Classical Potential Research Articles

Modelling technique trend (interatomic potential) to study the mineral surfaces: Review

Computational chemistry is another branch of chemistry that can be used to model the material which is based on the mathematical methods and combined that with the theories of the quantum mechanics. However, in this filed there are two different techniques or categories, classical interatomic potential and the electronic structure methodology. The aim of this paper is to describe how can modelling the structures and energetics of surface and interface processes of minerals surface, using the classical atomistic simulation methods. We will illustrate the types of potentials and some of Codes (Gulp and METADISE) which is needed to do these calculations to elucidate the structures and stabilities as well.

Surface stress calculations for nanoparticles and cavities in aluminum, silicon, and iron: influence of pressure and validity of the Young-Laplace equation

This study is dedicated to the determination of the surface energy and stress of nanoparticles and cavities in presence of pressure, and to the evaluation of the accuracy of the Young-Laplace equation for these systems. Procedures are proposed to extract those quantities from classical interatomic potentials calculations, carried out for three distinct materials: aluminum, silicon, and iron. Our investigations first reveal the increase of surface energy and stress of nanoparticles as a function of pressure. On the contrary we find a significant decrease for cavities, which can be correlated to the initiation of plastic deformation at high pressure. We show that the Young-Laplace equation should not be used for quantitative predictions when the Laplace pressure is computed with a constant surface energy value, as usually done in the literature. Instead, a significant improvement is obtained by using the diameter and pressure-dependent surface stress. In that case, the Young-Laplace equation can be used with a reasonable accuracy at low pressures for nanoparticles with diameters as low as 4 nm, and 2 nm for cavities. At lower sizes, or high pressures, a severely limiting factor is the challenge of extracting meaningful surface stress values.

Temporal Variabilities Provide Additional Category-Related Information in Object Category Decoding: A Systematic Comparison of Informative EEG Features.

How does the human brain encode visual object categories? Our understanding of this has advanced substantially with the development of multivariate decoding analyses. However, conventional electroencephalography (EEG) decoding predominantly uses the mean neural activation within the analysis window to extract category information. Such temporal averaging overlooks the within-trial neural variability that is suggested to provide an additional channel for the encoding of information about the complexity and uncertainty of the sensory input. The richness of temporal variabilities, however, has not been systematically compared with the conventional mean activity. Here we compare the information content of 31 variability-sensitive features against the mean of activity, using three independent highly varied data sets. In whole-trial decoding, the classical event-related potential (ERP) components of P2a and P2b provided information comparable to those provided by original magnitude data (OMD) and wavelet coefficients (WC), the two most informative variability-sensitive features. In time-resolved decoding, the OMD and WC outperformed all the other features (including the mean), which were sensitive to limited and specific aspects of temporal variabilities, such as their phase or frequency. The information was more pronounced in the theta frequency band, previously suggested to support feedforward visual processing. We concluded that the brain might encode the information in multiple aspects of neural variabilities simultaneously such as phase, amplitude, and frequency rather than mean per se. In our active categorization data set, we found that more effective decoding of the neural codes corresponds to better prediction of behavioral performance. Therefore, the incorporation of temporal variabilities in time-resolved decoding can provide additional category information and improved prediction of behavior.

Exploring the necessary complexity of interatomic potentials

The application of machine learning models and algorithms towards describing atomic interactions has been a major area of interest in materials simulations in recent years, as machine learning interatomic potentials (MLIPs) are seen as being more flexible and accurate than their classical potential counterparts. This increase in accuracy of MLIPs over classical potentials has come at the cost of significantly increased complexity, leading to higher computational costs and lower physical interpretability and spurring research into improving the speeds and interpretability of MLIPs. As an alternative, in this work we leverage “machine learning” fitting databases and advanced optimization algorithms to fit a class of spline-based classical potentials, showing that they can be systematically improved in order to achieve accuracies comparable to those of low-complexity MLIPs. These results demonstrate that high model complexities may not be strictly necessary in order to achieve near-DFT accuracy in interatomic potentials and suggest an alternative route towards sampling the high accuracy, low complexity region of model space by starting with forms that promote simpler and more interpretable interatomic potentials.

