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DOE OSTI2022

Krylov subspace recycling for evolving structures

Krylov subspace recycling is a powerful tool when solving a long series of large, sparse linear systems that change only slowly over time. In PDE constrained shape optimization, these series appear naturally, as typically hundreds or thousands of optimization steps are needed with only small changes in the geometry. In this setting, however, applying Krylov subspace recycling can be a difficult task. As the geometry evolves, in general, so does the finite element mesh defined on or representing this geometry, including the numbers of nodes and elements and element connectivity. This is especially the case if re-meshing techniques are used. As a result, the number of algebraic degrees of freedom in the system changes, and in general the linear system matrices resulting from the finite element discretization change size from one optimization step to the next. Changes in the mesh connectivity also lead to structural changes in the matrices. In the case of re-meshing, even if the geometry changes only a little, the corresponding mesh might differ substantially from the previous one. Obviously, this prevents any straightforward mapping of the approximate invariant subspace of the linear system matrix (the focus of recycling in this work) from one optimization step to the next; similar problems arise for other selected subspaces. In this paper, we present an algorithm to map an approximate invariant subspace of the linear system matrix for the previous optimization step to an approximate invariant subspace of the linear system matrix for the current optimization step, for general meshes. This is achieved by exploiting the map from coefficient vectors to finite element functions on the mesh, combined with interpolation or approximation of functions on the finite element mesh. We demonstrate the effectiveness of our approach numerically with several proof of concept studies for a specific meshing technique.

42 ENGINEERING↗

DOE OSTI2025

Proton, Electron, and Hydrogen-Atom Transfer Thermodynamics of the Metal–Organic Framework, Ti-MIL-125, Are Intrinsically Correlated to the Structural Disorder

Interfacial charge transfer reactions involving protons and/or electrons are fundamental to heterogeneous catalysis and many other reactions relevant to energy, chemical, and biological sectors. Metal–organic frameworks (MOFs) with redox-active metal-oxo nodes have emerged as candidate materials to examine these reactions with near-atomic-level precision, given their crystalline nature. Here, we employed a colloidally stable, Ti-based MOF, Ti-MIL-125, with different crystal sizes to examine catalytically relevant charge transfer thermodynamics. The Ti 8 (μ 2 -O) 8 (μ 2 -OH) 4 nodes structurally mimic TiO 2 , which has shown some PCET reactivity toward reactions of H 2 , O 2 , and others. In this report, we have demonstrated that a change in crystal size induces different amounts of structural disorder to the Ti-oxo node, further changing the thermodynamics of proton/electron/hydrogen-atom transfer reactions. Using electrochemical open-circuit potential (E OCP ) measurements, we have determined that all crystallites undergo a 1H + /1e – redox reaction, which, given the stoichiometry, can be considered as a net H atom transfer (HAT) reaction. The thermodynamics of this HAT reaction, the Ti 3+ O–H bond dissociation free energy (BDFE), was dependent on the crystal size of the MOF, as the decrease in crystal size induced more structural disorder. Our computational calculations have indicated that this difference in BDFE is due to a local change in the geometry of Ti cations, rather than the commonly invoked defects, such as the “missing-linker” defect sites. Individual proton/electron transfer (PT/ET) thermodynamics were also highly dependent on the crystal sizes. These were probed using pK a or band gaps (E g ), respectively. These findings suggest that, particularly when MOFs are nanosized with a large amount of structural disorder, they should no longer be considered “true” single-site catalysts; this is an implicit, but widespread assumption within the MOF-based catalysis field. Implications of these findings will be contrasted with structurally similar metal oxides like TiO 2 and other redox-active MOFs.

