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DOE OSTI2025

Heterogeneous Mixtures of Dictionary Functions to Approximate Subspace Invariance in Koopman Operators: Why Deep Koopman Operators Work

Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

Johnson, Charles A.↗

DOE OSTI2025

Characterization of the fractal dimension of helium plumes in laminar to turbulent transition

Abstract Schlieren imaging in conjunction with a high-speed camera was used to observe the behavior of metered helium plumes as they transition from laminar to turbulent flow in an air environment. The plumes were visualized at twelve jet Reynolds numbers ranging from 200 to 2980. The fractal dimension of the flows was obtained by applying a box counting algorithm to the recorded schlieren images. The results were analyzed to determine the correlation between the Reynolds number of the flow and the fractal dimension of the observed turbulence. A trend of increasing fractal dimension with increasing Reynolds number was observed for several different types of schlieren cutoffs including horizontal cutoff, vertical cutoff, circular cutoff, focused shadowgraphy and de-focused shadowgraphy. The vertical cutoff and focused shadowgraphy imaging methods showed the most consistent results for the fractal dimension characterization during the laminar to turbulent transition. For transitional plumes, it was observed that fractal dimension increased with distance from the jet outlet.

42 ENGINEERING↗

DOE OSTI2024

Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method

Abstract An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb’s oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler–Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.

25 ENERGY STORAGE↗

DOE OSTI2021

Time-temperature-superposition analysis of diverse datasets by the minimum-arclength method: long-term prediction with uncertainty margins

In a recent publication, we carried out an extensive analysis of an unsupervised method of determining optimum shift factors in time-temperature-superposition of accelerated-aging data that involves minimizing the vertical arclength to obtain the master curve. For synthetic Arrhenius data with a variety of noise distributions, the work showed that, in conjunction with bootstrap-resampling, the method can produce reliable estimates of the mean activation energy along with uncertainty quantification. Here, we apply the above method to six different datasets taken from the published literature and demonstrate accurate prediction of mean activation energy from the data as-is without the need for any pre-processing or fitting. We also compare uncertainty margins computed by second-order bootstrap with that by linear regression theory and show that the former appears to provide consistent margins in the presence of common noise types in real data, including intra-isotherm measurement-errors, sample-to-sample variations, and intrinsic deviation from perfect Arrhenius behavior.

36 MATERIALS SCIENCE↗

DOE OSTI2020

One Electron Multiple Proton Transfer in Model Organic Donor–Acceptor Systems: Implications for High-Frequency EPR

EPR spectroscopy is an important spectroscopic method for identification and characterization of radical species involved in many biological reactions. The tyrosyl radical is one of the most studied amino acid radical intermediates in biology. Often in conjunction with histidine residues, it is involved in many fundamental biological electron and proton transfer processes, such as in the water oxidation in photosystem II. As biological processes are typically extremely complicated and hard to control, molecular bio-mimetic model complexes are often used to clarify the mechanisms of the biological reactions. In this work, we present theoretical calculations to investigate the sensitivity of magnetic resonance parameters to proton-coupled electron transfer events, as well as conformational substates of the molecular constructs which mimic the tyrosine-histidine (Tyr-His) pairs found in a large variety of proteins. Upon oxidation of the phenol, the Tyr analog, these complexes can perform not only one-electron one-proton transfer (EPT), but also one-electron two-proton transfers (E2PT). It is shown that in aprotic environment the g X -components of the electronicg-tensor are extremely sensitive to the first proton transfer from the phenoxyl oxygen to the imidazole nitrogen (EPT product), leading to a significant increase of the g X -value of up to 0.003, but are not sensitive to the second proton transfer (E2PT). In the latter case, the change of the g X -value is much smaller (ca. 0.0001), which is too small to be distinguished even by high-frequency EPR. The 14 N hyperfine values are also too similar to allow differentiation between the different protonation states in EPT and E2PT. The magnetic resonance parameters were also calculated as a function of the rotation angles around single bonds. It was demonstrated that rotation of the phenoxyl group results in large positive changes (> 0.001) in the g X -values. Analysis of the data reveals that the main source of these changes is related to the strength of the H-bond between phenoxyl oxygen and the proton(s) on N 1 and N 2 positions of the imidazole.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2019

