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Results for “Mathematical Methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Electron-Donating para -Substituent (X) Enhances the Water Oxidation Activity of the Catalyst Ru(4'-X-terpyridine)(phenanthroline-SO 3 ) +

Recently, our group has developed a Ru-based water oxidation catalyst (WOC) with pendant sulfonate (1, Ru(4'-X-terpyridine)(phenanthroline-SO 3 )OTf (X = H, 1a) that shows high activity under both sacrificial oxidant (CAN, Ce(NH 4 ) 2 (NO 3 ) 6 , Ce IV ) and electrocatalytic conditions, in both acidic and neutral media. Here, we demonstrate that the functionalization of the 4'-X-terpyridine ligand with an electron-donating substituent X = OEt (1b) makes potentials of Ru II /Ru III redox catalysis more negative, whereas when X = NO 2 (1c) and CF 3 (1d), potentials are more positive. For 1b, full conversion of the sacrificial oxidant Ce IV occurred in 0.4 h (7 h for 1a), with an initial rate of 2.07 μmol O 2 s –1 and a turnover frequency of 7.6 s –1 , which is 30-fold faster than that for 1a at [cat] 0 = 20 μM. Under electrocatalytic conditions, water oxidation by 1b is three times faster than that by the parent catalyst 1a at close to the same potential. Extensive computations have identified differences in the initial PCET steps of the water oxidation by catalysts 1a, 1b, and 1d, and demonstrated the increased probability of the O 2 formation via the oxide relay pathway in the order 1b< 1a < 1d.

14 SOLAR ENERGY↗
DOE OSTI2025

U 4+/5+/6+ in a Conserved Pseudotetrahedral Imidophosphorane Coordination Sphere

While several ligand systems support uranium across a range of oxidation states, spanning more than two oxidation states in a conserved coordination geometry is uncommon among structurally authenticated complexes. Imidophosphorane ligands significantly stabilize high-valent lanthanide and actinide complexes. Here, we report a series of homoleptic uranium imidophosphorane complexes, spanning the +4, +5 and +6 oxidation states in a four-coordinate pseudotetrahedral ligand field. The +6 oxidation state is accessible using a mild ferrocenium oxidant, yielding a rare example of U6+ in a pseudotetrahedral coordination environment. As the formal oxidation state increases, the U–N distances gradually contract, consistent with the Shannon ionic radii of U 4+/5+/6+ . Compared to reported complexes, the short U–N distances observed in the U 6+ complex are more comparable to dianionic imido ligands than monoanionic amido ligands.

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

X-ray Spectroscopy Characterization of Electronic Structure and Metal–Metal Bonding in Dicobalt Complexes

Developing multimetallic complexes with tunable metal–metal interactions has long been a target of synthetic inorganic chemistry efforts due to the unique properties that such compounds can exhibit. However, understanding relationships between metal–metal bonding and chemical properties is challenging due to system-dependent factors that influence metal–metal and metal–ligand interactions, including ligand identity, coordination geometry, and metal–metal distance. In this work, we apply X-ray absorption and emission spectroscopy and quantum chemical calculations to describe electronic structure and bonding in a series of dicobalt complexes. The compounds with silane ligands and pseudo-octahedral coordination geometry exhibit Co–Co σ and multicentered bonding character, which we characterize from both the occupied and vacant perspectives via their contributions to the Co X-ray emission and absorption spectra, respectively. In contrast, the dicobalt complexes with a pseudotetrahedral coordination environment do not exhibit Co–Co bonding due to symmetry constraints on orbital overlap. We extend these insights to the theoretical evaluation of related dicobalt complexes to explain how ligand coordination and symmetry dictate the presence or absence of a Co–Co bond. In conclusion, this work highlights how fundamental insights into electronic structure and bonding through X-ray spectroscopy uncover important factors governing metal–metal interactions and guide the rational design of multimetallic complexes with tunable metal–metal bonds.

