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At least 199 records · Page 11

The effect of composition on helium bubble nucleation in complex concentrated alloys

Molecular dynamics simulations of helium implantation have been performed in the MoNbTaTi complex concentrated alloy (CCA) to determine the impact of composition on helium clustering and bubble nucleation. It was found that compositions with lower interstitial atomic volume resulted in smaller cluster sizes, higher helium-to-vacancy ratios, and larger migration barriers. As the atomic volume decreases, it is harder to accommodate additional helium in the lattice and for helium to diffuse between interstitial sites, resulting in smaller cluster sizes. In particular, increasing molybdenum directly correlated with a decreased interstitial atomic volume and increased migration barrier. Niobium exhibited the opposite trend, where more niobium in the material resulted in larger interstitial atomic volumes and cluster sizes but lower migration barriers. The atomic volume was determined to be an indicator of the susceptibility of the material to helium bubble growth and could potentially be used as a metric to screen compositions for resistance to helium damage. In this way, properties such as available interstitial volumes could be used to screen materials more rapidly given the vast compositional space of CCAs.

McCarthy, Megan Jeanne [Sandia National Laboratori↗

Materials Data on Ti2H2CSe4Cl16O5 by Materials Project

Ti2C(OCl2)3(HSeOCl)2(SeCl3)2Cl2 crystallizes in the monoclinic P2/c space group. The structure is two-dimensional and consists of two molecular chlorine molecules; four HSeOCl clusters; four SeCl3 clusters; and one Ti2C(OCl2)3 sheet oriented in the (0, 1, 0) direction. In each HSeOCl cluster, H1+ is bonded in a single-bond geometry to one O2- atom. The H–O bond length is 0.99 Å. Se3+ is bonded in a distorted L-shaped geometry to one O2- and one Cl1- atom. The Se–O bond length is 1.83 Å. The Se–Cl bond length is 2.50 Å. O2- is bonded in a distorted water-like geometry to one H1+ and one Se3+ atom. Cl1- is bonded in a distorted single-bond geometry to one Se3+ atom. In each SeCl3 cluster, Se3+ is bonded in a single-bond geometry to one Cl1- atom. The Se–Cl bond length is 2.76 Å. There are three inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a 1-coordinate geometry to one Cl1- atom. The Cl–Cl bond length is 2.30 Å. In the second Cl1- site, Cl1- is bonded in a 2-coordinate geometry to one Se3+ and one Cl1- atom. The Cl–Cl bond length is 2.32 Å. In the third Cl1- site, Cl1- is bonded in a distorted linear geometry to two Cl1- atoms. In the Ti2C(OCl2)3 sheet, Ti4+ is bonded in a 5-coordinate geometry to one O2- and four Cl1- atoms. The Ti–O bond length is 2.71 Å. There are a spread of Ti–Cl bond distances ranging from 2.15–2.47 Å. C4+ is bonded in a linear geometry to two equivalent O2- atoms. Both C–O bond lengths are 1.18 Å. There are two inequivalent O2- sites. In the first O2- site, O2- is bonded in a single-bond geometry to one Ti4+ and one C4+ atom. In the second O2- site, O2- is bonded in a bent 150 degrees geometry to two equivalent Cl1- atoms. Both O–Cl bond lengths are 1.93 Å. There are three inequivalent Cl1- sites. In the first Cl1- site, Cl1- is bonded in a single-bond geometry to one Ti4+ atom. In the second Cl1- site, Cl1- is bonded in a water-like geometry to one Ti4+ and one O2- atom. In the third Cl1- site, Cl1- is bonded in an L-shaped geometry to two equivalent Ti4+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on H12Cl2O13 by Materials Project

H7O3H5O2(ClO4)2 crystallizes in the monoclinic P2_1/c space group. The structure is zero-dimensional and consists of four molecular hydrogen;dihydrate molecules, eight ClO4 clusters, and four H7O3 clusters. In each ClO4 cluster, there are four inequivalent O sites. In the first O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.48 Å. In the second O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.46 Å. In the third O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.46 Å. In the fourth O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.46 Å. Cl is bonded in a tetrahedral geometry to four O atoms. In each H7O3 cluster, there are seven inequivalent H sites. In the first H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 1.02 Å. In the second H site, H is bonded in a linear geometry to two O atoms. There is one shorter (1.05 Å) and one longer (1.53 Å) H–O bond length. In the third H site, H is bonded in a linear geometry to two O atoms. There is one shorter (1.05 Å) and one longer (1.53 Å) H–O bond length. In the fourth H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 1.00 Å. In the fifth H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 1.00 Å. In the sixth H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 0.99 Å. In the seventh H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 0.98 Å. There are three inequivalent O sites. In the first O site, O is bonded in a 3-coordinate geometry to three H atoms. In the second O site, O is bonded in a trigonal non-coplanar geometry to three H atoms. In the third O site, O is bonded in a 3-coordinate geometry to three H atoms.

