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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Quantum-Inspired Bayesian Sampling for Uncertainty Quantification and Machine Learning (Final Technical Report)

With increasing simulation and measurement data, machine learning and artificial intelligence have been widely used in computational decision-making of complex engineering systems. The resulting tools, such as uncertainty quantification solvers, reinforcement learning, and physics-informed machine learning, have achieved great success in critical DOE tasks such as material discovery and design, energy system modeling and control, and numerical weather and climate prediction. A core topic in scientific machine learning and artificial intelligence is Bayesian inference: given an observed data set, people want to estimate the posterior distribution of a (possibly large) number of hidden parameters. Due to the flexibility and weak assumptions, Bayesian sampling has been the mainstream Bayesian inference solvers despite the rapid progress of approximate Bayesian inference. Classical Bayesian sampling methods such as Markov-chain Monte Carlo suffer from a low-acceptance rate due to the random walk nature, therefore state-of-the-art techniques use Hamiltonian Monte Carlo and its variants to efficiently draw posterior samples in a high dimension. The key idea of Hamiltonian Monte Carlo and its variants is to simulate the Hamiltonian dynamics of a classical particle with a fixed mass, and their performance significantly degrades when the posterior distribution is highly spiky or has multiple modes. Leveraging the idea of quantum physics, this project has investigated new theory, algorithms and applications of Bayesian inference (especially Bayesian sampling). The main results include: (1) novel quantum-inspired Bayesian sampling methods that can lead to better accuracy for challenging multi-modal or spiky distributions, (2) more scalable machine learning framework leveraging tensor-compressed Bayesian inference, and (3) Bayesian and sampling approaches for verifying the robustness of continuous and binary neural networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Understanding the chemical bonding of ground and excited states of HfO and HfB with correlated wavefunction theory and density functional approximations

Knowledge of the chemical bonding of HfO and HfB ground and low-lying electronic states provides essential insights into a range of catalysts and materials that contain Hf–O or Hf–B moieties. Here, we carry out high-level multi-reference configuration interaction theory and coupled cluster quantum chemical calculations on these systems. We compute full potential energy curves, excitation energies, ionization energies, electronic configurations, and spectroscopic parameters with large quadruple-ζ and quintuple-ζ quality correlation consistent basis sets. We also investigate equilibrium chemical bonding patterns and effects of correlating core electrons on property predictions. Differences in the ground state electron configuration of HfB(X 4 Σ - ) and HfO(X 1 Σ + ) lead to a significantly stronger bond in HfO than HfB, as judged by both dissociation energies and equilibrium bond distances. We extend our analysis to the chemical bonding patterns of the isovalent HfX (X = O, S, Se, Te, and Po) series and observe similar trends. We also note a linear trend between the decreasing value of the dissociation energy (D e ) from HfO to HfPo and the singlet–triplet energy gap (ΔE S–T ) of the molecule. Finally, we compare these benchmark results to those obtained using density functional theory (DFT) with 23 exchange–correlation functionals spanning multiple rungs of “Jacob’s ladder.” When comparing DFT errors to coupled cluster reference values on dissociation energies, excitation energies, and ionization energies of HfB and HfO, we observe semi-local generalized gradient approximations to significantly outperform more complex and high-cost functionals.

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

Distorted dislocation cores and asymmetric glide resistances in titanium

The determination of Critical Resolved Shear Stress (CRSS) in titanium for basal, prismatic, and pyramidal slip-planes without empirical constants is presented by combining Density Functional Theory (DFT) and anisotropic elasticity. A new mechanism leading to tension-compression (T-C) asymmetry in the CRSS levels has been revealed for the first time. The conditions for this asymmetry are established, involving a complex interplay between the dislocation core-structure and core-advance behavior. The three conditions for T-C asymmetry that need to be simultaneously satisfied can be summarized as: (1) a medium stacking fault width, d, (3 < d/b F < 10, where b F is the magnitude of the Burgers vector of the full dislocation), (2) an asymmetric core-structure of the extended dislocation (ξ 1 ≠ ξ 2 , where ξ 1 and ξ 2 are the core-widths of the first and second partials, respectively), and (3) intermittent motion of the partials (Δd/b F ≠ 0, where Δd is the magnitude of fluctuation in stacking fault width during intermittent motion). Pyramidal-slip in titanium satisfies all three conditions, resulting in significant T-C asymmetry. The CRSS theory considers a Wigner-Seitz (W-S) cell based domain area assigned to each lattice site for the calculations of core-energies accurately capturing the slip-plane lattice. The W-S based approach is essential due to the lower symmetry of the HCP crystal circumventing potential errors associated with the one-dimensional atomic-row approximation. Dislocation core structures are obtained for all the slip-systems in titanium showing significant distortion of the disregistry profile governing the core-advance behavior. The CRSS values predicted from the theory show agreement with the experimental CRSS levels reported in the literature.