Bond dissociation free energy↗

DOE OSTI2021

CaMn 3 IV O 4 Cubane Models of the Oxygen‐Evolving Complex: Spin Ground States S <9/2 and the Effect of Oxo Protonation

Abstract We report the single crystal XRD and MicroED structure, magnetic susceptibility, and EPR data of a series of CaMn 3 IV O 4 and YMn 3 IV O 4 complexes as structural and spectroscopic models of the cuboidal subunit of the oxygen‐evolving complex (OEC). The effect of changes in heterometal identity, cluster geometry, and bridging oxo protonation on the spin‐state structure was investigated. In contrast to previous computational models, we show that the spin ground state of CaMn 3 IV O 4 complexes and variants with protonated oxo moieties need not be S =9/2. Desymmetrization of the pseudo ‐ C 3 ‐symmetric Ca(Y)Mn 3 IV O 4 core leads to a lower S =5/2 spin ground state. The magnitude of the magnetic exchange coupling is attenuated upon oxo protonation, and an S =3/2 spin ground state is observed in CaMn 3 IV O 3 (OH). Our studies complement the observation that the interconversion between the low‐spin and high‐spin forms of the S 2 state is pH‐dependent, suggesting that the (de)protonation of bridging or terminal oxygen atoms in the OEC may be connected to spin‐state changes.

Lee, Heui Beom↗

DOE OSTI2021

CaMn 3 IV O 4 Cubane Models of the Oxygen‐Evolving Complex: Spin Ground States S <9/2 and the Effect of Oxo Protonation

Lee, Heui Beom↗

DOE OSTI2025

Toward Computation-Guided Design of Tunable Organic-Inorganic CdS Quantum Dot Binary Superlattices

Combining the advantages of structural programmability in sequence-defined biomimetic molecules and the controllable packing geometry in nanoparticle superlattices, we demonstrate a self-assembled organic-inorganic superlattice whose structure can be altered with the slightest change in the sequence of the organic counterpart. Here, oleate-coated CdS quantum dots (QDs) form a square-packed superlattice with a 1:1 molar equivalence of a di-block amphiphilic peptoid (Nbrpe6Dig) in chloroform. In contrast, no apparent structure is observed in the organic solvent alone. Based on theoretical evidence, we show that the assembly is a binary superlattice where both the CdS QDs and the peptoids serve as building blocks and further predict a correlation between the superlattice structure and the peptoid sequence. The computationally guided prediction is validated by experiments where superlattice transformation is observed with modified peptoids. The mechanism identified in our work inspires new ways to control and tune organic-inorganic hybrid nanomaterial self-assembly.

Qi, Xin↗

DOE OSTI2026

State-of-Charge Investigation of Lithium Manganese Dioxide Primary Batteries Utilizing X-ray Computed Tomography

Lithium primary batteries (LPBs) represent a class of energy storage devices, uniquely suited for mission-critical applications including emergency backup power, aerospace and defense electronics, implantable medical devices, and remote sensing. Despite their technological maturity and distinct advantages over rechargeable lithium-ion batteries (i.e., superior shelf life and operational simplicity), state-of-charge (SoC) estimation in these batteries remains a persistent challenge due to the lack of a reliable, quantifiable diagnostic technique. In this work, we investigate X-ray computed tomography (X-CT) as a transformative and accurate SoC estimation technique for LPBs. Results gained through X-CT measurements reveal systematic, quantifiable structural changes in cathode morphology and geometry during discharge, establishing a direct structural basis for SoC estimation, with a maximum relative standard deviation of 2.3%. This work establishes a pathway toward operando, imaging-driven SoC diagnostics that can significantly enhance the reliability of SoC estimation in LPBs.

25 ENERGY STORAGE↗

DOE OSTI2022

The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron–Sulfur Cubanes

Iron–sulfur clusters comprise an important functional motif in the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from correlated, large active space calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. Here, to provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of the [Fe(II/III) 4 S 4 (SMe) 4 ] -2 clusters using two complementary, correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (<1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the singlet and the spin state 2S + 1 = 19, corresponding to a maximal number of Fe-d electrons being unpaired and of parallel spin, is strongly geometry dependent, changing by a factor of 3 upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap compared to typical mean-field orbital approaches. Our results show the need for performing large active space calculations to unveil the challenging electronic structure of these complex catalytic centers and should serve as accurate starting points for fully correlated treatments upon inclusion of dynamical correlation outside the active space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Nanostructure‐Derived Antireflectivity in Leafhopper Brochosomes

