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DOE OSTI2024

Recent Advances on Computational Modeling of Supported Single-Atom and Cluster Catalysts: Characterization, Catalyst–Support Interaction, and Active Site Heterogeneity

To satisfy the need for catalyst materials with high activity, selectivity, and stability for energy conversion, material design and discovery guided by theoretical insights are a necessity. In the past decades, the rise in theoretical investigations into the properties of catalyst materials, reaction mechanisms, and catalyst design principles has shed light on the catalysis field. Quantitative structure–activity relationships have been developed through incorporating spectroscopic simulations, electronic structure calculations, and reaction mechanistic studies. Here, in this review, we report the state-of-the-art computational approaches to catalyst materials characterization for supported single-atom and cluster catalysts utilizing spectroscopic simulations, i.e., XANES simulation, and material properties investigation via electronic-structure calculations. Furthermore, approaches regarding reaction mechanisms, focusing on active site heterogeneity, are also discussed.

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

The design space of E(3)-equivariant atom-centred interatomic potentials

Abstract Molecular dynamics simulation is an important tool in computational materials science and chemistry, and in the past decade it has been revolutionized by machine learning. This rapid progress in machine learning interatomic potentials has produced a number of new architectures in just the past few years. Particularly notable among these are the atomic cluster expansion, which unified many of the earlier ideas around atom-density-based descriptors, and Neural Equivariant Interatomic Potentials (NequIP), a message-passing neural network with equivariant features that exhibited state-of-the-art accuracy at the time. Here we construct a mathematical framework that unifies these models: atomic cluster expansion is extended and recast as one layer of a multi-layer architecture, while the linearized version of NequIP is understood as a particular sparsification of a much larger polynomial model. Our framework also provides a practical tool for systematically probing different choices in this unified design space. An ablation study of NequIP, via a set of experiments looking at in- and out-of-domain accuracy and smooth extrapolation very far from the training data, sheds some light on which design choices are critical to achieving high accuracy. A much-simplified version of NequIP, which we call BOTnet (for body-ordered tensor network), has an interpretable architecture and maintains its accuracy on benchmark datasets.

Computer Science↗
DOE OSTI2025

Toward an Understanding of Linear Scaling Relations through Energy Decomposition Analysis

The discovery of linear scaling relations has fundamentally changed the field of heterogeneous catalysis. The scaling relations have been rationalized based on the d-band theory, specifically a separation of sp and d electron contributions to adsorption energies. Within the framework of energy decomposition analysis, a full understanding of such a separation would require one to further break down the adsorption energy into distinct energy components such as electrostatics, polarization, charge transfer, and van der Waals interactions, and to examine the sp and d contributions to each of them. As a step in this direction, we analyzed the interaction energy between CH x (x = 1–4) adsorbates and fcc(100) transition metal surfaces (M = Cu, Ag, Au, Rh, and Pt), with the surfaces represented both as slabs in plane-wave density functional theory (pw-DFT) calculations and as atomic clusters in atomic-orbital basis density functional theory (ao-DFT) calculations. Through an absolutely localized molecular orbital (ALMO) based energy decomposition analysis of the ao-DFT adsorption energy, each of the interaction energy components (electrostatics, polarization, van der Waals, and charge transfer) was found to follow its own scaling relations, with an intricate interplay among these energy components yielding the overall scaling relations for the total adsorption energies. Using the recently introduced ALMO-based polarization and charge-transfer analysis schemes, we further dissected polarization into metal surface and adsorbate contributions, and charge transfer into metal → adsorbate and adsorbate → metal contributions. The contributions from the sp and d electrons of the metal to these terms were further quantified, and the dominant role of the metal d electrons was reaffirmed. These results shed light on how CHx adsorbates interact with metal surfaces and further reveal the physical origin of the scaling relations.