Promoting microbial utilization of phenolic substrates from bio-oil

Abstract The economic viability of the biorefinery concept is limited by the valorization of lignin. One possible method of lignin valorization is biological upgrading with aromatic-catabolic microbes. In conjunction, lignin monomers can be produced by fast pyrolysis and fractionation. However, biological upgrading of these lignin monomers is limited by low water solubility. Here, we address the problem of low water solubility with an emulsifier blend containing approximately 70 wt% Tween® 20 and 30 wt% Span® 80. Pseudomonas putida KT2440 grew to an optical density (OD600) of 1.0 ± 0.2 when supplied with 1.6 wt% emulsified phenolic monomer-rich product produced by fast pyrolysis of red oak using an emulsifier dose of 0.076 ± 0.002 g emulsifier blend per g of phenolic monomer-rich product. This approach partially mitigated the toxicity of the model phenolic monomer p-coumarate to the microbe, but not benzoate or vanillin. This study provides a proof of concept that processing of biomass-derived phenolics to increase aqueous availability can enhance microbial utilization.

09 BIOMASS FUELS↗

DOE OSTI2024

Transition in ICF Capsule Implosions

Longstanding design and reproducibility challenges in inertial confinement fusion (ICF) capsule implosion experiments involve recognizing the need for appropriately characterized and modeled three-dimensional initial conditions and high-fidelity simulation capabilities to predict transitional flow approaching turbulence, material mixing characteristics, and late-time quantities of interest—e.g., fusion yield. We build on previous coarse graining simulations of the indirect-drive national ignition facility (NIF) cryogenic capsule N170601 experiment-a precursor of N221205 which resulted in net energy gain. We apply effectively combined initialization aspects and multiphysics coupling in conjunction with newly available hydrodynamics simulation methods, including directional unsplit algorithms and low Mach-number correction-key advances enabling high fidelity coarse grained simulations of radiation-hydrodynamics driven transition. Our presentation includes discussion of the capsule initialization and implosion dynamics, analysis of the vorticity production budget, transition signatures, quantities of interest—late-time ion temperature and fusion-neutron yield, numerical uncertainty quantification, and comparisons with NIF data.

42 ENGINEERING↗

DOE OSTI2021

Peptide nucleic acid Hoogsteen strand linker design for major groove recognition of DNA thymine bases

Sequence-specific targeting of double-stranded DNA and non-coding RNA via triple-helix-forming peptide nucleic acids (PNAs) has attracted considerable attention in therapeutic, diagnostic and nanotechnological fields. An E-base (3-oxo-2,3-dihydropyridazine), attached to the polyamide backbone of a PNA Hoogsteen strand by a side-chain linker molecule, is typically used in the hydrogen bond recognition of the 4-oxo group of thymine and uracil nucleic acid bases in the major groove. We report on the application of quantum chemical computational methods, in conjunction with spatial constraints derived from the experimental structure of a homopyrimidine PNA·DNA-PNA hetero-triplex, to investigate the influence of linker flexibility on binding interactions of the E-base with thymine and uracil bases in geometry-optimised model systems. Hydrogen bond formation between the N2 E-base atom and target pyrimidine base 4-oxo groups in model systems containing a β-alanine linker (J Am Chem Soc 119:11116, 1997) was found to incur significant internal strain energy and the potential disruption of intra-stand aromatic base stacking interactions in an oligomeric context. Additionally, in geometry-optimised model systems containing a 3-trans olefin linker (Bioorg Med Chem Lett 14:1551, 2004) the E-base swung out away from the target pyrimidine bases into the solvent. These findings are in qualitative agreement with calorimetric measurements in hybridisation experiments at T–A and U–A inversion sites. In contrast, calculations on a novel 2-cis olefin linker design indicate that it could permit simultaneous E-base hydrogen bonding with the thymine 4-oxo group, circumvention and solvent screening of the thymine 5-methyl group, and maintenance of triplex intra-stand base stacking interactions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2019

On the potential mechanisms of β to α' + β decomposition in two phase titanium alloys during additive manufacturing: a combined transmission Kikuchi diffraction and 3D atom probe study