Dislocation core↗
DOE OSTI2020

Theoretical, Solid-State, and Solution Quantification of the Hydrogen Bond-Enhanced Halogen Bond

Proximal noncovalent forces are commonplace in natural systems and understanding the consequences of their juxtaposition is critical. This paper experimentally quantifies for the first time a Hydrogen Bond-Enhanced Halogen Bond (HBeXB) without the complexities of protein structure or preorganization. An HBeXB is a halogen bond that has been strengthened when the halogen donor simultaneously accepts a hydrogen bond. In this work, our theoretical studies suggest that electron-rich halogen bond donors are strengthened most by an adjacent hydrogen bond. Furthermore, stronger hydrogen bond donors enhance the halogen bond the most. X-ray crystal structures of halide complexes (X - =Br - , I - ) reveal that HBeXBs produce shorter halogen bonds than non-hydrogen bond analogues. 19 F NMR titrations with chloride highlight that the HBeXB analogue exhibits stronger binding. Together, these results form the foundation for future studies concerning hydrogen bonds and halogen bonds in close proximity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Synergic Effects of Surface Chemistry and Applied Potentials on the Kinetics of the Electrocatalytic Oxygen Evolution Reaction in IrO 2

Improving the efficacy of the oxygen evolution reaction (OER) through water oxidation is critical for advancing photoelectrochemical water splitting. Among the catalysts, IrO 2 exhibits a high OER catalytic activity and stability under acidic conditions. The OER mechanism in this system has been a topic of intense research; however, many mechanistic understandings are lacking. In this work, we carried out first-principles calculations with an implicit solvation model at a constant potential to study the OER behavior on the IrO 2 (110) surface. We find that the surface hydrogen coverage has a significant effect on OER kinetics and transition states. We then develop a microkinetics model that accounts for the continuous evolution of both OER activation energy and hydrogen coverage as a function of an applied potential. We show that this inclusion leads to significant improvement in the simulated Tafel plot compared to available experiments. In conclusion, our results point to a complex interplay between surface chemistry and the applied potential on OER kinetics.

08 HYDROGEN↗
DOE OSTI2024

Structural modeling of high-entropy oxides battery anodes using x-ray absorption spectroscopy

High-entropy oxides (HEOs) are single phase solid solutions where five or more metals share the same sublattice, giving rise to unexpected features in various fields of applications. Recently, HEOs have emerged as an alternative conversion electrode anode material for next-generation Li-ion batteries, where the combination of several different elements in a single solid solution can synergistically act to overcome some of its main drawbacks, improving performance. Due to their chemical complexity, x-ray absorption spectroscopy (XAS) emerges as an appropriate technique to study the electronic (x-ray absorption near edge structure, XANES) and local structure (extended x-ray absorption fine structure, EXAFS) of these compounds as a function of cycling. This work aims to highlight the capabilities of XAS as an element-specific probe to understand a material’s structure at the atomistic level through EXAFS modeling of (MgFeCoNiCuZn)O high-entropy system and how to extract valuable information about the bond distance, number of near neighbors, and local disorder, which are crucial to a full understanding of the electrochemical reaction mechanisms of such battery electrodes.

