Configuration Space Research Articles

Constructing and Evaluating Machine-Learned Interatomic Potentials for Li-Based Disordered Rocksalts.

Lithium-based disordered rocksalts (LDRs), which are an important class of positive electrode materials that can increase the energy density of current Li-ion batteries, represent a significantly complex chemical and configurational space for conventional density functional theory (DFT)-based high-throughput screening approaches. Notably, atom-centered machine-learned interatomic potentials (MLIPs) are a promising pathway to accurately model the potential energy surface of highly disordered chemical spaces, such as LDRs, where the performance of such MLIPs has not been rigorously explored yet. Here, we represent a comprehensive evaluation of the accuracy, transferability, and ease of training of five atom-centered MLIPs, including the artificial neural network potentials developed by the atomic energy network (AENET), the Gaussian approximation potential (GAP), the spectral neighbor analysis potential (SNAP) and its quadratic extension (qSNAP), and the moment tensor potential (MTP), in modeling a 11-component LDR chemical space. Specifically, we generate a DFT-calculated data set of 10,842 configurations of disordered LiTMO2 and TMO2 compositions, where TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and/or Cu. To provide a point-of-comparison on the performance of atom-centered MLIPs, we also trained the neural equivariant interatomic potential (NequIP) on a subset of our data. Importantly, we find AENET to be the best potential in terms of accuracy and transferability for energy predictions, while MTP is the best for atomic forces. While AENET is the fastest to train among the MLIPs considered at low number of epochs (300), the training time increases significantly as epochs increase (3300), with a corresponding reduction in training errors (∼60%). Note that AENET and GAP tend to overfit in small data sets, with the extent of overfitting reducing with larger data sets. Finally, we observe AENET to provide reasonable predictions of average Li-intercalation voltages in layered, single-TM LiTMO2 frameworks, compared to DFT (∼10% error on average). Our study should pave the way both for discovering novel disordered rocksalt electrodes and for modeling other configurationally complex systems, such as high-entropy ceramics and alloys.

Dense-sparse quantum Monte Carlo algebraic diagrammatic construction and importance ranking.

Quantum Monte Carlo Algebraic Diagrammatic Construction (QMCADC) has been proposed as a reformulation of the second-order ADC scheme for the polarization propagator within the projection quantum Monte Carlo formalism. Dense-sparse partitioning and importance ranking filtering strategies are now exploited to accelerate its convergence and to alleviate the signproblem inherent in such calculations. By splitting the configuration space into dense and sparse subsets, the corresponding projection operator is decomposed into four distinct blocks. Deterministic calculations handle the dense-to-dense and sparse-to-dense blocks, while the remaining blocks, dense-to-sparse and sparse-to-sparse, are stochastically evaluated. The dense set is efficiently stored in a fixed-size array, and the sparse set is represented through conventional floating random Monte Carlo walks. The stochastic projection is further refined through importance ranking criteria, enabling a reduction in the required number of walkers with a controllable bias. Our results demonstrate the integration of dense-sparse partitioning with importance ranking filtering to significantly enhance the efficiency of QMCADC, enabling large-scale molecular excited-state calculations. Furthermore, this novel approach maximizes the utilization of the sparsity of ADC(2), transforming QMCADC into a tailored framework for ADC calculations.

Wave Function and Information

Two distinct measures of information, connected respectively to the amplitude and phase of the wave function of a particle, are proposed. There are relations between the time derivatives of these two measures and their gradients on the configuration space, which are equivalent to the wave equation. The information related to the amplitude measures the strength of the potential coupling of the particle (which is itself aspatial) with each volume of its configuration space, i.e., its tendency to participate in an interaction localized in a region of ordinary physical space corresponding to that volume. The information connected to the phase is that required to obtain the time evolution of the particle as a persistent entity starting from a random succession of bits. It can be considered as the information provided by conservation principles. The meaning of the so-called “quantum potential” in this context is briefly discussed.

On the canonicity of the singularities of quotients of the Fulton-MacPherson compactification

We prove that quotients of the Fulton-MacPherson compactification of configuration spaces of smooth projective varieties of dimension > 1 >1 by permutation groups have canonical singularities.