In this paper, we focus on the mechanisms of phase transformations in additively manufactured Ti–6Al–4V during cooling. In particular, the goal is to understand if the imposed thermal cycles during fabrication results in the complete transformation of the α' to the β phase or the sub-transus decomposition of α' (martensite) to α + β. To this effect, samples fabricated using electron beam melting and laser-directed energy deposition techniques were analyzed using atom probe tomography (APT) in conjunction with correlative transmission Kikuchi diffraction (TKD). While the composition measurement using APT shows partitioning of vanadium into the β phase, the crystallographic analysis suggests evidence of a shear-induced transformation. Despite the pronounced differences in the processing conditions, both of the additive manufacturing techniques lead to similar partitioning of vanadium to the β phase. Finally, calculations using THERMOCALC and DICTRA show that under the time and temperature regimes of additive manufacturing the microstructure could develop by the decomposition reaction of α' → α+β.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Quantitative analysis of Raman spectral parameters for carbon fibers: practical considerations and connection to mechanical properties

Although the literature on the Raman spectra of carbon fibers is vast, no consistent, robust predictive relationship between mechanical properties of carbon fibers and spectral parameters exists. This shortcoming is due to the use of numerous fitting functions to evaluate Raman spectra of carbon fibers and the inconsistencies in establishing the best fitting models in a statistically robust fashion. To address this gap, we present a comprehensive work on the Raman spectra of carbon fibers that combines a vast library of experimental data with a robust numerical analysis and a statistical evaluation of a wide range of suggested fitting models. This manuscript begins with a brief review of the commonly applied fitting models. Then, the Raman spectra of 32 commercially available polyacrylonitrile-based carbon fibers collected at excitation wavelengths 532, 633, and 785 nm are presented and the best fit for all fibers is evaluated based on several statistical criteria in conjunction with numerical calculations and physical arguments. The results suggest that high-performance fibers must be fit with at least five peaks, whereas high-tensile modulus fibers are best fit with at least six distinct peaks. Finally, we employ simultaneous fitting of the Raman spectra of specific fibers and wavelengths and demonstrate that strong correlations exist between mechanical properties and the D1 peak position and shape across the range of evaluated mechanical properties. Finally, we suggest straightforward improvements in fitting analysis procedures that can be implemented to increase coherency in the understanding of the underlying carbon fiber microstructure intuited from Raman spectroscopy.

36 MATERIALS SCIENCE↗

DOE OSTI2021

National nuclear forensics libraries: a case study on benefits and possibilities for identification of sealed radioactive sources

A National Nuclear Forensic Library (NNFL) is a useful nuclear forensics tool which consists of information and subject matter expertise on radioactive and nuclear (RN) materials produced, used or stored within a State. If RN material is found out of regulatory control the NNFL can be used as part of a nuclear forensics investigation to help identify whether or not the material is consistent with a country’s national holdings. In previous work, a number of signatures which can be useful to identify sealed sources of 241 Am were investigated. To validate the measurement results, an official query concerning information about two of the previously investigated 241 Am sources was sent to the United States Department of State, the international point-of-contact (POC) for the U.S. NNFL. The aim of this work is to show how data obtained in a characterization of a radioactive source can be used in conjunction with an NNFL to investigate the history of a source out of regulatory control.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2023

Optimal Sizing and Dispatch of Solar Power with Storage

Designers of utility-scale solar plants with storage, seeking to maximize some aspect of plant performance, face multiple challenges. In many geographic locations, there is significant penetration of photovoltaic generation, which depresses energy prices during the hours of solar availability. An energy storage system affords the opportunity to dispatch during higher-priced time periods, but complicates plant design and dispatch decisions. Solar resource variability compounds these challenges, because determining optimal system sizes requires simultaneously considering how the plant will be operated under the imposed market and weather conditions. We develop an approach to analyze the economic performance of hybrid and single-technology solar power plants, which incorporates optimal dispatch, and considers the expected electricity market and weather conditions. We utilize the System Advisor Model software package to simulate the operation of multiple renewable generation and energy storage technologies, in conjunction with hourly-fidelity generation decisions determined by a revenue-maximizing, mixed-integer linear program. We show that, under our assumed market and weather conditions, the lifetime benefit-to-cost ratio can be improved by 6 to 19 percent, relative to a baseline design without optimizing, and that a concentrating solar power with thermal energy storage design produces significantly more energy per year, but is less profitable under our cost assumptions.

black-box optimization↗

DOE OSTI2021

Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation

Abstract We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student- t observations; (ii) Student- t processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Full-Field Strain Measurement Integrated with Two Dimension Regression Analysis to Evaluate the Bi-Modulus Elastic Properties of Isotropic and Transversely Isotropic Materials

