Classical Potential Research Articles

The role of complement factor I rare genetic variants in age related macular degeneration in Finland.

Age-related macular degeneration (AMD) is the leading cause of irreversible blindness in the developed world. The alternative pathway (AP) of complement has been linked to the pathogenesis of AMD. In particular, rare variants (RVs) in the complement factor I (CFI) gene encoding the Factor I (FI) protein confer increased AMD risk. The prevalence of CFI RVs are well characterised in European AMD, however little is known about other populations. The Finnish population underwent genetic restriction events which have skewed allele frequencies in unexpected ways. A series of novel or enriched CFI RVs were identified in individuals with dry AMD from the Finnish Biobank Cooperative (FINBB), but the relationship between these genotypes and contribution to disease was unclear. Understanding how RVs impact the ability of FI to regulate the complement system is important to inform mechanistic understanding for how different genotypes contribute to disease development. To explore this a series of in vitro assays were used to functionally characterise the protein products of 3 CFI RVs enriched in FINBB dry AMD, where no prior data were available. The G547R variant resulted in almost complete loss of both classical pathway and AP regulatory potential. The c.982 g>a variant encoding G328R FI perturbed an exon splice enhancer site which resulted in exon skipping and a premature stop codon in vitro and low levels of FI in vivo. Despite detailed analysis no defect in levels or function was demonstrated in T107A. Functional characterization of all Finnish CFI RVs in the cohort allowed us to demonstrate that in Finnish dry AMD, collectively the type 1 CFI RVs (associated with FI haploinsufficiency) were significantly enriched with odds ratio (ORs) of 72.6 (95% confidence interval; CI 16.92 to 382.1). Meanwhile, type 2 CFI RVs (associated with FI dysfunction) collectively conferred a significant OR of 4.97 (95% CI 1.522 to 15.74), and non-impaired or normal CFI RV collectively conferred an of OR 3.19 (95% CI 2.410 to 4.191) although this was driven primarily by G261D. Overall, this study for the first time determined the ORs and functional effect for all CFI RVs within a Geographic Atrophy (GA) cohort, enabling calculations of combined risk scores that underline the risk conferred by type 1 and 2 CFI RVs in GA/AMD.

K-Means Clustering in Fingerprint-Based Configuration Selection for Fitting Interatomic Potentials.

In this study, we present a method for selecting an arbitrary number of distinct configurations from a larger data set by applying k-means clustering to atomistic configuration fingerprints based on the CrystalNN model and radial distribution function (RDF). This approach improves the accuracy of fitting classical molecular dynamics interatomic potentials to density functional theory (DFT) data for both energies and forces while requiring fewer configurations than random selection. We demonstrate this improvement by fitting an embedded-atom method (EAM) potential for titanium, using various configurational sizes from an initial set of 1800 configurations. The k-means clustering consistently achieves better precision and lower standard deviations for a smaller number of configurations than random selection. The results also suggest that only about 30 configurations are sufficient to obtain an EAM model that describes well the full set of 1800 configurations in terms of energies and forces. Additionally, t-distributed stochastic neighbor embedding (t-SNE) method was used to reduce the configuration fingerprints into 2D space, and it revealed an overlap between two configuration subsets with and without Ti vacancy, indicating similar atomic environments. This similarity is captured by k-means clustering but not by random selection. Furthermore, when the overlapping configurations with vacancies were excluded from the k-means algorithm and used only as a test set, their energy and force predictions showed similar precision to those when they were included. This indicates that the overlapping configurations in the 2D t-SNE space indeed imply potential information redundancy among the atomistic configurations.

Emergent potentials and non-perturbative open topological strings

We show that integrating out M2 branes ending on M5 branes inside Calabi-Yau manifolds captures non-perturbative open topological string physics. The integrating out is performed using a contour integral in complexified Schwinger proper time. For the resolved conifold, this contour can be extended to include the zero pole, which we argue captures the ultraviolet completion of the integrating out and yields the tree-level polynomial terms in the free energy. This is a manifestation of the Emergence Proposal, and provides further evidence for it. Unlike the case of closed strings, where the emergent terms are kinetic terms in the action, for these open strings it is tree-level potential terms which are emergent. This provides a first quantitative example of the proposal that classical tree-level potentials in string theory emerge from integrating out co-dimension one states.