Variational Integrators on Manifolds for Constrained Mechanical Systems

Abstract Variational integrators play a pivotal role in the simulation and control of constrained mechanical systems. Current Lagrange multiplier-free variational integrators for such systems are concise but inevitably face issues with parameterization singularities, hindering global integration. To tackle this problem, this paper proposes a novel method for constructing variational integrators on manifolds without introducing Lagrange multipliers, offering the benefit of avoiding singularities. Our approach unfolds in three key steps: (1) the local parameterization of configuration space; (2) the formulation of forced discrete Euler–Lagrange equations on manifolds; and (3) the construction and implementation of high-order variational integrators. Numerical tests are conducted for both conservative and forced mechanical systems, demonstrating the excellent global energy behavior of the proposed variational integrators.

Quotient singularities in the Grothendieck ring of varieties

Let G G be a finite group, X X be a smooth complex projective variety with a faithful G G -action, and Y Y be a resolution of singularities of X / G X/G . Larsen and Lunts asked whether [ X / G ] − [ Y ] [X/G]-[Y] is divisible by [ A 1 ] [\mathbb {A}^1] in the Grothendieck ring of varieties. We show that the answer is negative if B G BG is not stably rational and affirmative if G G is abelian. The case when X = Z n X=Z^n for some smooth projective variety Z Z and G = S n G=S_n acts by permutation of the factors is of particular interest. We make progress on it by showing that [ Z n / S n ] − [ Z ⟨ n ⟩ / S n ] [Z^n/S_n]-[Z\langle n\rangle / S_n] is divisible by [ A 1 ] [\mathbb {A}^1] , where Z ⟨ n ⟩ Z\langle n\rangle is Ulyanov’s polydiagonal compactification of the n n th configuration space of Z Z .

Six-dimensional quantum dynamics of an Eley-Rideal reaction between gaseous and adsorbed hydrogen atoms on Cu(111).

In the form of direct abstraction of a surface adsorbate by a gaseous projectile, the Eley-Rideal (ER) reaction at the gas-surface interface manifests interesting dynamics. Unfortunately, high-dimensional quantum dynamical (QD) studies for ER reactions remain very challenging, which demands a large configuration space and the coordinate transformation of wavefunctions. Here, we report the first six-dimensional (6D) fully coupled quantum scattering method for studying the ER reaction between gas phase H(D) atoms and adsorbed D(H) atoms on a rigid Cu(111) surface. Reaction probabilities and product rovibrational state distributions obtained by this 6D model are found to be quite different from those obtained by reduced-dimensional QD models, demonstrating the high-dimensional nature of the ER reaction. Using two distinct potential energy surfaces (PESs), we further discuss the influence of the PES on the calculated product vibrational and rotational state distributions, in comparison with experimental results. The lateral corrugation and the exothermicity of the PES are found to play a critical role in controlling the energy disposal in the ER reaction.

Renormalization group flows from the Hessian geometry of quantum effective actions

Abstract We explore a geometric perspective on quantum field theory by considering the configuration space, spanned by the correlation functions. Employing $n$-particle irreducible effective actions constructed via Legendre transforms of the Schwinger functional, this configuration space can be associated with a Hessian manifold. This allows for various properties and uses of the $n$-particle irreducible effective actions to be re-cast in geometrical terms. In the 2PI case, interpreting the two-point source as a regulator, this approach can be readily connected to the functional renormalization group. Renormalization group flows are then understood in terms of geodesics on this Hessian manifold.

Assessment of Anharmonicities in Clusters: Developing and Validating a Minimum-Information Partition Function.

Precise thermodynamic calculations are essential for understanding the dynamics of cluster systems and new particle formation. However, the widely employed harmonic statistical mechanical approach often falls short in terms of accuracy. In this study, we present an improved statistical model that incorporates vibrational anharmonicity via a novel partition function that requires only one additional system-specific input parameter. In addition to considering vibrational aspects, we also account for anharmonicity related to the configurational space. The role of anharmonicities is thoroughly examined in the case of general clusters, where the complete sets of conformers, mechanically stable spatial arrangements, are known up to clusters composed of 14 monomers. By performing consistent Monte Carlo simulations on these systems, we benchmark the statistical model's efficacy in reproducing key thermodynamic properties (formation free energy and potential energy) in the classical limit. The model exhibits exceptional alignment with simulations, accurately reproducing free energies within a precision of 2kBT and reliably capturing cluster melting temperatures. Furthermore, we demonstrate the significance and applicability of the model by reproducing thermodynamic barriers in homogeneous gas-phase nucleation of larger clusters. The transferability of our developed approach extends to more complex molecular systems and bears relevance for atmospheric multicomponent clusters, in particular.