Background: Measuring the physical properties of shale is critical for optimizing engineering activities such as geothermal energy generation and hydraulic fracturing. Shale is a transversely isotropic material. Furthermore, this material can also include micro and macro cracks at different locations and orientations that cause it to behave differently under tensile or compressive loading. Objective: In this work, a combined experimental–numerical approach is proposed to evaluate the bi-modulus elastic properties of isotropic and transversely isotropic materials. Methods: Full-field strain measurements for a circular disk under diametral compression are integrated with a regression analysis technique to evaluate the elastic properties of bi-modulus materials subjected to tensile and compressive loads using two loading configurations on the same specimen. Digital Image Correlation (DIC) is used to measure the full-field strains. Subsequently, in the case of an isotropic material, a linear least-squares approach is utilized to process the experimentally determined strains in conjunction with analytical expressions of the stress fields (in terms of far-field loading) to determine the elastic modulus E, the shear modulus G, and the Poisson’s ratio $v$. In the case of a transversely isotopic material, such as shale, a finite element model is implemented to determine the stress fields (again in terms of far-field loading), which is followed by repeating the previous regression analysis in an iterative process to estimate the elastic parameters. Results: The results show that the proposed technique successfully provides a complete set of elastic properties as a function of both the loading condition and the principal material directions. The technique is validated by measurements on a known isotropic material and then applied to determine the properties of shale. Conclusion: In this work, the proposed approach is successfully used to calculate the bi-modulus elastic response of poly(methyl meth- acrylate) (PMMA) and shale. As expected, PMMA exhibits an isotropic response with no bi-modulus effect, however, shale exhibits both transverse isotropy and a bi-modulus effect. Therefore, this approach holds promise for investigating the elastic properties of materials like rocks and fiber-reinforced composite laminates as functions of the principal material directions and the loading conditions.

42 ENGINEERING↗

DOE OSTI2020

An Alternative Casting Technique to Improve the Creep Resistance of Cast INCONEL Alloy 740H

The increasing performance requirements of power plant designs, such as advanced-ultra supercritical (A-USC), require the use of Ni-based superalloys to replace high-strength, ferritic-martensitic steels for components subjected to temperatures above 898 K (625 °C) and for austenitic stainless steels components at temperatures above 973 K (700 °C). To date, commercial Ni-based superalloy INCONEL 740H has been shown to be appropriate for use in A-USC power plants as boiler components in a wrought product. However, large complex components in boilers as well as other casings in the turbine and valve chest require castings of a thick-wall nature. Using the alloy in its cast form would be significantly valuable in terms of range of component size, geometry and complexity. Previous investigations revealed short creep lives from cast INCONEL alloy 740H. Here in this investigation, an alternative casting route that utilized a melt procedure resulting in a fine-grain casting, and in conjunction with a computationally optimized homogenization heat treatment, not only controlled the grain size and grain boundary structure but minimized chemistry variability and segregation. A primarily equiaxed and homogenous grain size distribution was obtained from this approach with better repartition of M 23 C 6 carbides along the grain boundaries. Furthermore, better than 38 pct increase was obtained for this material in comparison to the creep life obtained from the best performing conventionally cast material. More importantly, the fine-grain homogenized (FGH) casting route resulted in the Larson–Miller plot for this material that coincided with that of wrought alloy 740. At low creep stresses (with a test still in progress), the FGH casting is resulting in higher values of the LMP than the wrought alloy.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Accumulative Roll Bonding of Alloy 2205 Duplex Steel and the Accompanying Impacts on Microstructure, Texture, and Mechanical Properties

