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The unique properties exhibited in immiscible metals, such as excellent strength, hardness, and radiation-damage tolerance, have stimulated the interest of many researchers. As a typical immiscible metal system, the Cu–W nano-multilayers combine the plasticity of copper and the strength of tungsten, making it a suitable candidate for applications in aerospace, nuclear fusion engineering, and electronic packaging, etc. To understand the atomistic origin of the defects (e.g., vacancies, free surfaces, grain boundaries, and stacking faults and thermodynamical properties), we developed an accurate machine learning interatomic potential for Cu–W based on the atomic cluster expansion (ACE) method. The Cu–W ACE potential can faithfully reproduce the fundamental properties of Cu and W predicted by density functional theory (DFT) calculations. Moreover, the thermodynamical properties, such as the melting point, coefficient of thermal expansion, diffusion coefficient, and equation of the state curve of the Cu–W solid solution, are calculated and compared against DFT and experiments. Monte Carlo molecular dynamics simulations performed with the Cu–W ACE potential predict the experimentally observed phase separation and uphill diffusion phenomena. Our findings not only provide an accurate ACE potential for describing the Cu–W immiscible system but also shed light on understanding the atomistic mechanism during the Cu–W nano-multilayers formation process. [ABSTRACT FROM AUTHOR]

In this work, we systematically explore the effect of four-phonon (4ph) scattering on the lattice thermal conductivity (κ l) of γ -graphyne based on the atomic cluster expansion potential for carbon (C-ACE) combined with a phonon Boltzmann transport equation. The reliability of C-ACE in assessing the thermal transport properties of γ -graphyne is confirmed through comparing the results of phonon dispersion relation and κ 3 p h (only considering 3ph scattering) derived from C-ACE and density functional theory calculations. Regular residual analysis indicates that there might exist a strong 4ph interaction in γ -graphyne, and calculations further demonstrate κ 3 p h + 4 p h (considering 3ph scattering in an iterative solution and 4ph scattering in relaxation time approximation) is indeed reduced by 69.8% relative to κ 3 p h . From the analysis of scattering rates in γ -graphyne, one can intuitively observed that the 4ph scattering occupies a highly significant position in total phonon scattering, which greatly suppresses the κ l. The strong 4ph scattering in γ -graphyne is primarily due to the reflection symmetry selection rule less restricts 4ph scattering process for an out-of-plane flexural acoustic mode. The findings presented in this work demonstrate the reliability of C-ACE based accelerated calculations on the κ l of γ -graphyne, as well as reveal that the strong 4ph scattering in γ -graphyne significantly reduces its κ l , which will greatly promote the application of γ -graphyne and graphyne family in the field of thermoelectricity. [ABSTRACT FROM AUTHOR]

Large-scale atomistic molecular dynamics (MD) simulations provide an exceptional opportunity to advance the fundamental understanding of carbon under extreme conditions of high pressures and temperatures. However, the fidelity of these simulations depends heavily on the accuracy of classical interatomic potentials governing the dynamics of many-atom systems. This study critically assesses several popular empirical potentials for carbon, as well as machine learning interatomic potentials (MLIPs), in their ability to simulate a range of physical properties at high pressures and temperatures, including the diamond equation of state, its melting line, shock Hugoniot, uniaxial compressions, and the structure of liquid carbon. Empirical potentials fail to accurately predict the behavior of carbon under high pressure–temperature conditions. In contrast, MLIPs demonstrate quantum accuracy, with Spectral Neighbor Analysis Potential (SNAP) and atomic cluster expansion (ACE) being the most accurate in reproducing the density functional theory results. ACE displays remarkable transferability despite not being specifically trained for extreme conditions. Furthermore, ACE and SNAP exhibit superior computational performance on graphics processing unit-based systems in billion atom MD simulations, with SNAP emerging as the fastest. In addition to offering practical guidance in selecting an interatomic potential with a fine balance of accuracy, transferability, and computational efficiency, this work also highlights transformative opportunities for groundbreaking scientific discoveries facilitated by quantum-accurate MD simulations with MLIPs on emerging exascale supercomputers. [ABSTRACT FROM AUTHOR]

Physics-based, atom-centered machine learning (ML) representations have been instrumental to the effective integration of ML within the atomistic simulation community. Many of these representations build off the idea of atoms as having spherical, or isotropic, interactions. In many communities, there is often a need to represent groups of atoms, either to increase the computational efficiency of simulation via coarse-graining or to understand molecular influences on system behavior. In such cases, atom-centered representations will have limited utility, as groups of atoms may not be well-approximated as spheres. In this work, we extend the popular Smooth Overlap of Atomic Positions (SOAP) ML representation for systems consisting of non-spherical anisotropic particles or clusters of atoms. We show the power of this anisotropic extension of SOAP, which we deem AniSOAP, in accurately characterizing liquid crystal systems and predicting the energetics of Gay–Berne ellipsoids and coarse-grained benzene crystals. With our study of these prototypical anisotropic systems, we derive fundamental insights on how molecular shape influences mesoscale behavior and explain how to reincorporate important atom–atom interactions typically not captured by coarse-grained models. Moving forward, we propose AniSOAP as a flexible, unified framework for coarse-graining in complex, multiscale simulation. [ABSTRACT FROM AUTHOR]

We present an Atomic Cluster Expansion (ACE) machine learned potential developed for high-fidelity atomistic simulations of hydrocarbons, targeting pressures and temperatures near and above supercritical fluid regimes for molecular fluids. A diverse set of stoichiometries were covered in training, including 1:0 (pure carbon), 1:4 (methane), and 1:1 (benzene), and rich bonding environments sampled at supercritical temperatures, hydrogen rich, reactive mixtures where metastable stoichiometries arise, including 1:2 (ethylene) and 1:3 (ethane). A high-fidelity training database was constructed by performing large-scale quantum molecular dynamic simulations [density functional theory (DFT) MD] of diamond, graphite, methane, and benzene. A novel approach to selecting structures from DFT MD is also presented, which allows for the rapid selection of unique DFT MD frames from complex trajectories. Comparisons to DFT and experimental data demonstrate that the presented ACE potential accurately reproduces isotherms, carbon melting curves, radial distribution functions, and shock Hugoniots for carbon and hydrocarbon systems for pressures up to 100 GPa and temperatures up to 6000 K for hydrocarbon systems and up to 9000 K for pure carbon systems. This work delivers a potential that can be used for accurate, large-scale simulations of shocked hydrocarbons and demonstrates a methodology for fitting and validating machine learning interatomic potentials to complex molecular environments, which can be applied to energetic materials in future works. [ABSTRACT FROM AUTHOR]

Atomistic simulations often rely on interatomic potentials to access greater time and length scales than those accessible to first-principles methods, such as density functional theory. However, since a parameterized potential typically cannot reproduce the true potential energy surface of a given system, we should expect a decrease in accuracy and increase in error in quantities of interest calculated from these simulations. Quantifying the uncertainty on the outputs of atomistic simulations is thus an important, necessary step so that there is confidence in the results and available metrics to explore improvements in said simulations. Here, we address this research question by forming ensembles of atomic cluster expansion potentials, and using conformal prediction with ab initio training data to provide meaningful, calibrated error bars on several quantities of interest for silicon: the bulk modulus, elastic constants, relaxed vacancy formation energy, and the vacancy migration barrier. We evaluate the effects on uncertainty bounds using a range of different potentials and training sets. [ABSTRACT FROM AUTHOR]