Current-driven mechanical motion of double stranded DNA results in structural instabilities and chiral-induced-spin-selectivity of electron transport.

Chiral-induced-spin-selectivity of electron transport and its interplay with DNA's mechanical motion are explored in a double stranded DNA helix with spin-orbit-coupling. The mechanical degree of freedom is treated as a stochastic classical variable experiencing fluctuations and dissipation induced by the environment as well as force exerted by nonequilibrium, current-carrying electrons. Electronic degrees of freedom are described quantum mechanically using nonequilibrium Green's functions. Nonequilibrium Green's functions are computed along the trajectory for the classical variable taking into account dynamical, velocity dependent corrections. This mixed quantum-classical approach enables calculations of time-dependent spin-resolved currents. We showed that the electronic force may significantly modify the classical potential, which, at sufficient voltage, creates a bistable potential with a considerable effect on electronic transport. The DNA's mechanical motion has a profound effect on spin transport; it results in chiral-induced spin selectivity, increasing spin polarization of the current by 9% and also resulting in temperature-dependent current voltage characteristics. We demonstrate that the current noise measurement provides an accessible experimental means to monitor the emergence of mechanical instability in DNA motion. The spin resolved current noise also provides important dynamical information about the interplay between vibrational and spin degrees of freedom in DNA.

Accurate nuclear quantum statistics on machine-learned classical effective potentials.

The contribution of nuclear quantum effects (NQEs) to the properties of various hydrogen-bound systems, including biomolecules, is increasingly recognized. Despite the development of many acceleration techniques, the computational overhead of incorporating NQEs in complex systems is sizable, particularly at low temperatures. In this work, we leverage deep learning and multiscale coarse-graining techniques to mitigate the computational burden of path integral molecular dynamics (PIMD). In particular, we employ a machine-learned potential to accurately represent corrections to classical potentials, thereby significantly reducing the computational cost of simulating NQEs. We validate our approach using four distinct systems: Morse potential, Zundel cation, single water molecule, and bulk water. Our framework allows us to accurately compute position-dependent static properties, as demonstrated by the excellent agreement obtained between the machine-learned potential and computationally intensive PIMD calculations, even in the presence of strong NQEs. This approach opens the way to the development of transferable machine-learned potentials capable of accurately reproducing NQEs in a wide range of molecular systems.

The structural and electronic configuration of an amorphous silica surface, from its liquid to glassy state

Through classical molecular dynamics computational simulations, the surface of amorphous silica (vitreous silica) was generated for a system comprising 64 SiO2 molecules (192 atoms) via the classical three-body glass potential. Starting from the liquid state of silica at 3400 K, it was cooled in three different ways at intervals of 200, 400, and 2000 K, with a cooling rate of 4.4 K/ps and establishing relaxation at intermediate temperatures, yielding three groups of surfaces from 3400 to 1400 K. Subsequently, these systems underwent sudden cooling from 1400 to 300 K via the Andersen and Nosé‒Hoover thermostats, followed by relaxation at 300 K via a microcanonical ensemble (NVE constant). Each surface that underwent relaxation was analyzed through ab initio molecular dynamics for the following three physical properties, which are temperature dependent. The average electric charges of oxygen and silicon. Microstructures on the outermost part of the surface were observed and comprised nonbridging oxygen atoms, undercoordinated silicon, and N-membered rings (3 ≤ N ≤ 5). The radial distribution functions were analyzed for all surfaces. Below 2000 K, a type of freezing is observed in all the structures because of the glass transition. All analyses were performed at zero pressure.

