Pair Potential Research Articles

Interaction of complex particles: A framework for the rapid and accurate approximation of pair potentials using neural networks

Motivated by the limitations of conventional coarse-grained molecular dynamics for simulation of large systems of nanoparticles and the challenges in efficiently representing general pair potentials for rigid bodies, we present a method for approximating general rigid body pair potentials based on a specialized type of deep neural network that maintains essential properties, such as conservation of energy and invariance to the chosen origins of the particles. The network uses a specialized geometric abstraction layer to convert the relative coordinates of the rigid bodies to input more suitable to a conventional artificial neural network, which is trained together with the specialized layer. This results in geometric representations of the particles optimized for the specific potential. The network can be trained directly on scalar values to fit a model without explicit gradient and then used to efficiently evaluate the force and torque on the particles resulting from the potential. The concept is demonstrated with an atomistic interaction model for carbon nanotubes and the resulting model is compared with a common type of coarse-grained model optimized for the same potential, with even very small networks comparing favourably and larger networks achieving up to two orders of magnitude lower cost. The sensitivity to noise in the training data is investigated and the model is found to strongly reject noise up to 12.5% given a dataset of 107 samples. The performance of a proof-of-concept implementation is demonstrated on a variety of hardware, showing the models viability for large-scale simulations. Furthermore, generalization to soft bodies and potentials for polydisperse systems are discussed. Published by the American Physical Society 2024

Can one hear the shape of a crystal?

Isospectrality is a general fundamental concept often involving whether various operators can have identical spectra, i.e., the same set of eigenvalues. In the context of the Laplacian operator, the famous question “Can one hear the shape of a drum?” concerns whether different shaped drums can have the same vibrational modes. The isospectrality of a lattice in d-dimensional Euclidean space Rd is a tantamount to whether it is uniquely determined by its theta series, i.e., the radial distribution function g2(r). While much is known about the isospectrality of Bravais lattices across dimensions, little is known about this question of more general crystal (periodic) structures with an n-particle basis (n≥2). Here, we ask what is nmin(d), the minimum value of n for inequivalent (i.e., unrelated by isometric symmetries) crystals with the same theta function in space dimension d? To answer these questions, we use rigorous methods as well as a precise numerical algorithm that enables us to determine the minimum multiparticle basis of inequivalent isospectral crystals. Our algorithm identifies isospectral four-, three- and two-particle bases in one, two, and three spatial dimensions, respectively. For many of these isospectral crystals, we rigorously show that they indeed possess identically the same g2(r)'s for all values of r. Based on our analyses, we conjecture that nmin(d)=4, 3, 2 for d=1, 2, 3, respectively. The identification of isospectral crystals enables one to study the degeneracy of the ground-state under the action of isotropic pair potentials. Indeed, using inverse statistical-mechanical techniques, we find an isotropic pair potential whose low-temperature configurations in two dimensions obtained via simulated annealing can lead to both of two isospectral crystal structures with n=3, the proportion of which can be controlled by the cooling rate. Our findings provide general insights into the structural and ground-state degeneracies of crystal structures as determined by radial pair information. Published by the American Physical Society 2024

An explicitly magnetic modified embedded atom method formalism for coupled spin dynamics and molecular dynamics

Abstract In this paper, we augment the modified embedded atom method formalism to include magnetic spin-spin interactions for elements with a persistent magnetic moment. While previous spin coupling methods have been based on pair potentials, our Magnetic MEAM formalism, which we term MagMEAM, incorporates the many-body and angular effects of MEAM allowing for the strength of the magnetic interaction to vary with atomic environment. In particular, this allows potentials using this formalism to differentiate the magnetic interaction of different stable phases of magnetic elements such as the ferritic and austenitic phases of iron. This, in turn, allows for a more robust and realistic description of magnetism in polymorphic materials than was previously possible. The motivation for MagMEAM, including the insufficiency of magnetic pair potentials, is presented and the structure of the formalism is developed. A sample iron potential is developed using this formalism and shown to exceed the capabilities of existing magnetic pair potentials by simultaneously reproducing the magnetic energy of both martensite and austenite as well as the dynamic mechanical and magnetic properties of martensite. This newly designed formalism will allow for deeper explorations in the the complex interaction between different phases of polymorphic magnetic materials at the molecular dynamics scale.

Mechanical unfolding of RNA molecules using a knowledge-based model.