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

An Orbital Basis Set for Double Photoionization of Atoms and Molecules

The ab initio theoretical treatment of one-photon double photoionization processes has been limited to atoms and diatomic molecules by the challenges posed by large grid-based representations of the double ionized continuum wave function. To provide a path for extensions to polyatomics, an energy-adapted orbital basis approach is demonstrated that reduces the dimensions of such representations and simultaneously allows larger time steps in time-dependent computational descriptions of double ionization. Additionally, an algorithm that exploits the diagonal nature of the two-electron integrals in the grid basis and dramatically accelerates the transformation between grid and orbital representations is presented. Excellent agreement between the present results and benchmark theoretical calculations is found for H – and Be atoms, as well as the hydrogen molecule, including for the triply differential cross sections that relate the angular distribution and energy sharing of all of the particles in the molecular frame.

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

DONKEY: A Flexible and Accurate Algorithm for Clustering

We propose an accurate clustering algorithm suitable for the varied and multidimensional data sets that correspond to temporal snapshots from on-the-fly nonadiabatic trajectory-based simulations of photoexcited dynamics. The algorithm approximates the underlying probability density function using variable kernel density estimation, with local maxima corresponding to cluster centers. Each data point is then assigned to one of the maxima by employing a maximization procedure. Finally, clusters artificially separated by minor fluctuations in the probability density are merged. The algorithm does not require parameter tuning, which ensures flexibility and reduces the risk of bias. It is tested on several synthetic data sets, where it consistently outperforms conventional clustering algorithms. As a final example, the algorithm is applied to the excited dynamics of the norbornadiene ⇌ quadricyclane (C 7 H 8 ) molecular photoswitch, demonstrating how distinct reaction pathways can be identified.

algorithms↗
DOE OSTI2025

A Computational Framework for Simulations of Dissipative Nonadiabatic Dynamics on Hybrid Oscillator-Qubit Quantum Devices

Here, we introduce a computational framework for simulating nonadiabatic vibronic dynamics on circuit quantum electrodynamics (cQED) platforms. Our approach leverages hybrid oscillator-qubit quantum hardware with midcircuit measurements and resets, enabling the incorporation of environmental effects such as dissipation and dephasing. To demonstrate its capabilities, we simulate energy transfer dynamics in a triad model of photosynthetic chromophores inspired by natural antenna systems. We specifically investigate the role of dissipation during the relaxation dynamics following photoexcitation, where electronic transitions are coupled to the evolution of quantum vibrational modes. Our results indicate that hybrid oscillator-qubit devices, operating with noise levels below the intrinsic dissipation rates of typical molecular antenna systems, can achieve the simulation fidelity required for practical computations on near-term and early fault-tolerant quantum computing platforms.

Hamiltonians↗
DOE OSTI2025

Linearized Pair-Density Functional Theory with Spin–Orbit Coupling

Here, we include spin–orbit coupling (SOC) effects in linearized pair-density functional theory (L-PDFT), which is a multistate extension of multiconfiguration pair-density functional theory (MC-PDFT). Both 1-electron and 2-electron SOC integrals are computed using Breit-Pauli and Douglas–Kroll–Hess Hamiltonians in the atomic mean-field approximation. SO-L-PDFT removes the unphysical J-symmetry breaking observed in MC-PDFT. The accuracy of SO-L-PDFT is validated by calculations of zero-field splittings, fine-structure excitation energies, and low-energy excited-state spectra for a diverse group of atoms and molecules spanning the whole range of the periodic table, including atoms of groups 3, 11, and 13–17, the Ce 3+ and U 5+ ions, group 16 monohydrides, group 17 monoxides, lanthanide hexachlorides ([CeCl 6 ] 3− , [PrCl 6 ] 3− , and [NdCl 6 ] 3− ), actinyl ions ([UO 2 ] + , [NpO 2 ] 2+ ), and tricarbonatoactinyl complexes ([UO 2 (CO 3 ) 3 ] 5− , [NpO 2 (CO 3 ) 3 ] 4− ). We also compare the results to new spin–orbit-inclusive calculations by single-state and multistate multireference perturbation theory.

