Cluster Expansion Research Articles

Pressure of a dilute spin-polarized Fermi gas: Lower bound

Abstract We consider a dilute fully spin-polarized Fermi gas at positive temperature in dimensions $d\in \{1,2,3\}$ . We show that the pressure of the interacting gas is bounded from below by that of the free gas plus, to leading order, an explicit term of order $a^d\rho ^{2+2/d}$ , where a is the p-wave scattering length of the repulsive interaction and $\rho $ is the particle density. The results are valid for a wide range of repulsive interactions, including that of a hard core, and uniform in temperatures at most of the order of the Fermi temperature. A central ingredient in the proof is a rigorous implementation of the fermionic cluster expansion of Gaudin, Gillespie and Ripka (Nucl. Phys. A, 176.2 (1971), pp. 237–260).

Thermodynamic, electronic, and optical properties of ultra-wide bandgap zirconium-doped tin dioxide from a DFT perspective.

The effects of zirconium doping on the thermodynamic, electronic, and optical properties of tin dioxide are investigated by using density functional theory calculations combined with the cluster expansion method. In the whole composition range, the formation enthalpies of all structures are positive, indicating that SnO2-ZrO2 is an immiscible system and the ZrSnO2 alloy has a tendency of phase separation at low temperature. The x-T phase diagram of ZrSnO2 ternary alloy shows that the critical temperature is 979 K, which means that when the growth temperature of ZrSnO2 crystal is higher than the critical temperature, it is possible to realize the full-component solid solution. The bandgaps of ZrxSn1-xO2 alloys (0 ≤ x ≤ 1) are direct and increase as the Zr composition increases. Zr doping can tune the bandgap of SnO2 from the ultraviolet-B region to the deep ultraviolet region, and has a strong optical response to deep ultraviolet light. The projected density of states and band offsets clearly reveal the reason for the increase of bandgap, which provides useful information to design relevant optoelectronic devices such as quantum wells and solar-blind deep ultraviolet photodetectors.

Stability of the Spectral Gap and Ground State Indistinguishability for a Decorated AKLT Model

We use cluster expansion methods to establish local the indistiguishability of the finite volume ground states for the AKLT model on decorated hexagonal lattices with decoration parameter at least 5. Our estimates imply that the model satisfies local topological quantum order, and so, the spectral gap above the ground state is stable against local perturbations.

Phase Separation of Br-Doped CsPbI3: A Combined Cluster Expansion, Monte Carlo, and DFT Study.

Cluster expansion, which is a method that describes the concentration-dependent thermodynamic properties of materials while maintaining density functional theory accuracy, was used to predict new (CsPbIxBr1-x) structures. The cluster-expansion method generated 42 new stable (CsPb)xIyBrz (where x = 1 to 3 and y and z = 1 to 8) structures and these were ranked as meta-stable structures based on their enthalpies of formation. Monte Carlo calculations showed that CsPbI0.5Br0.5 composition separates into different phases at 300 K, but changes to a homogeneous phase at 700 K, suggesting that a different phase of CsPbI3 may exist at higher temperatures. Among the 42 predicted structures, randomly selected structures around iodide-rich, 50:50, and bromine-rich sites were studied further by determining their electronic, optical, mechanical, and thermodynamic properties using first-principle density functional theory. The materials possess similar properties as cubic Br-doped CsPbI3 perovskites. The mechanical properties of these compounds revealed that they are ductile in nature and mechanically stable. This work suggests that the introduction of impurities into CsPbI3 perovskite materials, as well as compositional engineering, can alter the electronic and optical properties, making them potential candidates for solar cell applications.

Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields.

The rational design of alloys and solid solutions relies on accurate computational predictions of phase diagrams. The cluster expansion method has proven to be a valuable tool for studying disordered crystals. However, the effects of vibrational entropy are commonly neglected due to the computational cost. Here, we devise a method for including the vibrational free energy in cluster expansions with a low computational cost by fitting a machine learning force field (MLFF) to the relaxation trajectories available from cluster expansion construction. We demonstrate our method for two (pseudo)binary systems, Na1-xKxCl and Ag1-xPdx, for which accurate phonon dispersions and vibrational free energies are derived from the MLFF. For both systems, the inclusion of vibrational effects results in significantly better agreement with miscibility gaps in experimental phase diagrams. This methodology can allow routine inclusion of vibrational effects in calculated phase diagrams and thus more accurate predictions of properties and stability for mixtures of materials.