25 ENERGY STORAGE↗
DOE OSTI2020

Transient Studies of Nonequilibrium Transport in Two-Dimensional Semiconductors

The overarching objective of research under DOE support has been to investigate emergent carrier phenomena in different two-dimensional (2D) systems, under conditions where they are driven far from equilibrium. The description of nonequilibrium transport has long represented one of the most enduring challenges in condensed-matter physics, in large part due to the need to invoke the role of complex many-body phenomena (electron-phonon and electron-electron coupling) in this regime. In this project, we have explored aspects of this problem in a variety of different two-dimensional systems. These include the modulation-doped two-dimensional electrons gas, or 2DEG, in GaAs/AlGaAs heterostructures; the electron and hole systems in graphene and its related hetero-structures, and; the strongly-confined electron layers in transition-metal dichalcogenide (MoS 2 and WS 2 ) and trichalcogenide (TiS 3 ) materials. Significant understanding has been achieved in a number of different areas, as we elaborate upon in subsequent sections of this proposal: Nanoscale spectroscopy of defect-related barriers in MoS2 Negative differential conductance due to inter-valley scattering in WS 2 under high fields Incipient localization due to scattering from frozen-phonon disorder in quantum point contacts High-field transient transport in graphene/hexagonal BN heterostructures Universal voltage scaling of quantum corrections in graphene under nonequilibrium A defining feature of much of this research has been an approach to problem solving in which novel experimental techniques (such as transient electrical pulsing and scanning-probe microscopy) are combined with the development (in collaboration with colleagues from condensed-matter theory) of sophisticated models, a strategy that we propose to continue in our future research. In recent years, we have developed an increasing capacity for handling atomically-thin materials, and their van der Waals systems, a capacity that is reflected in the balance of topics listed above.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Interpretable, extensible linear and symbolic regression models for charge density prediction using a hierarchy of many-body correlation descriptors

Here, density functional theory (DFT) is routinely used to make electronic structure predictions for high-throughput screening of materials and molecules for technologically relevant areas, like the identification of better catalysts, electronic materials, and drug discovery. However, the DFT formalism is limited by (a) its poor (quadratic-to-quartic) scaling, and (b) the need to perform repeated eigenvalue computations of the electronic Hamiltonian as part of its self-consistent field (SCF) iteration procedure to obtain the converged ground state electron density, ρ (r). Approaches that directly predict ρ (r) of a structure with high accuracy can accelerate conventional SCF calculations and can also be used in linearly scaling methods such as orbital-free DFT. To this end, we present a procedure to predict the ground state electron density of molecular and periodic three-dimensional systems directly from the atomic structure with a particular emphasis on physical interpretability. In our framework, ρ (r) is modeled using many-body correlation descriptors that accurately capture the effects of local atomic arrangements in the neighborhood of a grid point. Our use of a linear regression scheme to fit to charge density data enables transparent analysis of the relative contributions of various types of local atomic correlations. By systematically including increasingly complex correlations, our model is shown to accurately predict ρ (r) for a variety of chemically and electronically diverse systems — amorphous Ge, Al(001) slab, crystalline Ga 2 O 3 , molecular benzene, and polyethylene. We then demonstrate a symbolic regression-based protocol to construct easily computable, interpretable features from lower-order correlations that significantly improves our electron density predictions with effectively no increase in the computational cost.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Characterization of Deformational Isomerization Potential and Interconversion Dynamics with Ultrafast X-ray Solution Scattering

Dimeric complexes composed of d 8 square planar metal centers and rigid bridging ligands provide model systems to understand the interplay between attractive dispersion forces and steric strain in order to assist the development of reliable methods to model metal dimer complexes more broadly. [Ir 2 (dimen) 4 ] 2+ (dimen = para-diisocyanomenthane) presents a unique case study for such phenomena, as distortions of the optimal structure of a ligand with limited conformational flexibility counteract the attractive dispersive forces from the metal and ligand to yield a complex with two ground state deformational isomers. Here, in this work, we use ultrafast X-ray solution scattering (XSS) and optical transient absorption spectroscopy (OTAS) to reveal the nature of the equilibrium distribution and the exchange rate between the deformational isomers. The two ground state isomers have spectrally distinct electronic excitations that enable the selective excitation of one isomer or the other using a femtosecond duration pulse of visible light. We then track the dynamics of the nonequilibrium depletion of the electronic ground state population—often termed the ground state hole—with ultrafast XSS and OTAS, revealing a restoration of the ground state equilibrium in 2.3 ps. This combined experimental and theoretical study provides a critical test of various density functional approximations in the description of bridged d 8 –d 8 metal complexes. The results show that density functional theory calculations can reproduce the primary experimental observations if dispersion interactions are added, and a hybrid functional, which includes exact exchange, is used.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Molecular dynamics simulations for glass transition temperature predictions of polyhydroxyalkanoate biopolymers

