis. The experimental evidence for each functional characteristic is recorded, thereby enabling the scientific community to help review and improve the resource, which we have made publicly available.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Magnetic dipole γ-ray strength functions in the crossover from spherical to deformed neodymium isotopes

We calculate the magnetic dipole $\gamma$-ray strength functions in a chain of even-mass neodymium isotopes $^{144-152}$Nd in the framework of the configuration-interaction (CI) shell model. We infer the strength function by applying the maximum entropy method (MEM) to the exact imaginary-time response function calculated with the shell-model Monte Carlo (SMMC) method. The success of the MEM depends on the choice of a good strength function as a prior distribution. We investigate two choices for the prior strength function: the static path approximation (SPA) and the quasiparticle random-phase approximation (QRPA). We find that the QRPA is a better approximation at low temperatures (i.e., near the ground state), while the SPA is a better choice at finite temperatures. We identify a low-energy enhancement (LEE) in the MEM deexcitation $M1$ strength functions of the even-mass neodymium isotopes and compare with recent experimental results for the total deexcitation $\gamma$-ray strength functions. The LEE is already seen in the SPA strength function but not in the QRPA strength function, indicating the importance of large-amplitude static fluctuations around the mean field in reproducing the LEE. Our method is currently the only one which can reproduce LEE in heavy open-shell nuclei where conventional CI shell model calculations are prohibited. With the onset of deformation as number of neutrons increases along the chain of neodymium isotopes, we observe that some of the LEE strength transfers to a low-energy excitation, which we interpret as a finite-temperature ``scissors'' mode. Here, we also observe a finite-temperature spin-flip mode.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

A flexible class of priors for orthonormal matrices with basis function-specific structure

Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly factor the original data into the product of orthonormal basis functions and weights, where each basis function represents an independent feature of the data. However, the basis functions in these factorizations are typically computed using algorithmic methods that cannot quantify uncertainty or account for basis function correlation structure a priori. While there exist Bayesian methods that allow for a common correlation structure across basis functions, empirical examples motivate the need for basis function-specific dependence structure. We propose a prior distribution for orthonormal matrices that can explicitly model basis function-specific structure. The prior is used within a general probabilistic model for singular value decomposition to conduct posterior inference on the basis functions while accounting for measurement error and fixed effects. We discuss how the prior specification can be used for various scenarios and demonstrate favorable model properties through synthetic data examples. Finally, we apply our method to two-meter air temperature data from the Pacific Northwest, enhancing our understanding of the Earth system’s internal variability.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Chemical Functional Groups Regulate Ion Concentrations and pHs in Nanopores

Understanding ion behaviors in functionalized nanopores is essential to deciphering reactions in both natural and engineered systems, such as sediments, biological ion channels, and membranes. While many efforts have shown the modified ion behaviors in the functionalized nanopores, a direct measurement and analysis to show how chemical functional groups affect ion concentrations in nanopores are critically needed. In this work, we present a plasmonic nanosensor that can measure the local concentrations of protons, anions (phosphate, nitrate, sulfate, and arsenate), and cations (mercury, lead, and copper) in functionalized nanopores, and we compare their concentrations in nanopores with the corresponding bulk concentrations. Notably, chemical functional groups induced ion concentrations differently in nanopores. In pristine nanopores and methyl- and phenyl-functionalized nanopores, we discovered an unexpected concurrence of an enhanced anion concentration and a suppressed cation concentration. In addition, the nanopore pH is dependent on bulk solution compositions and can be lower by 2.5 units, even when the bulk solution is well-buffered. In contrast, for hydrophilic (amine, thiol, and carboxyl) nanopores, pH depended on the p K a of the functional groups, and the heavy metal concentrations depended on chemical interactions with the functional groups. Our findings provide a better understanding of water chemistry in nanopores and can help precisely control ions in nanopores to benefit the design of membrane-based desalination techniques, CO 2 storage, and porous catalysts.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

TRISO Fuel’s Safety Functions, Contributions to Reactor Safety, and Necessary Safety Limits