Controlled cluster expansion at a Zintl cluster surface

AbstractReaction of the tris‐hypersilyl nonagermanide Zintl cluster salt, K[Ge9(Hyp)3] (Hyp=Si(SiMe3)3) with [Rh(η2,η2‐L)Cl]2 (L=1,5‐cyclooctadiene, COD; norbornadiene, NBD) afforded eleven‐ and twelve‐vertex homo‐multimetallic clusters by cluster core expansion. Using a stepwise procedure, starting from the Zintl cluster [Rh(COD){Ge9(Hyp)3}] and [Ir(COD)Cl]2, this methodology was expanded for the synthesis of eleven‐vertex hetero‐multimetallic clusters. A mechanism for the formation of these first examples of closo eleven‐vertex Zintl clusters is proposed, informed by density functional theory calculations.

Controlled cluster expansion at a Zintl cluster surface.

Reaction of the tris-hypersilyl nonagermanide Zintl cluster salt, K[Ge9 (Hyp)3 ] (Hyp=Si(SiMe3 )3 ) with [Rh(η2 ,η2 -L)Cl]2 (L=1,5-cyclooctadiene, COD; norbornadiene, NBD) afforded eleven- and twelve-vertex homo-multimetallic clusters by cluster core expansion. Using a stepwise procedure, starting from the Zintl cluster [Rh(COD){Ge9 (Hyp)3 }] and [Ir(COD)Cl]2 , this methodology was expanded for the synthesis of eleven-vertex hetero-multimetallic clusters. A mechanism for the formation of these first examples of closo eleven-vertex Zintl clusters is proposed, informed by density functional theory calculations.

High-throughput Compositional Screening of PdxTi1-xHy and PdxNb1-xHy Hydrides for CO2 Reduction.

Electrochemical experiments and theoretical calculations have shown that Pd-based metal hydrides can perform well for the CO2 reduction reaction (CO2RR). Our previous work on doped-PdH showed that doping Ti and Nb into PdH can improve the CO2RR activity, suggesting that the Pd alloy hydrides with better performance are likely to be found in the PdxTi1-xHy and PdxNb1-xHy phase space. However, the vast compositional and structural space with different alloy hydride compositions and surface adsorbates, makes it intractable to screen out the stable and active PdxM1-xHy catalysts using density functional theory calculations. Herein, an active learning cluster expansion (ALCE) surrogate model equipped with Monte Carlo simulated annealing (MCSA), a CO* binding energy filter and a kinetic model are used to identify promising PdxTi1-xHy and PdxNb1-xHy catalysts with high stability and superior activity. Using our approach, we identify 24 stable and active candidates of PdxTi1-xHy and 5 active candidates of PdxNb1-xHy. Among these candidates, the Pd0.23Ti0.77H, Pd0.19Ti0.81H0.94, and Pd0.17Nb0.83H0.25 are predicted to display current densities of approximately 5.1, 5.1 and 4.6 μA cm-2 at -0.5 V overpotential, respectively, which are significantly higher than that of PdH at 3.7 μA cm-2.

Thermodynamic properties for metal oxides from first-principles

In this study, an efficient first-principles approach for calculating the thermodynamic properties of mixed metal oxides at high temperatures is demonstrated. More precisely, this procedure combines density functional theory and harmonic phonon calculations with tabulated thermochemical data to predict the heat capacity, formation energy, and entropy of important metal oxides. Alloy cluster expansions are, moreover, employed to represent phases that display chemical ordering as well as to calculate the configurational contribution to the specific heat capacity. The methodology can, therefore, be applied to compounds with vacancies and variable site occupancies. Results are, moreover, presented for a number of systems of high practical relevance: FeKTiO, KMnO, and CaMnO. For the reference materials, the agreement with experimental measurements is exceptional in the case of ilmenite (FeTiO3) and good for CaMnO3. When the generated data is used in multi-phase thermodynamic calculations to represent materials for which experimental data is not available, the predicted phase-diagrams for the KMnO and KTiO systems change dramatically. The demonstrated methodology is highly useful for obtaining approximate values on key thermodynamic properties in cases where experimental data is hard to obtain, inaccurate or missing.