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

Multiscale Physics of Atomic Nuclei from First Principles

Atomic nuclei exhibit multiple energy scales ranging from hundreds of MeV in binding energies to fractions of an MeV for low-lying collective excitations. As the limits of nuclear binding are approached near the neutron and proton drip lines, traditional shell structure starts to melt with an onset of deformation and an emergence of coexisting shapes. It is a long-standing challenge to describe this multiscale physics starting from nuclear forces with roots in quantum chromodynamics. Here, we achieve this within a unified and nonperturbative quantum many-body framework that captures both short- and long-range correlations starting from modern nucleon-nucleon and three-nucleon forces from chiral effective field theory. The short-range (dynamic) correlations which account for the bulk of the binding energy are included within a symmetry-breaking framework, while long-range (static) correlations (and fine details about the collective structure) are included by employing symmetry projection techniques. Our calculations accurately reproduce—within theoretical error bars—available experimental data for low-lying collective states and the electromagnetic quadrupole transitions in 20−30 Ne. In addition, we reveal coexisting spherical and deformed shapes in 30 Ne, which indicates the breakdown of the magic neutron number 𝑁 = 20 as the key nucleus 28 O is approached, and we predict that the drip line nuclei 32,34 Ne are strongly deformed and collective. By developing reduced-order models for symmetry-projected states, we perform a global sensitivity analysis and find that the subleading singlet 𝑆-wave contact and a pion-nucleon coupling strongly impact nuclear deformation in chiral effective field theory. The techniques developed in this work clarify how microscopic nuclear forces generate the multiscale physics of nuclei spanning collective phenomena as well as short-range correlations and allow one to capture emergent and dynamical phenomena in finite fermion systems such as atom clusters, molecules, and atomic nuclei.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Nanocluster Active Sites Formed on Heterogeneous Thermal Catalysts and Electrocatalysts by Operando Reactive Environments

Here, in this Viewpoint, we summarize our recent studies in this endeavor, ending with a forward-looking perspective into the remaining challenges and open questions for consideration by the catalysis community. Through a computationally efficient framework of systematically investigating metal atom ejection from and migration onto metal surfaces, leading to the formation of metal atom clusters, we show that the surface of a metal catalyst is dynamic and much less rigid than previously thought. We suggest that the operando formed metal atom clusters are novel active sites, which can dominate the activity of steps or kinks (let aside terraces) from where their constituent atoms were ejected. Through more readily responding to reaction conditions by forming catalytically active clusters, solid metal catalysts approach not only homogeneous catalyst motifs, thus establishing a bridge between homogeneous and heterogeneous catalysis, but also liquid metals which have been suggested to be better than traditional heterogeneous catalysts.

adsorption↗
DOE OSTI2022

Kuramoto synchronization of quantum tunneling polarons for describing the dynamic structure in cuprate superconductors

A major open topic in cuprates is the interplay between the lattice and electronic dynamics and the importance of their coupling to the mechanism of high-temperature superconductivity (HTSC). As evidenced by extended x-ray absorption fine structure (EXAFS) experiments, anharmonic structural effects are correlated with the charge dynamics and the transition to a superconducting phase in different HTSC compounds. Here, in this paper, we describe how structural anharmonic effects can be coupled to electronic and lattice dynamics in cuprate systems by performing the exact diagonalization of a prototype anharmonic many-body Hamiltonian on a relevant 6-atom cluster and show that the EXAFS results can be understood as a Kuramoto synchronization transition between coupled internal quantum tunneling of polarons associated with the two-site distribution of the copper–apical oxygen (Cu-O ap ) pair in the dynamic structure. The transition is driven by the anharmonicity of the lattice vibrations and promotes the pumping of charge, initially stored at the apical oxygen reservoirs, into the copper-oxide plane. Simultaneously, a finite projection of the internal quantum tunneling polaron extends to the copper–planar oxygen (Cu-O pl ) pair. All these findings allow an interpretation based on an effective quantum-mechanical triple-well potential associated with the oxygen sites of the 6-atom cluster, which accurately represents the phase synchronization of apical oxygens and lattice-assisted charge transfer to the CuO 2 plane.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Mechanistic insights into nitrogen activation on atomic Ru clusters in self-pillared pentasil using operando atomistic models and experimental kinetics