Safety functions are the actions, passive or active, that structures, systems, and components of nuclear facility that contribute to the safety of the workers, the public, or the environment. Well-defined safety functions are the foundation of a solid safety case for a reactor. For reactors that use TRISO-coated particles, the TRISO fuel plays an important part of the safety case because of its ability to contain radionuclides in the fuel itself. This ability enables the use of a functional containment strategy for the reactor where radionuclide retention is the primary safety function supported by the safety functions of controlling reactivity control and controlling heat rejection. This paper establishes at a deeper level the role that TRISO fuel plays in each of these safety functions and associated quality assurance and testing requirements for TRISO particle manufacturing to ensure these safety functions. Safety limits necessary to protect these safety functions include: operational limits, time at temperature limits, and fission gas release activity limits. In conclusion, this approach demonstrates the role that specific aspects of TRISO fuel play in protecting the safety of workers, the public, and the environment.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2025

Modest functional diversity decline and pronounced composition shifts of microbial communities in a mixed waste-contaminated aquifer

Background: Microbial taxonomic diversity declines with increased environmental stress. Yet, few studies have explored whether phylogenetic and functional diversities track taxonomic diversity along the stress gradient. Here, we investigated microbial communities within an aquifer in Oak Ridge, Tennessee, USA, which is characterized by a broad spectrum of stressors, including extremely high levels of nitrate, heavy metals like cadmium and chromium, radionuclides such as uranium, and extremely low pH (< 3). Results: Both taxonomic and phylogenetic α-diversities were reduced in the most impacted wells, while the decline in functional α-diversity was modest and statistically insignificant, indicating a more robust buffering capacity to environmental stress. Differences in functional gene composition (i.e., functional β-diversity) were pronounced in highly contaminated wells, while convergent functional gene composition was observed in uncontaminated wells. The relative abundances of most carbon degradation genes were decreased in contaminated wells, but genes associated with denitrification, adenylylsulfate reduction, and sulfite reduction were increased. Compared to taxonomic and phylogenetic compositions, environmental variables played a more significant role in shaping functional gene composition, suggesting that niche selection could be more closely related to microbial functionality than taxonomy. Conclusions: Overall, we demonstrated that despite a reduced taxonomic α-diversity, microbial communities under stress maintained functionality underpinned by environmental selection.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

How the choice of exchange–correlation functional affects DFT-based simulations of the hydrated electron

Hydrated electrons are anionic species that are formed when an excess electron is introduced into liquid water. Building an understanding of how hydrated electrons behave in solution has been a long-standing effort of simulation methods, of which density functional theory (DFT) has come to the fore in recent years. The ability of DFT to model the reactive chemistry of hydrated electrons is an attractive advantage over semi-classical methodologies; however, relatively few density functional approximations (DFAs) have been used for the hydrated electron simulations presented in the literature. Here, we simulate hydrated electron systems using a series of exchange–correlation (XC) functionals spanning Jacob’s ladder. We calculate a variety of experimental and other observables of the hydrated electron and compare the XC functional dependence for each quantity. We find that the formation of a stable localized hydrated electron is not necessarily limited to hybrid XC functionals and that some hybrid functionals produce delocalized hydrated electrons or electrons that react with the surrounding water at an unphysically fast rate. Here, we further characterize how different DFAs impact the solvent structure and predicted spectroscopy of the hydrated electron, considering several methods for calculating the hydrated electron’s absorption spectrum for the best comparison between structures generated using different density functionals. None of the dozen or so DFAs that we investigated are able to correctly predict the hydrated electron’s spectroscopy, vertical detachment energy, or molar solvation volume.

Ab-initio molecular dynamics↗

DOE OSTI2026

Rotational memory function of SPC/E water

Memory effects are essential for the dynamics of condensed materials and are responsible for non-exponential relaxation of correlation functions of dynamic variables through the memory function. Memory functions of dipole rotations for water have never been calculated directly from molecular dynamics simulations. We present here calculations of memory functions for single-dipole rotations and for the overall dipole moment of the sample for SPC/E water. The normalized memory functions for single-particle and collective dipole dynamics turn out to be nearly identical. This result validates theories of dielectric spectroscopy in terms of single-particle time correlation functions and the connection between the collective and single-particle relaxation times through the Kirkwood factor. The dielectric function in this formalism contains no new dynamic information that does not exist in the single-dipole correlation function. A short memory time, ≲1 fs, justifies the use of the mathematics of rotational diffusion to describe the dynamics of a single molecular dipole moment in bulk water. Here, an analytical equation for the rotational memory time is derived.