2329. What Causes a Cluster to Grow? Factors Associated with a Nosocomial COVID-19 Cluster at a University Hospital in Central Tokyo

Abstract Background Coronavirus disease 2019 (COVID-19) remains a significant threat to hospital infection control. Despite the decrease in severity and mortality associated with changes in the variants of concern and increased vaccination, SARS-CoV-2 transmissibility remains high, and nosocomial clusters continue to be reported in various countries. Although COVID-19 may be detected in multiple patients and healthcare workers (HCWs) in a given ward within a few days, it is uncertain whether these cases will develop into a large cluster. Methods The present, retrospective cohort study of nosocomial COVID-19 clusters was conducted at Tokyo Medical and Dental University Hospital from January 2022 to January 2023 using data from the hospital’s infection prevention and control team. A nosocomial COVID-19 cluster was defined as consisting of more than 2 COVID-19 cases occurring within 5 days in the same ward. Cases with a clear epidemiological link and clusters outside the ward were excluded. We collected information regarding community trends, the index case details, and each cluster's ward profile. Predictors of cluster expansion to more than 5 cases were also examined. Results 66 clusters were identified at the hospital during the study period. The median number of COVID-19 cases per cluster was 3 (range: 2-22), and their median duration was 5 days (range: 1-27). 37 (56.1%), 25 (37.9%), and 4 (6.1%) clusters comprised both inpatients and HCWs, only HCWs, and only patients, respectively. The index case of 51 clusters (77.3%) was a HCW. 18 (27.3%) and 47 (72.7%) clusters contained > 5 and < 5 cases, respectively. No significant intergroup difference was found in terms of community prevalence, index case and ward characteristics, the rate of close contact or history of previous clusters. However, “clusters occurring during the non-epidemic period” and “infections > 3 occurring within 3 days” tended to develop into clusters containing more than 5 cases. Conclusion Nosocomial clusters can occur anywhere, and predicting them is challenging. Further research is needed to identify the factors leading to cluster development and to establish effective infection prevention and control measures. Disclosures All Authors: No reported disclosures

Efficient time-dependent vibrational coupled cluster computations with time-dependent basis sets at the two-mode coupling level: Full and hybrid TDMVCC[2

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper, we report an efficient implementation of TDMVCC, covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: (i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and (ii) the use of a single function as an active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH (time-dependent Hartree) approach that can obtain even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] is illustrated for polyaromatic hydrocarbons with up to 264 modes. Finally, computations on the internal vibrational redistribution of benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom.

A central limit theorem for a classical gas

For a class of translation-invariant pair potentials ϕ in (mathbb{R}^{d},zlambda ) satisfying a stability and regularity condition, we choose z so small that the associated collection mathcal{ G}(phi,zlambda ) of Gibbs processes contains at least the stationary process G, which is a Gibbs process in the sense of DLR and is given by the limiting Gibbs process with empty boundary conditions. Using an abstract version of the method of cluster expansions and Dobrushin’s approach to the central limit theorem, we present a central limit theorem for the particle numbers of G.

Speeding up the Detection of Adsorbate Lateral Interactions in Graph-Theoretical Kinetic Monte Carlo Simulations.

Kinetic Monte Carlo (KMC) has become an indispensable tool in heterogeneous catalyst discovery, but realistic simulations remain computationally demanding on account of the need to capture complex and long-range lateral interactions between adsorbates. The Zacros software package (https://zacros.org) adopts a graph-theoretical cluster expansion (CE) framework that allows such interactions to be computed with a high degree of generality and fidelity. This involves solving a series of subgraph isomorphism problems in order to identify relevant interaction patterns in the lattice. In an effort to reduce the computational burden, we have adapted two well-known subgraph isomorphism algorithms, namely, VF2 and RI, for use in KMC simulations and implemented them in Zacros. To benchmark their performance, we simulate a previously established model of catalytic NO oxidation, treating the O* lateral interactions with a series of progressively larger CEs. For CEs with long-range interactions, VF2 and RI are found to provide impressive speedups relative to simpler algorithms. RI performs best, giving speedups reaching more than 150× when combined with OpenMP parallelization. We also simulate a recently developed methane cracking model, showing that RI offers significant improvements in performance at high surface coverages.

Phonon-mediated superconductivity in {text{Mg}}_{{1 - x}} {text{Mo}}_{x} {text{B}}_{2} compounds: a crystal prediction via cluster expansion and particle-swarm optimization

Investigating superconductivity represents one of the most significant phenomena in the field of condensed matter physics. Our simulations aim to elucidate the structures in the metallic state of Mg1−xMoxB2, which is essential for predicting their superconducting properties. By employing a first-principle cluster expansion and particle-swarm optimization, we have predicted the structures of Mg1−xMoxB2 ternary alloys, including Mg0.667Mo0.333B2, Mg0.5Mo0.5B2, and Mg0.333Mo0.667B2, and have determined their thermodynamically stable configurations under both atmospheric and high-pressure conditions. To investigate the potential for superconductivity in these structures, we have conducted a detailed examination of electronic properties that are pertinent to determining the superconducting state. Regarding superconducting properties, Mg0.333Mo0.667B2 exhibits superconductivity with a critical temperature (Tc) of 7.4 K at ambient pressure. These findings suggest that the theoretically predicted structures in Mg/Mo-substituted metal borides could play a significant role in synthesis and offer valuable insights into superconducting materials.