Asymptotics for 2D whispering gallery modes in optical micro-disks with radially varying index

Abstract Whispering gallery modes [WGM] are resonant modes displaying special features: they concentrate along the boundary of the optical cavity at high polar frequencies and they are associated with complex scattering resonances very close to the real axis. As a classical simplification of the full Maxwell system, we consider 2D Helmholtz equations governing transverse electric or magnetic modes. Even in this 2D framework, very few results provide asymptotic expansion of WGM resonances at high polar frequency $m\to \infty $ for cavities with radially varying optical index. In this work, using a direct Schrödinger analogy, we highlight three typical behaviors in such optical micro-disks, depending on the sign of an ‘effective curvature’ that takes into account the radius of the disk and the values of the optical index and its derivative. Accordingly, this corresponds to abruptly varying effective potentials (step linear or step harmonic) or more classical harmonic potentials, leading to three distinct asymptotic expansions for ground state energies. Using multiscale expansions, we design a unified procedure to construct families of quasi-resonances and associate quasi-modes that have the WGM structure and satisfy eigenequations modulo a super-algebraically small residual ${\mathscr{O}}(m^{-\infty })$. We show using the black box scattering approach that quasi-resonances are ${\mathscr{O}}(m^{-\infty })$ close to true resonances.

Guest–Host Interactions in Clathrate Hydrates: Benchmark MP2 and CCSD(T)/CBS Binding Energies of CH4, CO2, and H2S in (H2O)20Cages

We present benchmark binding energies of naturally occurring gas molecules CH4, CO2, and H2S in the small cage, namely, the pentagonal dodecahedron (512) (H2O)20, which is one of the constituent cages of the 3 major lattices (structures I, II, and H) of clathrate hydrates. These weak interactions require higher levels of electron correlation and converge slowly with an increasing basis set to the complete basis set (CBS) limit, necessitating the use of large basis sets up to the aug-cc-pV5Z and subsequent correction for basis set superposition error (BSSE). For the host hollow (H2O)20 cages, we have identified a most stable isomer with binding energy of -200.8 ± 2.1 kcal/mol at the CCSD(T)/CBS limit (-199.2 ± 0.5 kcal/mol at the MP2/CBS limit). Additionally, we report converged second order Møller-Plesset (MP2) CBS binding energies for the encapsulation of guests in the (H2O)20 cage of -4.3 ± 0.1 for CH4@(H2O)20, -6.6 ± 0.1 for CO2@(H2O)20, and -8.5 ± 0.1 kcal/mol for H2S@(H2O)20, respectively. For CH4@(H2O)20, exhibiting the weakest encapsulation affinity among the three, we report CCSD(T)/aug-cc-pVTZ binding energies and, based on them, a CCSD(T)/CBS estimate of -4.75 ± 0.1 kcal/mol. To the best of our knowledge, the CCSD(T)/aug-cc-pVTZ calculation for CH4@(H2O)20 is the largest one reported to date (168 valence electrons, 1978 basis functions, and the correlation of 84 doubly occupied and 1873 virtual orbitals) and required a scalable implementation of the (T) module on 6144 nodes (350 208 cores) of the "Cori" supercomputer at the National Energy Research Supercomputing Center (NERSC) for a total execution time of 195 min (for the (T) part). These efficient scalable implementations of highly correlated methods offer the capability to obtain long-lasting benchmarks of intermolecular interactions in complex systems. They also provide a path toward parametrizing classical potentials needed to study the dynamical and transport properties in these complex systems as well as assess the accuracy of lower scaling electronic structure methods such as density functional theory (DFT) and MP2 including its spin-biased variants.

