Results for “Computer implementation” — Page 27

DOE OSTI2026

Magnus method for electronic structure calculations at extreme conditions

We present the application of Magnus based methods to the solution of first order coupled ordinary differential equations in High Energy Density (HED) physics applications. Our focus is on the application to quantum mechanical methods, specifically on the solution of the radial Dirac equation for real and complex energies. HED applications require accurate solutions across a wide range of spatial and energy domains, including regimes where the solutions exhibit pronounced oscillatory behavior. Such cases pose significant computational challenges. We demonstrate that Magnus-based integrators can efficiently and accurately address these challenges. We discuss the implementation of the Magnus method for the solution of the radial Dirac equation, including practical considerations such as the evaluation of matrix exponentials, numerical integration, error estimation, and adaptive step size control. We also discuss the application of these methods to complex energy Green’s function techniques and the efficient approximation of integrals of the solutions relevant to HED electronic structure calculations. Here, we demonstrate the accuracy and robustness of the resulting method in applications to the free-particle case, for which analytic solutions are available for comparison, as well as the challenging case of gold at HED conditions.

general physics↗

DOE OSTI2025

Solving k –SAT problems with generalized quantum measurement

We generalize the projection–based quantum measurement–driven k –SAT algorithm of Benjamin, Zhao, and Fitzsimons to arbitrary strength quantum measurements, including the limit of continuous monitoring. In doing so, we clarify that this algorithm is a particular case of the measurement–driven quantum control strategy elsewhere referred to as “Zeno dragging”. We argue that the algorithm is most efficient with finite time and measurement resources in the continuum limit, where measurements have an infinitesimal strength and duration. Moreover, for solvable k -SAT problems, the dynamics generated by the algorithm converge deterministically towards target dynamics in the long–time (Zeno) limit, implying that the algorithm can successfully operate autonomously via Lindblad dissipation, without detection. We subsequently study both the conditional and unconditional dynamics of the algorithm implemented via generalized measurements, quantifying the advantages of detection for heralding errors. These strategies are investigated first in a computationally–trivial 2-qubit 2-SAT problem to build intuition, and then we consider the scaling of the algorithm on 3-SAT problems encoded with 4–10 qubits. We numerically investigate the scaling of 3-SAT with respect to algorithmic runtime and find that the optimized time to solution scales with qubit number n as λ n , where λ is slightly larger than $\sqrt{2}$ for unconditional dynamics and less than $\sqrt{2}$ for conditional dynamics. We assess the implications for using this analog measurement–driven approach to quantum computing in practice.

quantum information↗

DOE OSTI2025

Transient Modeling and Simulation of a Generic Stable Salt Reactor

A SAM system-level model of a generic stable salt reactor has been developed to investigate thermal-hydraulic behavior and safety performance under steady and transient conditions. The model integrates information generated from a reactor physics analysis using PROTEUS and PERSENT, and a computation fluid dynamics (CFD) analysis using STAR-CCM+. A loose, iterative coupling scheme between PROTEUS and SAM is implemented to calculate the equilibrium power and temperature distributions in the steady-state critical core condition. The converged steady-state model is then used in PERSENT to calculate the four reactivity feedback temperature coefficients (Doppler, fuel density, coolant density, and core radial expansion) and kinetic parameters that are needed in SAM to model the temperature feedback effects in transient simulations. Within the fully enclosed liquid fuel pins, natural convection is the dominant heat transfer mechanism. The STAR-CCM+ model of the fuel pin considers conjugate heat transfer from the liquid fuel salt to the pin cladding and external reactor coolant. The CFD results of the axial and radial temperature profiles are used to empirically determine an effective fuel salt thermal conductivity in the SAM fuel pin model so that the temperatures predicted by the SAM model match as closely as possible the CFD results. In the central region of the fuel pin, the effective thermal conductivity is as high as similar to 60 times the physical fuel salt thermal conductivity. The whole-plant SAM model is then used to simulate an unprotected station blackout transient. The results of this simulation showed that the large negative fuel axial expansion reactivity feedback reduces fission power to similar to 2.4% nominal power. The core is cooled by natural circulation, which removes heat in the core to the emergency heat removal system, and ultimately, to the ambient. However, peak fuel salt and cladding temperatures can potentially reach as high as 1500 K, albeit briefly, if the shutdown mechanism fails to operate.