Enhancing thermal stability of optimal magnetization reversal in nanoparticles

Energy-efficient switching of nanoscale magnets requires application of a time-varying magnetic field characterized by microwave frequency. At finite temperatures, even weak thermal fluctuations induce perturbations in the magnetization that can accumulate in time, disrupt the phase locking between the magnetization and the applied field, and eventually compromise magnetization switching. It is demonstrated here that the magnetization reversal is mostly disturbed by unstable perturbations arising in a certain domain of the configuration space of a nanomagnet. The instabilities can be suppressed and the probability of magnetization switching enhanced by applying an additional stimulus such as a weak longitudinal magnetic field that ensures bounded dynamics of the perturbations. Application of the stabilizing longitudinal field to a uniaxial nanomagnet makes it possible to reach a desired probability of magnetization switching even at elevated temperatures. The principle of suppressing instabilities provides a general approach to enhancing thermal stability of magnetization dynamics. Published by the American Physical Society 2024

Effect of Dynamic and Preferential Decoration of Pt Catalyst Surfaces by WOx on Hydrodeoxygenation Reactions.

Catalysts containing Pt nanoparticles and reducible transition-metal oxides (WOx, NbOx, TiOx) exhibit remarkable selectivity to aromatic products in hydrodeoxygenation (HDO) reactions for biomass valorization, contrasting the undesired aromatic hydrogenation typically observed for metal catalysts. However, the active site(s) responsible for the high selectivity remains elusive. Here, theoretical and experimental analyses are combined to explain the observed HDO reactivity by interrogating the organization of reduced WOx domains on Pt surfaces at sub-monolayer coverage. The SurfGraph algorithm is used to develop model structures that capture the configurational space (∼1000 configurations) for density functional theory (DFT) calculations of a W3O7 trimer on stepped Pt surfaces. Machine-learning models trained on the DFT calculations identify the preferential occupation of well-coordinated Pt sites (≥8 Pt coordination number) by WOx and structural features governing WOx-Pt stability. WOx/Pt/SiO2 catalysts are synthesized with varying W loadings to test the theoretical predictions and relate them to HDO reactivity. Spectroscopy- and microscopy-based catalyst characterizations identify the dynamic and preferential decoration of well-coordinated sites on Pt nanoparticles by reduced WOx species, consistent with theoretical predictions. The catalytic consequences of this preferential decoration on the HDO of a lignin model compound, dihydroeugenol, are clarified. The effect of WOx decoration on Pt nanoparticles for HDO involves WOx inhibition of aromatic ring hydrogenation by preferentially blocking well-coordinated Pt sites. The identification of preferential decoration on specific sites of late-transition-metal surfaces by reducible metal oxides provides a new perspective for understanding and controlling metal-support interactions in heterogeneous catalysis.

Tuning structural and electronic properties of metal-organic framework 5 by metal substitution and linker functionalization.

The chemical flexibility of metal-organic frameworks (MOFs) offers an ideal platform to tune structure and composition for specific applications, from gas sensing to catalysis and from photoelectric conversion to energy storage. This variability gives rise to a large configurational space that can be efficiently explored using high-throughput computational methods. In this work, we investigate from first principles the structural and electronic properties of MOF-5 variants obtained by replacing Zn with Be, Mg, Cd, Ca, Sr, and Ba and by functionalizing the originally H-passivated linkers with CH3, NO2, Cl, Br, NH2, OH, and COOH groups. To build and analyze the resulting 56 structures, we employ density-functional theory calculations embedded in an in-house developed library for automatized calculations. Our findings reveal that structural properties are mainly defined by metal atoms and large functional groups, which distort the lattice and modify coordination. The formation energy is largely influenced by functionalization and enhanced by COOH and OH groups, which promote the formation of hydrogen bonds. The charge distribution within the linker is especially influenced by functional groups with electron-withdrawing properties, while the metal nodes play a minor role. Likewise, the bandgap size is crucially determined by ligand functionalization. The smallest gaps are found with NH2 and OH groups, which introduce localized orbitals at the top of the valence band. This characteristic makes these functionalizations particularly promising for the design of MOF-5 variants with enhanced gas uptake and sensing properties.

Multisimplicial chains and configuration spaces

We define an E∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_\\infty $$\\end{document}-coalgebra structure on the chains of multisimplicial sets. Our primary focus is on the surjection chain complexes of McClure-Smith, for which we construct a zig-zag of complexity preserving quasi-isomorphisms of E∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_\\infty $$\\end{document}-coalgebras relating them to both the singular chains on configuration spaces and the Barratt–Eccles chain complexes.