Point Group (PG) symmetries play a fundamental role in many aspects of theoretical chemistry and computational materials science. With the objective to automatize the search of PG symmetry operations of generic atomic clusters, we present a new algorithm called Symmetry Operation FInder (SOFI). SOFI addresses the problem of identifying PG symmetry by framing it as a degenerate shape-matching problem, where the multiple solutions correspond to distinct symmetry operations. The developed algorithm is compared against three other algorithms dedicated to PG identification on a large set of atomic clusters. The results, along with some illustrative use cases, showcase the effectiveness of SOFI. The SOFI algorithm is released as part of the iterative rotations and assignments library, accessible at https://github.com/mammasmias/IterativeRotationsAssignments. [ABSTRACT FROM AUTHOR]

We present a four-component relativistic unitary coupled cluster method for atoms and molecules. We have used commutator-based non-perturbative approximation using the "Bernoulli expansion" to derive an approximation to the relativistic unitary coupled cluster method. The performance of the full quadratic unitary coupled-cluster singles and doubles method (qUCCSD), as well as a perturbative approximation variant (UCC3), has been reported for both energies and properties. It can be seen that both methods give results comparable to those of the standard relativistic coupled cluster method. The qUCCSD method shows better agreement with experimental results due to the better inclusion of relaxation effects. The relativistic UCC3 and qUCCSD methods can simulate the spin-forbidden transition with easy access to transition properties. A natural spinor-based scheme to reduce the computational cost of relativistic UCC3 and qUCCSD methods has been discussed. [ABSTRACT FROM AUTHOR]

In the past decade, natural orbital functional (NOF) approximations have emerged as prominent tools for characterizing electron correlation. Despite their effectiveness, these approaches, which rely on natural orbitals and their associated occupation numbers, often require hybridization with other methods to fully account for all correlation effects. Recently, a global NOF (GNOF) has been proposed [Piris, Phys. Rev. Lett. 127, 233001 (2021)] to comprehensively address both dynamic and static correlations. This study evaluates the performance of GNOF on strongly correlated model systems, including comparisons with highly accurate Full Configuration Interaction calculations for hydrogen atom clusters in one, two, and three dimensions. Additionally, the investigation extends to a BeH2 reaction, involving the insertion of a beryllium atom into a hydrogen molecule along a C2v pathway. According to the results obtained using GNOF, consistent behavior is observed across various correlation regions, encompassing a range of occupations and orbital schemes. Furthermore, distinctive features are identified when varying the dimensionality of the system. [ABSTRACT FROM AUTHOR]

We describe a method to compute photon–matter interaction and atomic dynamics with x-ray lasers using a hybrid code based on classical molecular dynamics and collisional-radiative calculations. The forces between the atoms are dynamically determined based on changes to their electronic occupations and the formation of a free electron cloud created from the irradiation of photons in the x-ray spectrum. The rapid transition from neutral solid matter to dense plasma phase allows the use of screened potentials, reducing the number of non-bonded interactions. In combination with parallelization through domain decomposition, the hybrid code handles large-scale molecular dynamics and ionization. This method is applicable for large enough samples (solids, liquids, proteins, viruses, atomic clusters, and crystals) that, when exposed to an x-ray laser pulse, turn into a plasma in the first few femtoseconds of the interaction. We present four examples demonstrating the applicability of the method. We investigate the non-thermal heating and scattering of bulk water and damage-induced dynamics of a protein crystal using an x-ray pump–probe scheme. In both cases, we compare to the experimental data. For single particle imaging, we simulate the ultrafast dynamics of a methane cluster exposed to a femtosecond x-ray laser. In the context of coherent diffractive imaging, we study the fragmentation as given by an x-ray pump–probe setup to understand the evolution of radiation damage in the time range of hundreds of femtoseconds. [ABSTRACT FROM AUTHOR]

The crystal orientation and the temperature of the substrate are crucial factors that influence clusters deposition and, consequently, the properties of thin films. In this study, the molecular dynamics simulation method was employed to investigate the deposition of Cu55 clusters on Fe(001), Fe(011), and Fe(111) substrates with varying crystal orientations. The incident energies used ranged from 0.1 to 20.0 eV/atom, and the substrates were maintained at temperatures of 300, 500, and 800 K. Analysis of cluster and substrate atom snapshots, along with the physical properties of clusters, revealed how the crystal orientation of Fe substrates affects the morphology and structure of the cluster at different temperatures. Additionally, specific microscopic mechanisms responsible for these effects were identified. The simulation results demonstrate that the crystal orientation of Fe substrate significantly influences the deposition of Cu55 clusters. The structures of the clusters on the three crystal substrates undergo similar changes as the substrate temperature increases, with the Cu55 clusters on the Fe(111) substrate exhibiting the most significant changes in response to the temperature rise. [ABSTRACT FROM AUTHOR]

31P nuclear magnetic resonance (NMR) chemical shifts were shown to be very sensitive to the basis set used at the geometry optimization stage. Commonly used energy-optimized basis sets for a phosphorus atom containing only one polarization d-function were shown to be unable to provide correct equilibrium geometries for the calculations of phosphorus chemical shifts. The use of basis sets with at least two polarization d-functions on a phosphorus atom is strongly recommended. In this paper, an idea of creating the basis sets purposed for the geometry optimization that provide the least possible error coming from the geometry factor of accuracy in the resultant NMR shielding constants is proposed. The property-energy consisted algorithm with the target function in the form of the molecular energy gradient relative to P–P bond lengths was applied to create new geometry-oriented pecG-n (n = 1, 2) basis sets for a phosphorus atom. New basis sets have demonstrated by far superior performance as compared to the other commonly used energy-optimized basis sets in massive calculations of 31P NMR chemical shifts carried out at the gauge-including atomic orbital-coupled cluster singles and doubles/pecS-2 level of the theory by taking into account solvent, vibrational, and relativistic corrections. [ABSTRACT FROM AUTHOR]

Thermal transport in wurtzite aluminum nitride (w-AlN) significantly affects the performance and reliability of corresponding electronic devices, particularly when lattice strains inevitably impact the thermal properties of w-AlN in practical applications. To accurately model the thermal properties of w-AlN with high efficiency, we develop a machine learning interatomic potential based on the atomic cluster expansion (ACE) framework. The predictive power of the ACE potential against density functional theory (DFT) is demonstrated across a broad range of properties of w-AlN, including ground-state lattice parameters, specific heat capacity, coefficients of thermal expansion, bulk modulus, and harmonic phonon dispersions. Validation of lattice thermal conductivity is further carried out by comparing the ACE-predicted values to the DFT calculations and experiments, exhibiting the overall capability of our ACE potential in sufficiently describing anharmonic phonon interactions. As a practical application, we perform a lattice dynamics analysis using the potential to unravel the effects of biaxial strains on thermal conductivity and phonon properties of w-AlN, which is identified as a significant tuning factor for near-junction thermal design of w-AlN-based electronics. [ABSTRACT FROM AUTHOR]

