Hyperuniformity of Weighted Particle Systems

arXiv (Cornell University) · 2026-03-03

Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights: internal degrees of freedom such as scalars, vectors, pseudovectors, directors, tensors, or extrinsic local attributes. Our generalization extends hyperuniformity from fluctuations in particle positions to fluctuations in the spatial distribution of weights. We derive generalized weighted pair correlation, autocovariance, and spectral functions, and show their relation to the local variance in weighted many-particle systems. Applying this formalism to bond-orientational ordered phases, dipolar liquid water, Voronoi-cell volumes, and certain ionic liquids, we demonstrate that hyperuniformity in the particle system does not necessarily translate to hyperuniformity of the weighted system. In fact, cases exist where a hyperuniform particle system becomes antihyperuniform when weighted, and others where nonhyperuniform or antihyperuniform particle systems yield hyperuniform weighted systems. This theoretical framework provides a road map for quantifying large-scale fluctuations in weighted many-particle systems, offering a powerful tool for identifying systems with novel physical properties.

Hyperuniformity of Weighted Particle Systems

Physical Review X · 2026-01-30

Hyperuniform particle arrangements are characterized by a local number variance within a spherical window of radius <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>R</a:mi> </a:math> that grows more slowly than the volume of the window, i.e., <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>R</c:mi> <c:mi>d</c:mi> </c:msup> </c:math> , in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>d</e:mi> </e:math> -dimensional Euclidean space. We generalize this concept to describe the large-scale behavior of particle systems in which particles carry weights: internal degrees of freedom such as scalars (charges and masses), vectors (electric dipole moments, velocities, and torques), pseudovectors (spins and angular momenta), directors (bond orientations), tensors (quadrupole moments), or extrinsic local attributes (Voronoi-cell characteristics). The underlying hyperuniform arrangement may be ordered (crystals and quasicrystals) or disordered, the latter of which has been extensively studied for its novel properties. Our generalization extends hyperuniformity from fluctuations in particle positions to fluctuations in the spatial distribution of weights and examines how weighted fluctuations compare to their unweighted counterparts. We derive generalized weighted pair correlation functions, autocovariance functions, and spectral functions and show their relation to formulas for the local variance in weighted many-particle systems. Then, we apply our formalism to determine the hyperuniformity or nonhyperuniformity of bond-orientational ordered phases, dipolar liquid water, Voronoi-cell volumes, and certain ionic liquids in various Euclidean space dimensions. We demonstrate that hyperuniformity in the particle system does not necessarily translate to hyperuniformity of the weighted system. In fact, cases exist where a hyperuniform particle system becomes antihyperuniform when weighted and others where nonhyperuniform or antihyperuniform particle systems yield hyperuniform weighted systems. This theoretical framework provides a road map for quantifying large-scale fluctuations in weighted many-particle systems, offering a powerful tool for identifying systems with novel physical properties.

fix pimd/langevin: An Efficient Implementation of Path Integral Molecular Dynamics in LAMMPS

Open MIND · 2026-02-14

Path integral molecular dynamics (PIMD), which maps a quantum particle onto a fictitious classical system of ring polymers and propagates the "beads" of this extended classical system using molecular dynamics, is widely used to capture nuclear quantum effects (NQEs) in molecular simulations. Accurate PIMD calculations typically require a large number of beads and are therefore computationally demanding. While software packages such as i-PI offer comprehensive PIMD functionality, the high efficiency of simulations driven by machine learning interatomic potentials, such as Deep Potential (DP), calls for more efficient PIMD implementations that fully exploit modern massively parallel supercomputers. Here we present fix pimd/langevin, an efficient PIMD implementation in LAMMPS that supports commonly used features and leverages the Message Passing Interface architecture of LAMMPS to achieve high computational efficiency. We demonstrate the usage and validate the correctness of our code using liquid water as a representative example, and provide a comprehensive overview of the supported features. Then we discuss several important technical aspects of the implementation. Using DP simulations of water as a benchmark, we show that our implementation achieves several-fold acceleration compared to i-PI. Finally, we report strong and weak scaling results that demonstrate the favorable parallel performance of our code.

fix pimd/langevin: An Efficient Implementation of Path Integral Molecular Dynamics in LAMMPS