Deep Learning-Enhanced Sampling-Based Path Planning for LTL Mission Specifications.

The presented paper introduces a novel path planning algorithm designed for generating low-cost trajectories that fulfill mission requirements expressed in Linear Temporal Logic (LTL). The proposed algorithm is particularly effective in environments where cost functions encompass the entire configuration space. A core contribution of this paper is the presentation of a refined approach to sampling-based path planning algorithms that aligns with the specified mission objectives. This enhancement is achieved through a multi-layered framework approach, enabling a simplified discrete abstraction without relying on mesh decomposition. This abstraction is especially beneficial in complex or high-dimensional environments where mesh decomposition is challenging. The discrete abstraction effectively guides the sampling process, influencing the selection of vertices for extension and target points for steering in each iteration. To further improve efficiency, the algorithm incorporates a deep learning-based extension, utilizing training data to accurately model the optimal trajectory distribution between two points. The effectiveness of the proposed method is demonstrated through simulated tests, which highlight its ability to identify low-cost trajectories that meet specific mission criteria. Comparative analyses also confirm the superiority of the proposed method compared to existing methods.

Machine learning-enabled chemical space exploration of all-inorganic perovskites for photovoltaics

The vast compositional and configurational spaces of multi-element metal halide perovskites (MHPs) result in significant challenges when designing MHPs with promising stability and optoelectronic properties. In this paper, we propose a framework for the design of B-site-alloyed ABX3 MHPs by combining density functional theory (DFT) and machine learning (ML). We performed generalized gradient approximation with Perdew–Burke–Ernzerhof functional for solids (PBEsol) on 3,159 B-site-alloyed perovskite structures using a compositional step of 1/4. Crystal graph convolution neural networks (CGCNNs) were trained on the 3159 DFT datasets to predict the decomposition energy, bandgap, and types of bandgaps. The trained CGCNN models were used to explore the compositional and configurational spaces of 41,400 B-site-alloyed ABX3 MHPs with a compositional step of 1/16, by accessing all possible configurations for each composition. The electronic band structures of the selected compounds were calculated using the hybrid functional (PBE0). Then, we calculated the optical absorption spectra and spectroscopic limited maximum efficiency of the selected compounds. Based on the DFT/ML-combined screening, 10 promising compounds with optimal bandgaps were selected, and from among these 10 compounds, CsGe0.3125Sn0.6875I3 and CsGe0.0625Pb0.3125Sn0.625Br3 were suggested as photon absorbers for single-junction and tandem solar cells, respectively. The design framework presented herein is a good starting point for the design of mixed MHPs for optoelectronic applications.

Comparative Life-Cycle Assessment of Steel and GFRP Rebars for Procurement Sustainability in the Construction Industry

This research examines the potential impact on the procurement sustainability of replacing steel rebars with Glass Fiber-Reinforced Polymer (GFRP) rebars in the construction industry, focusing on screed pre-cast hollow core topping in a project in the Kingdom of Saudi Arabia. A comparative life cycle assessment (LCA) is conducted using One Click LCA (Version 0.26.0) software for cradle-to-grave analysis. The assessment covers various stages, including raw material extraction, manufacturing, transportation, usage, and recycling. The comprehensive LCA highlights GFRP rebars as a more sustainable alternative to steel, emitting 17% less CO2 equivalent (2e) per kilogram throughout its life cycle. Additionally, GFRP requires substantially less mass compared to steel, resulting in a dramatic reduction in CO2e emissions ranging from 77.89% to 85.26% across different spacing configurations in real-world construction scenarios, as presented in this research case study. These findings suggest that GFRP rebars offer a promising solution for reducing the environmental impact of construction activities while potentially yielding significant cost savings over the project’s life cycle. Integrating environmental considerations into material selection processes can prioritize sustainability without compromising performance or safety, contributing to a more sustainable future for the construction industry globally.

In-silico Studies, Design, and Synthesis of Pyrimidine-linked Benzothiazoles for its Anticonvulsant Potential.