Nanoscale magnesium clusters are important potential hydrogen storage materials, and density functional theory (DFT) is mainly used for their theoretical investigation. The results of the coupled-cluster theory at the singles and doubles level with a perturbative treatment of triples [CCSD(T)] were employed previously to choose proper exchange–correlation (XC) functionals in DFT calculations for magnesium clusters, but it is too expensive to be applied to Mgn with n > 7. The diffusion Monte Carlo (DMC) method is employed in this work to study magnesium clusters up to nanosize. The error of atomization energies with DMC using single-determinant-Jastrow (SDJ) trial wavefunctions has been shown to be somewhat larger than that of CCSD(T) for many molecules. However, cohesive energies with DMC using SDJ for Mgn with n ≤ 7 are in excellent agreement with those of CCSD(T) using the aug-cc-pVQZ basis set, with a difference of less than 1 kcal/mol. DMC results are employed to investigate the performance of different XC functionals on magnesium clusters. Our results indicate that the PBE0 functional is the best XC functional for determining the lowest-energy isomer when compared with DMC results, while the RPBE functional is the best XC functional for calculating cohesive energies per atom of these magnesium clusters with a mean absolute error of 0.5 kcal/mol. These XC functionals are expected to provide reasonable results for even larger magnesium clusters. [ABSTRACT FROM AUTHOR]

We introduce ACEpotentials.jl, a Julia-language software package that constructs interatomic potentials from quantum mechanical reference data using the Atomic Cluster Expansion [R. Drautz, Phys. Rev. B 99, 014104 (2019)]. As the latter provides a complete description of atomic environments, including invariance to overall translation and rotation as well as permutation of like atoms, the resulting potentials are systematically improvable and data efficient. Furthermore, the descriptor's expressiveness enables use of a linear model, facilitating rapid evaluation and straightforward application of Bayesian techniques for active learning. We summarize the capabilities of ACEpotentials.jl and demonstrate its strengths (simplicity, interpretability, robustness, performance) on a selection of prototypical atomistic modelling workflows. [ABSTRACT FROM AUTHOR]

The unique physical properties of carbyne, a novel carbon nanostructure, have attracted considerable interest in modern nanotechnology. While carbyne synthesis has been accomplished successfully using diverse techniques, the underlying mechanisms governing the carbon monoxide-dependent catalytic synthesis of endohedral carbyne remain poorly understood. In this simulation-based study, we investigate the synthesis of endohedral carbyne from carbon and carbon monoxide radicals in the presence of a nickel catalyst inside double-walled carbon nanotubes with a (5,5)@(10,10) structure. The outcome of our investigation demonstrates that the incorporation of the carbon atom within the Nin@(5,5)@(10,10) model system initiates the formation of an elongated carbon chain. In contrast, upon the introduction of carbon monoxide radicals, the growth of the carbyne chain is inhibited as a result of the oxidation of endohedral nickel clusters by oxygen atoms after the initial steps of nucleation. Our findings align with prior theoretical, simulation, and experimental investigations, reinforcing their consistency and providing valuable insights into the synthesis of carbyne-based nanodevices that hold promising potential for future advancements in nanotechnology. [ABSTRACT FROM AUTHOR]

Dense atom ensembles with Rydberg excitations display intriguing collective effects mediated by their strong, long-range dipole–dipole interactions. These collective effects, often modeled using Rydberg superatoms, have gained significant attention across various fields due to their potential applications in quantum information processing and quantum optics. In this review article, we delve into the theoretical foundations of Rydberg interactions and explore experimental techniques for their manipulation and detection. We also discuss the latest advancements in harnessing Rydberg collective effects for quantum computation and optical quantum technologies. By synthesizing insights from theoretical studies and experimental demonstrations, we aim to provide a comprehensive overview of this rapidly evolving field and its potential impact on the future of quantum technologies. [ABSTRACT FROM AUTHOR]

High pressure has been recognized as an important tool in molecule and materials research, and thus, it is expected to be used to understand the evolution of electronic states and geometric structures in superatoms. In this work, by studying three characteristic axial compressions on a typical endohedral metallofullerene superatom U@C28 with Td symmetry, we find that the triplet ground electronic state is preserved when the compression moves along the direction that reduces the symmetry to D2d, but the electronic state of the structure compressed along the direction of symmetry reduction to C2v or Cs is transformed into a singlet. The transition is attributed to the distinction in the response of electron spin to different axial compressions, which results in a change in the electron occupation mode of the system. Furthermore, we also confirm the gradual evolution from stereo to near-plane superatoms and the connection between their electron structures. This is reflected in the fact that the electron density distributions of the superatomic molecular orbitals (SAMOs) with extension along the restricted degrees of freedom ( D z 2 , F z 3 SAMOs) gradually contract, and the delocalization destruction of special orbitals is associated with this freedom. In addition, Raman and ultraviolet–visible spectra show a hyperchromic effect and redshift of characteristic peaks during axial compression, which are expected to be used for fingerprinting the superatomic planarization. Therefore, our work provides new insights based on high pressure for future research toward the discovery of physical properties and applications of superatoms. [ABSTRACT FROM AUTHOR]

Spectra of rare gas atom clusters containing a single carbon dioxide molecule are observed using a tunable mid-infrared (4.3 µm) source to probe a pulsed slit jet supersonic expansion. There are relatively few previous detailed experimental results on such clusters. The assigned clusters include CO2–Arn with n = 3, 4, 6, 9, 10, 11, 12, 15, and 17, and CO2–Krn and CO2–Xen with n = 3, 4, and 5. Each spectrum has (at least) a partially resolved rotational structure, and each yields precise values for the shift of the CO2 vibrational frequency (ν3) induced by the nearby rare gas atoms, together with one or more rotational constants. These results are compared with theoretical predictions. The more readily assigned CO2–Arn species tend to be those with symmetric structures, and CO2–Ar17 represents completion of a highly symmetric (D5h) solvation shell. Those not assigned (e.g., n = 7 and 13) are probably also present in the observed spectra but with band structures that are not well-resolved and, thus, are not recognizable. The spectra of CO2–Ar9, CO2–Ar15, and CO2–Ar17 suggest the presence of sequences involving very low frequency (≈2 cm−1) cluster vibrational modes, an interpretation which should be amenable to theoretical confirmation (or rejection). [ABSTRACT FROM AUTHOR]

A promising research area in nanomaterials is the use of superatomic clusters as building blocks for creating novel molecules or materials with tailored properties. However, assembling these superatoms into functional materials is challenging, and a thorough understanding of this process is still lacking. In this study, we introduce a new concept called the "superatomic family," which refers to superatoms that share similar valence electron structures but differ in size. We demonstrate this concept with the synthesized [Au6{Ni3(CO)6}4]2− cluster and the designed [Au16{Ni6(CO)10}4]2− and [Au31{Ni10(CO)15}4]5− clusters. These serve as analogs to simple hydrocarbons, such as methane (CH4), silicon hydride (SiH4), and germanium hydride (GeH4). In these supermolecular structures, the central cores of Au6, Au16, and Au31 exhibit the formation of superatomic SP3 hybridized orbitals, which influence the molecular shape and bonding. Moreover, we explored superatomic bonding involving SP3–SP3 hybridized cores, representing a single superatomic bond between members of the superatomic family, analogous to CH3–SiH3 bonds. By integrating the concept of group superatoms into the Lewis structure framework, we present a powerful approach for predicting and engineering cluster properties, thus opening a vast landscape of nanomaterial design possibilities. [ABSTRACT FROM AUTHOR]