Polyhydroxyalkanoates (PHAs) represent an emerging class of biosynthetic and biodegradable polyesters that exhibit considerable potential to replace petroleum-based plastics towards a sustainable future. Despite the promise, general structure–property mappings within this class of polymers remain largely unexplored. An efficient exploration of this vast chemical space calls for the development and validation of predictive methods for accurate estimation of a diverse range of properties for PHA-based polymers. Towards this aim, we present and validate in this work the results of our molecular dynamics (MD) simulation based approach aimed at predicting glass transition temperatures (T g ) of PHA-based polymers. Since generally available and widely used polymer forcefields exhibit a relatively poor performance for T g predictions, we have developed a new forcefield by modifying the polymer consistent force field (PCFF) via refining a selected set of torsion potentials of the polymer backbone using accurate density functional theory (DFT) computations. After carefully assessing the dependence of critical simulation parameters, such as, polymer chain length, number of polymer chains, supercell size, and thermal quenching rate used in the simulation, the applicability and transferability of the modified PCFF (mPCFF) is demonstrated by directly comparing the computed T g predictions of various polymers with different chemistries, polymer side chain lengths and functional groups forming the polymer side chains against the respective experimentally measured values. Furthermore, the transport properties such as self-diffusion coefficient and viscosity are computationally determined and their well-known correlation with the target properties is demonstrated. Lastly, we have employed the developed approach to predict T g values for a number of yet-to-be-synthesized PHA-based polymers with a diverse set of functional groups in the polymer side chains. The results are further rationalized by correlating the predicted T g values with the inter-chain H-bond formation tendencies of the different side chain functional groups. This work represents an important first step towards computationally guided design of PHA-based functional polymers and opens up new directions for a systematic investigation of composition- and configuration-dependent structure–property relationships in more complex binary and ternary copolymer systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Sparsity of the electron repulsion integral tensor using different localized virtual orbital representations in local second-order Møller–Plesset theory

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree–Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller–Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the “ragged list”) and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Here, our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the “fixed sparsity pattern”) for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.

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

A DFT-based kinetic Monte Carlo simulation of multiphase oxide-metal thin film growth

Functional thin films of nanoscale metal pillars in oxide or nitride matrices known as vertically aligned nanocomposite (VAN) have gained much interest owing to their unique strain-coupled and highly anisotropic properties. So far, the deposition of these films has been explored mostly experimentally. In this work, a density functional theory (DFT)-based kinetic Monte Carlo simulation model using Bortz–Kalos–Lebowitz algorithm was developed to understand the growth of VAN films deposited by pulsed laser technique on mismatching substrates. The model has been parameterized and applied to understand the kinetics of growth thin films consisting of Au pillars in CeO2 matrix deposited on SrTiO3 substrates. The effects of pulsed laser deposition (PLD) conditions including the pulse frequency, deposition flux, and substrate temperature were explored. The simulations indicate that the Au pillar size and shape exhibit significant dependence on the PLD conditions. Namely, increasing the temperature increases the average pillar size and lowers the pillar density, and vice versa. In addition, the simulations revealed that increasing the deposition rate results in lowering the average pillar size and increasing the density. Particularly, the DFT results suggest that Au pillar size can be tuned during the initial growth of the first monolayer due to the significantly low activation barrier. Our analysis showed that the relationship between the average pillar size and pillar density is influenced by the kinetics. Furthermore, autocorrelation analysis showed that pillars self-organize in quasi-ordered patterns at certain windows of the deposition conditions, which is attributed to the complex nature of the chemical interactions in the system, the kinetics, and the deposition parameters.

Physics↗
DOE OSTI2026

Effects of Composition and Oxidation States on the Structures of Chromium-Containing Sodium Silicate Glasses: Molecular Dynamics Simulations using Machine Learning Interatomic Potentials