Understanding how insect‐derived biomaterials interact with light has led to new advances and interdisciplinary insights in entomology and physics. Leafhoppers are insects that coat themselves with highly ordered biological nanostructures known as brochosomes. Brochosomes are thought to provide a range of protective properties to leafhoppers, such as hydrophobicity and antireflectivity, which has inspired the development of synthetic brochosomes that mimic their structures. Despite recent progress, the high antireflective properties of brochosome structures are not fully understood. Herein, a combination of experiments and computational modeling is used to understand the structure‐, material‐, and polarization‐dependent optical properties of brochosomes modeled on the geometries found in three leafhopper species. The results qualitatively represent that light interference interaction with nanostructures naturally occurring in brochosomes is responsible for the spectral tuning and the asymmetric line shape of the reflectance spectra. Whereas prior work has focused on the computational modeling of idealized pitted particles, this work shows that light–matter interactions with brochosome structures can be tuned by varying the geometry of their cage‐like nanoscale features and by changing the arrangement of multiparticle assemblies. Broadly, this work establishes principles for the guided design of new optically active materials inspired by these unique insect nanostructures.

Banerjee, Progna↗

DOE OSTI2022

Asphericity Can Cause Nonuniform Lithium Intercalation in Battery Active Particles

Uniform intercalation is desired to enable next-generation Li-ion batteries. While we expect nonuniformity in materials undergoing a phase change, single-phase intercalation materials such as nickel manganese cobalt oxide are believed to lithiate uniformly at the particle/electrolyte interface. However, recent imaging reveals nonuniform lithiation. Motivated by this discrepancy, we examine if aspherical particle shape can cause such nonuniformity since the conventional belief is based on spherical particle theory. We obtain real particle geometries using rapid lab-based X-ray computed tomography and subsequently perform physics-based calculations accounting for electrochemical reactions at the particle/electrolyte interface and lithium transport inside the particle bulk. The aspherical geometry breaks the symmetry and causes nonuniform reaction distribution. Such nonuniformity is exacerbated as the particle becomes more aspherical. We report the proposed mechanism represents a fundamental limit on achievable lithiation uniformity in aspherical particles in the absence of other mechanisms causing inhomogeneity, such as grain structure, nonuniform carbon-binder coating, etc.

25 ENERGY STORAGE↗

DOE OSTI2024

Effect of Heat Treatment on Microstructure and Mechanical Property of 316L Stainless Steel Produced by Laser Powder Bed Fusion