Due to the transient interaction between laser and powder and layer-by-layer rapid melting and solidification, laser additive manufacturing-fabricated metal components can exhibit unique microstructure evolution behaviors and strengthening mechanisms that are normally not available in traditional processes. In this work, a previously unreported rapid hardening behavior at the very early stage of isothermal aging for laser powder bed fusion-processed high-strength Al-5024 alloy was revealed. The microstructures and mechanical properties of specimens aged from 10 min to 120h were systematically analyzed. It showed that the specimens underwent two peak hardening processes during an isothermal aging at 325 °C. The mechanical properties of the specimens including microhardness, yield strength, and elastic modulus were significantly enhanced after an extremely short aging time of 10 min and then reached a secondary peak hardening at an aging time of 4h, where the yield strength of 450 ± 10.3 and 463.2 ± 13.2 MPa were obtained, respectively. The unusual aging responses were attributed to the formation and decomposition of Sc-rich clusters with a high number density of 2.7 × 1023 m−3 and nano-size of 2.71 nm. These clusters were characterized by transmission electron microscopy analyses and further supported by differential scanning calorimetry measurements, where a significantly higher activation energy of 147.6 ± 21.1 kJ/mol corresponding to the precipitation/coarsening process of Al3(Sc,Zr) was measured for rapid hardening specimens. In addition, the relationship between the aging process, the evolution of nano-precipitates, and the mechanical properties was systematically demonstrated. [ABSTRACT FROM AUTHOR]

Single atom alloy AgCu catalysts have attracted great attention, since doping the single Cu atom introduces narrow free-atom-like Cu 3d states in the electronic structure. These peculiar electronic states can reduce the activation energies in some reactions and offer valuable guidelines for improving catalytic performance. However, the geometric tuning effect of single Cu atoms in Ag catalysts and the structure–activity relationship of AgCu catalysts remain unclear. Here, we prepared well-resolved pristine Agn− as well as single atom alloy Agn−1Cu− and Agn−1Au− (n = 7–20) clusters and investigated their reactivity with O2. We found that replacing an Ag atom in Agn− (n = 15–18) with a Cu atom significantly increases the reactivity with O2, while replacement of an Ag with an Au atom has negligible effects. The adsorption of O2 on Agn− or Agn−1Cu− clusters follows the single electron transfer mechanism, in which the cluster activity is dependent on two descriptors, the energy level of α-HOMO (strong correlation) and the α-HOMO–LUMO gap (weak correlation). Our calculation demonstrated that the cluster arrangements caused by single Cu atom alloying would affect the above activity descriptors and, therefore, regulates clusters' chemical activity. In addition, the observed reactivity of clusters in the representative sizes with n = 17–19 can also be interpreted using the symmetry-adapted orbital model. Our work provides meaningful information to understand the chemical activities of related single-atom-alloy catalysts. [ABSTRACT FROM AUTHOR]

We present our latest advancements of machine-learned potentials (MLPs) based on the neuroevolution potential (NEP) framework introduced in Fan et al. [Phys. Rev. B 104, 104309 (2021)] and their implementation in the open-source package gpumd. We increase the accuracy of NEP models both by improving the radial functions in the atomic-environment descriptor using a linear combination of Chebyshev basis functions and by extending the angular descriptor with some four-body and five-body contributions as in the atomic cluster expansion approach. We also detail our efficient implementation of the NEP approach in graphics processing units as well as our workflow for the construction of NEP models and demonstrate their application in large-scale atomistic simulations. By comparing to state-of-the-art MLPs, we show that the NEP approach not only achieves above-average accuracy but also is far more computationally efficient. These results demonstrate that the gpumd package is a promising tool for solving challenging problems requiring highly accurate, large-scale atomistic simulations. To enable the construction of MLPs using a minimal training set, we propose an active-learning scheme based on the latent space of a pre-trained NEP model. Finally, we introduce three separate Python packages, viz., gpyumd, calorine, and pynep, that enable the integration of gpumd into Python workflows. [ABSTRACT FROM AUTHOR]

We examine the many-body expansion (MBE) for alkaline earth metal clusters, Ben, Mgn, Can (n = 4, 5, 6), at the Møller–Plesset second order perturbation theory, coupled-cluster singles and doubles with perturbative triples, multi-reference perturbation theory, and multi-reference configuration interaction levels of theory. The magnitude of each term in the MBE is evaluated for several geometrical configurations. We find that the behavior of the MBE for these clusters depends strongly on the geometrical arrangement and, to a lesser extent, on the level of theory used. Another factor that affects the MBE is the in situ (ground or excited) electronic state of the individual atoms in the cluster. For most geometries, the three-body term is the largest, followed by a steady decrease in absolute energy for subsequent terms. Though these systems exhibit non-negligible multi-reference effects, there was little qualitative difference in the MBE when employing single vs multi-reference methods. Useful insights into the connectivity and stability of these clusters have been drawn from the respective potential energy surfaces and quasi-atomic orbitals for the various dimers, trimers, and tetramers. Through these analyses, we investigate the similarities and differences in the binding energies of different-sized clusters for these metals. [ABSTRACT FROM AUTHOR]

Determining the atomic structure of clusters has been a long-term challenge in theoretical calculations due to the high computational cost of density-functional theory (DFT). Deep learning potential (DP), as an alternative way, has been demonstrated to be able to conduct cluster simulations with close-to DFT accuracy but at a much lower computational cost. In this work, we update 34 structures of the 41 Cu clusters with atomic numbers ranging from 10 to 50 by combining global optimization and the DP model. The calculations show that the configuration of small Cun clusters (n = 10–15) tends to be oblate and it gradually transforms into a cage-like configuration as the size increases (n > 15). Based on the updated structures, their relative stability and electronic properties are extensively studied. In addition, we select three different clusters (Cu13, Cu38, and Cu49) to study their electrocatalytic ability of CO2 reduction. The simulation indicates that the main product is CO for these three clusters, while the selectivity of hydrocarbons is inhibited. This work is expected to clarify the ground-state structures and fundamental properties of Cun clusters, and to guide experiments for the design of Cu-based catalysts. [ABSTRACT FROM AUTHOR]