stable salt reactor; transient simulations; system↗

DOE OSTI2026

FAIR Data and Interpretable AI Framework for Architectured Metamaterials (Final Report)

This research program established a transformative framework for the discovery and design of mechanical metamaterials, which are architected structures engineered to control physical phenomena like sound and vibration in ways natural materials cannot. To overcome the traditional reliance on trial-and-error, the project developed an interpretable Artificial Intelligence (AI) framework that moves beyond "black box" models to reveal the specific geometric patterns—such as "unit-cell templates"—that govern a material’s performance. A major breakthrough was the development of a hierarchical design method, which allows a single material to block vibrations across multiple frequency ranges simultaneously by layering patterns at different scales without them interfering with one another. This was further expanded to include irregular, graph-based designs that use spanning tree algorithms to ensure structural connectivity while allowing for customized, direction-dependent properties like stiffness and acoustic impedance. Beyond design, the project addressed the practicalities of real-world production by developing uncertainty quantification techniques that account for manufacturing defects and material variability, reducing the need for expensive physical testing by orders of magnitude. To speed up the discovery process, the team implemented Gaussian Process Regression and other surrogate models that provide accurate performance predictions at a fraction of the traditional computational cost. The AI-generated designs were successfully validated through fabrication of physical samples and wave propagation experiments, confirming their ability to accurately guide or reflect waves as predicted. By contributing these tools and high-quality FAIR benchmark datasets to the wider scientific community, this work provides a scalable foundation for advancing technologies in aerospace vibration control, medical imaging, and noise reduction.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Hydrogeological assessment of CO2 containment assurance and wellbore integrity at a Gulf Coast storage site

Abstract A large-scale carbon capture and storage (CCS) initiative on the Texas Gulf Coast serves as a premier demonstration of the U.S. Department of Energy’s CarbonSAFE program. Targeting deep saline formations, specifically Oligo-Miocene deltaic sequences, the project aims to establish technical and commercial viability for geologic CO2 storage within a major industrial corridor. This study provides a rigorous hydrogeological assessment to support Class VI permitting by quantifying the high degree of containment security. Utilizing a compositional reservoir simulator, we developed a suite of 27 distinct simulation cases to evaluate vertical plume dynamics near both planned injection wells and proximal legacy infrastructure. To ensure numerical accuracy near wellbores, we implemented a refined mesh strategy, determining that a 5.6 ft × 5.6 ft grid refinement offered the optimal balance between computational efficiency and descriptive precision. The modeling framework utilized a systematic sensitivity-based approach to evaluate the mechanical redundancy of the subsurface system by performing a bounding analysis of wellbore interfaces against hypothetical high-permeability microannuli. By systematically isolating competing physical drivers, including permeability, porosity, gas hysteresis, thermal gradients, salinity, and solubility trapping (quantified via Henry’s law with dynamically adjusted coefficients), this work moves beyond binary assessments to establish a nuanced hierarchy of containment factors. The results confirm that primary trapping mechanisms (e.g., gas hysteresis and solubility), combined with the site's unique geomechanical stratigraphy, significantly restrict vertical mobility and reinforce the robust containment security of the reservoir. Baseline results demonstrate substantial vertical separation between the CO2 plume and the upper confining system, ensuring robust containment. Sensitivity analysis reveals that even under highly conservative bounding scenarios—assuming theoretical 10-Darcy pathways at specific wellbore locations—the 2,900-ft thick multi-layered confining zone remains a reliable barrier. In these hypothetical upper-bound cases, peak upward fluxes of CO2 and saltwater after 15 years of injection remain localized and dissipate rapidly within the lower sections of the confining interval, leaving the integrity of the seal uncompromised. Furthermore, the study identifies that while localized wellbore pathways define theoretical upper bounds of vertical migration, the Area of Review (AoR) is primarily sensitive to regional thermal gradients and hysteresis, which can influence the AoR by over 3,000 acres in pessimistic configurations. Also, primary trapping mechanisms, specifically gas hysteresis and solubility, work in tandem with the Gulf Coast’s unique geomechanical stratigraphy to significantly restrict vertical mobility. Ductile, smectite-rich mudstones facilitate natural borehole convergence and the self-healing of potential conduits, creating a natural geomechanical bridge that effectively mitigates migration potential at both current injection points and legacy-well locations. This comprehensive modeling effort demonstrates that the integration of high-resolution wellbore simulations and regional geomechanical observations confirms the long-term storage security of the studied site, providing a physics-based foundation for industrial-scale CCS deployments. This modeling framework establishes a baseline for future research into coupled geomechanical effects, such as time-dependent borehole convergence, to further refine long-term containment projections. Acknowledgements We thank the Gulf Coast Carbon Center (GCCC) at the Bureau of Economic Geology for foundational research support. We appreciate Alex Bump for technical guidance and David Hoffman for model mesh generation. This work used TACC’s Frontera cluster for simulations and CMG Ltd. software licenses provided to UT-Austin. This material is based upon work supported by the Department of Energy under Award Number DE-FE0032338. Disclaimer This material is based upon work supported by the U.S. Department of Energy’s Fossil Energy and Carbon Management Office under the CarbonSAFE program, award Number DE-FE0032338. The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