The advanced non-light water reactor designs (Gen IV reactors), including molten salt/ very high temperature/ sodium-cooled and lead-cooled fast reactors, typically operate at higher temperatures and more extreme radiation conditions than light water reactors. An intrinsic part of the deployment and progress of Gen IV reactor designs is selecting the most suitable structural material for a specific application. Additive manufacturing (AM), a fairly new process of making physical, three-dimensional objects from a computer design file, is going to completely change the way of design, build and certify nuclear systems. It offers a range of opportunities to produce complex geometries from existing materials, offers new routes for processing of previously difficult to process materials, allows for design of new high-performance materials, and finally facilitates hybridization of dissimilar materials. This emerging technology has successfully produced cars, wind turbine blade molds and even live cells. It could also open up big opportunities for the nuclear industry to quickly deploy technologies at a fraction of the cost. So far, AM techniques have been preliminarily applied in the field of nuclear reactors, including the classical parts such as the pressure vessel of a small reactor with 508-III steel, the bottom nozzle of a fuel assembly with 304L steel, the fuel cladding with zirconium alloy and the integrated impeller of a pump and the multi-channel valve body with 316L steel [6,7]. The AM applications for operating nuclear reactors started in auxiliary plant components and have slowly migrated to metallic reactors and core components, but many of these are not safety critical components. Although many parts used for nuclear reactors have been fabricated by AM techniques, practical applications in engineering are still a long way off due to the uncertainty factors focused on the processing, material properties, analysis methods and application standards, which feeds the safety and life-cycle of the nuclear reactor. Due to rapid, repeated heating and cooling during production, a high dislocation density was present in the AM material. This microstructure feature is unstable at elevated temperature while high temperature is one of the typical operation environments for nuclear reactors. Thus, it is important to understand the thermal effect on the microstructure of AM material. The objectives of this study are to investigate the effect of heat treatment on the microstructure and mechanical properties of 316L stainless steel produced by laser powder bed fusion additive manufacturing, and to determine an appropriate heat treatment practice that will be applied to the lightweight AM lattice-structured material with the same chemistry. The heat treatment study consisted of annealing the samples at a temperature range of 800 to 1200 oC with a 50 oC increment for different times (1-24 hours), followed by vacuum or air cooling. Microstructural characterization was carried out by Scanning Electron Microscope (SEM). Grain size and crystallographic orientation were investigated by Electron Backscatter Diffraction (EBSD). Vickers hardness tests with a 0.5 kg load were employed to determine the hardness of samples after different heat treatments. After heat treatment, the random crystallographic orientation was preserved, and the volume fraction of high-angle grain boundaries (grain boundary misorientation =15 oC) remained the same. The dislocation density decreased with annealing temperature due to recovery. The fine subgrain structures in the as-printed specimen were quite stable up to 1200 oC. Minimal recrystallization was observed up to 1200 oC. Recrystallization initiated only after 8.5 hours at 1200 oC. The SEM images did not show obvious dependence of microstructure on cooling rate. The hardness of the specimens decreased with increasing annealing temperature as a result of the decrease in dislocation density. It is interesting to note that the AM material showed very similar hardness to the wrought material when annealing at similar temperature, although the microstructures are very different. Annealing at 1050 oC for 1 hour followed by air cooling was selected as the heat treatment procedure for the lattice designed lightweight AM 316L material.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Phase-Field Modeling of Materials Interfaces and Nanostructures

Nanostructured materials offer unique properties for a wide range of energy applications. Among various known processing methods, liquid metal dealloying (LMD)—the selective dissolution of a base alloy element into a metallic melt—has emerged as a powerful technique to produce a new class of nano-/meso-scale open porous and bicontinuous composite structures with ultra-high interfacial area. LMD has recently been complemented by the advent of vapor phase dealloying (VPD), a novel technique that exploits the selective evaporation of one element from a parent alloy containing elements with very different vapor pressures, thereby enabling to fabricate open nanoporous structures of various elements from less-noble metals to inorganic elements regardless of their chemical activity without requiring high LMD temperatures and chemical etching. Together LMD and VPD have greatly expanded the scope of dealloying techniques, limited by traditional electrochemical means to noble metals, and boosted the design of new functional and structural materials that combine a wide variety of elements. Topologically-connected open porous structures with ultra-high surface area allow mass transport within the structure while preserving structural integrity, enabling them to serve as catalysts, fuel cells, supercapacitors, or high-capacity battery materials. Bicontinuous composite structures in turn can display high strength and high ductility or superior radiation-damage resistance due to the ultra-high interface area between interpenetrating solid phases. This research program makes use of state-of-the-art computational methods to understand at a basic level the self-organizing dealloying process with main focus on dealloying kinetics and interfacial pattern formation at the dealloying front controlling initial structure size, topology, and phase compositions. Phase-field simulation studies of LMD focus on solid solutions, line compounds, and intermetallic systems that can form ternary composites by nucleation and growth of a new phase. Studies of VPD employ phase-field modeling and a hybrid method combining a kinetic Monte Carlo (KMC) model of evaporation and surface diffusion with molecular dynamics for vapor-phase transport inside nanopores. Simulations explore mechanisms of interface- and diffusion-controlled dealloying kinetics, both observed in VPD but not fundamentally understood. In addition, our newly developed multi-physics phase-field approach of large-volume-change phase transformations is being used to model novel 3D anode geometries based on dealloyed nanoporous structures including novel sandwiched graphene/Si/silica for highrate Li ion battery. Those studies are aimed at elucidating geometric design principles that improve mechanical stability. We expect this research to enhance the capability to tailor nano-/mesoscale structures for a wide range of energy-related materials applications and to yield further advances in computational methodologies that benefit a broad materials research community.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