We revisit a coarse-grained model to study the dynamics of ribonucleic acid (RNA). In our model, each nucleotide is replaced by an interaction center located at the center of mass. The interaction between nucleotides is carried out by a series of effective pair potentials obtained from the statistical analysis of 501 RNA molecules of high molecular weight from the Protein Data Bank. In addition to the Watson-Crick interactions, we also include non-canonical interactions, which provide stability to the three-dimensional (3D) structure of the molecule. The resulting knowledge-based interactions for the nucleotides (KIN) model allow us to perform efficient Brownian dynamics simulations under different conditions. First, we simulate the stretch of a set of hairpins at a loading rate similar to the values employed in unfolding experiments near equilibrium using optical tweezers. Additionally, we explore unfolding a set of pseudoknots under conditions farther from equilibrium, namely, at loading rates higher than the experimental equilibrium values. The results of our simulations are compared with those obtained from experimental measurements and theoretical models intended to estimate transition states and activation energies. Our KIN model is able to reproduce the intermediate states observed during mechanical unfolding experiments. Moreover, the results of the KIN model are in good agreement with the measured data.

Design of self-emulsifying oral delivery systems for semaglutide: reverse micelles versus hydrophobic ion pairs.

It was the aim of this study to evaluate the potential of reverse micelles (RM) and hydrophobic ion pairs (HIP) for incorporation of semaglutide into self-emulsifying oral drug delivery systems. Reverse micelles loaded with semaglutide were formed with a cationic (ethyl lauroyl arginate, ELA) and an anionic surfactant (docusate, DOC), whereas HIP were formed between semaglutide and ELA. Maximum solubility of the peptide and the rate of dissolution was evaluated in various lipophilic phases (glycerol monocaprylocaprate:caprylic acid 1:4 (m/m), glycerol monolinoleate:caprylic acid 1:4 (m/m) and glycerol monocaprylocaprate:glycerol monolinoleate 1:4 (m/m)). Self-emulsifying drug delivery systems (SEDDS) loaded with RM and HIP were characterized regarding size distribution, zeta potential, cytocompatibility and Caco-2 permeability. Droplet sizes between 50 and 300nm with polydispersity index (PDI) around 0.3 and zeta potentials between - 45 mV (RMDOC) and 36 mV (RMELA) were obtained. RM provided an almost 2-fold higher lipophilicity of semaglutide than HIP resulting in a 4.2-fold higher payload of SEDDS compared to HIP. SEDDS containing RM or HIP showed high cytocompatibilities with a cell survival above 75% for concentrations up to 0.1% on Caco-2 cells and acceptable hemolytic activity. Permeation studies across Caco-2 monolayer revealed an at least 2-fold increase in permeability of semaglutide for the developed formulations.

Infinite cycles of interacting bosons

Abstract In the first-quantized description of bosonic systems permutation cycles formed by the particles play a fundamental role. In the ideal Bose gas Bose-Enstein condensation (BEC) is signaled by the appearance of infinite cycles. When the particles interact, the two phenomena may not be simultaneous, the existence of infinite cycles is necessary but not sufficient for BEC. We demonstrate that their appearance is always accompanied by a singularity
in the thermodynamic quantities
which in three and four dimensions can be as strong as a one-sided divergence of the isothermal compressibility. Arguments are presented that long-range interactions can give rise to unexpected results, such as the absence of infinite cycles in three dimensions for long-range repulsion or their presence in one and two dimensions if the pair potential has a long attractive tail.

Enlarged Curvature, Torsion and Torque in Helical Conformations and the Stability and Growth of α-Peptide under the Isochoric and Isobaric Conditions: Variatonal Optimization

