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DOE OSTI2026

Development of local hybrid density functionals to treat self-interaction error and many-electron effects

The goal of this project was to improve density functional theory (DFT) for systems where conventional semilocal approximations are limited by self-interaction error (SIE) and by near-degeneracy or strong many-electron effects. While DFT remains the only broadly practical first-principles framework for large-scale materials simulations, its predictive accuracy is often challenged in situations involving stretched bonds, charge transfer, transition-metal chemistry, magnetic couplings, band gaps, and correlated electronic states. This project addressed these limitations by developing physically grounded and numerically robust exchange–correlation functionals that retain the efficiency of modern DFT while extending its predictive scope.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Automated workflow for non-empirical Wannier-localized optimal tuning of range-separated hybrid functionals

Here, we introduce an automated workflow for generating non-empirical Wannier-localized optimally-tuned screened range-separated hybrid (WOT-SRSH) functionals. WOT-SRSH functionals have been shown to yield highly accurate fundamental band gaps, band structures, and optical spectra for bulk and 2D semiconductors and insulators. Our workflow automatically and efficiently determines the WOT-SRSH functional parameters for a given crystal structure and composition, approximately enforcing the correct screened long-range Coulomb interaction and an ionization potential ansatz. In contrast to previous manual tuning approaches, our tuning procedure relies on a new search algorithm that only requires a few hybrid functional calculations with minimal user input. We demonstrate our workflow on 23 previously studied semiconductors and insulators, reporting the same high level of accuracy. By automating the tuning process and improving its computational efficiency, the approach outlined here enables applications of the WOT-SRSH functional to compute spectroscopic and optoelectronic properties for a wide range of materials.

Gant, Stephen E. [University of California, Berkel↗

DOE OSTI2025

Deciphering the small-angle scattering of polydisperse hard spheres using deep learning

We introduce a deep learning approach for analyzing the scattering function of the polydisperse hard sphere system. We use a variational autoencoder-based neural network to learn the bidirectional mapping between the scattering function and the system parameters, including the volume fraction and polydispersity. Such that the trained model serves both as a generator that produces a scattering function from the system parameters and an inferrer that extracts system parameters from the scattering function. We first generate a scattering dataset by carrying out molecular dynamics simulations of the polydisperse hard spheres modeled by the truncated-shifted Lennard-Jones model, then analyze the scattering function dataset using singular value decomposition to confirm the feasibility of dimensional compression. Then, we split the dataset into training and testing sets and train our neural network on the training set only. Our generator model produces a scattering function with significantly higher accuracy compared to the traditional Percus–Yevick approximation and β correction, and the inferrer model can extract the volume fraction and polydispersity with much higher accuracy than traditional model functions.

Ding, Lijie [ORNL] (ORCID:0000000227454606)↗

DOE OSTI2025

Nonresonant two-photon x-ray absorption in Cu

We present a real-space Green's function theory and calculations of two-photon x-ray absorption (TPA). Our focus is on nonresonant 𝐾-shell TPA in metallic Cu, which has been observed experimentally at intense x-ray free electron laser (XFEL) sources. The theory is based on an independent particle Green's function treatment of the Kramers-Heisenberg equation and an approximation for the sum over nonresonant intermediate states in terms of a static quadrupole transition operator. XFEL effects are modeled by a partially depleted 𝑑 band. This approach is shown to give results for 𝐾-shell TPA in quantitative agreement with XFEL experiment and with a Bethe-Salpeter equation approach. Furthermore, we also briefly discuss many-body corrections and TPA sum rules.

Approximation methods for many-body systems↗

DOE OSTI2024

Time-dependent density-functional theory study on nonlocal electron stopping for inertial confinement fusion

Understanding laser–target coupling is of the utmost importance for achieving high performance in laser-direct-drive (LDD) inertial confinement fusion (ICF) experiments. Thus, accurate modeling of electron transport and deposition through ICF-relevant materials and conditions is necessary to quantify the total thermal conduction and ablation. The stopping range is a key transport quantity used in thermal conduction models; in this work, we review the overall role that the electron mean free path (MFP) plays in thermal conduction and hydrodynamic simulations. The currently used modified Lee–More model employs various physics approximations. We discuss a recent model that uses time-dependent density functional theory (TD-DFT) to eliminate these approximations in both the calculation of the electron stopping power and corresponding MFP in conduction zone polystyrene (CH) plasma. In general, the TD-DFT calculations showed a larger MFP (lower stopping power) than the standard modified Lee–More model. Using the TD-DFT results, an analytical model for the electron deposition range, λTD−DFT(ρ,T,K), was devised for CH plasmas between ρ=[0.05−1.05] g/cm3, kBT=[100−1000] eV. We implemented this model into LILAC, for simulations of a National Ignition Facility-scale LDD implosion and compared key physics quantities to ones obtained by simulations using the standard model. The implications of the obtained results and the path moving forward to calculate this same quantity in conduction-zone deuterium–tritium plasmas are further discussed, to hopefully close the understanding gap for laser target coupling in LDD-ICF simulations.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Many-body perturbation theory with hybrid density functional theory starting points accelerated by adaptively compressed exchange