Hamiltonians↗
DOE OSTI2025

Determining the Ensemble N -Representability of Reduced Density Matrices

The N-representability problem for reduced density matrices remains a fundamental challenge in electronic structure theory. Following our previous work that employs a unitary-evolution algorithm based on an adaptive derivative-assembled pseudo-Trotter variational quantum algorithm to probe pure-state N-representability of reduced density matrices [J. Chem. Theory Comput. 2024, 20, 9968], in this work we propose a practical framework for determining the ensemble N-representability of a p-body matrix. This is accomplished using a purification strategy that embeds an ensemble state into a pure state defined on an extended Hilbert space, such that the reduced density matrices of the purified state reproduce those of the original ensemble. By iteratively applying variational unitaries to an initial purified state, the proposed algorithm minimizes the Hilbert-Schmidt distance between its p-body reduced density matrix and a specified target p-body matrix, which serves as a measure of the N-representability of the target. This methodology facilitates both error correction of defective ensemble reduced density matrices and quantum-state reconstruction on a quantum computer, offering a route for density-matrix refinement. We validate the algorithm with numerical simulations on systems of two, three, and four electrons in both simple models as well as molecular systems at finite temperature, demonstrating its robustness.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Learning Latent Representations to Bridge Coarse-Grained and Atomistic Resolutions in Polymer Simulations

We present a machine-learning-based framework for learning reduced-order representations of polymer chain conformations across coarse-grained (CG) and united-atom (UA) fidelities. By employing linear singular value decomposition and nonlinear autoencoders, we compress high-dimensional polymer configurations into latent spaces with minimal loss of structural accuracy. Crucially, we demonstrate a near-perfect linear mapping between CG and UA latent spaces, enabling an efficient super-resolution back-mapping procedure that reconstructs high-fidelity UA configurations from CG simulations. While minor structural inaccuracies occur, they are effectively corrected through a brief molecular dynamics relaxation, forming a practical hybrid machine learning−physics scheme. This approach establishes the key structural prerequisites for accelerated polymer dynamics simulations: a compact and accurate latent encoding of polymer chain conformations and a validated multi-fidelity mapping that permits reconstruction of UA structures from CG configurations. The extension of this framework to explicit time evolution within the latent space, enabling dynamics to be propagated at CG fidelity and decoded to UA resolution only when required, represents a natural and well-motivated direction for future work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

SCF Framework, HF Stability, and RPA Correlation for Jordan–Wigner-Transformed Spin Hamiltonians on Arbitrary Coupling Topologies

Mapping spins to fermions via the Jordan–Wigner (JW) transformation can render mean-field (Hartree–Fock, HF) descriptions effective for strongly correlated spin systems. As established in recent work, the application of such approaches is not limited by the nonlocal structure of JW strings or by site ordering because string operators can be absorbed into Thouless rotations of a Slater determinant, and the variational optimization of a unitary Lie-algebraic similarity transformation removes any ordering dependence. Leveraging these ideas, we develop a self-consistent field (SCF) scheme that expresses the mean-field energy as a functional of the single-particle density matrix, providing an alternative to gradient-based optimization of Thouless parameters. We derive the analytical orbital Hessian to diagnose HF stability and compute the ground-state correlation energy through the random-phase approximation (RPA). Benchmark results for the XXZ and J 1 –J 2 model on one- and two-dimensional lattices demonstrate that RPA significantly improves mean-field accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Charge Transport in Solvated Donor–Acceptor Functionalized Peptoids: Molecular Dynamics and Rate Theory