The influence of intrinsic point defects on the electronic band structures and swelling behaviors of 4H-SiC

In this work, both the first principles calculations and molecular dynamics simulations are adopted to investigate the formation ability of various intrinsic point defects in 4H-SiC as well as the electronic band structure changes and the swelling effects caused by them. Our results demonstrate that the classical MEAM potential has an unsatisfactory performance on the defect formation energies as compared with the ab initio calculations based on the advanced SCAN functional, but provides a reasonable description on the volumetric swelling caused by single point defect. Both the SCAN and MEAM calculations indicate that the VC monovacancy and the CSi antisite defect will cause the lattice shrinkage, while the VSi monovacancy, the SiC antisite, the IC and the ISi interstitials will induce the volumetric swelling. Besides that, first principles calculations reveal that monovacancies and interstitials would induce defective electronic states near the Fermi level, while antisites have negligible influence on the electronic band structures as compared with the pristine case. Furthermore, the molecular statics relaxations are employed to explore the influence of point defect densities on the swelling behaviors of 4H-SiC, which reveals that the volume swelling ratios present good linear relationships with the increased density of the VC monovacancy, CSi antisite, SiC antisite and IC interstitial defects, but express complex non-linear tendencies with the VSi monovacancy and ISi interstitial defects. Therefore, our research deepens the understanding of the point defects’ effects on the electronic properties and swelling behaviors of 4H-SiC.

Analytical potential energy functions for CO in its ground and excited electronic states.

Accurate functions to analytically represent the potential energy interactions of CO diatomic system in , , and electronic states are proposed. The new functions depend upon only four parameters directly obtained from experimental data, without any fitting procedure. These functions have been developed from the modified generalized potential proposed by Araújo and Ballester. The function for the electronic state represents a significant improvement to the previously proposed model. To quantify the accuracy of the potential energy functions, the Lippincont test is used. The novel potential was also compared with the classical Morse potential and with the recently proposed Improved Generalized Pöschl-Teller potential. Furthermore, the main spectroscopic constants and vibrational energy levels are calculated and compared for all potentials. The present results agree excellently with the experiment Rydberg-Klein-Rees (RKR) potentials. The rovibrational energy levels of the proposed diatomic potentials were asserted by solving radial the Schrödinger equation of the nuclear motion with the aid of the LEVEL program.

Implementing reactivity in molecular dynamics simulations with harmonic force fields

The simulation of chemical reactions and mechanical properties including failure from atoms to the micrometer scale remains a longstanding challenge in chemistry and materials science. Bottlenecks include computational feasibility, reliability, and cost. We introduce a method for reactive molecular dynamics simulations using a clean replacement of non-reactive classical harmonic bond potentials with reactive, energy-conserving Morse potentials, called the Reactive INTERFACE Force Field (IFF-R). IFF-R is compatible with force fields for organic and inorganic compounds such as IFF, CHARMM, PCFF, OPLS-AA, and AMBER. Bond dissociation is enabled by three interpretable Morse parameters per bond type and zero energy upon disconnect. Use cases for bond breaking in molecules, failure of polymers, carbon nanostructures, proteins, composite materials, and metals are shown. The simulation of bond forming reactions is included via template-based methods. IFF-R maintains the accuracy of the corresponding non-reactive force fields and is about 30 times faster than prior reactive simulation methods.

A theoretical perspective on solid-state ionic interfaces.

Solid-state ionic conductors find application across various domains in materials science, particularly showcasing their significance in energy storage and conversion technologies. To effectively utilize these materials in high-performance electrochemical devices, a comprehensive understanding and precise control of charge carriers' distribution and ionic mobility at interfaces are paramount. A major challenge lies in unravelling the atomic-level processes governing ion dynamics within intricate solid and interfacial structures, such as grain boundaries and heterophases. From a theoretical viewpoint, in this Perspective article, my focus is to offer an overview of the current comprehension of key aspects related to solid-state ionic interfaces, with a particular emphasis on solid electrolytes for batteries, while providing a personal critical assessment of recent research advancements. I begin by introducing fundamental concepts for understanding solid-state conductors, such as the classical diffusion model and chemical potential. Subsequently, I delve into the modelling of space-charge regions, which are pivotal for understanding the physicochemical origins of charge redistribution at electrified interfaces. Finally, I discuss modern computational methods, such as density functional theory and machine-learned potentials, which offer invaluable tools for gaining insights into the atomic-scale behaviour of solid-state ionic interfaces, including both ionic mobility and interfacial reactivity aspects. This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.