The mechanical and microstructural evolution of Alloy 2205 during severe plastic deformation is examined in this study. A combination of accumulative roll bonding (ARB) and cold rolling results in the successful formation of a nanograined dual-phase microstructure of austenite and ferrite with some transformed martensite. Severe deformation to cumulative reductions of 80.5, 92.5, 95, and 97 pct were performed. Microscopy indicates that grain dimensions in the sheet normal direction is less than 100 nm for reductions ≥ 92.5 pct. Shear banding is observed at reductions ≥ 95 pct while twinning is only observed at reductions < 92.5 pct. Neutron diffraction measurements indicated the presence of martensite for reductions ≥ 95 pct at ~ 8 pct volume fraction. Taken in conjunction, it appears that during initial ARB processing, both slip and twinning are active plastic mechanisms. As twinning becomes exhausted, martensitic transformation, slip, and intermittent shear banding account for the active plasticity mechanisms. Material hardness saturates at 92.5 pct reduction, with a maximum hardness of 45 HRC. Sub-sized tensile testing confirms this approximate hardness with measurements indicating a UTS of ~ 1440 MPa. Texture analysis of crystal orientation distributions in the plate normal direction suggest an approximate Kurdjumov–Sachs orientation relationship at all reductions above 80 pct indicating stability of the orientation relationship at high strains. The intragranular structure develops a fine scale sub-grain content with increasing deformation, resulting in a continual evolution of texture up to and including 97 pct reduction. The final structure presents strong components of Goss and rotated cube texture in both the austenite and ferrite. In this body of work we aim to compare ARB of an industrially relevant FCC/BCC system (Alloy 2205) to historical model FCC/BCC systems such as Cu/Nb.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Investigating the Interaction Between Circulating Tumor Cells and Local Hydrodynamics via Experiment and Simulations

Introduction: The biological and mechanical properties of circulating tumor cells (CTCs) in combination with the hemodynamics affect the preference of metastatic sites in the vasculature. Despite the extensive literature on the effects of biological properties on cell adhesion, the effects of hydrodynamic forces on primary attachment remains an active area of research. Here, using simulations in conjunction with experimentation, we provide new insight into the interplay of CTCs dynamics and local hydrodynamics. Methods: A flow experiment of CTC attachment was performed within a bioprinted, double branching endothelialized vessel. Simulations of fluid flow and CTC transport in the reconstructed and idealized bifurcated vessel were respectively performed by HARVEY, our in-house massively parallel computational fluid dynamics solver. HARVEY is based on the lattice Boltzmann and finite element methods to model the fluid and cells dynamics. The immersed boundary method is employed for resolving the fluid–structure interaction. Results: CTC attachment was quantified experimentally at all regions of the complex vessel. The results demonstrate a clear preference for CTCs to attach at the branch points. To elucidate the effect of the vessel topology on the location of attachment, a fluid-only simulation was performed assessing the differences in the hydrodynamics along the vessel. CTC transport in idealized bifurcated vessels was subsequently studied to examine the effects of cell deformability on the local hydrodynamics patterns and, thus, the preference of attachment sites. Conclusions: The current work provides evidence on the correlation of the hydrodynamics forces arising from the vessel topology and CTC properties on the attachment regions.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Co-adsorption of O{sub 2} and C{sub 2}H{sub 4} on a Free Gold Dimer Probed via Infrared Photodissociation Spectroscopy

Infrared multiple photon dissociation (IR-MPD) spectroscopy in conjunction with density functional theory (DFT) calculations has been employed to study the activation of molecular oxygen and ethylene co-adsorbed on a free gold dimer cation Au{sub 2}{sup +}. Both studied complexes, Au{sub 2}O{sub 2}(C{sub 2}H{sub 4}){sup +} and Au{sub 2}O{sub 2}(C{sub 2}H{sub 4}){sub 2}{sup +}, show distinct features of both intact O{sub 2} and ethylene co-adsorbed on the cluster. However, the ethylene C=C double bond is activated, increasing in length by up to 0.07 Å compared with the free molecule, and the red shift of the O–O vibration frequency increases with the number of adsorbed ethylene molecules, indicating a small but increasing activation of the O–O bond. The small O{sub 2} activation and the rather weak interaction between O{sub 2} and C{sub 2}H{sub 4} are also reflected in the calculated electronic structure of the co-adsorption complexes which shows only a small occupation of the empty anti-bonding O{sub 2} 2π{sup *}{sub 2p} orbital as well as the localization of most of the Kohn–Sham orbitals on O{sub 2} and C{sub 2}H{sub 4}, respectively, with only limited mixing between O{sub 2} and C{sub 2}H{sub 4} orbitals. The results are compared with theoretical studies on neutral Au{sub x}O{sub 2}(C{sub 2}H{sub 4}) (x = 3, 5, 7, 9) complexes. .

74 ATOMIC AND MOLECULAR PHYSICS↗