ArXiv.org · 2026-02-14

Path integral molecular dynamics (PIMD), which maps a quantum particle onto a fictitious classical system of ring polymers and propagates the "beads" of this extended classical system using molecular dynamics, is widely used to capture nuclear quantum effects (NQEs) in molecular simulations. Accurate PIMD calculations typically require a large number of beads and are therefore computationally demanding. While software packages such as i-PI offer comprehensive PIMD functionality, the high efficiency of simulations driven by machine learning interatomic potentials, such as Deep Potential (DP), calls for more efficient PIMD implementations that fully exploit modern massively parallel supercomputers. Here we present fix pimd/langevin, an efficient PIMD implementation in LAMMPS that supports commonly used features and leverages the Message Passing Interface architecture of LAMMPS to achieve high computational efficiency. We demonstrate the usage and validate the correctness of our code using liquid water as a representative example, and provide a comprehensive overview of the supported features. Then we discuss several important technical aspects of the implementation. Using DP simulations of water as a benchmark, we show that our implementation achieves several-fold acceleration compared to i-PI. Finally, we report strong and weak scaling results that demonstrate the favorable parallel performance of our code.

fix pimd/langevin: An efficient implementation of path integral molecular dynamics in LAMMPS

The Journal of Chemical Physics · 2026-04-13

Path integral molecular dynamics (PIMD), which maps a quantum particle onto a fictitious classical system of ring polymers and propagates the "beads" of this extended classical system using molecular dynamics, is widely used to capture nuclear quantum effects in molecular simulations. Accurate PIMD calculations typically require a large number of beads and are, therefore, computationally demanding. While software packages such as i-PI offer comprehensive PIMD functionality, the high efficiency of simulations driven by machine learning interatomic potentials, such as deep potential (DP), calls for more efficient PIMD implementations that fully exploit modern massively parallel supercomputers. Here, we present fix pimd/langevin, an efficient PIMD implementation in LAMMPS that supports commonly used features and leverages the Message Passing Interface architecture of LAMMPS to achieve high computational efficiency. We demonstrate the usage, validate the correctness of our code using liquid water as a representative example, and provide a comprehensive overview of the supported features. Then, we discuss several important technical aspects of the implementation. Using DP simulations of water as a benchmark, we show that our implementation achieves several-fold acceleration compared to i-PI. Finally, we report strong and weak scaling results that demonstrate the favorable parallel performance of our code.

From Bulk to Surface: Structure and Dynamics of Amorphous Alumina from Deep Potential Molecular Dynamics

arXiv (Cornell University) · 2026-05-06

Understanding the atomic-scale structure and dynamics of amorphous oxide surfaces is essential for interpreting their chemical reactivity, mechanical stability, and interfacial behavior, yet direct experimental characterization remains challenging. We employ Deep Potential (DP) molecular dynamics to generate large-scale, ab initio-quality models of amorphous Al$_2$O$_3$ bulk glasses and melt-quenched free surfaces, enabling a quantitative analysis of both structure and relaxation dynamics with statistical confidence inaccessible to direct ab initio simulation. The trained DP model reproduces experimental liquid and glass structure, captures the cooling-rate dependence of the bulk glass transition, and corrects systematic biases in the polyhedral populations predicted by widely used classical force fields. At the free surface, mass density recovers to bulk values over ~10 $\unicode{x212B}$, while local coordination requires a slightly wider subsurface region to fully converge. The outermost layer is oxygen-enriched, exhibits altered polyhedral connectivity with contracted Al-O bonds, and hosts a broad population of under-coordinated motifs (notably AlO$_3$ and OAl$_2$) whose abundances are governed by glass stability. These reactive Lewis acid and Br$\unicode{x00F8}$nsted base sites are locally paired in a manner consistent with bond-valence compensation, yet remain spatially dispersed rather than aggregating into extended clusters. Despite this pronounced structural heterogeneity, the surface relaxes on the same timescale as the bulk and exhibits a comparable glass transition temperature, suggesting that the disordered surface is kinetically stable once formed. Together, these results establish a molecular-level picture of amorphous alumina surfaces and demonstrate the capability of machine-learned potentials to resolve structure-property relationships in disordered oxide interfaces.