Scalable solar-energy conversion requires photoactive materials that combine the efficiency of natural photosynthetic systems with the stability and processability needed for practical applications. Achieving reliable charge transport in soft, self-assembled organic materials remains challenging, as structural fluctuations and environmental effects strongly influence charge-transfer (CT) rates. Here, we present a broadly applicable computational framework for evaluating CT rates in the condensed phase, combining Fermi’s golden rule rate theory with inputs from all-atom molecular dynamics (MD) simulations and first-principles electronic-structure calculations. The approach does not rely on system-specific parametrization and is applicable to a wide range of soft and disordered materials. We demonstrate the applicability and usefulness of the framework on redox-active peptoids functionalized with iron–porphyrin (Fe–P) complexes, a bioinspired platform with programmable donor–acceptor units and tunable three-dimensional organization. The calculated CT rates exhibit strong sensitivity to molecular conformation, with variations spanning several orders of magnitude. This dependence is shown to arise from the pronounced variation in diabatic electronic coupling with the relative orientations and separations of the Fe–P complexes across the conformational ensemble. The framework provides a consistent route for connecting atomistic structure to CT kinetics in the condensed phase and enables analysis of structure–rate relations in organic semiconducting systems.

Charge transfer↗
DOE OSTI2024

Comparison of Machine Learning Approaches for Prediction of the Equivalent Alkane Carbon Number for Microemulsions Based on Molecular Properties

The chemical properties of oils are vital in the design of microemulsion systems. The hydrophilic–lipophilic difference equation used to predict microemulsions’ phase behavior expresses the oils’ physiochemical properties as the equivalent alkane carbon number (EACN). The experimental determination of EACN requires knowledge of the temperature dependence of the microemulsion system and the effects of different surfactant concentrations. Thus, the experimental determination is time-intensive and tedious, requiring days to months for proper separations. Furthermore, the experiments require high purity of chemicals because microemulsions are sensitive to impurities. Our work focuses on the quick and reliable predictions of the EACN with machine learning (ML) models. Due to the immaturity of ML chemical predictions, we compare three graph neural networks (GNNs) and a gradient-boosted tree algorithm, known as XGBoost. The GNNs use the molecular structures represented as simplified molecular-input line-entry system (SMILES) codes for the initial input, which allows us to assess whether geometry optimization is necessary for reliable results. The XGBoost model also begins with the SMILES representations of the molecules but uses molecular descriptors instead of geometry optimizations. As a result, the best model tested (crystal graph convolutional neural network with Merck molecular force field-94) has an error of 1.15 EACN units of the true EACN for unknown data with the errors skewed toward zero and an R² score of 0.9

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

Toward a Machine Learning Approach to Interpreting X-ray Spectra of Trace Impurities by Converting XANES to EXAFS

The fact that the photoabsorption spectrum of a material contains information about the atomic structure, commonly understood in terms of multiple scattering theory, is the basis of the popular extended X-ray absorption spectroscopy (EXAFS) technique. How much of the same structural information is present in other complementary spectroscopic signals is not obvious. Here we use a machine learning approach to demonstrate that within theoretical models that accurately predict the EXAFS signal, the extended near-edge region does indeed contain the EXAFS-accessible structural information. We do this by exhibiting deep operator neural networks (DeepONets) that have learned the relationship between the extended and near edge portions of the X-ray absorption spectrum to predict the former from the latter. We find that we can accurately predict the EXAFS spectrum between 6 and 14 Å –1 from the first 6 Å –1 (≈100 eV) of the absorption spectrum of Cu 2 + substitutional defects in the Fe 3+ mineral hematite (α-Fe 2 O 3 ). This surprising finding implies that theoretical analyses of X-ray absorption spectra could be implemented that extract the same conclusions as high-quality EXAFS studies from spectra collected over a much smaller range of photon energies. This relaxes a host of experimental limitations related to the X-ray source and measurement sample, including collection time, minimum dopant concentration, source brilliance, and energy range. We describe the theoretical data sets and DeepONet construction and show that the resulting DeepONets produce EXAFS that recovers linear combination fits to experimental data with accuracy approaching the original ab initio calculations. We discuss the implications of our findings for minor constituent characterization and for understanding the information content of spectroscopic data more broadly, including how this approach might be applied to measured experimental spectra. In conclusion, to encourage similar efforts, the simulated X-ray spectra, machine learning, and fitting code are publicly available.