F-theory flux vacua at large complex structure

We compute the flux-induced F-term potential in 4d F-theory compactifications at large complex structure. In this regime, each complex structure field splits as an axionic field plus its saxionic partner, and the classical F-term potential takes the form V = ZABρAρB up to exponentially-suppressed terms, with ρ depending on the fluxes and axions and Z on the saxions. We provide explicit, general expressions for Z and ρ, and from there analyse the set of flux vacua for an arbitrary number of fields. We identify two families of vacua with all complex structure fields fixed and a flux contribution to the tad- pole Nflux which is bounded. In the first and most generic one, the saxion vevs are bounded from above by a power of Nflux. In the second their vevs may be unbounded and Nflux is a product of two arbitrary integers, unlike what is claimed by the Tadpole Conjecture. We specialise to type IIB orientifolds, where both families of vacua are present, and link our analysis with previous results in the literature. We illustrate our findings with several examples.

A Data-Driven Dimensionality Reduction Approach to Compare and Classify Lipid Force Fields.

Molecular dynamics simulations of all-atom and coarse-grained lipid bilayer models are increasingly used to obtain useful insights for understanding the structural dynamics of these assemblies. In this context, one crucial point concerns the comparison of the performance and accuracy of classical force fields (FFs), which sometimes remains elusive. To date, the assessments performed on different classical potentials are mostly based on the comparison with experimental observables, which typically regard average properties. However, local differences of the structure and dynamics, which are poorly captured by average measurements, can make a difference, but these are nontrivial to catch. Here, we propose an agnostic way to compare different FFs at different resolutions (atomistic, united-atom, and coarse-grained), by means of a high-dimensional similarity metrics built on the framework of Smooth Overlap of Atomic Position (SOAP). We compare and classify a set of 13 FFs, modeling 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayers. Our SOAP kernel-based metrics allows us to compare, discriminate, and correlate different FFs at different model resolutions in an unbiased, high-dimensional way. This also captures differences between FFs in modeling nonaverage events (originating from local transitions), for example, the liquid-to-gel phase transition in dipalmitoylphosphatidylcholine (DPPC) bilayers, for which our metrics allows us to identify nucleation centers for the phase transition, highlighting some intrinsic resolution limitations in implicit versus explicit solvent FFs.

Neural-network model for force prediction in multi-principal-element alloys

Atomistic simulations can provide useful insights into the physical properties of multi-principal-element alloys. However, classical potentials mostly fail to capture key quantum (electronic-structure) effects. We present a deep 3D convolutional neural network (3D CNN) based framework combined with a voxelization technique to design interatomic potentials for chemically complex alloys. We highlight the performance of the 3D CNN model and its efficacy in computing potentials using the medium-entropy alloy TaNbMo. In order to provide insights into the effect of voxel resolution, we implemented two approaches based on the inner and outer bounding boxes. An efficient 3D CNN model, which is as accurate as the density-functional theory (DFT) approach, for calculating potentials will provide a promising schema for accurate atomistic simulations of structure and dynamics of general multi-principle element alloys.

Defect Properties and Lithium Incorporation in Li2ZrO3

Lithium zirconate is a candidate material in the design of electrochemical devices and tritium breeding blankets. Here we employ an atomistic simulation based on the classical pair-wise potentials to examine the defect energetics, diffusion of Li-ions, and solution of dopants. The Li-Frenkel is the lowest defect energy process. The Li-Zr anti-site defect cluster energy is slightly higher than the Li-Frenkel. The Li-ion diffuses along the c axis with an activation energy of 0.55 eV agreeing with experimental values. The most favorable isovalent dopants on the Li and Zr sites were Na and Ti respectively. The formation of additional Li in this material can be processed by doping of Ga on the Zr site. Incorporation of Li was studied using density functional theory simulation. Li incorporation is exoergic with respect to isolated gas phase Li. Furthermore, the semiconducting nature of LZO turns metallic upon Li incorporation.