Alternative catalysts to the industrial Haber Bosch process have been of significant interest in the field of heterogeneous catalysis, yet realizing ammonia synthesis under mild conditions (e.g., 300 °C and 10 bar) is challenging due to the low per-pass conversion. One strategy is to promote the associative ammonia synthesis mechanism which eschews direct N-N bond cleavage. Here, in this work, we use self-pillared pentasil, a self-pillared hierarchical zeolite built by thin MFI zeolite nanosheets, as a support for subnanometric Ru clusters to synthesize ammonia. We show that Ru remains well-dispersed during reaction and further demonstrate that ammonia synthesis rates are higher than Cs-Ru/MgO. Reaction kinetics show a positive order in H 2 providing evidence for the associative mechanism, which then becomes negative in H 2 if Ru is allowed to aggregate into nanoparticles. Operando Density Functional Theory models for Ru speciation in SPP, free energy diagrams, and microkinetic modeling were then applied to develop a reaction mechanism that involves sequential hydrogenation of N 2 from metallic Ru clusters. For this hydrogenation to occur, there are site requirements for N 2 to adopt a bridge-bound configuration that facilitates sequential hydrogenation on single sites and metal clusters. These site requirements in turn inform the design of improved zeolite-supported ammonia synthesis catalysts.

36 MATERIALS SCIENCE↗
DOE OSTI2026

From closed shells to open shells: Coupled-cluster calculations of atomic nuclei

Coupled-cluster theory is a powerful tool for first-principles calculations of atomic nuclei, enabling accurate predictions of nuclear observables across the Segrè chart. While coupled-cluster computations are especially efficient at shell closures, extensions have been developed to tackle open-shell nuclei, by exploiting the equation-of-motion method or by expanding the coupled-cluster wave function on top of a symmetry-breaking (either deformed or superfluid) reference state. In this study, we provide a comprehensive comparison of these different formulations applied to the calcium and nickel isotopes using nuclear two-and three-body interactions from chiral effective field theory. Here, based on ground-state energies, two-neutron separation energies, and two-neutron shell gaps, different coupled-cluster computations—based on symmetry-broken reference states and equationof-motion techniques— offer consistent descriptions of bulk properties across medium-mass isotopic chains.

Marino, Francesco [Johannes Gutenberg-Universität ↗
DOE OSTI2023

Proper orthogonal descriptors for efficient and accurate interatomic potentials

Here, we present the proper orthogonal descriptors for efficient and accuracy representation of the potential energy surface. The potential energy surface is represented as a many-body expansion of parametrized potentials in which the potentials are functions of atom positions and parameters. The proper orthogonal decomposition is employed to decompose the parametrized potentials into a set of proper orthogonal descriptors (PODs). Because of the rapid convergence of the proper orthogonal decomposition, relevant snapshots can be sampled exhaustively to represent the atomic neighborhood environment accurately with a small number of descriptors. The proper orthogonal descriptors are used to develop interatomic potentials by using a linear expansion of the descriptors and determining the expansion coefficients from a weighted least-squares regression against a density functional theory (DFT) training set. We present a comprehensive evaluation of the POD potentials on previously published DFT data sets comprising Li, Mo, Cu, Ni, Si, Ge, and Ta elements. The data sets represent a diverse pool of metals, transition metals, and semiconductors. The accuracy of the POD potentials are comparable to that of state-of-the-art machine learning potentials such as the spectral neighbor analysis potential (SNAP) and the atomic cluster expansion (ACE).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Bayesian prior construction for uncertainty quantification in first-principles statistical mechanics