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

Chemist: A Domain-Specific Language by Chemists for Chemists

Managing the complexity of quantum chemistry (QC) software is key to ensuring it remains accessible, maintainable, and reusable. Noticeably missing from the QC ecosystem are modules targeting bottleneck routines. Here we argue that this is likely due to the difficulty in defining interfaces for such modules. To that end, we introduce the open-source, publicly available Chemist library https://github.com/NWChemEx/Chemist. Chemist is a domain-specific language targeting the QC domain. Chemist has been developed focusing on performance and user-friendliness. Using Chemist, QC tasks are defined using familiar domain concepts such as molecules, wave functions, and operators. The domain objects are hierarchical to ensure a systematic encapsulation of information. Key features of Chemist include: extensibility, the ability to alias existing data, and the ability to succinctly define many common QC tasks. The usefulness of Chemist is demonstrated by discussing the interface of NWChemEx’s Fock build module and by showcasing a proof-of-concept self-consistent field algorithm containing uncertainty propagation.

Algorithms↗
DOE OSTI2025

How Thermodynamic, Electronic, and Steric Factors Influence Mesitylcopper Oligomers

Mesitylcopper (CuMes) is a highly versatile organocopper reagent used in both organic and inorganic syntheses. It has previously been shown that CuMes exists as a tetrameric or pentameric cyclic oligomer [CuMes] n (n = 4, 5), both in solution and in the solid state. The bonding arrangement between the [CuMes] units has qualitatively been described as localized three-center twoelectron (3c-2e) bonds. However, the electronic, structural, and thermodynamic forces driving this aggregation are still not well understood. For this reason, we employed density functional theory (DFT) calculations to study mesitylcopper as a monomeric [CuMes] unit and [CuMes]n oligomers with n = 2 to n = 7. We found that there is a strong electronic driving force for aggregation caused by strong mixing between the Cu’s d orbitals and Mes’s π orbitals in oligomers larger than the dimer. This mixing is only optimized in oligomers with n ≥ 3, where the mesityl group is no longer bonded to a single copper center but instead becomes a bridging ligand. Beyond the trimer, steric and entropic factors become relevant for determining the relative stabilities of the different aggregates, with midsized oligomers (n = 4−5) having the optimal balance between the electronic Cu−C bonding character, Cu···Cu attractive forces, entropy, reduced internal ring strain, and reduced steric interactions between the mesityl groups.

Copper↗
DOE OSTI2025

The UV Photoinduced Ring-Closing Reaction of Cyclopentadiene Probed with Ultrafast Electron Diffraction

Conjugated cyclic organic molecules are common across many fields such as pharmaceuticals, are naturally occurring in biological systems, and are used in synthetic materials. One particular area of interest from a photochemical point of view is the formation of highly strained cyclic organics. We investigate the photoinduced reaction of cyclopentadiene, a five-membered organic ring molecule which can form strained three and four carbon rings after photoexcitation with UV light, with the gas-phase ultrafast electron diffraction instrument at the SLAC MeV-UED facility. Electron diffraction offers a direct probe sensitive to the nuclear geometry during the reaction, allowing for the determination of the distribution of products formed following photoexcitation. We observe the simultaneous formation of the highly strained ring- closed bicyclo[2.1.0]pentene and vibrationally hot cyclopentadiene within the temporal resolution of the experiment, and determine the relative yield of all reaction products. Furthermore, the experimental results are in good agreement with the predictions of trajectory simulations.

Computational Chemistry↗