A major challenge for atom probe tomography (APT) quantification is the inability to decouple ions that possess the same mass–charge (m/n) ratio but a different mass. For example, 75As+ and 75As22+ at ∼75 Da or 14N+ and 28Si2+ at ∼14 Da cannot be differentiated without the additional knowledge of their kinetic energy or a significant improvement of the mass resolving power. Such mass peak overlaps lead to ambiguities in peak assignment, resulting in compositional uncertainty and an incorrect labeling of the atoms in a reconstructed volume. In the absence of a practical technology for measuring the kinetic energy of the field-evaporated ions, we propose and then explore the applicability of a post-experimental analytical approach to resolve this problem based on the fundamental process that governs the production of multiply charged molecular ions/clusters in APT, i.e., post-field ionization (PFI). The ability to predict the PFI behavior of molecular ions as a function of operating conditions could offer the first step toward resolving peak overlap and minimizing compositional uncertainty. We explore this possibility by comparing the field dependence of the charge-state-ratio for Si clusters (Si2, Si3, and Si4) with theoretical predictions using the widely accepted Kingham PFI theory. We then discuss the model parameters that may affect the quality of the fit and the possible ways in which the PFI of molecular ions in APT can be better understood. Finally, we test the transferability of the proposed approach to different material systems and outline ways forward for achieving more reliable results. [ABSTRACT FROM AUTHOR]

Crystal-glass nanocomposites with the synergy of high strength and exceptional ductility are promising for future applications in micro-electromechanical systems. Deformation behaviors of crystal-glass nanocomposites are governed by the formation and propagation of their plastic deformation carriers, namely, dislocations in the crystalline phase and strain-activated atomic clusters (e.g., shear transformation zones and shear bands) in the glassy phase. Yet, it is challenging to unveil the size effect of a glassy domain on the propagation of plastic deformation carriers in crystal-glass nanocomposites. To clarify the above issue, in this work, we perform molecular dynamics simulation on simple configurations fabricated by embedding a series of cylinder glass domains with different radii into the single-crystal matrix. Their stress–strain response and microstructures, especially the deformation carriers in the two phases evolving with the applied compressive strain, are quantitively analyzed. The average shear strain of glassy atoms is found to significantly decrease with the increased glassy domain volume, accordingly alleviating the strain localization in the glassy phase. The formation and propagation of strain-activated atomic clusters are also suppressed by enlarging the glassy domain volume due to the lowered shear strains sustained by glassy atoms. Moreover, dislocation densities in the crystalline matrix also decrease in the configuration with a larger-volume glassy domain, which can be ascribed to the enhanced dislocation absorption effect from the amorphous-crystal interfaces. This work indicates that the mechanical properties of multi-phase nanocomposites can be improved by rationally optimizing the phase contents and provides new knowledge on designing high-performance nanocomposites. [ABSTRACT FROM AUTHOR]

Swelling of metals under irradiation is commonly assessed by calculating the volume fraction of voids, which appear at temperatures where vacancies are mobile. However, other clusters are formed, which may also have an impact on swelling. In particular, interstitial loops have recently been considered to give a significant contribution to swelling owing to their large relaxation volume. In this work, we perform calculations in nickel, based on interatomic potentials, to estimate the contributions of the various point defect clusters. We show that voids produce much more swelling than loops and stacking fault tetrahedra, whose contribution is essentially due to the dislocation core field, inducing a dilatation per unit length of around 1 b 2 , where b is the Burgers vector. Evaluation of swelling should indeed be done by summing formation volumes, not relaxation volumes, the latter being related to lattice parameter change as measured by x-ray diffraction. We also discuss the case of "lattice swelling" occurring when vacancies are immobile. When self-interstitial atoms cluster as dislocation loops, this swelling mode turns out to be nothing but "void" swelling in a regime where vacancy mobility is so low that vacancies do not cluster appreciably, leaving only interstitial loops visible in transmission electron microscopy. [ABSTRACT FROM AUTHOR]

The search for new superhydrides, promising materials for both hydrogen storage and high temperature superconductivity, made great progress, thanks to atomistic simulations and Crystal Structure Prediction (CSP) algorithms. When they are combined with Density Functional Theory (DFT), these methods are highly reliable and often match a great part of the experimental results. However, systems of increasing complexity (number of atoms and chemical species) become rapidly challenging as the number of minima to explore grows exponentially with the number of degrees of freedom in the simulation cell. An efficient sampling strategy preserving a sustainable computational cost then remains to be found. We propose such a strategy based on an active-learning process where machine learning potentials and DFT simulations are jointly used, opening the way to the discovery of complex structures. As a proof of concept, this method is applied to the exploration of tin crystal structures under various pressures. We showed that the α phase, not included in the learning process, is correctly retrieved, despite its singular nature of bonding. Moreover, all the expected phases are correctly predicted under pressure (20 and 100 GPa), suggesting the high transferability of our approach. The method has then been applied to the search of yttrium superhydrides (YHx) crystal structures under pressure. The YH6 structure of space group Im-3m is successfully retrieved. However, the exploration of more complex systems leads to the appearance of a large number of structures. The selection of the relevant ones to be included in the active learning process is performed through the analysis of atomic environments and the clustering algorithm. Finally, a metric involving a distance based on x-ray spectra is introduced, which guides the structural search toward experimentally relevant structures. The global process (active-learning and new selection methods) is finally considered to explore more complex and unknown YHx phases, unreachable by former CSP algorithms. New complex phases are found, demonstrating the ability of our approach to push back the exponential wall of complexity related to CSP. [ABSTRACT FROM AUTHOR]

155, 164702 (2021).10.1063/5.0059912 44 S. Valtera, J. Jasik, M. Vaidulych, J. E. Olszówka, M. Zlámalová, H. Tarábková, L. Kavan, and S. Vajda, "Atom by atom built subnanometer copper cluster catalyst for the highly selective oxidative dehydrogenation of cyclohexene", J. Chem. Phys. 156, 114302 (2022).10.1063/5.0065350 45 T. Matsuyama, S. Kikkawa, Y. Fujiki, M. Tsukada, H. Takaya, N. Yasuda, K. Nitta, N. Nakatani, Y. Negishi, and S. Yamazoe, "Thermal stability of crown-motif [Au9(PPh3)8]3+ and [MAu8(PPh3)8]2+ (M = Pd, Pt) clusters: Effects of gas composition, single-atom doping, and counter anions", J. Chem. Phys. 155, 054301 (2021).10.1063/5.0059607 15 K. O. Sulaiman, R. W. Purves, and R. W. J. Scott, "Exploring the structure of atom-precise silver-palladium bimetallic clusters prepared via improved single-pot co-reduction synthesis protocol", J. Chem. Phys. Nanometer-sized atomic clusters constitute a unique phase of matter that lies between the atoms and their bulk. [Extracted from the article]

Fe–Cr alloys are at the forefront for high radiation tolerant materials with long-standing validated performance. Yet, the detailed mechanism behind their high radiation resistance is in question and understanding the effect of varying Cr percentage is a grand challenge limiting further improvements. Here, we applied depth-resolved positron annihilation lifetime spectroscopy and Doppler broadening spectroscopy to study the effect of Cr alloying on the formation and evolution of atomic size clusters induced by ion-irradiation in Fe. We also used atom probe tomography to investigate the possible presence of Cr clusters or α′ phase precipitates with high Cr composition. The study reveals that the well-known resistance to radiation in Fe–Cr alloys may arise from the stabilization of vacancy clusters around Cr atoms, which act as sinks for radiation-induced defects. This implies that Cr atoms do not provide a direct sink for interstitials; rather defect complexes that consist of Cr atoms and vacancies, in turn, act as sinks for irradiation-induced vacancies and interstitials. we also find that lower amounts of Cr create smaller defect clusters that act as efficient sinks for radiation damage, but larger quantities of Cr form a defect structure that is less homogenous and larger in size, resulting in less efficient damage recombination. No evidence of α′ was found before or after irradiation, which indicates that it does not contribute to the observed radiation tolerance. [ABSTRACT FROM AUTHOR]