First-principles statistical mechanics enables the prediction of thermodynamic and kinetic properties of materials, but is computationally expensive. Many approaches require surrogate models to calculate energies within Monte Carlo or molecular dynamics simulations. Inexpensive surrogates such as cluster expansions enable otherwise intractable calculations by interpolating data from higher accuracy methods, such as Density Functional Theory (DFT). Surrogate models introduce uncertainty into downstream calculations, in addition to any uncertainty inherent to DFT calculations. Bayesian frameworks address this by quantifying uncertainty and incorporating expert knowledge through priors. However, constructing effective priors remains challenging. This work introduces and describes practical strategies for building Bayesian cluster expansions, focusing on basis truncation, hyperparameter selection, and ground state replication. We analyze multiple basis truncation schemes, compare cross-validation to the evidence-approximation for hyperparameter optimization, and provide methods to find and enforce ground-state-preserving models through priors. Additionally, we compare the uncertainties between different approximations to DFT (LDA, PBE, SCAN) against the uncertainty introduced with the use of cluster expansion surrogate models. These approaches are demonstrated on the BCC Li x Mg 1-x and Li x Al 1-x alloys, which are both of interest for solid-state Li batteries. Our results provide guidelines for constructing and utilizing Bayesian cluster expansions, thereby improving the transparency of materials modeling. Furthermore, the approaches and insights developed in this work can be transferred to a wide range of cluster expansion surrogate models, including the atomic cluster expansion and related machine-learned interatomic potential architectures.

Alloy theory↗
DOE OSTI2022

Superatomic chemistry

Superatoms are atomic clusters with tailored size and composition that mimic the chemistry of atoms in the periodic table. However, unlike the atoms whose chemistry is governed by their valence electron orbitals, the chemistry of superatoms is governed by their highest occupied molecular orbitals. In addition, due to their large size and non-spherical geometry, superatoms can promote unusual reactions and serve as the building blocks of cluster assembled materials with properties very different from conventional materials. This perspective highlights the unique role of superatoms in chemical and material sciences by focusing on superhalogens, which not only possess electron affinities larger than those of halogens but also can be stable when multiply charged. We discuss how these unique features of superhalogens enable noble gas atoms like argon to form chemical bonds at room temperature and zinc to exhibit an oxidation state of +3. Here, the advantages of using superhalogens in the synthesis of water-resistant materials for solar cells, halogen-free electrolytes for solid-state batteries, and multiferroic materials are also discussed.

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

Ru/MgO catalyst with dual Ru structure sites for efficient CO production from CO 2 hydrogenation

The development and comprehension of supported metal catalysts for CO 2 hydrogenation is of paramount importance in mitigating the net CO 2 emissions. Supported Ru catalysts have been widely recognized in facilitating CO 2 methanation, on which recent findings suggest that the CO 2 hydrogenation process can be manipulated to favor the reverse water–gas shift (RWGS) pathway by precisely adjusting the size of Ru particles. However, the size-dependent impact of Ru remains a topic of lively debate. In this work, Ru/MgO catalysts with Ru in the form of single atoms (Ru 1 ) and few-atom cluster (Ru FAC ) structures were prepared for CO 2 hydrogenation. The 1.0Ru/MgO catalyst (with 1 wt.% of Ru), featuring a mixture of Ru 1 and Ru FAC with a size of 0.6–1.0 nm, showed the highest CO yield (38% at 500 °C) with balanced CO 2 conversion and CO selectivity. Transient CO 2 hydrogenation and temperature-programmed surface reaction (TPSR) studies suggested that the adsorbed CO 2 species participated in CO 2 hydrogenation. On Ru 1 sites, CO 2 hydrogenation followed the RWGS pathway, resulting in the production of CO. In contrast, on Ru FAC sites, the enhanced H 2 dissociation ability, along with the presence of adsorbed bidentate and monodentate carbonate species at the Ru-MgO interfaces, facilitated the formation of CH 4 through the CO 2 methanation pathway. In conclusion, this study highlights the critical roles of Ru structure and local environment in defining the CO 2 hydrogenation pathways and provides new design principles for highly active Ru-based catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Reversible disorder-order transitions in atomic crystal nucleation