Asthagiri, Dilipkumar N. [Oak Ridge National Labor↗

DOE OSTI2025

Identifying microbial functional guilds performing cryptic organotrophic and lithotrophic redox cycles in anaerobic granular biofilms

Granular biofilms used in anaerobic digester systems contain diverse microbial populations that interact to hydrolyze organic matter and produce methane within controlled environments. Prior research investigated the feasibility of utilizing granular biofilms obtained from an anaerobic digester to remove nitrate without the addition of exogenous electron donors. These granules possessed a unique structure of alternating light and dark iron sulfide and pyrite rich layers that potentially served as both an electron source and sink, linking carbon, nitrogen, sulfur, and iron cycles. To characterize the functional roles of diverse microbial populations enriched within these layered biofilms, we analyzed metagenomes obtained from three different granules. Comparisons between the functional gene content of forty metagenome assembled genomes (MAGs) identified phylogenetically cohesive functional guilds. Each of these functional MAG clusters was assigned to specific steps in anaerobic digestion (hydrolysis, acidogenesis, acetogenesis, and methanogenesis) and anaerobic respiration (denitrification and sulfate reduction). Comparisons with metagenomes derived from a variety of natural and engineered ecosystems confirmed that the enriched denitrifying bacteria were similar to populations typically found in wetlands and biological nitrogen removal systems. Analysis of read alignments to individual genes within the forty MAGs identified conserved genomic features that were representative of the functions that distinguished functional guilds. Overall, this research illustrates the utility of functional based classification of microorganisms for characterizing ecosystem functions and highlights the potential application of engineered ecosystems to serve as experimental models for complex natural ecosystems.

Ecosystem engineering↗

DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Noncollinear ground states of solids with a source-free exchange correlation functional

In this paper, we expand upon the source-free (SF) exchange correlation (XC) functional developed by Sangeeta Sharma and coworkers to plane-wave density functional theory (DFT) based on the projector augmented wave (PAW) method. This constraint is implemented by the current authors within the VASP source code, using a fast Poisson solver that capitalizes on the parallel three-dimensional fast Fourier transforms (FFTs) implemented in VASP. Using this modified XC functional, we explore the improved convergence behavior that results from applying this constraint to the GGA-PBE+U+J functional. In the process, we compare the noncollinear magnetic ground state computed by each functional and their SF counterpart for a select number of magnetic materials in order to provide a metric for comparing with experimentally determined magnetic orderings. We observe significantly improved agreement with experimentally measured magnetic ground-state structures after applying the source-free constraint. Furthermore, we explore the importance of considering probability current densities in spin-polarized systems, even under no applied field. We analyze the XC torque as well, in order to provide theoretical and computational analyses of the net XC magnetic torque induced by the source-free constraint. Along these lines, we highlight the importance of properly considering the real-space integral of the source-free local magnetic XC field. Our analyses on probability currents, net torque, and constant terms draw additional links to the rich body of previous research on spin-current density functional theory (SCDFT), and pave the way for future extensions and corrections to the SF corrected XC functional.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Improved loss functions for machine-learned atomic potentials

Machine learning (ML) has become an invaluable tool across a wide array of domains in science as researchers find new ways to leverage its predictive power. This is especially true in chemistry, where ML is used to fit chemical properties or desirable attributes to the local structure of molecules and materials. In the pursuit of greater accuracy, it is relatively simple to increase the size or complexity of such models, although this often requires simultaneously seeking larger datasets in order to both fit and interpret the larger number of parameters. However, it is equally important to assess the quality and relative importance of the data and how these factors impact the training process. We, therefore, investigate the impact of using different loss functions for training neural network potentials (NNPs), as the loss function defines the error and parameter gradients used to train the NNP. In particular, we test the mean-squared error and Huber loss functions and, using insight from these functions, derive a new loss function based on the Asinh function, which yields significant improvement in the accuracy and generality of NNPs. We show that by discounting/minimizing errors and anomalies in the optimization process, both the Huber and Asinh loss functions improve the training of NNPs, leading to a final potential with a greater effective dimensionality.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Finite-range pairing in nuclear density functional theory