Angular-dependent interatomic potential for large-scale atomistic simulation of iron: Development and comprehensive comparison with existing interatomic models

The development of classical interatomic potential for iron is a quite demanding task with a long history background. A new interatomic potential for simulation of iron was created with a focus on description of crystal defects properties. In contrast with previous studies, here the potential development was based on force-matching method that requires only ab initio data as reference values. To verify our model, we studied various features of body-centered-cubic iron including the properties of point defects (vacancy and self-interstitial atom), the Peierls energy barrier for dislocations (screw and mix types), and the formation energies of planar defects (surfaces, grain boundaries, and stacking fault). The verification also implies thorough comparison of a potential with 11 other interatomic potentials reported in literature. This potential correctly reproduces the largest number of iron characteristics which ensures its advantage and wider applicability range compared to the other considered classical potentials. Here application of the model is illustrated by estimation of self-diffusion coefficients and the calculation of fcc lattice properties at high temperature.

High-pressure Effect of Elastic and Mechanical Properties of Hexagonal Gallium Nitride

This study examines an effect of pressure up to 50 GPa on the elastic and mechanical properties of wurtzite gallium nitride (w-GaN) by using classical potential within the Atomistic Tool Kit (ATK)-force field. The obtained results show that the elastic constants and other related parameters, such as Young’s modulus, shear modulus, bulk modulus, Poisson’s ratio, Pugh’s ratio, Zener anisotropy factor and Kleinman parameter increase monotonically with increase of pressure up to 32 GPa. Beyond this pressure, we observed a non-linear behavior with increase in pressure. This might be attributed to the phase transition in GaN in the pressure range of 33.4 - 44.6 GPa. The results obtained for zero pressure are consistent with both experimental data and the theoretical data shown in references.

Thermo-mechanical properties of nitrogenated holey graphene (C2N): A comparison of machine-learning-based and classical interatomic potentials

Thermal and mechanical properties of two-dimensional nanomaterials are commonly studied by calculating force constants using the density functional theory (DFT) and classical molecular dynamics (MD) simulations. Although DFT simulations offer accurate estimations, the computational cost is high. On the other hand, MD simulations strongly depend on the accuracy of interatomic potentials. Here, we investigate thermal conductivity and elastic modulus of nitrogenated holey graphene (C2N) using passively fitted machine-learning interatomic potentials (MLIPs), which depend on computationally inexpensive ab-initio molecular dynamics trajectories. Thermal conductivity of C2N is investigated via MLIP-based non-equilibrium molecular dynamics simulations (NEMD). At room temperature, the lattice thermal conductivity of 85.5 ± 3 W/m-K and effective phonon mean free path of 36.7 ± 1 nm are found. By carrying out uniaxial tension simulations, the elastic modulus, ultimate strength, and fractural strain of C2N are predicted to be 390 ± 3 GPa, 42 ± 2 GPa, and 0.29 ± 0.01, respectively. It is shown that the passively fitted MLIPs can be employed as an efficient interatomic potential to obtain the thermal conductivity and elastic modulus of C2N utilizing classical MD simulations. Moreover, the possibility of employing MLIPs to simulate C2N with point defects has been investigated. By training MLIP with point defect configurations, the mechanical properties of defective structures were studied. Although using the MLIP is more costly than classical interatomic potentials, it could efficiently predict the thermal and mechanical properties of 2D nanostructures.