Chromium represents a significant challenge for the vitrification of high-level nuclear waste into silicate and borosilicate glasses due to its low solubility and variable oxidation states, which can limit the waste loading due to promotion of crystallization or phase separation during processing. In this study, we modeled chromium containing silicate glasses using molecular dynamics simulations with three machine learning interatomic potentials (MLIPs), MACE, CHGNet, and PFP were employed, to gain insights on glass composition and oxidation states on the structures of these glasses. One of the goals is to evaluate their ability of these MLIPs to accurately represent the general structure of silicate glasses and chromium local environments as a function of chromium oxidation states. Density Functional Theory (DFT) based calculations and experimental data such as neutron structure factors were used to validate the structural models. It was found that the foundation models of all three MLIPs are able to reproduce general structural features of the sodium silicate glass structure consistent with experimental and DFT data, but only CHGNet and PFP can accurately capture the oxidation states and local environment of chromium: tetrahedral for Cr6+ and octahedral for Cr3+. Furthermore, we studied the effect of varying Cr3+/ Cr6+ (Cr3+/Crtotal) ratio and total chromium content using PFP. Our results show that Cr6+ enhances network polymerization by reducing non-bridging oxygens through Na? charge compensation required due to the formation of chromate (CrO42-) species, while Cr³? acts as a network modifier that disrupts connectivity. System size effects on the structural characteristics and chromium environments were also tested using the PFP potential. This work highlights the importance of careful validation on the precision, transferability, and potential of MLIPs for modeling glasses containing transition metal elements that can exist in multiple oxidation states. It is also encouraging to see the foundational models are all three MLFFs are able to reproduce the basic sodium silicate glass structures, while suggesting additional training or refining is needed to improve the description of more complex systems containing transition metals.

Puga, Christina L.↗
DOE OSTI2023

Supported Electrophilic Organoruthenium Catalyst for the Hydrosilylation of Olefins

A series of supported electrophilic organoruthenium complexes has been synthesized via surface organometallic chemistry (SOMC) techniques and applied to the selective hydrosilylation of olefins. The air-sensitive 16e - complex Cp*RuMes(PCy 3 ) (1) (Cp* = pentamethylcyclopentadienyl, Mes = mesityl) was synthesized by the treatment of Cp*RuCl(PCy 3 ) with mesityl Grignard MesMgBr. This species was chemisorbed onto sulfated zirconia SO 4 /ZrO 2 , but the resulting material was inactive toward cyclohexene hydrosilylation with phenylsilane. Instead, Cp*RuMes(PCy 3 ) was treated with phenylsilane (PhSiH 3 ) to provide a ruthenium disilyl hydride complex Cp*RuH(SiH 2 Ph) 2 (PCy 3 ) (3), which was fully characterized by NMR spectroscopy and single-crystal X-ray diffraction. Grafting this species onto SO 4 /ZrO 2 resulted in the formation of phenylsilane along with the surface electrophilic species [Cp*RuH(R)(X-SiHPh)(PCy 3 )] (R = H, O 3 S-O or O 3 Zr-O; 4a, 4b, X = O 3 S-O, and O 3 Zr-O, respectively) as the major species. Material 4 was characterized via a combination of spectroscopic techniques including dynamic nuclear polarization (DNP)-enhanced solid-state NMR spectroscopy, diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), X-ray absorption spectroscopy (XAS), and density function theory (DFT) calculations. Further, capping the remaining acid sites on 4 with Me 3 Si-SiMe 3 provides 5, which significantly reduces side reactions, such as olefin isomerization and silane redistribution. Catalyst 5 is a highly robust and selective hydrosilylation catalyst and can be recycled up to 5 times without significant diminishment of activity. Exclusive anti-Markovnikov regiochemistry, cis-addition selectivity, and the inactivity of secondary and tertiary silanes provide support for the proposed Glaser-Tilley mechanism involving cationic ruthenium silylene species analogous to homogeneous systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

A critical comparison of CH∙∙∙π versus π∙∙∙π interactions in the benzene dimer: obtaining benchmarks at the CCSD(T) level and assessing the accuracy of lower scaling methods