The Expansion of House Mouse Major Urinary Protein Genes Likely Did Not Facilitate Commensalism with Humans.

Mouse wild-derived strains (WDSs) combine the advantages of classical laboratory stocks and wild animals, and thus appear to be promising tools for diverse biomedical and evolutionary studies. We employed 18 WDSs representing three non-synanthropic species (Mus spretus, Mus spicilegus, and M. macedonicus) and three house mouse subspecies (Mus musculus musculus, M. m. domesticus, M. m. castaneus), which are all important human commensals to explore whether the number of major urinary protein (MUP) genes and their final protein levels in urine are correlated with the level of commensalism. Contrary to expectations, the MUP copy number (CN) and protein excretion in the strains derived from M. m. castaneus, which is supposed to be the strongest commensal, were not significantly different from the non-commensal species. Regardless of an overall tendency for higher MUP amounts in taxa with a higher CN, there was no significant correlation at the strain level. Our study thus suggests that expansion of the Mup cluster, which appeared before the house mouse diversification, is unlikely to facilitate commensalism with humans in three house mouse subspecies. Finally, we found considerable variation among con(sub)specific WDSs, warning against generalisations of results based on a few strains.

Analysis of medium-frequency oscillation based on bifurcation theory and joint modelling of SVG and direct-drive wind turbine

With the expansion of wind power clusters in power system, medium and high frequency oscillations in wind farm area are preliminarily emerging. At present, linear analysis such as impedance analysis are mainly used to analyse the grid-connected oscillation of renewable energy generation. However, the explanation of the oscillation mechanism is not intuitive and does not take into account the nonlinearity of converter. Considering the influence of external loop control of SVG and direct-drive wind turbine on the medium-frequency characteristics of the parallel system, a reduced-order nonlinear model under voltage time scale is established. The conjoint analysis of Jacobi matrix, bifurcation diagram and phase space trajectory are applied to study the influence rule of machine-side output power and short-circuit ratio on the oscillation behaviour of the parallel system. In addition, the oscillation evolution process is analysed from the dynamic standpoint. It is found that the system operates on the limit-loop state when the medium-frequency oscillation occurs, which reveals the mapping relationship between the oscillation amplitude and the limit-loop trajectory. The experimental results ultimately validate the theoretical analysis conducted on the StarSim-HIL (hardware-in-the-loop) experiment platform.

Atomic cluster expansion for a general-purpose interatomic potential of magnesium

Atomic cluster expansion for a general-purpose interatomic potential of magnesium

Structural changes in the lithium cobalt dioxide electrode: A combined approach with cluster expansion and Bayesian optimization

Structural changes in the lithium cobalt dioxide electrode: A combined approach with cluster expansion and Bayesian optimization

Impact of hydrogen concentration for [formula omitted] reduction on [formula omitted]: A combination study of cluster expansion and kinetics analysis

Pd hydride has shown better electrochemical CO2 reduction reaction (CO2RR) performance compared to metal Pd implying that H in the PdHx surface plays a vital role in affecting the performance. Using density functional theory (DFT) calculations in combination with active learning cluster expansion and Monte Carlo simulated annealing we identify 12 stable PdHx(111) configurations on the DFT convex hull and investigate the binding energies of intermediates in the CO2RR and the competing hydrogen evolution reaction. Through analysis of intermediate binding energies and a microkinetic model, we identify the atomic structures of the PdHx phase most likely to produce syngas. The high activity of the PdH0.6 surface can be attributed to the fact that H segregation in the PdHx(111) surface breaks the linear relation between HOCO* and CO* adsorbates.

Health inequalities, multimorbidity and primary care in Scotland

Scotland has an ageing population and the widest health inequalities in Western Europe. Multiple health conditions develop ∼10-15 years earlier in deprived areas than in affluent areas. General practice is central to the effective and safe management of such complex multiple health conditions, but the inverse care law has permeated deprived communities ('Deep End' general practices) for the past 50 years. A new, radical, Scottish GP contract was introduced in April 2018, which has a vision to improve quality of care through cluster working and expansion of the multidisciplinary team (MDT), enabling GPs to deliver 'expert generalism' to patients with complex needs. It states a specific intention to address health inequalities and also to support the integration of health and social care. Here, we discuss recent evidence for whether the ambition of the new GP contract, to reduce health inequalities, is being achieved.