58 GEOSCIENCES↗

DOE OSTI2026

Hydrogeological assessment of CO2 containment assurance and wellbore integrity at a Gulf Coast storage site

Abstract A large-scale carbon capture and storage (CCS) initiative on the Texas Gulf Coast serves as a premier demonstration of the U.S. Department of Energy’s CarbonSAFE program. Targeting deep saline formations, specifically Oligo-Miocene deltaic sequences, the project aims to establish technical and commercial viability for geologic CO2 storage within a major industrial corridor. This study provides a rigorous hydrogeological assessment to support Class VI permitting by quantifying the high degree of containment security. Utilizing a compositional reservoir simulator, we developed a suite of 27 distinct simulation cases to evaluate vertical plume dynamics near both planned injection wells and proximal legacy infrastructure. To ensure numerical accuracy near wellbores, we implemented a refined mesh strategy, determining that a 5.6 ft × 5.6 ft grid refinement offered the optimal balance between computational efficiency and descriptive precision. The modeling framework utilized a systematic sensitivity-based approach to evaluate the mechanical redundancy of the subsurface system by performing a bounding analysis of wellbore interfaces against hypothetical high-permeability microannuli. By systematically isolating competing physical drivers, including permeability, porosity, gas hysteresis, thermal gradients, salinity, and solubility trapping (quantified via Henry’s law with dynamically adjusted coefficients), this work moves beyond binary assessments to establish a nuanced hierarchy of containment factors. The results confirm that primary trapping mechanisms (e.g., gas hysteresis and solubility), combined with the site's unique geomechanical stratigraphy, significantly restrict vertical mobility and reinforce the robust containment security of the reservoir. Baseline results demonstrate substantial vertical separation between the CO2 plume and the upper confining system, ensuring robust containment. Sensitivity analysis reveals that even under highly conservative bounding scenarios—assuming theoretical 10-Darcy pathways at specific wellbore locations—the 2,900-ft thick multi-layered confining zone remains a reliable barrier. In these hypothetical upper-bound cases, peak upward fluxes of CO2 and saltwater after 15 years of injection remain localized and dissipate rapidly within the lower sections of the confining interval, leaving the integrity of the seal uncompromised. Furthermore, the study identifies that while localized wellbore pathways define theoretical upper bounds of vertical migration, the Area of Review (AoR) is primarily sensitive to regional thermal gradients and hysteresis, which can influence the AoR by over 3,000 acres in pessimistic configurations. Also, primary trapping mechanisms, specifically gas hysteresis and solubility, work in tandem with the Gulf Coast’s unique geomechanical stratigraphy to significantly restrict vertical mobility. Ductile, smectite-rich mudstones facilitate natural borehole convergence and the self-healing of potential conduits, creating a natural geomechanical bridge that effectively mitigates migration potential at both current injection points and legacy-well locations. This comprehensive modeling effort demonstrates that the integration of high-resolution wellbore simulations and regional geomechanical observations confirms the long-term storage security of the studied site, providing a physics-based foundation for industrial-scale CCS deployments. This modeling framework establishes a baseline for future research into coupled geomechanical effects, such as time-dependent borehole convergence, to further refine long-term containment projections. Acknowledgements We thank the Gulf Coast Carbon Center (GCCC) at the Bureau of Economic Geology for foundational research support. We appreciate Alex Bump for technical guidance and David Hoffman for model mesh generation. This work used TACC’s Frontera cluster for simulations and CMG Ltd. software licenses provided to UT-Austin. This material is based upon work supported by the Department of Energy under Award Number DE-FE0032338. Disclaimer This material is based upon work supported by the U.S. Department of Energy’s Fossil Energy and Carbon Management Office under the CarbonSAFE program, award Number DE-FE0032338. The views expressed herein do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