36 MATERIALS SCIENCE↗

Density functional theory (DFT) study of UF 6 hydrolysis: reaction pathways, spectroscopy, and chemical kinetics

Depleted uranium hexafluoride (UF 6 ), a stockpiled byproduct of the nuclear fuel cycle, reacts readily with atmospheric humidity, but the gas-phase reaction mechanism and associated chemical kinetics are poorly understood. During the performance period we undertook development of a state-of-the-art ab initio gas-phase chemical kinetics simulation workflow to model the hydrolysis of uranium hexafluroride (UF 6 ). In doing so, we addressed several outstanding issues in the theoretical treatment of uranium-containing systems. At the outset it was unclear how to generate accurate estimates of kinetic and thermodynamic data for U-containing chemical reactions. Generation of such data has been made routine. Prior to our work, the literature associated with UF 6 hydrolysis were disparate and inaccurate. This body of work provides a modern and comprehensive theoretical assessment of the reaction mechanism, molecular clustering towards deposition, and chemical kinetics. New methodological implementations and software integrations resulting from this work are also highlighted. As much as possible, our predictions were validated against experimental data including particle morphologies, vibrational spectroscopy, atomization enthalpies, and kinetic rate constants. Nevertheless, we were unable to reconcile kinetic measurements with high-accuracy simulations.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Exploring the Structural, Dynamic, and Functional Properties of Metal–Organic Frameworks through Molecular Modeling

This review spotlights the role of atomic-level modeling in research on metal-organic frameworks (MOFs), especially the key methodologies of density functional theory (DFT), Monte Carlo (MC) simulations, and molecular dynamics (MD) simulations. The discussion focuses on how periodic and cluster-based DFT calculations can provide novel insights into MOF properties, with a focus on predicting structural transformations, understanding thermodynamic properties and catalysis, and providing information or properties that are fed into classical simulations such as force field parameters or partial charges. Classical simulation methods, highlighting force field selection, databases of MOFs for high-throughput screening, and the synergistic nature of MC and MD simulations, are described. By predicting equilibrium thermodynamic and dynamic properties, these methods offer a wide perspective on MOF behavior and mechanisms. Additionally, the incorporation of machine learning (ML) techniques into quantum and classical simulations is discussed. These methods can enhance accuracy, expedite simulation setup, reduce computational costs, as well as predict key parameters, optimize geometries, and estimate MOF stability. By charting the growth and promise of computational research in the MOF field, the aim is to provide insights and recommendations to facilitate the incorporation of computational modeling more broadly into MOF research.

36 MATERIALS SCIENCE↗

Using Density-Corrected DFT to Understand Density-Driven and Functional-Dependent Errors in Ab Initio Simulations of the Hydrated Electron

The hydrated electron, an excess electron in liquid water, plays a crucial role in a plethora of chemical processes, motivating extensive research efforts to characterize its structure, dynamics, and reactivity in solution. Recent theoretical approaches to understanding this intriguing object have involved ab initio simulations based on density functional theory (DFT). Although DFT allows for the study of hydrated electron reactivity and quantum mechanical behavior, it is well-known that anionic systems can suffer from significant density-driven errors (DDEs). Density-corrected DFT (DC-DFT) provides a framework to mitigate such errors; the method reduces DDEs by replacing the self-consistent (SC) density associated with a given density functional with the Hartree–Fock (HF) density. Since HF densities tend to be more localized than DFT SC densities, the DC-DFT scheme significantly improves errors in calculations where the SC density is spuriously delocalized. Here, we investigate how the use of density correction affects the calculated properties of the DFT-simulated (PBEh) hydrated electron, a particularly challenging diffuse anionic system to simulate. First, we analyze charge delocalization in a system consisting of a model octahedral hydrated electron water cluster (the so-called Kevan structure) along with a spatially separated sulfur atom. We show that the use of density correction indeed reduces DDEs in comparison to a standard DFT global hybrid functional. We then propagate molecular dynamics trajectories of the hydrated electron using DC-DFT, where we find that DC further localizes electron density in the cavity region, a signature of reduced charge delocalization. Unfortunately, the decreased radius of gyration of the spin density and corresponding tightening of the local solvation structure from density correction causes predicted observables to deviate further from experimental measurements than when density correction is not employed. Here, we argue that DC’s worse agreement with experiment results from the removal of a fortuitous cancellation of errors that is intrinsic to the PBEh functional. This indicates that the difficulties with DFT to simulate hydrated electrons are primarily due to the inherent approximations in DFT rather than to density-driven errors.