EAPOTs: An integrated empirical interatomic potential optimization platform for single elemental solids

The development of high-fidelity, empirical, interatomic potentials is in high demand since it determines the reliability and quality of atomistic simulations, such as molecular dynamics/statics (MD/MS) and Monte Carlo (MC) simulations; however, it is a challenging and difficult process. In this paper, we present a flexible, extensible, and user-friendly platform called EAPOTs, i.e., Empirical interAtomic POTentials for single elemental solids, which provides a graphical user interface for the routine construction, optimization, and evaluation of classical empirical interatomic potentials by integrating various potential functions, local and global optimization schemes, and flexible combinations of various targets. A high-throughput flowchart was also implemented in EAPOTs through automatic processing of model construction with various modifications, data delivery, and retrieval with first-principles calculations, alongside highly efficient batches of operations. In addition, EAPOTs also realized multiple combinations of “energy-stress-force-elasticity” and multi-level, objective optimization schemes, which ensured that the fitting strategy could meet the demands of different simulation scenarios. Compared with other similar software, such as POTFIT, MEAMfit, and ATOMICREX, this software exhibited a series of advantages, such as a more maneuverable and concise graphical user interface, richer potential function forms, more robust optimization schemes, and a higher degree of functional integration. To demonstrate its efficiency and flexibility, the software was critically validated by several evaluations and tests on various elemental metallic and covalent solids, including high-throughput construction, extreme scenarios, and tunable targets, which provided guidance and confidence for its broad applications in atomistic simulations as a core component.

Atomistic two-, three- and four-body potentials. Spatial and material settings

In molecular dynamics or molecular statics (MD/MS) multi-body potentials empirically capture the energetic interactions in atomistic systems enabling the computation of the corresponding atomistic forces as energetic conjugates to the atomistic positions. We distinguish here between spatial and material atomistic positions and consequently between the corresponding spatial and material atomistic forces. In quasi-statics, i.e. MS, the former, also denoted as deformational atomistic forces, contribute to the classical deformational mechanics (i.e., equilibrium) problem that seeks to minimise the total potential energy of an atomistic system with respect to the atomistic positions relative to the ambient space. The latter, also denoted as configurational atomistic forces, contribute to the configurational mechanics (i.e., non-equilibrium) problem that determines the release of total potential energy of an atomistic system upon variation of the atomistic positions relative to the ambient material, i.e., due to perturbations of the material (initial) atomistic configuration. The importance of material atomistic forces is that they drive energetically favourable re-organisations of the material atomistic configuration, thereby characterising the tendency of generic atomistic defects to propagate. In this contribution we focus on two-, three-, and four-body potentials, whereby we distinguish between novel stretch- and classical angle-based potentials for the two latter cases. Taken together, as the main contribution, we derive expressions for the corresponding spatial and, for the first time, material atomistic forces and highlight their striking formal similarity. The derivations are detailed but the final expression compact and well-suited for numerical implementation.

Investigation of alumino-silicate glasses by coupling experiments and simulations: Part I - Structures

A set of alumino-silicate glasses with SiO2-Al2O3-Na2O-CaO compositions was investigated using Raman and NMR spectroscopy techniques and by classical molecular dynamics, in order to study the structural modifications which occur when CaO progressively replaces Na2O and when Al2O3 progressively replaces SiO2. The effect of a gradual increase in the Al2O3 content was also studied. Al was always 4 coordinated for all the compositions studied, including the peraluminous glasses. An increase in the number of Al-O-Al bonds was found when the Al2O3 or CaO content increases. The study confirmed that AlO4 groupings are preferentially compensated by Na rather than by Ca, and that there are non-bridging oxygens surrounded by mixed environments containing both Na and Ca. Combining the information given by the Raman and NMR spectroscopy results enabled the attribution of the Raman band at 570cm-1 to the Si-O-Al bonds. It confirmed that the band at 510cm-1 can be attributed to the Al-O-Al bonds, while that at 985cm-1 can be attributed to the Q4-Al entities. Lastly, it was demonstrated that the classical molecular dynamics potentials of Deng et al., specifically developed for this type of glasses, permit the reproduction of a large number of the experimental results quantitatively or sometimes simply qualitatively.