The effect of particle size and support on the catalytic performance of supported subnanometer copper clusters was investigated in the oxidative dehydrogenation of cyclohexene. From among the investigated seven size-selected subnanometer copper particles between a single atom and clusters containing 2–7 atoms, the highest activity was observed for the titania-supported copper tetramer with 100% selectivity toward benzene production and being about an order of magnitude more active than not only all the other investigated cluster sizes on the same support but also the same tetramer on the other supports, Al2O3, SiO2, and SnO2. In addition to the profound effect of cluster size on activity and with Cu4 outstanding from the studied series, Cu4 clusters supported on SiO2 provide an example of tuning selectivity through support effects when this particular catalyst also produces cyclohexadiene with about 30% selectivity. Titania-supported Cu5 and Cu7 clusters supported on TiO2 produce a high fraction of cyclohexadiene in contrast to their neighbors, while Cu4 and Cu6 solely produce benzene without any combustion, thus representing odd–even oscillation of selectivity with the number of atoms in the cluster. [ABSTRACT FROM AUTHOR]

The Greifswald multi-reflection time-of-flight setup has been extended with a magnetron sputtering gas aggregation source for the production of atomic cluster ions with sizes ranging from a single to thousands of atoms. This source, combined with a newly added quadrupole mass filter and a linear Paul trap, opens up the possibility of many new atomic-cluster studies not feasible with the setup before. The new components and their interfacing with the previous setup are described, and benchmarking as well as the first experimental results are presented. The capability of the system to handle singly charged ions with masses of several ten thousand atomic mass units is demonstrated. [ABSTRACT FROM AUTHOR]

The knowledge of atomic structure for liquids, especially for liquid alloys with complex crystal structure and high liquidus temperatures, remains poorly understood. In this work, we have extended the development of deep neural network (DNN) potential for liquid Nb5Si3. The DNN potential captures the structural features of liquid alloys compared with ab initio results. The chemical short-range order parameter suggests that there exists strong affinity between Nb and Si atoms. The dynamic property was investigated, and the diffusion coefficient obeys the Arrhenius relationship. The atomic structure has been subsequently explored for normal and undercooled liquid Nb5Si3. Large amounts of fivefold symmetry Honeycutt–Andersen pairs have been identified in liquid Nb5Si3. However, due to the violent thermal motion in a high-temperature Nb5Si3 melt, icosahedral symmetry and distorted icosahedrons (ICOs) account for little proportion according to Voronoi polyhedron (VP) analysis. The effect of thermal motion on VPs has been discussed. Except from the well documented ⟨0,2,8,2⟩ and ⟨0,1,10,2⟩ distorted ICOs, six more quasi-ICOs (⟨0,1,9,3⟩, ⟨0,2,8,1⟩, ⟨0,2,8,4⟩, ⟨0,2,8,5⟩, ⟨0,1,10,3⟩, and ⟨0,1,10,4⟩) have been proven to deform from ICOs at high temperatures. The local environment motif obtained by the atomic cluster alignment method demonstrates the existence of dominant distorted ICOs. At last, the atomic structure during melting process is discussed by VP analysis. It is found that ⟨0,2,8,1⟩, ⟨0,2,8,2⟩, ⟨0,2,8,5⟩, and ⟨0,1,10,4⟩ prefer to form at the beginning of the melting but rapidly reduce when it is fully melted. [ABSTRACT FROM AUTHOR]

The properties of semiconductor surfaces can be modified by the deposition of metal clusters consisting of a few atoms. The properties of metal clusters and of cluster-modified surfaces depend on the number of atoms forming the clusters. Deposition of clusters with a monodisperse size distribution thus allows tailoring of the surface properties for technical applications. However, it is a challenge to retain the size of the clusters after their deposition due to the tendency of the clusters to agglomerate. The agglomeration can be inhibited by covering the metal cluster modified surface with a thin metal oxide overlayer. In the present work, phosphine-protected Au clusters, Au9(PPh3)8(NO3)3, were deposited onto RF-sputter deposited TiO2 films and subsequently covered with a Cr2O3 film only a few monolayers thick. The samples were then heated to 200 °C to remove the phosphine ligands, which is a lower temperature than that required to remove thiolate ligands from Au clusters. It was found that the Cr2O3 covering layer inhibited cluster agglomeration at an Au cluster coverage of 0.6% of a monolayer. When no protecting Cr2O3 layer was present, the clusters were found to agglomerate to a large degree on the TiO2 surface. [ABSTRACT FROM AUTHOR]

The field of cluster science is drawing increasing attention due to the strong size and composition-dependent properties of clusters and the exciting prospect of clusters serving as the building blocks for materials with tailored properties. However, identifying a unifying central paradigm that provides a framework for classifying and understanding the diverse behaviors is an outstanding challenge. One such central paradigm is the superatom concept that was developed for metallic and ligand-protected metallic clusters. The periodic electronic and geometric closed shells in clusters result in their properties being based on the stability they gain when they achieve closed shells. This stabilization results in the clusters having a well-defined valence, allowing them to be classified as superatoms—thus extending the Periodic Table to a third dimension. This Perspective focuses on extending the superatomic concept to ligated metal–chalcogen clusters that have recently been synthesized in solutions and form assemblies with counterions that have wide-ranging applications. Here, we illustrate that the periodic patterns emerge in the electronic structure of ligated metal-chalcogenide clusters. The stabilization gained by the closing of their electronic shells allows for the prediction of their redox properties. Further investigations reveal how the selection of ligands may control the redox properties of the superatoms. These ligated clusters may serve as chemical dopants for two-dimensional semiconductors to control their transport characteristics. Superatomic molecules of multiple metal–chalcogen superatoms allow for the formation of nano-p–n junctions ideal for directed transport and photon harvesting. This Perspective outlines future developments, including the synthesis of magnetic superatoms. [ABSTRACT FROM AUTHOR]

Property-optimized Gaussian basis sets of split-valence, triple-zeta valence, and quadruple-zeta valence quality are developed for the lanthanides Ce–Lu for use with small-core relativistic effective core potentials. They are constructed in a systematic fashion by augmenting def2 orbital basis sets with diffuse basis functions and minimizing negative static isotropic polarizabilities of lanthanide atoms with respect to basis set exponents within the unrestricted Hartree–Fock method. The basis set quality is assessed using a test set of 70 molecules containing the lanthanides in their common oxidation states and f electron occupations. 5d orbital occupation turns out to be the determining factor for the basis set convergence of polarizabilities in lanthanide atoms and the molecular test set. Therefore, two series of property-optimized basis sets are defined. The augmented def2-SVPD, def2-TZVPPD, and def2-QZVPPD basis sets balance the accuracy of polarizabilities across lanthanide oxidation states. The relative errors in atomic and molecular polarizability calculations are ≤8% for augmented split-valence basis sets, ≤ 2.5% for augmented triple-zeta valence basis sets, and ≤1% for augmented quadruple-zeta valence basis sets. In addition, extended def2-TZVPPDD and def2-QZVPPDD are provided for accurate calculations of lanthanide atoms and neutral clusters. The property-optimized basis sets developed in this work are shown to accurately reproduce electronic absorption spectra of a series of L n C p 3 ′ − complexes (Cp′ = C5H4SiMe3, Ln = Ce–Nd, Sm) with time-dependent density functional theory. [ABSTRACT FROM AUTHOR]