Density functional theory↗

Electrocatalytic alkene epoxidation at disrupted metal ensembles in blended electrolytes

The project aims to achieve a molecular understanding of oxygen-atom transfer from water to alkenes at electrocatalytic interfaces. Molecular oxygen is the most common oxygen-atom source for epoxidations, and our group is developing sustainable routes through which epoxidation of olefins is achieved using water as the oxygen source. This route can improve the safety of the reaction while also co-producing hydrogen, demonstrating the relevance of this reaction to the energy transition. If successful in our efforts, we may enable oxygen-atom transfer reactions at the anode of water electrolyzers in the place of conventional oxygen evolution, allowing for the synthesis of sustainable value-added co-products. In this vein, we explore several approaches to acquiring high selectivity toward epoxidation over competing reactions, such as oxygen evolution. One of our aims is to allow for rational control of epoxide selectivity by disrupting contiguous metal ensembles at the surface of catalytic metal oxide nanoparticles. Specifically, we aim to synthesize single-atom, few-atom, and many-atom clusters supported on metal oxides and study the mechanism of oxygen evolution and alkene epoxidation on these materials. Thus, this approach will determine the impact of disrupting metal ensembles on the selectivity for alkene epoxidation versus oxygen evolution in blended electrolytes. Another aim is to develop a molecular-level understanding of how a blended electrolyte (i.e., a mixture of aqueous and organic solvents) influences rates of alkene epoxidation versus oxygen evolution. In other words, we are interested in understanding the catalytic influence of the solvent, as our preliminary work shows that the selectivity and reactivity of epoxidation depend strongly on the solvent composition. This investigation includes blended electrolytes and electrolytes containing redox mediator species that improve selectivity toward the desired epoxidation reaction. Overall, our proposed work will help to provide a detailed molecular-level picture of how solvents interact with substrates at the electrode-electrolyte interface, including their involvement in proton transfer reactions and screening of electric fields.

14 SOLAR ENERGY↗

Parallel algorithms for hyperdynamics and local hyperdynamics

Hyperdynamics (HD) is a method for accelerating the timescale of standard molecular dynamics (MD). It can be used for simulations of systems with an energy potential landscape that is a collection of basins, separated by barriers, where transitions between basins are infrequent. HD enables the system to escape from a basin more quickly while enabling a statistically accurate renormalization of the simulation time, thus effectively boosting the timescale of the simulation. In [Kim, Perez, Voter, J Chem Phys, 139:144110, 2013)1, a local version of HD was formulated, which exploits the intrinsic locality characteristic typical of most systems to mitigate the poor scaling properties of standard HD as the system size is increased. In this paper, we discuss how both HD and local HD can be formulated to run efficiently in parallel. We have implemented these ideas in the LAMMPS MD code, which means HD can be used with any interatomic potential LAMMPS supports. Together, these parallel methods allow simulations of any size to achieve the time acceleration offered by HD (which can be orders of magnitude), at a cost 3-5x that of standard MD. As examples, we performed two simulations of a million-atom system to model the diffusion and clustering of Pt adatoms on a large patch of Pt(100) surface for 80 and 160 μs.

74 ATOMIC AND MOLECULAR PHYSICS↗

Many-body reactive force field development for carbon condensation in C/O systems under extreme conditions

In this paper, we describe the development of a reactive force field for C/O systems under extreme temperatures and pressures, based on the many-body Chebyshev Interaction Model for Efficient Simulation (ChIMES). The resulting model, which targets carbon condensation under thermodynamic conditions of 6500 K and 2.5 g cm –3 , affords a balance between model accuracy, complexity, and training set generation expense. We show that the model recovers much of the accuracy of density functional theory for the prediction of structure, dynamics, and chemistry when applied to dissociative condensed phase systems at 1:1 and 1:2 C:O ratios, as well as molten carbon. Our C/O modeling approach exhibits a 104 increase in efficiency for the same system size (i.e., 128 atoms) and a linear system size scalability over standard quantum molecular dynamics methods, allowing the simulation of significantly larger systems than previously possible. We find that the model captures the condensed-phase reaction-coupled formation of carbon clusters implied by recent experiments, and that this process is susceptible to strong finite size effects. Overall, we find the present ChIMES model to be well suited for studying chemical processes and cluster formation at pressures and temperatures typical of shock waves. We expect that the present C/O modeling paradigm can serve as a template for the development of a broader high pressure–high temperature force-field for condensed phase chemistry in organic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules

Abstract Maximum diversification of data is a central theme in building generalized and accurate machine learning (ML) models. In chemistry, ML has been used to develop models for predicting molecular properties, for example quantum mechanics (QM) calculated potential energy surfaces and atomic charge models. The ANI-1x and ANI-1ccx ML-based general-purpose potentials for organic molecules were developed through active learning; an automated data diversification process. Here, we describe the ANI-1x and ANI-1ccx data sets. To demonstrate data diversity, we visualize it with a dimensionality reduction scheme, and contrast against existing data sets. The ANI-1x data set contains multiple QM properties from 5 M density functional theory calculations, while the ANI-1ccx data set contains 500 k data points obtained with an accurate CCSD(T)/CBS extrapolation. Approximately 14 million CPU core-hours were expended to generate this data. Multiple QM calculated properties for the chemical elements C, H, N, and O are provided: energies, atomic forces, multipole moments, atomic charges, etc. We provide this data to the community to aid research and development of ML models for chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Domain Separated Density Functional Theory for Reaction Energy Barriers and Optical Excitations

We recently proposed Domain Separated Density Functional Theory (DS-DFT), a framework that allows for the combination of different levels of theory for the computation of the electronic structure of molecules. Here, this work discusses the application of DS-DFT to the computation of transition-state energy barriers and optical absorption spectra. We considered several hydrogen abstraction reactions and optical spectra of molecule/metal cluster systems, including the absorption of individual species such as carbon monoxide, methane, and molecular hydrogen to a Li6 cluster. We present and discuss two domain-separated methods: i), the screened-density approximation (SDA), and, ii), linearly weighted exchange (LWE). We find that SDA, which is applied as a hybridization based on atomic domains, could be useful to computing energy barriers, whereas LWE is suited for the analysis of electronic properties such as ground-state gaps, excitation energies, and oscillator strengths.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Immobilization of “Capping Arene” Cobalt(II) Complexes on Ordered Mesoporous Carbon for Electrocatalytic Water Oxidation

We report the synthesis, characterization, and electrocatalytic water oxidation activity of two cobalt complexes, (6-FP)Co(NO 3 ) 2 (1) (6-FP = 8,8'-(1,2-phenylene)diquinoline) and (5-FP)Co(NO 3 ) 2 (2) (5-FP = 1,2-bis(N-7-azaindolyl)benzene), containing "capping arene" bidentate ligands with nitrogen atom donors. The cobalt complexes 1 and 2 were supported on ordered mesoporous carbon (OMC) by π-π stacking, resulting in heterogenized cobalt materials 6-FP-Co-OMC-1 and 5-FP-Co-OMC-2, respectively, and studied for electrocatalytic water oxidation. We find that 6-FP-Co-OMC-1 exhibits an overpotential of 355 mV for a current density of 10 mA cm -2 and a turnover frequency (TOF) of ~0.53 s -1 at an overpotential of 400 mV at pH 14. 6-FP-Co-OMC-1 exhibits activity that is ~1.6 times that of 5-FP-Co-OMC-2, which gives a TOF of 0.32 s -1 at 400 mV overpotential. The structural stability of the single-atom Co site was demonstrated for 6-FP-Co-OMC-1 using X-ray absorption spectroscopy for the molecular complex supported on OMC, but slow degradation in catalyst activity can be attributed to eventual formation of Co oxide clusters. DFT computations of electrocatalytic water oxidation using the molecular complexes as models provide a description of the catalytic mechanism. These studies reveal that the mechanism for O-O bond formation involves an intermediate Co IV oxo complex that undergoes an intramolecular reductive O-O coupling to form a Co II -OOH species. Further, the calculations predict that the molecular 6-FP-Co structure is more active for electrocatalytic water oxidation than 5-FP-Co, which is consistent with experimental studies of 6-FP-Co-OMC-1 and 5-FP-Co-OMC-2, highlighting the possibility that the ligand structure influences the catalytic activity of the supported molecular catalysts.