We report on the use of the adaptively compressed exchange (ACE) operator to accelerate many-body perturbation theory (MBPT) calculations, including G 0 W 0 and the Bethe–Salpeter equation (BSE), for hybrid density functional theory starting points. We show that by approximating the exact exchange operator with the low-rank ACE operator, substantial computational savings can be achieved with systematically controllable errors in the quasiparticle energies computed with full-frequency G 0 W 0 and the optical absorption spectra and vertical excitation energies computed by solving the BSE within density matrix perturbation theory. Our implementation makes use of the ACE-accelerated electronic Hamiltonian to carry out both G 0 W 0 and BSE without explicitly computing empty states. We show the robustness of the approach and present the computational gains obtained on both the central processing unit and graphics processing unit nodes. In conclusion, our work will facilitate the exploration and evaluation of fine-tuned hybrid starting points aimed at enhancing the accuracy of MBPT calculations without involving computationally demanding self-consistency in Hedin’s equations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Filtered Rayleigh-Ritz is all you need

Recent work has shown that the (block) Lanczos algorithm can be used to extract approximate energy spectra and matrix elements from (matrices of) correlation functions in quantum field theory, and identified exact coincidences between Lanczos analysis methods and others. In this work, we note another coincidence: the Lanczos algorithm is equivalent to the well-known Rayleigh-Ritz method applied to Krylov subspaces. Rayleigh-Ritz provides optimal eigenvalue approximations within subspaces; we find that spurious-state filtering allows these optimality guarantees to be retained in the presence of statistical noise. We explore the relation between Lanczos and Prony's method, their block generalizations, generalized pencil of functions (GPOF), and methods based on the generalized eigenvalue problem (GEVP), and find they all fall into a larger "Prony-Ritz equivalence class", identified as all methods which solve a finite-dimensional spectrum exactly given sufficient correlation function (matrix) data. This equivalence allows simpler and more numerically stable implementations of (block) Lanczos analyses.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A Meta-Generalized Gradient Approximation for the Cavity-Dependent Exchange-Correlation Interaction in Strongly Coupled Light–Matter Systems

Strong light–matter coupling in optical cavities enables the manipulation of chemical and physical properties without altering molecular composition. Theoretical modeling of such phenomena requires exchange-correlation (XC) functionals that account for both electron–electron and electron–photon (ep) interactions within quantum electrodynamical density functional theory (QEDFT). In this work, we develop a meta-generalized gradient approximation (meta-GGA) specifically targeting the cavity-dependent XC interaction in strongly coupled light–matter systems. This novel approximation is built upon a new semilocal polarizability approximation, which draws from the jellium-with-a-gap model, and can be extended to a “global hybrid” variant that goes beyond the isotropic model from previous approximations. The polarizability model yields significantly improved dispersion coefficients and benchmark calculations with the cavity-dependent XC functional demonstrate improved agreement with QED Hartree–Fock (QED-HF) reference energies. Application to the regioselectivity of brominated nitrobenzene intermediates reveals the functional’s capacity to capture cavity-induced energetic shifts. In conclusion, our results advance the Jacob’s ladder of functionals for QEDFT and provide a practical tool for modeling polaritonic chemistry.

Approximation↗

DOE OSTI2025

A Bayesian Framework for Spectral Reprojection

Abstract Fourier partial sum approximations yield exponential accuracy for smooth and periodic functions, but produce the infamous Gibbs phenomenon for non-periodic ones. Spectral reprojection resolves the Gibbs phenomenon by projecting the Fourier partial sum onto a Gibbs complementary basis, often prescribed as the Gegenbauer polynomials. Noise in the Fourier data and the Runge phenomenon both degrade the quality of the Gegenbauer reconstruction solution, however. Motivated by its theoretical convergence properties, this paper proposes a new Bayesian framework for spectral reprojection, which allows a greater understanding of the impact of noise on the reprojection method from a statistical point of view. We are also able to improve the robustness with respect to the Gegenbauer polynomials parameters. Finally, the framework provides a mechanism to quantify the uncertainty of the solution estimate.