The torsional deformation behavior of an elastic bar with a circular cross-section was investigated by applying invariant dyadic analysis, where the small finite displacement functions advocated by Saint-Venant (1855) were fully employed. It was found that the previously overlooked circumferential shear force field generated by pure torsion on the side walls of a bar produces an unusual torque term induced by the skew-symmetric part of the deformation tensor and exhibits quadratic length dependence along the z-axis of the bar. The adaptation of this torque term for a helical conformation of α-peptides creates moments acting on the circular cross-sections and is directed along the surface normal of circular cross-sections, which coincides with the tangent vector of the helix. The projection of this torque along the z-axis of the helix varies quadratically with the azimuthal angle. The radial component of the unusual torque, which also lies along the principal normal vector of the helix, starts to perform a precession motion by tracking a spiral orbit around the z-axis, whereas its apex angle decreases asymptotically with the azimuthal angle and finally reaches a finite value depending on the height of the helix along the z-axis. The ordinary torque terms, which are also deduced from the self- and anti-self-conjugate parts of the deformation tensor, have magnitudes half that of the full torque term reported in the literature. The present results were applied to the helical conformation of α-peptides designated by {3.611} to show that the mechanical stability of strained open-ended helical conformations can be successfully achieved by spontaneous readjustments of the surface and bulk Helmholtz free energies under isothermal isochoric conditions. It has been demonstrated that the main contribution to the mechanical stability of α-peptide 3.611 cannot come alone from the electrostatic dipole-dipole interaction potential of the anti-align excess dipole pairs but also from the surface Helmholtz free energy, which is characterized by a binding free energy of -15.5 eV/molecule (-32.56 Kcal/mole) for an alpha-peptide composed of 11 amino acid residues with a critical arc length of approximately 10 nm, assuming that the shear modulus is G = 1GPa and the surface Helmholtz specific free energy density is fs = 800 erg/cm2. This result was in excellent agreement with the experimental observations of the AH-1 conformation of (Glu)n Cys at pH 8. The present theory indicates that only two excess permanent anti-align dipole pairs for one α-Helical peptide molecule is requirement to stabilize the whole secondary structure of the protein that is exposed to heavy torsional deformation during the folding processes which amounts to 7.75 eV/molecule stored electrostatic energy compared to the interfacial Helmholtz free energy of -23.25 eV/molecule, which is exposed to hydrophobic environments.

Quantum geometry encoded to pair potentials

Quantum geometry encoded to pair potentials

Emergent pair symmetries in systems with poor man's Majorana modes

Few-site Kitaev chains are promising for realizing Majorana zero modes without topological protection but fully nonlocal, which are known as poor man's Majorana modes. While several signatures have already been reported both theoretically and experimentally, it still remains unknown what is the nature of superconducting correlations in the presence of poor man's Majorana modes. In this paper, we study few-site Kitaev chains and demonstrate that they host pair correlations with distinct symmetries, entirely determined by the underlying quantum numbers. In particular, we find that a two-site Kitaev chain hosts local (odd-frequency) and nonlocal (odd- and even-frequency) pair correlations, both spin polarized and highly tunable by the system parameters. Interestingly, the odd-frequency pair correlations exhibit a divergent behavior around zero frequency when the nonlocal p-wave pair potential and electron tunneling are of the same order, an effect that can be controlled by the on-site energies. Since a divergent odd-frequency pairing is directly connected to the intrinsic spatial nonlocality of Majorana zero modes in topological superconductors, the divergent odd-frequency pairing here reflects the intrinsic Majorana nonlocality of poor man's Majorana modes but without any relation to topology. Our findings could help understanding the emergent pair correlations in few-site Kitaev chains. Published by the American Physical Society 2024

Shot noise and tunneling magnetoresistance in silicene-based ferromagnet/antiferromagnet/ferromagnet/p-wave superconductor junctions

We investigate the transport properties in silicene-based ferromagnet/antiferromagnet/ferromagnet/p-wave superconductor junctions within the Blonder–Tinkham–Klapwijk formalism by solving the Dirac–Bogoliubov-de Gennes equation. The results show that the conductance and the shot noise strongly depend on the p-wave superconducting pair potentials and the magnetic configurations of the ferromagnetic regions. The simultaneous diminution of the conductance and enhancement of the shot noise can be achieved with the increase of the antiferromagnetic exchange field strength. The conductance and the shot noise can be effectively modulated by the external electric field and the ferromagnetic exchange field strength, and the corresponding switch effects are also achieved. The tunneling magnetoresistance (TMR) outside the subgap energy interval is always larger than the one obtained in the subgap energy interval. When the antiferromagnetic exchange field strength is large enough, a larger TMR can be obtained by tuning the external electric field.

Yu-Shiba-Rusinov States in s-Wave Kagome Superconductors: Self-Consistent Bogoliubov-de Gennes Calculations.

Significant research has recently been conducted into the Yu-Shiba-Rusinov (YSR) states in kagome superconductors through theoretical modeling and experimental investigations. However, additional efforts are still needed to further understand the local superconductivity near magnetic impurities in the kagome lattice and clarify how relevant quantities depend on the interaction strength, J, between such impurities and electrons. In this study, we explore a self-consistent numerical solution of the Bogoliubov-de Gennes equations for an s-wave superconducting Kagome model with a single classical magnetic impurity. Our study reveals that with increasing J, the local pair potential is systematically depressed in the vicinity of the impurity, similar to previous results obtained for the square and triangular lattices. Moreover, when J is further increased, the system undergoes a first-order phase transition with the appearance of stable and metastable states, reflecting the presence of the hysteresis loop in the pertinent quantities. As a consequence of this transition, the minimal energy of the stable YSR state is nonzero at any J, contrary to the expectations based on the assumption of a constant pair potential. A distinctive feature of the kagome lattice is that characteristics of the first-order transition are very sensitive to the position of the chemical potential within the kagome energy spectrum.