58 GEOSCIENCES↗

DOE OSTI2024

A low-latency graph computer to identify metastable particles at the Large Hadron Collider for real-time analysis of potential dark matter signatures

Abstract Image recognition is a pervasive task in many information-processing environments. We present a solution to a difficult pattern recognition problem that lies at the heart of experimental particle physics. Future experiments with very high-intensity beams will produce a spray of thousands of particles in each beam-target or beam-beam collision. Recognizing the trajectories of these particles as they traverse layers of electronic sensors is a massive image recognition task that has never been accomplished in real time. We present a real-time processing solution that is implemented in a commercial field-programmable gate array using high-level synthesis. It is an unsupervised learning algorithm that uses techniques of graph computing. A prime application is the low-latency analysis of dark-matter signatures involving metastable charged particles that manifest as disappearing tracks.

47 OTHER INSTRUMENTATION↗

DOE OSTI2024

Design and implementation of a verified interpreter for additive manufacturing programs: Experience report

Explore the source record for details and available documents.

Computer science↗

DOE OSTI2025

Mantaray: A Rust Package for Ray Tracing Ocean Surface Gravity Waves

Ocean surface gravity waves are an important component of air-sea interaction, influencing energy, momentum, and gas exchanges across the ocean-atmosphere interface. In specific applications such as refraction by ocean currents or bathymetry, ray tracing provides a computationally efficient way to gain insight into wave propagation. In this paper, we introduce Mantaray, an open-source software package implemented in Rust, with a Python interface, that solves the ray equations for ocean surface gravity waves. Mantaray is designed for performance, robustness, and ease of use. The package is modular to facilitate further development and can currently be applied to both idealized and realistic wave propagation problems (Fig. 1).

16 TIDAL AND WAVE POWER↗

DOE OSTI2024

Computing the Instantaneous Collision Probability between Satellites using Characteristic Function Inversion

The probability that two satellites overlap in space at a specified instant of time is called their instantaneous collision probability. Assuming Gaussian uncertainties and spherical satellites, this probability is the integral of a Gaussian distribution over a sphere. This paper shows how to compute the probability using an established numerical procedure called characteristic function inversion. The collision probability in the short-term encounter scenario is also evaluated with this approach, where the instant at which the probability is computed is the time of closest approach between the objects. Python and R code is provided to evaluate the probability in practice. Overall, the approach has been established for over fifty years, is implemented in existing software, does not rely on analytical approximations, and can be used to evaluate two and three dimensional collision probabilities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Computational Optimization of Room Temperature Usable Capacity for Hydrogen Storage in MFU-4-Type Metal–Organic Frameworks via Pairwise Metal Substitutions

The efficient storage of hydrogen is a critical challenge in the quest for sustainable energy solutions. Current adsorbent-based methods achieve satisfactory storage densities predominantly under cryogenic temperatures and/or high pressures, which imposes problems with cost-efficient and safe implementation of this technology. Materials that can bind hydrogen gas reversibly at ambient temperatures and more moderate pressures could play a pivotal role in enabling hydrogen-powered technologies. In this study, we use reliable computational modeling to investigate two synthetically feasible paths for tuning the enthalpy of H2 binding in MFU-4-type metal–organic frameworks (MOFs), aiming to maximize usable capacity. This study examines MIM4 IICl3(bta)6 (bta– = benzotriazolate) Kuratowski-type clusters as a model for strong binding sites in MFU-4l frameworks. We systematically evaluate the impact of separately tuning the central MII metal ion (which plays a structural role) and the peripheral MI metal ion (which binds the substrate) on the energetics of H2 binding. Our computational study reveals that H2 binding at an MI site mostly follows the trend AgI < CuI < NiI < CoI < AuI while a larger central MII site generally weakens the H2 binding at a MI site. Importantly, we have identified three new combinations of MI and MII to achieve high fractional usable capacities of the total H2 adsorbed under a pressure swing from 5 to 100 bar at room temperature. Additionally, we examine the nature of the binding interaction between the peripheral metal atom and the hydrogen molecule. While charge transfer predominantly induces this interaction, for several atom combinations, a change in the polarization (associated with variations in the ionic radius of the MI binding atom) is another important factor for adjusting the strength of the interaction. We suggest that the proposed compositions of Kuratowski-type clusters are highly desirable synthetic targets for future laboratory study.