Li, Tongtong (ORCID:0000000276644764)↗

DOE OSTI2025

Surrogate-driven design optimization with uncertainty constraints in Monte Carlo simulations

In multi-objective design tasks, the computational cost increases rapidly when high-fidelity simulations are used to evaluate objective functions. Surrogate models help mitigate this cost by approximating the simulation output, simplifying the design process. However, under high uncertainty, surrogate models trained on noisy data can produce inaccurate predictions, as their performance depends heavily on the quality of training data. This study investigates the impact of data uncertainty on two multi-objective design problems modelled using Monte Carlo transport simulations: a neutron moderator and an ion-to-neutron converter. For each, a grid search was performed using five different tally uncertainty levels to generate training data for neural network surrogate models. These models were then optimized using NSGA-III. The recovered Pareto-fronts were analyzed across uncertainty levels: in the moderator problem, normalized hypervolume dropped from 0.886 at 1.0% uncertainty to 0.748 at 10% uncertainty, while in the converter problem it remained near 0.50 for all cases. Average simulation times were also compared to evaluate the trade-off between accuracy and computational cost. Results show that the influence of simulation uncertainty is strongly problem-dependent. In the neutron moderator case, higher uncertainties led to exaggerated objective sensitivities and distorted Pareto-fronts, reducing normalized hypervolume. In contrast, the ion-to-neutron converter task was less affected—low-fidelity simulations produced results similar to those from high-fidelity data. These findings suggest that a fixed-fidelity approach is not optimal. Surrogate models can recover the Pareto-front under noisy conditions, and multi-fidelity studies help identify suitable uncertainty levels for each problem to balance efficiency and accuracy.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2024

CO 2 storage site characterization using ensemble-based approaches with deep generative models

Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO 2 storage operations. In this paper, a deep generative model that can accurately capture complex subsurface structure is tested with an ensemble-based inversion method for accurate and accelerated characterization of CO 2 storage sites. We chose Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) for its realistic reservoir property representation and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for its robust data fitting and uncertainty quantification capability. WGAN-GP are trained to generate high-dimensional permeability fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface site characterization examples including Gaussian, channelized, and fractured reservoirs are used to evaluate the accuracy and computational efficiency of the proposed method and the main features of the unknown permeability fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method in several benchmark cases. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

42 ENGINEERING↗

DOE OSTI2025

Improving the Quasi‐Biennial Oscillation via a Surrogate‐Accelerated Multi‐Objective Optimization

Accurate simulation of the quasi-biennial oscillation (QBO) is challenging due to uncertainties in representing convectively generated gravity waves. We develop an end-to-end uncertainty quantification workflow that calibrates these gravity wave processes in E3SM for a realistic QBO. Central to our approach is a domain knowledge-informed, compressed representation of high-dimensional spatio-temporal wind fields. By employing a parsimonious statistical model that learns the fundamental frequency from complex observations, we extract interpretable and physically meaningful quantities capturing key attributes. Building on this, we train a probabilistic surrogate model that approximates the fundamental characteristics of the QBO as functions of critical physics parameters governing gravity wave generation. Leveraging the Karhunen–Loève decomposition, our surrogate efficiently represents these characteristics as a set of orthogonal features, capturing cross-correlations among multiple physics quantities evaluated at different pressure levels and enabling rapid surrogate-based inference at a fraction of the computational cost of full-scale simulations. Finally, we analyze the inverse problem using a multi-objective approach. Our study reveals a tension between amplitude and period that constrains the QBO representation, precluding a single optimal solution. To navigate this, we quantify the bi-criteria trade-off and generate a set of Pareto optimal parameter values that balance the conflicting objectives. This integrated workflow improves the fidelity of QBO simulations and offers a versatile template for uncertainty quantification in complex geophysical models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Shock Hugoniot calculations using on-the-fly machine learned force fields with ab initio accuracy

We present a framework for computing the shock Hugoniot using on-the-fly machine learned force field (MLFF) molecular dynamics simulations. In particular, we employ an MLFF model based on the kernel method and Bayesian linear regression to compute the free energy, atomic forces, and pressure, in conjunction with a linear regression model between the internal and free energies to compute the internal energy, with all training data generated from Kohn–Sham density functional theory (DFT). We verify the accuracy of the formalism by comparing the Hugoniot for carbon with recent Kohn–Sham DFT results in the literature. In so doing, we demonstrate that Kohn–Sham calculations for the Hugoniot can be accelerated by up to two orders of magnitude, while retaining ab initio accuracy. We apply this framework to calculate the Hugoniots of 14 materials in the FPEOS database, comprising 9 single elements and 5 compounds, between temperatures of 10 kK and 2 MK. We find good agreement with first principles results in the literature while providing tighter error bars. In addition, we confirm that the inter-element interaction in compounds decreases with temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Physics-informed neural networks for heterogeneous poroelastic media