The objective of the study was to design and synthesize a series of N-(6-substituted-1,3-benzothiazole- 2-yl)-2-{[6-(3-substitutedphenyl)-5-cyano-2-sulfanylpyrimidine-4-yl)]amino}acetamide derivatives BPD (1-15) that contains key pharmacophores required for anticonvulsant action. The titled compounds (BPD 1-15) were synthesized by reacting 2-substituted-N-(6-chlorobenzo[d]thiazol2-yl)acetamide with 4-amino-6-(4-substituted phenyl)-2-mercapto pyrimidine 5-carbonitrile in the presence of potassium carbonate and dry acetone. The synthesized compounds BPD (1-15) were assessed in vivo by the maximum electric shock (MES) test and the subcutaneous pentylenetetrazol (scPTZ) test in mice. The neurotoxicity test was performed by the rotarod test. A molecular docking study of title compounds with a sodium channel receptor (PDB ID: 1BYY) was carried out using the SP Docking protocol of the Glide module of the Maestro. Pharmacophore modeling was used to qualitatively identify the chemical characteristics for ligand binding and their spatial configurations in the 3D space of the active site. Among the studied compounds, BPD-15 and BPD-5 compounds showed significant action in both the MES and scPTZ models, with no neurotoxicity. BPD-15 & BPD-5 were relatively safe in acute toxicity testing. Compounds BPD-15 and BPD-5 showed good dock scores of -6.434 and -6.191, respectively. Thus, the compounds BPD-15 and BPD-5 have shown a considerable affinity towards the sodium channel as compared to the standard drug Riluzole. Compound BPD-14 showed good drug compatibility, and compounds BPD-1, BPD-2, BPD-11, BPD-12, BPD-13, BPD-14, BPD-15 showed good ADME values.

Network science: Ising states of matter

Network science provides very powerful tools for extracting information from interacting data. Although recently the unsupervised detection of phases of matter using machine learning has raised significant interest, the full prediction power of network science has not yet been systematically explored in this context. Here we fill this gap by providing an in-depth statistical, combinatorial, geometrical, and topological characterization of 2D Ising snapshot networks (IsingNets) extracted from Monte Carlo simulations of the 2D Ising model at different temperatures, going across the phase transition. Our analysis reveals the complex organization properties of IsingNets in both the ferromagnetic and paramagnetic phases and demonstrates the significant deviations of the IsingNets with respect to randomized null models. In particular percolation properties of the IsingNets reflect the existence of the symmetry between configurations with opposite magnetization below the critical temperature and the very compact nature of the two emerging giant clusters revealed by our persistent homology analysis of the IsingNets. Moreover, the IsingNets display a very broad degree distribution and significant degree-degree correlations and weight-degree correlations demonstrating that they encode relevant information present in the configuration space of the 2D Ising model. The geometrical organization of the critical IsingNets is reflected in their spectral properties deviating from the one of the null model. This work reveals the important insights that network science can bring to the characterization of phases of matter. The set of tools described hereby can be applied as well to numerical and experimental data. Published by the American Physical Society 2024

Homology and Euler characteristic of generalized anchored configuration spaces of graphs

AbstractIn this paper we consider the generalized anchored configuration spaces on n labeled points on a graph. These are the spaces of all configurations of n points on a fixed graph G, subject to the condition that at least q vertices in some pre-determined set K of vertices of G are included in each configuration. We give a non-alternating formula for the Euler characteristic of such spaces for arbitrary connected graphs, which are not trees. Furthermore, we completely determine the homology groups of the generalized anchored configuration spaces of n points on a circle graph.

A realist interpretation of unitarity in quantum gravity

Unitarity is a difficult concept to implement in canonical quantum gravity because of state non-normalisability and the problem of time. We take a realist approach based on pilot-wave theory to address this issue in the Ashtekar formulation of the Wheeler–DeWitt equation. We use the postulate of a definite configuration in the theory to define a global time for the gravitational-fermionic system recently discussed in Alexander et al (2022 Phys. Rev. D 106 106012), by parameterising a variation of a Weyl-spinor that depends on the Kodama state. The total Hamiltonian constraint yields a time-dependent Schrodinger equation, without semi-classical approximations, which we use to derive a local continuity equation over the configuration space. We implement the reality conditions at the level of the guidance equation, and obtain a real spin-connection, extrinsic curvature and triad along the system trajectory. We obtain quantum corrections to deSitter spacetime from the guidance equation. The non-normalisable Kodama state is naturally factored out of the full quantum state in the conserved current density, opening the possibility for quantum-mechanical unitarity. We also give a pilot-wave generalisation of the notion of unitarity applicable to non-normalisable states, and show the existence of equilibrium density for our system. Lastly, we find unitary states in mini-superspace by finding an approximate solution to the Hamiltonian constraint.