In this study, we have established CCSD(T)/CBS (Complete Basis Set) limits for 3 stationary points on the benzene dimer potential energy surface, corresponding to the π∙∙∙π (parallel displaced or PD(C 2h ), minimum) and CH∙∙∙π (T-shaped or T(C 2v ), transition state) and tilted T-shaped (or TT(Cs), minimum) bonding scenarios considering both the structure and binding energy. The CCSD(T)/CBS binding energies are -2.65 ± 0.02 (PD), -2.74 ± 0.03 (T), and -2.83 ± 0.01 kcal mol -1 (TT). To this end, the CH∙∙∙π is ~0.2 kcal mol -1 stronger than the π∙∙∙π interaction, whereas the tilting of the CH donating benzene molecule with respect to the other benzene is worth 0.1 kcal mol -1 . As previously discussed in the literature, the MP2 level of theory does not provide a close match for either the energy or structure, yet the SCS-MP2 yields structures in excellent agreement with respect to the CCSD(T) result. It is found that the SCS-MI-MP2 also gives optimized structures very close to SCS-MP2 (within ~0.01 Å of the benchmark). Despite the closer match in structure, the spin-biased MP2 methods (SCS-, SCS-MI-, and SOS-MP2) incorrectly predict the relative stabilities of the isomers. That said, none of the spin biased MP2 methods offers a good compromise between energy and structure for the systems examined. Finally, the CCSD(T)/CBS benchmarks were used to assess the performance of 13 DFT functionals selected from different rungs of Jacob's ladder. Several functionals such as TPSS-D3, B3LYP-D3, B97-D, B97-D3, and B2PLYP-D3 provided a good description of the binding energies for both CH∙∙∙π and π∙∙∙π interactions, yielding values within 6% of the CCSD(T)/CBS benchmark values. Unlike the MP2 methods, these functionals correctly predict the relative stability of the PD(C 2h ) and T(C 2v ) dimers. Further, we find that there is no systematic improvement as Jacob's ladder is ascended (increased complexity of functional). The best functionals that result in a good compromise between structure and energy accuracy are B97-D3 and B2PLYP-D3 for both the CH∙∙∙π and π∙∙∙π interaction. Despite the impressive performance of these functionals, a challenge that remains is ensuring the transferability of these density functionals in accurately describing the interaction between dimers of larger aromatic molecules, the latter requiring high-level benchmarks for these systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Implementation of Perturbation Theory and Sensitivity Capabilities in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor Multiphysics analysis application, jointly developed by Argonne and Idaho National Laboratories under the DOE-NE NEAMS program. This fiscal year, capabilities for reactivity and sensitivity evaluation using perturbation methods were implemented and verified. The First Order Perturbation Method (FOPT) was employed to compute reactivity worth resulting from small perturbations in input parameters, while the Generalized Perturbation Theory (GPT) was used to evaluate sensitivities of a range of response types, including reaction rate ratio, k-eigenvalue, neutron generation time, and effective delayed neutron fraction. These perturbation methods enable users to quantify how response quantities change due to a perturbation in a input parameter without explicitly performing an additional transport simulation for each perturbed state. In particular, the GPT formulation accounts for indirect effects arising from flux changes by solving generalized inhomogeneous equations, for which a Neumann series-based iterative solution method was developed and implemented in Griffin. The implemented reactivity and sensitivity evaluation capabilities were verified using two test problems: an infinite homogeneous system and a two-dimensional hexagonal core. The results showed excellent agreement with reference solutions obtained by a direct method based on finite difference approximation as well as GPT-based results from the PERSENT code, confirming the accuracy of both reactivity and sensitivity evaluations. Additionally, preliminary uncertainty quantification (UQ) results were obtained by combining the sensitivity values computed using GPT and external covariance data, demonstrating that the implemented sensitivity results can be reliably used for uncertainty calculations. To further demonstrate the generality and practical strength of the implementation, the sensitivity evaluation capability was successfully applied to the Empire microreactor with a geometrically complex design that poses significant modeling challenges. The results confirm that Griffin enables sensitivity evaluations even for irregular and highly heterogeneous reactor configurations, thereby establishing a foundation for UQ applications in advanced reactor designs and analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Structure of the Majorana Clifford group

In quantum information science, Clifford operators and stabilizer codes play a central role for systems of qubits (or qudits). In this study, we study their analogs for systems composed of Majorana fermions. In this case, a crucial role is played by fermion parity symmetry, which is an unbreakable symmetry present in any system with fundamentally fermionic degrees of freedom. We prove that the subgroup of parity-preserving Majorana Cliffords can be represented by the orthogonal group over the binary field 𝔽 2 , and we show how it can be generated by braiding operators and used to construct any (even-parity) Majorana stabilizer code. We also analyze the frame potential for this so-called p-Clifford group when acting on a fixed-parity sector of the Hilbert space, proving that it is equivalent to the frame potential of the ordinary Clifford group acting on the same sector.

Computational complexity↗