Pairing correlations are ubiquitous in low-energy states of atomic nuclei. To incorporate them within nuclear density functional theory, often used for global computations of nuclear properties, pairing functionals that generate nucleonic pair densities and pairing fields are introduced. Many pairing functionals currently used can be traced back to zero-range nucleon-nucleon interactions. Unfortunately, such functionals are plagued by deficiencies that become apparent in large model spaces that contain unbound single-particle (continuum) states. In particular, the underlying computational schemes diverge as the single-particle space increases, and the results depend on how marginally occupied states are incorporated. These problems become more pronounced for pairing functionals that contain gradient-density dependence, such as in the Fayans functional. To remedy this, finite-range pairing functionals are introduced. In this study, this is done by folding the pair density with Gaussians. Here, we show that a folding radius of about 1 fm offers the best compromise between quality and stability, and substantially reduces the pathological behavior in different numerical applications.

Nuclear density functional theory↗

DOE OSTI2025

Explainable Machine Learning for Functional Data

Black-box machine learning models are recognized as useful tools for prediction applications, but the algorithmic complexity of some models causes interpretation challenges. Explainability methods have been proposed to provide insight into these models, but there is little research focused on supervised modeling with functional data inputs. We argue that, especially in applications of high consequence, it is important to explicitly model the functional dependence in a black-box analysis to not obscure or misrepresent patterns in explanations. As such, we propose the V ariable importance E xplainable E lastic S hape A nalysis (VEESA) pipeline for training supervised machine learning models with functional inputs. The pipeline is an analysis process that includes the data preprocessing, modeling, and post-hoc explanations. The preprocessing is done using elastic functional principal components analysis, which accounts for vertical and horizontal variability in functional data and, ultimately, allows for explanations in the original data space that identify the important functional variability without bias due to correlated variables. Here, we demonstrate the pipeline on two high-consequence applications: explosives classification for national security and inkjet printer identification in forensic science. The applications exhibit the VEESA pipeline’s ability to provide an understanding of the characteristics of the functional data useful for prediction. Code for implementing the pipeline is available in the veesa R package (and supplemental python code).

Elastic Shape Analysis↗

DOE OSTI2026

FunDiff: diffusion models over function spaces for physics-informed generative modeling

Recent advances in generative modeling-particularly diffusion models and flow matching-have been widely used for synthesizing discrete data such as images and videos. However, adapting these models to physical applications remains challenging, as the quantities of interest are continuous functions governed by complex physical laws. To address this, we introduce FunDiff, an efficient and robust framework for generative modeling in function spaces. FunDiff combines a latent diffusion process with a function autoencoder architecture to handle input functions with varying discretizations, generates continuous functions that can be evaluated at arbitrary locations, and seamlessly incorporate physical priors. These priors are enforced through architectural constraints or physics-informed loss functions, ensuring that generated samples satisfy fundamental physical laws. We theoretically establish minimax optimality guarantees for density estimation in function spaces, demonstrating that diffusion-based estimators achieve optimal convergence rates under suitable regularity conditions. We further demonstrate the practical effectiveness of FunDiff across diverse applications in fluid dynamics and solid mechanics. Empirical results indicate that our method can generate physically consistent samples with high fidelity to the target distribution, and exhibit robustness to noisy and low-resolution data.

Wang, Sifan [Yale University, New Haven, CT (Unite↗

DOE OSTI2024

Exploring the exact limits of the real-time equation-of-motion coupled cluster cumulant Green’s functions

In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green’s function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green’s function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green’s function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green’s function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green’s function approach and other Green’s function approaches in the numerical exact limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