Flat-Bottom Elastic Network Model for Generating Improved Plausible Reaction Paths.

Rapid generation of a plausible reaction path connecting a given reactant and product in advance is crucial for the efficient computation of precise reaction paths or transition states. We propose a computationally efficient potential energy based on the molecular structure to generate such paths. This potential energy has a flat bottom consisting of structures without atomic collisions while preserving nonreactive chemical bonds, bond angles, and partial planar structures. By combining this potential energy with the direct MaxFlux method, a recently developed reaction-path/transition-state search method, we can find the shortest plausible path passing within the bottom. Numerical results show that this combination yields lower energy paths compared to the paths obtained by the well-known image-dependent pair potential. We also theoretically investigate the differences between these two potential energies. The proposed potential energy and path generation routine are implemented in our Python version of the direct MaxFlux method, available on GitHub.

Predicting phase coexistence and adsorption isotherms of classical and quantum fluids using the microcanonical-ensemble perturbation theory (MEPT)

The Microcanonical-Ensemble Perturbation Theory (MEPT) of Sastre et al. (2018) [7] has been extended to study the vapor-liquid phase coexistence of binary and ternary mixtures of fluids. The attractive interactions between chains of molecules are represented as monomer segments interacting via a square-well pair potential. Calculations for the thermodynamic properties and phase behavior of square-well monomer chains are considered and compared with experimental data. Molecular parameters have been obtained to model the phase behavior of real fluids such as n-alkanes (from C1 to C12), nitrogen, perfluoromethane, carbon dioxide, i-butane, i-pentane, neon, and hydrogen. Furthermore, the capability of the MEPT approach in predicting critical and azeotropic lines of binary and ternary mixtures is explored. The results demonstrate that the MEPT approach provides a robust description of the phase behavior of mixtures containing chains of fluids. Additionally, we have integrated the MEPT approach with the two-dimensional Statistical Associating Fluid Theory for fluids interacting via variable range potentials (SAFT-VR-2D) to investigate the effect of quantum contributions on both phase behavior and adsorption. Remarkable improvements are observed when both higher order perturbation terms of the Helmholtz free energy and quantum contributions are included in the predictions of the phase behavior of quantum fluids such as neon and hydrogen. In all cases, the theoretical results exhibit favorable comparisons with experimental data in a wide range of compositions, pressures, and temperatures.

Pair Potential between Poloxamer 407 Micelles in 14 wt % Aqueous Solution Clarifying the Sol-Gel-Sol Transition by Temperature Rise.

Poloxamer 407 (P407) is used as a safety-guaranteed, invaluable pharmaceutical nanocarrier. The aqueous solution of P407 exhibits sol-to-gel and gel-to-sol transitions, specifically during a temperature rise. Here, we develop a method to determine the pair potential between colloidal particles based primarily on experimental small-angle scattering data. Using this approach, the pair potential between the P407 micelles in the sol-gel-sol transition state is revealed without prelimiting any type of interaction forces. The results indicate that the increase in the attractive interaction contributes to enhancing the volume fraction, which is the decisive parameter for the gelation in terms of the Alder transition theory, i.e., the fluid-to-crystal phase transition of the hard-sphere model in the micelle system. This study demonstrates that one of the key mechanisms of the gel-to-sol transition upon heating is the enhancement of the structural fluctuation due to widening of the potential well in the intermicellar pair potential.

Disorder and demixing in bidisperse particle systems assembling bcc crystals.

Colloidal and nanoparticle self-assembly enables the creation of ordered structures with a variety of electronic and photonic functionalities. The outcomes of the self-assembly processes used to synthesize such structures, however, strongly depend on the uniformity of the individual nanoparticles. Here, we explore the simplest form of particle size dispersity-bidispersity-and its impact on the self-assembly process. We investigate the robustness of self-assembling bcc-type crystals via isotropic interaction potentials in binary systems with increasingly disparate particle sizes by determining their terminal size ratio-the most extreme size ratio at which a mixed binary bcc crystal forms. Our findings show that two-well pair potentials produce bcc crystals that are more robust with respect to particle size ratio than one-well pair potentials. This suggests that an improved self-assembly process is accomplished with a second attractive length scale encoded in the particle-particle interaction, which stabilizes the second-nearest neighbor shell. In addition, we document qualitative differences in the process of ordering and disordering: in bidisperse systems of particles interacting via one-well potentials, we observe a breakdown of order prior to demixing, while in systems interacting via two-well potentials, demixing occurs first and bcc continues to form in parts of the droplet down to low size ratios.