From Bulk to Surface: Structure and Dynamics of Amorphous Alumina from Deep Potential Molecular Dynamics

ArXiv.org · 2026-05-06

Understanding the atomic-scale structure and dynamics of amorphous oxide surfaces is essential for interpreting their chemical reactivity, mechanical stability, and interfacial behavior, yet direct experimental characterization remains challenging. We employ Deep Potential (DP) molecular dynamics to generate large-scale, ab initio-quality models of amorphous Al$_2$O$_3$ bulk glasses and melt-quenched free surfaces, enabling a quantitative analysis of both structure and relaxation dynamics with statistical confidence inaccessible to direct ab initio simulation. The trained DP model reproduces experimental liquid and glass structure, captures the cooling-rate dependence of the bulk glass transition, and corrects systematic biases in the polyhedral populations predicted by widely used classical force fields. At the free surface, mass density recovers to bulk values over ~10 $\unicode{x212B}$, while local coordination requires a slightly wider subsurface region to fully converge. The outermost layer is oxygen-enriched, exhibits altered polyhedral connectivity with contracted Al-O bonds, and hosts a broad population of under-coordinated motifs (notably AlO$_3$ and OAl$_2$) whose abundances are governed by glass stability. These reactive Lewis acid and Br$\unicode{x00F8}$nsted base sites are locally paired in a manner consistent with bond-valence compensation, yet remain spatially dispersed rather than aggregating into extended clusters. Despite this pronounced structural heterogeneity, the surface relaxes on the same timescale as the bulk and exhibits a comparable glass transition temperature, suggesting that the disordered surface is kinetically stable once formed. Together, these results establish a molecular-level picture of amorphous alumina surfaces and demonstrate the capability of machine-learned potentials to resolve structure-property relationships in disordered oxide interfaces.

Benchmarking universal machine learning interatomic potentials for supported nanoparticles: decoupling energy accuracy from structural exploration

npj Computational Materials · 2026-04-02

Spectral Similarity Masks Structural Diversity at Hydrophobic Water Interfaces

Physical Review Letters · 2026-01-07 · 4 citations

The air-water and graphene-water interfaces represent quintessential examples of the liquid-gas and liquid-solid boundaries, respectively. While the sum-frequency generation (SFG) spectra of these interfaces show similarities, a consensus on their signals and interpretations has yet to be reached. Leveraging deep learning, we computed first-principles SFG spectra for both systems, addressing experimental discrepancies. Our findings reveal that similarities in SFG signals do not translate into comparable interfacial microscopic properties. Instead, graphene-water and air-water interfaces exhibit fundamental differences in SFG-active thicknesses, hydrogen-bonding networks, and surface dynamics. These distinctions underscore roughness suppression and electronic interactions present at the solid-liquid interface but absent at the gas-liquid interface.

Dynamic Metal–Support Interaction Dictates Cu Nanoparticle Sintering on Al₂O₃ Surfaces

ACS Nano · 2025-08-08 · 18 citations

Nanoparticle sintering remains a critical challenge in heterogeneous catalysis. In this work, we present a unified deep potential (DP) model based on the Perdew–Burke–Ernzerhof approximation of density functional theory for Cu nanoparticles on three Al2O3 surfaces (γ-Al2O3(100), γ-Al2O3(110), and α-Al2O3(0001)). Using DP-accelerated simulations, we reveal that the nanoparticle size-mobility relationship strongly depends on the supporting surface. The diffusion of nanoparticles on the two γ-Al2O3 surfaces is almost independent of the size of the nanoparticle, while the diffusion on α-Al2O3(0001) decreases rapidly with increasing size. Interestingly, nanoparticles with fewer than 55 atoms diffuse several times faster on α-Al2O3(0001) than on γ-Al2O3(100) at 800 K while expected to be more sluggish based on their larger binding energy at 0 K. The diffusion on α-Al2O3(0001) is facilitated by dynamic metal–support interaction (MSI), where Al atoms move out of the surface plane to optimize contact with the nanoparticle and relax back to the plane as the nanoparticle moves away. In contrast, the MSI on γ-Al2O3(100) and on γ-Al2O3(110) is dominated by more stable and directional Cu–O bonds, consistent with the limited diffusion observed on these surfaces. Our extended MD simulations provide insight into the sintering processes, showing that the dispersity of the nanoparticles strongly influences the coalescence driven by nanoparticle diffusion. We observed that the coalescence of Cu13 nanoparticles on α-Al2O3(0001) can occur in a short time (10 ns) at 800 K even with an initial internanoparticle distance increased to 3 nm, while the coalescence on the two γ-Al2O3 surfaces are inhibited significantly by increasing the initial internanoparticle distance. These findings demonstrate that the dynamics of the supporting surface is crucial to understanding the sintering mechanism and offer guidance for designing sinter-resistant catalysts by engineering the support morphology.