25 ENERGY STORAGE↗

Exploring electron beam induced atomic assembly via reinforcement learning in a molecular dynamics environment

We report atom-by-atom assembly of functional materials and devices is perceived as one of the ultimate targets of nanotechnology. Recently it has been shown that the beam of a scanning transmission electron microscope can be used for targeted manipulation of individual atoms. However, the process is highly dynamic in nature rendering control difficult. One possible solution is to instead train artificial agents to perform the atomic manipulation in an automated manner without need for human intervention. As a first step to realizing this goal, we explore how artificial agents can be trained for atomic manipulation in a simplified molecular dynamics environment of graphene with Si dopants, using reinforcement learning. We find that it is possible to engineer the reward function of the agent in such a way as to encourage formation of local clusters of dopants under different constraints. This study shows the potential for reinforcement learning in nanoscale fabrication, and crucially, that the dynamics learned by agents encode specific elements of important physics that can be learned.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Molecular dynamics study of interstitial He clusters in nickel

This study presents a molecular dynamics analysis focusing on the behavior of interstitial helium (He) clusters in nickel (Ni), examining their formation, stability, and migration energetics. Consistent with previous research, we found that the binding energies of interstitial helium within a helium cluster are positive and increase with the cluster size, indicating a preference for helium atoms to cluster together. However, our findings also reveal that while the formation energy increases monotonically with cluster size, the increase in binding energy is non-monotonic. Importantly, small He clusters were observed to be thermally unstable at reactor operational temperatures (approximately 600 K), with the He 2 cluster exhibiting instability even at room temperature. With a binding energy of 0.49 eV for a He 4 cluster, we hypothesize that for helium bubbles to form via homogeneous nucleation (i.e., through trap mutation) at reactor operating temperatures, the helium concentration must be high enough to facilitate the formation of helium clusters of at least size 4 or larger. As expected, interstitial helium and small helium clusters are highly mobile. This mobility was observed not only at room temperature but also at temperatures as low as approximately 200 K. Furthermore, the mean squared displacement method has been utilized to determine the migration barriers and the corresponding prefactors for clusters ranging from He 1 to He 6

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

The Reactivity and Structural Dynamics of Supported Metal Nanoclusters Using Electron Microscopy, in-situ X-Ray Spectroscopy, Electronic Structure Theories, and Molecular Dynamics Simulations

This research will provide new methods to determine the structures and compositions of heterogeneous catalysts as they exist in reaction conditions. The new tools will make it possible to understand how extremely small material structures—ones in a size range spanning from single atoms to larger polyatomic clusters—make it possible to carry out highly selective chemical transformations required to synthesize useful materials as well as for efficient energy production and utilization. The tools will make it possible to see how the atomic structures of catalytic materials evolve over time under the conditions of their use, and in this way provide understandings to guide the design of new energy-efficient catalysts. The work will make it possible to answer long standing questions that include the following. How does catalyst structure help guide molecules along specific reaction pathways? What are the important intermediates involved in these transformations? How do the structures and reactivity of catalytic materials, as well as the chemistry of their interfaces, vary with reaction conditions? Is it possible to develop new catalytic materials using new knowledge of the active structures and reaction mechanisms? The work will provide heretofore unavailable experimental tools that can be applied in advanced programs of research addressing such questions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Structural adaptation of oxygen tolerance in 4-hydroxybutyrl-CoA dehydratase, a key enzyme of archaeal carbon fixation

Abstract Autotrophic microorganisms that convert inorganic carbon into organic matter were key players in the evolution of life on Earth. As the early atmosphere became oxygenated, microorganisms needed to develop mechanisms for oxygen protection, especially those relying on enzymes containing oxygen-sensitive metal clusters (e.g., Fe-S). Here we investigated how 4-hydroxybutyryl-CoA dehydratase (4HBD) - the key enzyme of the 3-hydroxypropionate/4-hydroxybutyrate (HP/HB) cycle for CO 2 -fixation - adapted as conditions shifted from anoxic to oxic. 4HBD is found in both anaerobic bacteria and aerobic ammonia-oxidizing archaea (AOA). The oxygen-sensitive bacterial 4HBD and oxygen-tolerant archaeal 4HBD share 59 % amino acid identity. To examine the structural basis of oxygen tolerance in archaeal 4HBD, we determined the atomic resolution structure of the enzyme. Two tunnels providing access to the canonical [4Fe-4S] cluster in oxygen-sensitive bacterial 4HBD were closed with four conserved mutations found in all aerobic AOA and other archaea. Further biochemical experiments and molecular dynamics simulations support our findings that restricting access to the active site is the key to oxygen tolerance, explaining how active site evolution drove a major evolutionary transition. Significance statement Autotrophy (primary production) was the first life strategy on Earth. Before photosynthesis (using solar energy to fix carbon dioxide), life relied on chemical reactions for energy. These chemosynthetic reactions are present in all domains of life, including archaea possessing the most energy-efficient carbon fixation pathway - the 3-hydroxypropionate/4-hydroxybutyrate cycle. This efficiency results from enzyme modifications, including enhanced enzyme stability and catalysis of multiple reactions. We reveal the first structure of aerobic 4-hydroxybutyryl-CoA dehydratase (4HBD) from ammonia-oxidizing archaea. These archaea are among the most abundant organisms on the planet, and their 4HBD active site evolved oxygen tolerance to support aerobic metabolism. This modification can provide further insight into enzyme evolution on early earth, as photosynthesis developed and began oxygenating the atmosphere.