Tkachenko, Nikolay V↗

DOE OSTI2025

Sharp front tracking with geometric interface reconstruction

Here, this paper presents a novel sharp front-tracking method designed to address limitations in classical front-tracking approaches, specifically their reliance on smooth interpolation kernels and extended stencils for coupling the front and fluid mesh. In contrast, the proposed method employs exclusively sharp, localized interpolation and spreading kernels, restricting the coupling to the interfacial fluid cells–those containing the interface/front. This localized coupling is achieved by integrating a divergence-preserving velocity interpolation method with a piecewise parabolic interface calculation (PPIC) and a polyhedron intersection algorithm to compute the indicator function and local interface curvature. Surface tension is computed using the Continuum Surface Force (CSF) method, maintaining consistency with the sharp representation. Additionally, we propose an efficient local roughness smoothing implementation to account for surface mesh undulations, which is easily applicable to any triangulated surface mesh. Building on our previous work, the primary innovation of this study lies in the localization of the coupling for both the indicator function and surface tension calculations. By reducing the interface thickness on the fluid mesh to a single cell, as opposed to the 4–5 cell spans typical in classical methods, the proposed sharp front-tracking method achieves a highly localized and accurate representation of the interface. This sharper representation mitigates parasitic currents and improves force balancing, making it particularly suitable for scenarios where the interface plays a critical role, such as microfluidics, fluid-fluid interactions, and fluid-structure interactions. The proposed method is comprehensively validated and tested on canonical interfacial flow problems, including stationary and translating Laplace equilibria, oscillating droplets, and rising bubbles. The presented results demonstrate that the sharp front-tracking method significantly outperforms the classical approach in terms of accuracy, stability, and computational efficiency. Notably, parasitic currents are reduced by approximately two orders of magnitude and stable results are obtained for parameter ranges where classical front tracking fails to converge.

42 ENGINEERING↗

DOE OSTI2025

Using system identification in modeling the yaw response of tail fins for small wind turbines with bearing friction

Here, we describe three main developments of our previous study of the nonlinear yaw dynamics of the tail fins for small wind turbines [Khedr et al., J. Renewable Sustainable Energy 16, 053305 (2024)]. First, the model constants derived from archived computational and experimental studies are adjusted by employing system identification (SI) to maximize the model's agreement with wind tunnel tests. This adjustment was done for high wind speeds, where yaw bearing friction can be ignored. When starting a turbine at low wind speed, however, friction can become important. Our second development is to implement a model for the frictional resistive torque and use SI to maximize its accuracy. These developments used wind tunnel experiments on generic delta, elliptical, and rectangular planforms that were described by Khedr et al. [J. Renewable Sustainable Energy 16, 053305 (2024)]. Since the aerodynamic and friction models employ a large number of constants, we describe ways to constrain the values using linearized solutions of the response equations for small and large yaw angles. Third, we test the generality of the aerodynamic and friction modeling using the complex planform from a commercial small turbine, for which limited theoretical and computational guidance is available in selecting the model constants. The model implemented with SI is shown to provide an accurate description of the yaw response of the complex planform. Guidelines are given for the use of wind tunnel tests to determine the model constants for tail fins of any planform.

17 WIND ENERGY↗

DOE OSTI2025

Using nuclear observations to improve climate research and GHG emission estimates – the NuClim project

Project NuClim (Nuclear observations to improve Climate research and GHG emission estimates) aims to use high-quality measurements of atmospheric radon activity concentration and ambient radioactivity to advance climate science and improve radiation protection and nuclear surveillance capabilities. It is supported by new metrological capabilities developed in the EMPIR project 19ENV01 traceRadon. This work reviews the scientific objectives of project NuClim in terms of both climate science and radiological protection, and provides an overview of the NuClim field campaign and the various nuclear measurements being implemented within the scope of the project.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