Pressure and temperature diagram of C60 from atomistic simulations.

Although widely studied experimentally in the 1990s, the structure and properties of low-dimensional or high-pressure phases of fullerenes have recently been re-examined. Remarkably, recent experiments have shown that transparent, nearly pure amorphous sp3-bonded carbon phases can be obtained by heating a C60 molecular crystal at a high pressure. With the additional aim of testing the ability of three classical carbon potentials reactive empirical bond order, environment-dependent interatomic potential, and reactive force-field to reproduce these results, we investigate the details of the structural transformations undergone by fullerene crystals over a wide range of pressures and temperatures. All the potentials tested show that the initial polymerization of fullerenes is accompanied by negative thermal expansion, albeit in slightly different ranges. However, more significant differences in structural and mechanical properties are observed in the amorphous phases, in particular the sp3 carbon fraction and the existence of layered amorphous carbon. Overall, these results indicate to which extent classical reactive potentials can be used to explore phase transitions over a wide range of pressures and temperatures.

Accuracy, transferability, and computational efficiency of interatomic potentials for simulations of carbon under extreme conditions.

Large-scale atomistic molecular dynamics (MD) simulations provide an exceptional opportunity to advance the fundamental understanding of carbon under extreme conditions of high pressures and temperatures. However, the fidelity of these simulations depends heavily on the accuracy of classical interatomic potentials governing the dynamics of many-atom systems. This study critically assesses several popular empirical potentials for carbon, as well as machine learning interatomic potentials (MLIPs), in their ability to simulate a range of physical properties at high pressures and temperatures, including the diamond equation of state, its melting line, shock Hugoniot, uniaxial compressions, and the structure of liquid carbon. Empirical potentials fail to accurately predict the behavior of carbon under high pressure-temperature conditions. In contrast, MLIPs demonstrate quantum accuracy, with Spectral Neighbor Analysis Potential (SNAP) and atomic cluster expansion (ACE) being the most accurate in reproducing the density functional theory results. ACE displays remarkable transferability despite not being specifically trained for extreme conditions. Furthermore, ACE and SNAP exhibit superior computational performance on graphics processing unit-based systems in billion atom MD simulations, with SNAP emerging as the fastest. In addition to offering practical guidance in selecting an interatomic potential with a fine balance of accuracy, transferability, and computational efficiency, this work also highlights transformative opportunities for groundbreaking scientific discoveries facilitated by quantum-accurate MD simulations with MLIPs on emerging exascale supercomputers.

Lattice dynamics and free energies of Fe–V alloys with thermal and chemical disorder

Molecular dynamics simulations of Fe-V binary alloys with body-centered cubic as the underlying lattice were performed using a classical potential for chemically ordered and disordered states at finite temperatures for a common set of volumes. The equation of state was fitted to the computational data to obtain temperature- and chemical-order-dependent state functions via the Moruzzi-Janak-Schwarz approximation. Additionally, vibrational entropies that account for both thermal and chemical disorder were calculated for the equiatomic compositions from phonon density-of-states curves computed using effective force constants obtained from fits to the simulations. The latter predicts that the vibrational entropy at room temperature at equiatomicity is higher for the ordered phase than for the solid solution, a peculiar behavior previously observed experimentally. The internal energy of mixing favors ordering at all compositions, with a maximum at equiatomicity that decreases as the solute concentration decreases. The configurational entropy contribution to the free energy of mixing is almost entirely responsible for the stability of the high-temperature disordered phase.