Nucleation in atomic crystallization remains poorly understood, despite advances in classical nucleation theory. The nucleation process has been described to involve a nonclassical mechanism that includes a spontaneous transition from disordered to crystalline states, but a detailed understanding of dynamics requires further investigation. In situ electron microscopy of heterogeneous nucleation of individual gold nanocrystals with millisecond temporal resolution shows that the early stage of atomic crystallization proceeds through dynamic structural fluctuations between disordered and crystalline states, rather than through a single irreversible transition. Our experimental and theoretical analyses support the idea that structural fluctuations originate from size-dependent thermodynamic stability of the two states in atomic clusters. These findings, based on dynamics in a real atomic system, reshape and improve our understanding of nucleation mechanisms in atomic crystallization.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Analysis of Dynamical Peculiarities in Nanoalloys at Subsystems Level: Dynamical Degrees of Freedom, Temperature Differences, and the Chameleon Effect

Abstract A novel analysis of the dynamical behavior of nanoalloy systems, as represented by model Ni/Al 13‐atom clusters, over a broad range of energies that cover the stage‐wise transition of the systems from their solid‐like to liquid‐like state is presented. Conceptually, the analysis is rooted in partitioning the systems into judiciously chosen subsystems and characterizing the latter in terms of subsystem‐specific dynamical descriptors that include dynamical degrees of freedom , root‐mean‐square bond‐length fluctuation , and element‐specific subsystem temperature . The analysis reveals a host of intriguing new peculiarities in the dynamical behavior of the Ni/Al 13‐mers, among which are what we call the chameleon effect and the difference in the temperatures of the Ni and Al subsystems at high energies, a difference that strongly depends on the cluster composition and also changes with energy. These do not have an analog in pure Ni 13 and Al 13 and are explained in terms of the coupled effects of the difference between the masses of the Ni and Al atoms (the mass effect) and of the difference in the anharmonicity of the overall interaction potential as experienced by the Ni and Al subsystems of the clusters (the potential effect).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Evolution of Charge-Lattice Dynamics across the Kuramoto Synchronization Phase Diagram of Quantum Tunneling Polarons in Cuprate Superconductors

Because of its sensitivity to the instantaneous structure factor, S(Q,t = 0), Extended X-ray Absorption Fine Structure (EXAFS) is a powerful tool for probing the dynamic structure of condensed matter systems in which the charge and lattice dynamics are coupled. When applied to hole-doped cuprate superconductors, EXAFS has revealed the presence of internal quantum tunneling polarons (IQTPs). An IQTP arises in EXAFS as a two-site distribution for certain Cu–O pairs, which is also duplicated in inelastic scattering but not observed in standard diffraction measurements. The Cu–Sr pair distribution has been found to be highly anharmonic and strongly correlated to both the IQTPs and to superconductivity, as, for example, in YSr 2 Cu 2.75 Mo 0.25 O 7.54 (T c =84 K). In order to describe such nontrivial, anharmonic charge-lattice dynamics, we have proposed a model Hamiltonian for a prototype six-atom cluster, in which two Cu-apical-O IQTPs are charge-transfer bridged through Cu atoms by an O atom in the CuO 2 plane and are anharmonically coupled via a Sr atom. By applying an exact diagonalization procedure to this cluster, we have verified that our model indeed produces an intricate interplay between charge and lattice dynamics. Then, by using the Kuramoto model for the synchronization of coupled quantum oscillators, we have found a first-order phase transition for the IQTPs into a synchronized, phase-locked phase. Most importantly, we have shown that this transition results specifically from the anharmonicity. Finally, we have provided a phase diagram showing the onset of the phase-locking of IQTPs as a function of the charge-lattice and anharmonic couplings in our model. We have found that the charge, initially confined to the apical oxygens, is partially pumped into the CuO 2 plane in the synchronized phase, which suggests a possible connection between the synchronized dynamic structure and high-temperature superconductivity (HTSC) in doped cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