Optimized interatomic potential for atomistic simulation of Zr-Nb alloy

We present a new classical interatomic potential for a study of the binary Zr-Nb system, taking into account a wide range of the components concentrations. The potential was developed by virtue of the force-matching method that is capable of ensuring a high accuracy at the description of the complex systems containing diverse crystal phases. At simulation of pure Zr, the potential correctly describes a relative stability of Zr phases (α-Zr, β-Zr and ω-Zr) and qualitatively reproduces the right arrangement of these phases in the phase diagram. It is remarkable that β-Zr phase is found to have a dynamically unstable structure at the low temperature, in agreement with the ab initio calculations. The potential can also play a role in considering the tasks related to the crystal defects in the Zr-Nb system. In support of this statement, we show the simulation results proving adequate representation of a number of key properties of the crystal defects in Zr-Nb system. In particular, the offered potential reproduces formation/solution energies of point defects with well accuracy. To illustrate wide application possibilities for the model, we made a prediction of atomic self-diffusion and impurity diffusion in Zr and Nb. Also, the potential ensures correct description of a screw dislocation in niobium, which is a crucial point for the investigation of plasticity.

P -band stability of an ultracold-atom gas in an anharmonic optical-lattice potential with large energy scales

Using an optical potential with subwavelength resolution in the form of sharp $\delta$-like peaks, new potential landscapes are created with increased anharmonicity in placement of lattice band energies and more favorable energy scales. In particular, this makes the ultracold atom p-band gas more stable. The article outlines the details of the construction and discusses the p-band stability in canonical cosine optical lattice potential, double well potential, and a combination of a classical cosine potential with dark state peaked potential.

Molecular-statistical theory of elasticity in nematic liquid crystals composed of polar and nonpolar molecules.

A molecular-statistical theory of the orientational elasticity of nematic liquid crystals has been developed employing the orientational deformation tensor which describes the rotation of the director. An explicit expression for the general elasticity tensor of the nematic phase has been obtained and the Frank elastic constants are expressed in terms of the three independent parameters of this tensor. Explicit expressions for the Frank elastic constants have been derived in the molecular field approximation in terms of the orientational order parameters and the corresponding coefficients of expansion of the intermolecular potential in spherical invariants. Frank elastic constants have been calculated numerically for nematic liquid crystals composed of both polar and nonpolar molecules together with the orientational order parameters using the classical Gay-Berne model interaction potential and the two of its popular modifications. The polarity of the uniaxial molecular shape has been directly introduced into the model potential by modifying the distance of closest approach. The elastic constants are presented as functions of temperature for different values of the molecular elongation, the anisotropy of the potential well and the molecular shape polarity. It has been shown that the elastic constants are much more sensitive to the details of the intermolecular interaction potential in comparison with the orientational order parameters. In particular, a relatively weak polarity of the molecular shape may result in an unusual decrease of the splay constant K_{11} which may vanish at some temperature leading to the instability of the homogeneous nematic phase. This may represent a mechanism of the formation of the splay-bend phase.

Defect and dopant properties in CaMnO3

CaMnO3-based ceramics have been the subject of considerable research due to their potential application in solid oxide fuel cells, thermoelectric generators, and catalysis. The computational modeling technique based on the classical pair-wise potentials has allowed atomic-scale insights into the defect chemistry, diffusion of Ca2+ and O2− ions, and solution of various dopants in this material. The Ca/Mn anti-site was found to be the most favorable intrinsic defect suggesting disorder, which would be sensitive to synthesis conditions. The second most favorable disorder in CaMnO3 involves loss of CaO, resulting in calcium and oxygen vacancies, which in turn can promote vacancy mediated self-diffusion. The activation energy for oxygen migration (1.25 eV) is much lower than that for calcium (4.42 eV). Favorable isovalent dopants on the Ca and Mn sites were found to be Fe2+ and Ge4+, respectively. The formation of O vacancies can be facilitated by doping of single dopants Fe2+ and Al3+ on the Mn site. Dual dopants Ni–Fe and Al–Ga on the Mn site can also facilitate the introduction of oxygen vacancies required for the vacancy assisted oxygen diffusion.