Vanadium oxide clusters in substellar atmospheres. A quantum chemical study

As a refractory material, vanadia (solid V$_2$O$_5$) is likely to be found as a condensate in the atmospheres of substellar objects such as exoplanets and brown dwarfs. However, the nature of the nanometer-sized vanadium oxide clusters that partake in the nucleation process is not well understood. We aim to understand the formation of cloud condensation nuclei in oxygen-rich substellar atmospheres by calculating the relevant fundamental properties of the energetically most favorable vanadium oxide molecules and clusters and, investigate how they contribute to the formation of condensation seeds. We applied a hierarchical optimization approach in order to find the most favourable structures for clusters of (VO) N and (VO$_2$) N for N=1-10, and of (V$_2$O$_5$) N for N=1-4, and to calculate their thermodynamical potentials. The candidate geometries are initially optimized by applying classical interatomic potentials; these are then refined at the B3LYP/cc-pVTZ level of theory to obtain accurate zero-point energies and thermochemical quantities. We present previously unreported vanadium oxide cluster structures as the lowest-energy isomers. Moreover, we report revised cluster energies and their thermochemical properties. Chemical equilibrium calculations are used to asses the impact of the updated and newly derived thermodynamic potentials on the gas-phase abundances of vanadium-bearing species. In chemical equilibrium, larger clusters from different stoichiometric families are found to be the most abundant vanadium-bearing species for temperatures below sim 1000 K, while molecular VO is the most abundant between sim 1000 K and sim 2000 K. We determine the nucleation rates of each stoichiometric family for a given (T$_ gas $, p$_ gas $) profile of a brown dwarf using both classical and non-classical nucleation theory. Small differences in the revised Gibbs free energies of the clusters have a large impact on the abundances of vanadium-bearing species in chemical equilibrium at temperatures below sim 1000 K. These abundance changes subsequently have an impact on the nucleation rates of each stoichiometric family. We find that with the revised and more accurate cluster data, non-classical nucleation rates are up to 15 orders of magnitude higher than classical nucleation rates.

Modeling the unsteady wake of an impulsively started circular cylinder using refined potential flow theory

Cylindrical structures find usage in many engineering applications including tethered oil drums and engine canisters slung beneath helicopters in flight. The motion of air around such circular cylindrical structures and the helicopter presents interesting phenomena including flow separation, wakes and turbulence. The physics of these are enshrined in the continuity equation and the Navier–Stokes equations. Therefore, their studies are not only important in mathematics and physics, but they are also required for efficient helicopter operations. In practice, reduced-order models of these operations that take in aerodynamics models of the tethered loads are utilized for stability analysis, flight certification and pilot training because of the prohibitive cost of experimentation and computational analyses of these configurations. However, there is a dearth of realistic analytical models of finite cylinder flows because of the Navier–Stokes problem. Classical potential flow theory provides an avenue to develop such models, but the extant gaps in its predictions significantly preclude its usage for engineering applications. Attempting to bridge these gaps, this article introduces refined potential flow theory in which the governing equations and boundary conditions are satisfied. Viscous effects, fluctuations of the mean flow and three-dimensional effects are also incorporated. For characterization, refined potential flow theory is employed on an incompressible flow over an impulsively started circular cylinder for Reynolds numbers and non-dimensional times in the range 30<Re<104 and 0.2 ≤ T ≤ 77, 047 respectively. There is an excellent prediction of 0.209 for the Strouhal number at Re=3,900 . At this transitional Reynolds number, the harmonics of the Strouhal frequency are also captured, and the characteristic irregular fluctuations at sub-Strouhal frequencies are discernible in the velocity spectra. As the flow becomes more turbulent, these become more pronounced at Re=9,500 when the predicted Strouhal number is within 10% of experimental result. In the fully developed stage, spectra analyses of the wake velocity components at some downstream locations also display Kolmogorov's Five-Thirds law of homogeneous isotropic turbulence. The present model can thus aid the development of reduced-order models of helicopter operations that feature tethered cylindrical loads.

POTENTIAL PARAMETERS FOR EVALUATING THE ACTIVATION CHARACTERISTICS OF ION DIFFUSION IN SOLID ELECTROLYTES BASED ON STABILIZED ZIRCONIUM OXIDE

The activation energy values of oxygen ion diffusion in yttria-stabilized zirconia (one of the most promising solid electrolytes for fuel cell technologies), estimated in molecular dynamics studies with the classical Buckingham potential, turn out to be significantly lower than experimental ones. A possible reason is the incorrect calibration of the potential, the parameters of which were selected earlier using simple model systems. In this paper, three sets of potential parameters have been developed based on the calibration of the interatomic potential based on the results of periodic DFT calculation in an extended system. The results of molecular dynamic modeling using the developed parameter sets reproduce much better the experimental values of activation energies with a variation of the molar fraction of the dopant in a solid electrolyte.