A robust approach to Gaussian process implementation

Abstract. Gaussian process (GP) regression is a flexible modeling technique used to predict outputs and to capture uncertainty in the predictions. However, the GP regression process becomes computationally intensive when the training spatial dataset has a large number of observations. To address this challenge, we introduce a scalable GP algorithm, termed MuyGPs, which incorporates nearest-neighbor and leave-one-out cross-validation during training. This approach enables the evaluation of large spatial datasets with state-of-the-art accuracy and speed in certain spatial problems. Despite these advantages, conventional quadratic loss functions used in the MuyGPs optimization, such as root mean squared error (RMSE), are highly influenced by outliers. We explore the behavior of MuyGPs in cases involving outlying observations and, subsequently, develop a robust approach to handle and mitigate their impact. Specifically, we introduce a novel leave-one-out loss function based on the pseudo-Huber function (LOOPH) that effectively accounts for outliers in large spatial datasets within the MuyGPs framework. Our simulation study shows that the LOOPH loss method maintains accuracy despite outlying observations, establishing MuyGPs as a powerful tool for mitigating unusual observation impacts in the large data regime. In the analysis of US ozone data, MuyGPs provides accurate predictions and uncertainty quantification, demonstrating its utility in managing data anomalies. Through these efforts, we advance the understanding of GP regression in spatial contexts.

Mukangango, Juliette↗

DOE OSTI2024

Synchronization for CXL Based Memory

Compute Express Link (CXL) is an important emerging standard for disaggregated memory. While this standard provisions coherency across numerous hosts and devices, implementing hardware support for type three devices is challenging. In this work, we look at the overhead of software synchronization and using software-based coherency. Moreover, we discuss the limits of software-based coherency in fully expressing modern synchronization techniques for a CXL-based disaggregate memory system. We demonstrate our approach using a CXL hardware prototype and running a version of the famous Peterson Lock (enhanced to run with more than two threads). We analyze its performance and share how more advanced synchronization techniques might interact with software-based coherence CXL hardware and program execution models.

High Performance Computing (HPC)↗

DOE OSTI2026

FastrSHWFS Analysis

This code analyzes the reflection geometry of modified Shack-Hartmann Wavefront Sensor (SHWFS) masks, with a focus on the fastrSHWFS designs. It takes a height map of a reflective mask, divides it into sub apertures, removes the global focus term by referencing a central block, and fits local surface planes to each sub aperture. From these fits it computes reflection angles and propagates the corresponding rays downstream to determine spot positions and the overall reflected beam footprint as a function of distance. The implementation is parameterized in sub aperture size, number of sub apertures, focal length, and mask dimensions, so it can be adapted to different mask designs beyond the two current fastrSHWFS masks. The code: Converts mask bitmaps into physical height in microns and reconstructs a focus subtracted mask, divides the mask into a grid of sub apertures and assigns pixel and micron coordinates to each block, excludes user specified unused sub apertures from the analysis, fits a plane to each sub aperture to obtain local surface normals, propagates reflected rays to a range of z positions to compute ray spots and the full reflected beam width, computes the effective mask tilt angle with respect to the incoming beam as a function of propagation distance, and provides helper routines for plotting the grid over the mask and for visualizing the beam geometry. These tools are intended for iterating on fastrSHWFS mask designs and for planning downstream optical layouts, for example choosing lens positions and apertures that capture the reflected beam given known focal plane distances and beam widths.

Gerard, BenjaminL [Lawrence Livermore National Lab↗

DOE OSTI2024

Molecular NMR shieldings, J -couplings, and magnetizabilities from numeric atom-centered orbital based density-functional calculations

This paper reports and benchmarks a new implementation of nuclear magnetic resonance shieldings, magnetizabilities, and J-couplings for molecules within semilocal density functional theory, based on numeric atom-centered orbital (NAO) basis sets. NAO basis sets are attractive for the calculation of these nuclear magnetic resonance (NMR) parameters because NAOs provide accurate atomic orbital representations especially near the nucleus, enabling high-quality results at modest computational cost. Moreover, NAOs are readily adaptable for linear scaling methods, enabling efficient calculations of large systems. Here, the paper has five main parts: (1) It reviews the formalism of density functional calculations of NMR parameters in one comprehensive text to make the mathematical background available in a self-contained way. (2) The paper quantifies the attainable precision of NAO basis sets for shieldings in comparison to specialized Gaussian basis sets, showing similar performance for similar basis set size. (3) The paper quantifies the precision of calculated magnetizabilities, where the NAO basis sets appear to outperform several established Gaussian basis sets of similar size. (4) The paper quantifies the precision of computed J-couplings, for which a group of customized NAO basis sets achieves precision of ~Hz for smaller basis set sizes than some established Gaussian basis sets. (5) The paper demonstrates that the implementation is applicable to systems beyond 1000 atoms in size.

74 ATOMIC AND MOLECULAR PHYSICS↗