The structural, electronic, and optical properties of the protected Au clusters with icosahedral (Ih) and face-centered cubic (FCC)-like Au13 cores were studied to understand the origin of the difference in the optical gaps of these clusters. It has been demonstrated that the choice of density functionals does not qualitatively affect the properties of Au23 and Au25 clusters with Ih and FCC cores. The density of states, molecular orbitals, and natural charges were analyzed in detail using the B3LYP functional. The substantial energy difference in the lowest-energy absorption peaks for the clusters with the Ih and FCC cores is attributed to the difference in the natural charges of the central Au atoms (Auc) in the Ih and FCC cores, the former of which is more negative than the latter. Natural population analysis demonstrates that the excess negative charge of the Auc atom in clusters with Ih cores occupies the 6p atomic orbitals. This difference in Auc is attributed to the smaller size of the Ih core compared to the FCC core, as a less bulky ligand allows a smaller core with increased electron density, which, in turn, increases the highest occupied molecular orbital energy and decreases the optical gap. [ABSTRACT FROM AUTHOR]

We probe the accuracy of linear ridge regression employing a three-body local density representation derived from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies and atomic forces in molecules and solids. We find that such a simple regression framework performs on par with state-of-the-art machine learning methods which are, in most cases, more complex and more computationally demanding. Subsequently, we look for ways to sparsify the descriptor and further improve the computational efficiency of the method. To this aim, we use both principal component analysis and least absolute shrinkage operator regression for energy fitting on six single-element datasets. Both methods highlight the possibility of constructing a descriptor that is four times smaller than the original with a similar or even improved accuracy. Furthermore, we find that the reduced descriptors share a sizable fraction of their features across the six independent datasets, hinting at the possibility of designing material-agnostic, optimally compressed, and accurate descriptors. [ABSTRACT FROM AUTHOR]

Boron (B) containing III-nitride materials, such as wurtzite (wz) (B, Ga)N alloys, have recently attracted significant interest due to their ability to tailor the electronic and optical properties of optoelectronic devices operating in the visible and ultraviolet spectral range. However, the growth of high quality samples is challenging and B atom clustering is often observed in (B, Ga)N alloys. To date, a fundamental understanding of the impact of such clustering on the electronic and optical properties of these alloys is sparse. In this work, we employ density functional theory (DFT) in the framework of the meta-generalized gradient approximation [modified Becke Johnson (mBJ) functional] to provide insight into this question. We use mBJ DFT calculations, benchmarked against state-of-the-art hybrid functional DFT, on (B, Ga)N alloys in the experimentally relevant B content range of up to 7.4%. Our results reveal that B atom clustering can lead to a strong reduction in the bandgap of such an alloy, in contrast to alloy configurations where B atoms are not forming clusters, thus not sharing nitrogen (N) atoms. We find that the reduction in bandgap is linked mainly to carrier localization effects in the valence band, which stem from local strain and polarization field effects. However, our study also reveals that the alloy microstructure of a B atom cluster plays an important role: B atom chains along the wz c axis impact the electronic structure far less strongly when compared to a chain formed within the c-plane. This effect is again linked to local polarization field effects and the orbital character of the involved valence states in wz BN and GaN. Overall, our calculations show that controlling the alloy microstructure of (B, Ga)N alloys is of central importance when it comes to utilizing these systems in future optoelectronic devices with improved efficiencies. [ABSTRACT FROM AUTHOR]

Molecular gas species for gas cluster ion beams (GCIBs), such as carbon dioxide and water, were examined with a range of beam energies and cluster sizes to compare with the "universal relation" of the sputter yield, Y, per cluster atom against incident beam energy, E, per cluster atom of Arn cluster beam using Irganox 1010. In this work, we compare Arn, (CO2)n, and (H2O)n gas clusters to the universal equations for Arn clusters. To discuss molecular gas species for GCIBs, energy per nucleon (E/N) needs to replace energy per atom. We monitored sputter rate, depth resolution, and secondary ion yield as a function of the beam parameters: gas species, beam energy, and cluster size. (H2O)n GCIB shows reduced sputter rates and improved depth resolution with high sensitivity compared to Arn and (CO2)n GCIBs. These initial results indicate the potential to achieve high-depth resolution with high sensitivity and suggest that (H2O)n cluster ion beam has the potential to play a significant role in surface analysis techniques with organic materials. Results also show that no single set of conditions will provide the "best gas cluster ion beam" for all applications. However, it is possible to choose a set of conditions that will be more or less optimal depending on the experimental goals, such as maximizing the sputter rate, depth resolution, and molecular ion yield. In this work, we recommend the following three guidelines for GCIB users to set their own conditions: (1) to maximize the sputter rate, select a smaller cluster (higher E/N), but be aware that this will increase fragmentation and reduce molecular ion yield; (2) to maximize the depth resolution, select a larger cluster (lower E/N), and use (H2O)n GCIB, if possible; and (3) to maximize the molecular ion signal, use the highest beam energy available, and select a cluster with 0.15–0.25 eV/nucleon for Ar and (CO2)n GCIBs or around 0.1 eV/nucleon if using (H2O)n GCIB. These results are valid for XPS, SIMS, and any technique that utilizes GCIBs. [ABSTRACT FROM AUTHOR]

The magnetic response of valence electrons in doped gold-based M @ A u 8 L 8 q superatoms (M = Pd, Pt, Ag, Au, Cd, Hg, Ir, and Rh; L = PPh3; and q = 0, +1, +2) is studied by calculating the gauge including magnetically induced currents (GIMIC) in the framework of the auxiliary density functional theory. The studied systems include 24 different combinations of the dopant, total cluster charge, and cluster structure (cubic-like or oblate). The magnetically induced currents (both diatropic and paratropic) are shown to be sensitive to the atomic structure of clusters, the number of superatomic electrons, and the chemical nature of the dopant metal. Among the cubic-like structures, the strongest aromaticity is observed in Pd- and Pt-doped M @ A u 8 L 8 0 clusters. Interestingly, Pd- and Pt-doping increases the aromaticity as compared to a similar all-gold eight-electron system A u 9 L 8 + 1 . With the recent implementation of the GIMIC in the deMon2k code, we investigated the aromaticity in the cubic and butterfly-like M@Au8 core structures, doped with a single M atom from periods 5 and 6 of groups IX–XII. Surprisingly, the doping with Pd and Pt in the cubic structure increases the aromaticity compared to the pure Au case not only near the central atom but encompassing the whole metallic core, following the aromatic trend Pd > Pt > Au. These doped (Pd, Pt)@Au8 nanoclusters show a closed shell 1S21P6 superatom electronic structure corresponding to the cubic aromaticity rule 6n + 2. [ABSTRACT FROM AUTHOR]