Bending and twisting rigidities of 2D materials

A novel torus-based surface parametrization is proposed and used to evaluate the bending and twisting rigidities of 2D materials of arbitrary symmetries. A generalized constitutive model is used to capture the effects of simultaneous bending and twisting curvatures on the strain energy density of a 2D material. The flexural rigidities are evaluated by subjecting the 2D material specimens to different curvature states, including simultaneous bending and twisting, evaluating the corresponding strain energy densities and curve fitting the constitutive model to the data. The proposed methodology is independent of the method used to evaluate the strain energy of the 2D materials, e.g., density functional theory or classical interatomic potentials. The flexural rigidities of graphene, molybdenum disulfide, and black phosphorus are evaluated and compared to those published in the literature. The directional dependence of the flexural rigidities is investigated. Dimensionless coefficients are presented for quantifying the bidirectional bending and bending-twisting coupling effects in 2D materials. Lastly, this study includes an analysis of the flexural anisotropy and flexure-thickness distension coefficients of black phosphorus.

Deciphering diffuse scattering with machine learning and the equivariant foundation model: the case of molten FeO

Bridging the gap between diffuse x-ray or neutron scattering measurements and predicted structures derived from atom–atom pair potentials in disordered materials, has been a longstanding challenge in condensed matter physics. This perspective gives a brief overview of the traditional approaches employed over the past several decades. Namely, the use of approximate interatomic pair potentials that relate three-dimensional structural models to the measured structure factor and its’ associated pair distribution function. The use of machine learned interatomic potentials has grown in the past few years, and has been particularly successful in the cases of ionic and oxide systems. Recent advances in large scale sampling, along with a direct integration of scattering measurements into the model development, has provided improved agreement between experiments and large-scale models calculated with quantum mechanical accuracy. However, details of local polyhedral bonding and connectivity in meta-stable disordered systems still require improvement. Here we leverage MACE-MP-0; a newly introduced equivariant foundation model and validate the results against high-quality experimental scattering data for the case of molten iron(II) oxide (FeO). These preliminary results suggest that the emerging foundation model has the potential to surpass the traditional limitations of classical interatomic potentials.

Amorphous MoS2 from a machine learning inter-atomic potential.

Amorphous molybdenum disulfide has shown potential as a hydrogen evolution catalyst, but the origin of its high activity is unclear, as is its atomic structure. Here, we have developed a classical inter-atomic potential using the charge equilibration neural network method, and we have employed it to generate atomic models of amorphous MoS2 by melting and quenching processes. The amorphous phase contains an abundance of molybdenum and sulfur atoms in low coordination. Besides the 6-coordinated molybdenum typical of the crystalline phases, a substantial fraction displays coordinations 4 and 5. The amorphous phase is also characterized by the appearance of direct S-S bonds. Density functional theory shows that the amorphous phase is metallic, with a considerable contribution of the 4-coordinated molybdenum to the density of states at the Fermi level. S-S bonds are related to the reduction of sulfur, with the excess electrons spread over several molybdenum atoms. Moreover, S-S bond formation is associated with a distinctive broadening of the 3s states, which could be exploited for experimental characterization of the amorphous phases. The large variety of local environments and the high density of electronic states at the Fermi level may play a positive role in increasing the electrocatalytic activity of this compound.

Calabi-Yau Meets Gravity: A Calabi-Yau Threefold at Fifth Post-Minkowskian Order.

We study geometries occurring in Feynman integrals that contribute to the scattering of black holes in the post-Minkowskian (PM) expansion. These geometries become relevant to gravitational-wave production from binary mergers through the classical conservative potential. At 4PM, a K3 surface is known to occur in a three-loop integral, leading to elliptic integrals in the result. In this Letter, we identify a Calabi-Yau threefold in a four-loop integral, contributing at 5PM. The presence of this Calabi-Yau geometry indicates that completely new functions occur in the full analytical results.