Simulated structure and thermodynamics of decagonal Al-Co-Cu quasicrystals

Atomic structures of Al-Co-Cu decagonal quasicrystals (dQCs) are investigated using empirical oscillating pair potentials (EOPP) in molecular dynamic (MD) simulations that we enhance by Monte Carlo (MC) swapping of chemical species and replica exchange. Predicted structures exhibit planar decagonal tiling patterns and are periodic along the perpendicular direction. We then recalculate the energies of promising structures using first-principles density functional theory (DFT), along with energies of competing phases. We find that our τ-inflated sequence of QC approximants (QCAs) are energetically unstable at low temperature by at least 3 meV/atom. Extending our study to finite temperatures by calculating harmonic vibrational entropy, as well as anharmonic contributions that include chemical species swaps and tile flips, our results suggest that the quasicrystal phase is entropically stabilized at temperatures in the range 600-800 K and above. It decomposes into ordinary (though complex) crystal phases at low temperatures, including a partially disordered B2-type phase. We discuss the influence of density and composition on QC phase stability; we compare the structural differences between Co-rich and Cu-rich quasicrystals; and we analyze the role of entropy in stabilizing the quasicrystal, concluding with a discussion of the possible existence of “high entropy” quasicrystals. Published by the American Physical Society 2024

Non-hyperuniformity of Gibbs point processes with short-range interactions

Abstract We investigate the hyperuniformity of marked Gibbs point processes that have weak dependencies among distant points whilst the interactions of close points are kept arbitrary. Various stability and range assumptions are imposed on the Papangelou intensity in order to prove that the resulting point process is not hyperuniform. The scope of our results covers many frequently used models, including Gibbs point processes with a superstable, lower-regular, integrable pair potential, as well as the Widom–Rowlinson model with random radii and Gibbs point processes with interactions based on Voronoi tessellations and nearest-neighbour graphs.

Semi‐partial Quadratic Subtraction Set Pair Potential (SQSSPP) method for regional drought risk assessment: A case study in Suzhou City, China

AbstractDrought risk assessment plays a crucial role in effective drought management. However, it is often challenging due to the intricate relationships among various indicators and the lack of practical guidance. This study presents a drought risk assessment model developed using the Semi‐partial Quadratic Subtraction Set Pair Potential (SQSSPP) method, which is derived from the theory of set pair analysis. The indicator system comprises 21 indicators divided into four subsystems. The SQSSPP method utilizes uncertainty information in the overall development trend of regional drought risk states by extracting connection numbers from the Subtraction Set Pair Potential (SSPP), improving the reliability of evaluation results. The SQSSPP method is validated through a case study of Suzhou City, China, from 2007 to 2017. Three grades are used to evaluate comprehensive drought risk. The result shows an overall decreasing trend over time, with a level III risk in 2010 and consistently at level II from 2011 to 2017. Indicators in the hazard and resilience subsystems are the primary factors influencing drought risk in the Suzhou City. Specific indicators requiring emphasis for improvement are identified, including arable land rate, agricultural population ratio, reservoir regulation rate, current water supply capacity, and irrigation index. The SQSSPP method not only provides targeted drought risk assessment but also provides valuable guidance for future water resource management. While the study focuses on Suzhou City, the proposed approach is applicable to broader‐scale risk management evaluations and practices.

Dynamical Coulomb blockade as a signature of the sign-reversing Cooper pairing potential

Dynamical Coulomb blockade as a signature of the sign-reversing Cooper pairing potential

Depletion potential, correlation functions and demixing transition in model colloid-polymer mixtures

We describe a theoretical framework to calculate depletion potential between colloid particles induced by non-adsorbing ideal polymer chains (s-species) and correlation functions in a coarse-grained one-component system of colloids (c-species). A Padé approximant is used to express the depletion potential as a pair potential with many-body contributions subsumed in it. The depletion potential and correlation functions of c-species are calculated using a self-consistent procedure. Results for several values of size ratio q=σsσc (σs and σc are, respectively diameters of the polymer chain and a colloid particle) and packing fractions of s- and c-species are reported. The spinodal curve and critical point of demixing transition are determined for several values of q. Calculated values are compared with values found from other theories and simulations.