DIF3D-VARIANT 12.0: Updates and New Features

The DIF3D code has been a workhorse of fast reactor analysis work at Argonne National Laboratory for over 40 years. In 1995, a transport option called VARIANT was added to DIF3D to improve the flux solutions for fast reactor problems which we term DIF3D-VARIANT today. DIF3D-VARIANT performs nodal neutron transport calculations using P N or SP N theory in Cartesian and hexagonal two- and three-dimensional geometries. The limited computing capabilities of the time restricted DIF3D-VARIANT to use at most a 6 th order spatial approximation combined with a P3 flux approximation and P1 scattering kernel for a 33 group structure on most studied reactor problems. Computer capabilities have increased steadily since 1995 and today much larger space-angle-energy approximations are possible. This manuscript serves as an update to the theory section of the original DIF3D-VARIANT manual and details more than twenty years of changes made to DIF3D to make version 12 which was released on November 1 st , 2024. The primary focus of the initial work was to extend the space-angle approximations available in DIF3D-VARIANT such that the error due to transport approximations could be better understood. This work was started and completed in 2002 and marked the official version 10. Unfortunately, those higher order approximations could not be used at that time due to the memory constraints of the BPOINTER part of DIF3D (limited to 2 GB). In version 11, completed in 2012, BPOINTER was circumvented in DIF3D-VARIANT for the largest arrays by introducing a Fortran 90 module called LMA (Large Memory Array). This seamlessly replaces all of the functionality of the BPOINTER concept, but it allows 64 bit addressing for every array such that they can be larger than 2 GB. It is now common for DIF3D-VARIANT jobs to consume 50 GB of memory on modern workstations when using high order space-angle approximations and a large number of groups. Many improvements were made to version 11 from 2012 to 2022 when work to create version 12 started. For version 12, several parts of DIF3D were updated to improve performance and thread parallelism was introduced to further reduce the runtime. Numerous minor bugs were discovered in DIF3D-VARIANT as part of the process of creating the perturbation and sensitivity code PERSENT. All of these algorithmic problems were identified in the transition from version 10 to version 11 which prevented DIF3D-VARIANT from running efficiently and reliably. Firstly, the coarse mesh rebalance scheme would routinely diverge and a study detailed in this report demonstrates how it was also typically not effective. This is not a failure of the coarse mesh rebalance methodology, but a failure of its implementation in DIF3D-VARIANT for hexagonal geometries. The fission source extrapolation algorithm was also found to be unreliable on larger group structure problems, leading to divergence in some cases and a negligible improvement in performance overall. Finally, the “Omega” acceleration applied to the partial current solver routine of DIF3D-VARIANT was found to cause DIF3D-VARIANT to converge to the wrong answer. To resolve these issues, both the coarse mesh rebalance and fission source extrapolation were permanently disabled in version 11. The Tchebychev acceleration was put in as a temporary reliable alternative but it is generally inferior to coarse mesh rebalance or coarse mesh finite difference. For the Omega acceleration, the factor was restricted to guarantee that it would not cause follow-on errors in PERSENT. Due to limited funding to support maintenance and development of DIF3D in the last 10 years, no effort was spent since to resolve the outer iteration acceleration. Except for the threading work, all of the changes discussed in this manuscript refer to changes made between version 10 and version 11. Performance comparisons are done to demonstrate the improvements from version 9 to version 12. As will be demonstrated, the updated versi

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Assessment of Microstructure Prediction Capabilities for Powder Bed Fusion Stainless Steel 316