DeMirci, Hasan (ORCID:0000000291355397)↗

Materials Data on H5ClO6 by Materials Project

H5O2(H2O)4(HClO4)2H5O6ClClO4 crystallizes in the triclinic P1 space group. The structure is zero-dimensional and consists of one molecular hydrogen;dihydrate molecule, four water molecules, one ClO4 cluster, one H5O6Cl cluster, and two HClO4 clusters. In the ClO4 cluster, there are four inequivalent O sites. In the first O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.47 Å. In the second O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.47 Å. In the third O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.47 Å. In the fourth O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.46 Å. Cl is bonded in a tetrahedral geometry to four O atoms. In the H5O6Cl cluster, there are five inequivalent H sites. In the first H site, H is bonded in a single-bond geometry to two O atoms. There is one shorter (1.00 Å) and one longer (1.71 Å) H–O bond length. In the second H site, H is bonded in a linear geometry to two O atoms. There is one shorter (1.20 Å) and one longer (1.24 Å) H–O bond length. In the third H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 0.99 Å. In the fourth H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 0.99 Å. In the fifth H site, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 0.98 Å. There are six inequivalent O sites. In the first O site, O is bonded in a distorted single-bond geometry to one Cl atom. The O–Cl bond length is 1.46 Å. In the second O site, O is bonded in a distorted bent 120 degrees geometry to one H and one Cl atom. The O–Cl bond length is 1.47 Å. In the third O site, O is bonded in a trigonal non-coplanar geometry to three H atoms. In the fourth O site, O is bonded in a trigonal non-coplanar geometry to three H atoms. In the fifth O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.49 Å. In the sixth O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.45 Å. Cl is bonded in a tetrahedral geometry to four O atoms. In one of the HClO4 clusters, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 1.00 Å. There are four inequivalent O sites. In the first O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.43 Å. In the second O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.44 Å. In the third O site, O is bonded in a distorted water-like geometry to one H and one Cl atom. The O–Cl bond length is 1.63 Å. In the fourth O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.43 Å. Cl is bonded in a tetrahedral geometry to four O atoms. In one of the HClO4 clusters, H is bonded in a single-bond geometry to one O atom. The H–O bond length is 1.00 Å. There are four inequivalent O sites. In the first O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.43 Å. In the second O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.43 Å. In the third O site, O is bonded in a single-bond geometry to one Cl atom. The O–Cl bond length is 1.43 Å. In the fourth O site, O is bonded in a distorted water-like geometry to one H and one Cl atom. The O–Cl bond length is 1.64 Å. Cl is bonded in a tetrahedral geometry to four O atoms.

36 MATERIALS SCIENCE↗

Quantum chemical calculation of the equilibrium structures of small metal atom clusters

The application of ab initio quantum mechanical approaches in the study of metal atom clusters requires simplifying techniques that do not compromise the reliability of the calculations. Various aspects of the implementation of the effective core potential (ECP) technique for the removal of the metal atom core electrons from the calculation were examined. The ECP molecular integral formulae were modified to bring out the shell characteristics as a first step towards fulfilling the increasing need to speed up the computation of the ECP integrals. Work on the relationships among the derivatives of the molecular integrals that extends some of the techniques pioneered by Komornicki for the calculation of the gradients of the electronic energy was completed and a formulation of the ECP approach that quite naturally unifies the various state-of-the-art "shape- and Hamiltonian-consistent" techniques was discovered.

Kahn, L. R.↗