This study presents a novel physics-informed neural network (PINN) framework for modeling poroelasticity in heterogeneous media with material interfaces. The approach introduces a composite neural network (CoNN) where separate neural networks predict displacement and pressure variables for each material. While sharing identical activation functions, these networks are independently trained for all other parameters. To address challenges posed by heterogeneous material interfaces, the CoNN is integrated with the Interface-PINNs (I-PINNs) framework (Sarma et al., Comput. Methods Appl. Mech. Eng. 429: 117135, 2024), allowing different activation functions across material interfaces. Further, this ensures accurate approximation of discontinuous solution fields and gradients. Performance and accuracy of this combined architecture were evaluated against the conventional PINNs approach, a single neural network (SNN) architecture, and the eXtended PINNs (XPINNs) framework through two one-dimensional benchmark examples with discontinuous material properties. The results show that the proposed CoNN with I-PINNs architecture achieves an RMSE that is two orders of magnitude better than the conventional PINNs approach and is at least 40 times faster than the SNN framework. Compared to XPINNs, the proposed method achieves an RMSE at least one order of magnitude better and is 40% faster.

42 ENGINEERING↗

DOE OSTI2026

Cooperative spin coupling in PrFeO3

A transition from crystal-field to spin wave excitations has been experimentally observed in PrFeO3 using inelastic neutron scattering. Theoretical modeling with density functional theory and the mean field random phase approximation successfully reproduces the experimental observations and allows extraction of the values for the various exchange interactions. The study reveals that the strong coupling between the two magnetic sublattices of Pr and Fe is the fundamental mechanism underlying the low-temperature Pr magnetism. This coupling, analogous to the Dicke cooperative interaction between atoms and photons, polarizes the Pr moments, enhances the Pr-Pr interactions, and contributes to the formation of a quasidoublet, leading to the transition from single-particle to collective excitations within the Pr sublattice. Furthermore, this coupling induces spin reorientation on the Fe sublattice. The manipulation of magnetic moments via spin waves is achievable through the coupling between different magnetic sublattices in a bulk material containing multiple magnetic ions.

Garlea, Vasile [ORNL] (ORCID:0000000253227271)↗

DOE OSTI2025

Towards excitations and dynamical quantities in correlated lattices with density matrix embedding theory

Density matrix embedding theory (DMET) provides a framework to describe ground-state expectation values in strongly correlated systems, but its extension to dynamical quantities is still an open problem. We show one route to obtaining excitations and dynamical spectral functions by using the techniques of DMET to approximate the matrix elements that arise in a single-mode inspired excitation ansatz. We demonstrate this approach in the one-dimensional Hubbard model, comparing the neutral excitations, single-particle density of states, charge, and spin dynamical structure factors to benchmarks from the Bethe ansatz and density matrix renormalization group. Finally, our work highlights the potential of these ideas in building computationally efficient approaches for dynamical quantities.

1-dimensional systems↗

DOE OSTI2026

Intermediate Bandgap (IB) Cu 3 VS x Se 4−x Nanocrystals as a New Class of Light Absorbing Semiconductors

A new family of highly uniform, cubic-shaped Cu 3 VS x Se 4−x (CVSSe; 0 ≤ x ≤ 4) nanocrystals based on earth-abundant materials with intermediate bandgaps (IB) in the visible range is reported, synthesized via a hot-injection method. The IB transitions and optical band gap of the novel CVSSe nanocrystals are investigated using ultraviolet-visible spectroscopy, revealing tunable band gaps that span the visible and near-infrared regimes. The composition-dependent relationships among the crystal phase, optical band gap, and photoluminescence properties of the novel IB semiconductors with progressive substitution of Se by S are examined in detail. High-resolution transmission electron microscopy and scanning electron microscopy characterization confirm the high crystallinity and uniform size (~19.7 nm × 17.2 nm for Cu 3 VS 4 ) of the cubic-shaped nanocrystals. Density functional theory (DFT) calculations based on virtual crystal approximation support the experimental findings, showing good agreement in lattice parameters and band gaps across the CVSSe series and lending confidence that the targeted phases and compositions have been successfully realized. A current conversion efficiency, i.e., incident photon-to-current efficiency, of 14.7% was achieved with the p-type IB semiconductor Cu 3 VS 4 . These novel p-type IB semiconductor nanocrystals hold promise for enabling thin film solar cells with efficiencies beyond the Shockley–Queisser limit by allowing sub-band-gap photon absorption through intermediate-band transitions, in addition to the conventional direct-band-gap transition.

Cu3VSxSe4−x↗