The Advanced Materials and Manufacturing Technologies program aims to accelerate the development, qualification, demonstration, and deployment of advanced materials and manufacturing technologies to enable reliable and economical nuclear energy. However, the characteristic process-structure-property relationships of additive manufacturing (AM) materials pose challenges for the qualification and certification of AM nuclear components. In particular, component-scale variations in microstructure and properties can be driven by localized changes in melt pool dynamics due to how process parameters interact with different part geometries. Computational modeling tools can play a crucial role in predicting and controlling this variability. This report presents final results on process modeling tools designed to predict microstructure variability in additively manufactured stainless steel 316 parts. It details the software packages and physical modeling approaches employed to simulate an AM component within an automated process modeling workflow. Results are demonstrated through comparisons between predicted microstructures and experimental measurements across various representative processing conditions. The report concludes by discussing identified challenges and future opportunities for connecting the developed simulation workflow with mechanics simulations for prediction of part performance.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Development and Validation of Resistance-Capacitance Model (RCM) for Phase Change Material (PCM) Embedded in 3D Periodic Structures

The low thermal conductivity of Phase Change Materials (PCM) can be improved with extended surfaces such as additively manufactured 3D periodic lattice structures. Three different aluminum alloy-based lattices (base sizes 10, 20, and 40 mm) with average porosity of 0.95 filled with paraffin wax, with a nominal phase change temperature of 55°C, were experimentally investigated. In this work, a computationally efficient 2D Resistance Capacitance-based model (RCM) was developed for predicting the thermal characteristics of these geometries. Non-uniform porosity in the PCM-metal domain was estimated using image processing and served as model input. The solver does not solve for higher-order physics as in CFD but still can provide a good prediction of thermal resistance and energy storage at a very low computational cost. The simulation-to-real-time factor for this geometry is of the order of 10-4, while CFD simulations typically have a real-time factor greater than 1. The model was validated against the experimental data for melting under three different heat fluxes (6250 W/m2, 12500 W/m2, and 18750 W/m2). The mean deviation of the predicted average PCM temperature was between 1.34 K-2.81 K for different cases. The maximum average temperature deviation of 5.45 K was observed for the 20 mm geometry at the highest heat flux test condition. The effects of natural convection were neglected in the model, but the predicted PCM temperature and energy storage still showed good agreement with the experimental data.

25 ENERGY STORAGE↗

DOE OSTI2024

Resolving local ordering and structure in Mn x Ge 1- x Te alloys through thermodynamic ensembles of pair distribution functions

Characterizing local bonding environments in complex materials is essential for understanding and optimizing their properties. Equally as important is the ability to predict local motifs as a function of synthesis conditions, enhancing chemists’ ability to design properties into materials. In this study, we present an approach to leverage statistical mechanics to generate temperature- and energy-informed ensemble averaged pair distribution functions (PDFs). This method, which we have named Thermodynamic Ensemble Averages of PDFs for Ordering and Transformations (TEAPOT), utilizes density functional theory (DFT) to relax supercells while incorporating energetic penalties for local order, enabling accurate and computationally efficient analysis of local structure. We apply this method to the neutron PDF measurements of the pseudobinary MnTe–GeTe (MGT) alloy, demonstrating its capability to resolve complex local distortions and chemical ordering. Our results reveal detailed insights into phase transformations and local distortions driven by Mn substitution. For compositions that globally present as rock salt, our analysis reveals that Ge coordination geometry is heavily impacted by synthesis temperature. We propose that high temperature synthesis conditions promote a lowered Ge polyhedra distortion, promoting high charge carrier mobility due to the alignment of local and global structure. Incorporating statistical mechanics and computation into experimental analysis thus guides synthesis of tailored local structure.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Controlling Molecular Structure and Spin with Multiconfigurational Quantum Chemistry (Final Technical Report)