The recent advent of cutting-edge experimental techniques allows for a precise synthesis of subnanometer metal clusters composed of just a few atoms, opening new possibilities for subnanometer science. In this work, via first-principles modeling, we show how the decoration of perfect and reduced TiO2 surfaces with Ag5 atomic clusters enables the stabilization of multiple surface polarons. Moreover, we predict that Ag5 clusters are capable of promoting defect-induced polarons transfer from the subsurface to the surface sites of reduced TiO2 samples. For both planar and pyramidal Ag5 clusters, and considering four different positions of bridging oxygen vacancies, we model up to 14 polaronic structures, leading to 134 polaronic states. About 71% of these configurations encompass coexisting surface polarons. The most stable states are associated with large inter-polaron distances (>7.5 Å on average), not only due to the repulsive interaction between trapped Ti3+ 3d1 electrons, but also due to the interference between their corresponding electronic polarization clouds [P. López-Caballero et al., J. Mater. Chem. A 8, 6842–6853 (2020)]. As a result, the most stable ferromagnetic and anti-ferromagnetic arrangements are energetically quasi-degenerate. However, as the average inter-polarons distance decreases, most (≥70%) of the polaronic configurations become ferromagnetic. The optical excitation of the midgap polaronic states with photon energy at the end of the visible region causes the enlargement of the polaronic wave function over the surface layer. The ability of Ag5 atomic clusters to stabilize multiple surface polarons and extend the optical response of TiO2 surfaces toward the visible region bears importance in improving their (photo-)catalytic properties and illustrates the potential of this new generation of subnanometer-sized materials. [ABSTRACT FROM AUTHOR]

Superatoms have exciting properties, including diverse functionalization, redox activity, and magnetic ordering, so the resulting cluster-assembled solids hold the promise of high tunability, atomic precision, and robust architectures. By utilizing adamantane-like clusters as building blocks, a new class of superatoms N4Mg6M (M = Li, Na, K) is proposed here. The studied superalkalis feature low adiabatic ionization energies, an antibonding character in the interactions between magnesium and nitrogen atoms, and highly delocalized highest occupied molecular orbital (HOMO). Consequently, the N4Mg6M superalkalis might easily lose their HOMO electrons when interacting with superhalogen electrophiles to form stable superatom [superalkali]+[superhalogen]− compounds. Moreover, the studied superalkalis interact strongly with carbon dioxide, and the resulting N4Mg6M/CO2 systems represent two strongly interacting ionic fragments (i.e., N4Mg6M+ and CO2−). In turn, the electron affinity of the N2 molecule (of −1.8 eV) is substantially lower than that observed for carbon dioxide (EA = −0.6 eV) and consequently, the N2 was found to form the weakly bound [N4Mg6M][N2] complex rather than the desired ionic [N4Mg6M]+[N2]− product. Thus, the N4Mg6M superalkalis have high selectivity over N2 when it comes to CO2 reduction and also are themselves stable. We believe that the results described within this paper will be useful for understanding CO2 activation, which is the first step for producing fuels from CO2. Moreover, we demonstrate that designing novel superatomic systems and exploring their physicochemical features might be used to create desirable functional materials. [ABSTRACT FROM AUTHOR]

We analyze the probability distribution of rare first passage times corresponding to transitions between product and reactant states in a kinetic transition network. The mean first passage times and the corresponding rate constants are analyzed in detail for two model landscapes and the double funnel landscape corresponding to an atomic cluster. Evaluation schemes based on eigendecomposition and kinetic path sampling, which both allow access to the first passage time distribution, are benchmarked against mean first passage times calculated using graph transformation. Numerical precision issues severely limit the useful temperature range for eigendecomposition, but kinetic path sampling is capable of extending the first passage time analysis to lower temperatures, where the kinetics of interest constitute rare events. We then investigate the influence of free energy based state regrouping schemes for the underlying network. Alternative formulations of the effective transition rates for a given regrouping are compared in detail to determine their numerical stability and capability to reproduce the true kinetics, including recent coarse-graining approaches that preserve occupancy cross correlation functions. We find that appropriate regrouping of states under the simplest local equilibrium approximation can provide reduced transition networks with useful accuracy at somewhat lower temperatures. Finally, a method is provided to systematically interpolate between the local equilibrium approximation and exact intergroup dynamics. Spectral analysis is applied to each grouping of states, employing a moment-based mode selection criterion to produce a reduced state space, which does not require any spectral gap to exist, but reduces to gap-based coarse graining as a special case. Implementations of the developed methods are freely available online. [ABSTRACT FROM AUTHOR]

Size reduction of the barrier and liner stack for copper interconnects is a major bottleneck in further down-scaling of transistor devices. The role of the barrier is to prevent diffusion of Cu atoms into the surrounding dielectric, while the liner (also referred to as a seed layer) ensures that a smooth Cu film can be electroplated. Therefore, a combined barrier + liner material that restricts the diffusion of Cu into the dielectric and allows for copper electro-deposition is needed. In this paper, we have explored barrier + liner materials composed of 1 and 2 monolayers (MLs) of Ru-passivated ϵ -TaN and Ru doped ϵ -TaN and focused on their interactions with Cu through the adsorption of small Cu clusters with 1–4 atoms. Moreover, different doping patterns for Ru doping in TaN are investigated to understand how selective doping of the ϵ -TaN surface influences surface stability. We found that an increased concentration of Ru atoms in the outermost Ta layer improves the adhesion of Cu. The strongest binding of the Cu atoms was found on the 100% Ru doped surface followed by the 1 ML Ru passivated surface. These two surfaces are recommended for the combined barrier + liner for Cu interconnects. The closely packed arrangements of Cu were found to exhibit weak Cu–slab and strong Cu–Cu interactions, whereas the sparse arrangements of Cu exhibit strong Cu–slab and weak Cu–Cu interactions. The Cu atoms seem to bind more favorably when they are buried in the doped or passivated surface layer due to the increase in their coordination number. This is facilitated by the surface distortion arising from the ionic radius mismatch between Ta and Ru. We also show that the strong Cu–Cu interaction alone cannot predict the association of Cu atoms as a few 2D Cu clusters showed stronger Cu–Cu interaction than the 3D clusters, highlighting the importance of Cu–surface interactions. [ABSTRACT FROM AUTHOR]

The atomic pair-distribution function of simple liquid and glass shows exponentially decaying oscillations beyond the first peak, representing the medium-range order (MRO). The structural coherence length that characterizes the exponential decay increases with decreasing temperature and freezes at the glass transition. Conventionally, the structure of liquid and glass is elucidated by focusing on a center atom and its neighboring atom shell characterized by the short-range order (SRO) and describing the global structure in terms of overlapping local clusters of atoms as building units. However, this local bottom-up approach fails to explain the strong drive to form the MRO, which is different in nature from the SRO. We propose to add an alternative top-down approach based upon the density wave theory. In this approach, one starts with a high-density gas state and seeks to minimize the global potential energy in reciprocal space through density waves using the pseudopotential. The local bottom-up and global top-down driving forces are not mutually compatible, and the competition and compromise between them result in a final structure with the MRO. This even-handed approach provides a more intuitive explanation of the structure of simple liquid and glass. [ABSTRACT FROM AUTHOR]