For many first-row transition metal complexes, structure-property relationships can be obtained from high-level molecular geometry optimizations and subsequent electronic structure studies. The project funded under this award utilized newly implemented fully internally contracted (FIC) nuclear gradients for extended multi-state (XMS) complete active space second-order multireference perturbation theory (CASPT2) to explore geometry changes in first-row transition metal coordination complexes. At the start of the project, only one full geometry optimization using FIC-CASPT2 analytical gradients had been reported (J. Chem. Theory Comput., 2016, 12 (8), 3781), and many open-questions regarding the performance and achievable accuracy in applying such computations to larger complexes persisted. Key deliverables in the report include the implementation of the numerical Hessian and subsequent vibrational analysis in the BAGEL program package. This includes both full Hessian vibrational analysis (FHVA) and a partial Hessian vibrational analysis (PHVA). The latter of which allows us to reduce the significant cost of computing the vibrational frequencies in a large molecule by focusing on the modes of highest interest. The gradient code also proved useful in the development of an approach to improve the Hubbard-U correction by removing bias in predicting spin-splitting in Fe(II) complexes via plane-wave density functional theory (DFT). Finally, we showed for three families of complexes (spin-crossover (SCO) complexes, metallocorroles complexes, and those with metal-metal bonds) that CASPT2 can result in good molecular geometries and established best practices in undertaking this work. We are now using this approach in collaborative projects with experimental groups, which would not have been possible at the start of this project. A common theme also arose through this work that static and dynamic correlation must be recovered in a balanced way to yield quantitative results. By systematically varying how both effects were included, we were able to make key chemical insights. This work supported the training of two postdoctoral scholars, one graduate student, and one undergraduate student in applying high-level wavefunction based methods to challenging systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Cu site differentiation in tetracopper(I) sulfide clusters enables biomimetic N 2 O reduction

Copper clusters feature prominently in both metalloenzymes and synthetic nanoclusters that mediate catalytic redox transformations of gaseous small molecules. Such reactions are critical to biological energy conversion and are expected to be crucial parts of renewable energy economies. However, the precise roles of individual metal atoms within clusters are difficult to elucidate, particularly for cluster systems that are dynamic under operating conditions. Here, we present a metal site-specific analysis of synthetic Cu 4 (μ 4 -S) clusters that mimic the Cu Z active site of the nitrous oxide reductase enzyme. Leveraging the ability to obtain structural snapshots of both inactive and active forms of the synthetic model system, we analyzed both states using resonant X-ray diffraction anomalous fine structure (DAFS), a technique that enables X-ray absorption profiles of individual metal sites within a cluster to be extracted independently. Using DAFS, we found that a change in cluster geometry between the inactive and active states is correlated to Cu site differentiation that is presumably required for efficient activation of N 2 O gas. More precisely, we hypothesize that the Cu δ+ ∙∙∙Cu δ- pairs produced upon site differentiation are poised for N 2 O activation, as supported by computational modeling. These results provide an unprecedented level of detail on the roles of individual metal sites within the synthetic cluster system and how those roles interplay with cluster geometry to impact the reactivity function. We expect this fundamental knowledge to inform understanding of metal clusters in settings ranging from (bio)molecular to nanocluster to extended solid systems involved in energy conversion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Methods to Calculate Electronic Excited-State Dynamics for Molecules on Large Metal Clusters with Many States: Ensuring Fast Overlap Calculations and a Robust Choice of Phase

Here, we present an efficient set of methods for propagating excited-state dynamics involving a large number of configuration interaction singles (CIS) or Tamm-Dancoff approximation (TDA) single-reference excited states. Specifically, (i) following Head-Gordon et al., we implement an exact evaluation of the overlap of singly-excited CIS/TDA electronic states at different nuclear geometries using a biorthogonal basis and (ii) we employ a unified protocol for choosing the correct phase for each adiabat at each geometry. For many-electron systems, the combination of these techniques significantly reduces the computational cost of integrating the electronic Schrodinger equation and imposes minimal overhead on top of the underlying electronic structure calculation. As a demonstration, we calculate the electronic excited-state dynamics for a hydrogen molecule scattering off a silver metal cluster, focusing on high-lying excited states, where many electrons can be excited collectively and crossings are plentiful. Interestingly, we find that the high-lying, plasmon-like collective excitation spectrum changes with nuclear dynamics, highlighting the need to simulate non-adiabatic nuclear dynamics and plasmonic excitations simultaneously. In the future, the combination of methods presented here should help theorists build a mechanistic understanding of plasmon-assisted charge transfer and excitation energy relaxation processes near a nanoparticle or metal surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