Classical Potential Research Articles

Modeling of Diffusion of Acetone in UiO-66

Highly porous zirconium-based metal–organic frameworks (MOFs) have been widely studied as materials for sorption and destruction of chemical warfare agents (CWAs). It is important to understand the diffusion of CWAs, their reaction products, and environmental molecules through MOFs to utilize these materials for protection against CWA threats. As a first step toward this goal, we study adsorption and diffusion of acetone in pristine UiO-66. We have chosen to study UiO-66 because it has been demonstrated to be effective for destruction of CWAs and simulants; we use acetone because it is a prototypical polar organic molecule small enough to be expected to diffuse fairly rapidly through nondefective UiO-66. We specifically examine the impact of framework flexibility and hydrogen bonding between acetone and the OH groups on the nodes of the framework on the diffusivity of acetone. We find that inclusion of flexibility is essential for meaningful predictions of diffusion of acetone. We have identified the dynamics of the three linkers making up the triangular window between adjacent pores as the critical factor in controlling diffusion of acetone. We demonstrate from experiments and first-principles calculations that acetone readily hydrogen bonds to UiO-66 framework OH groups. We have modified the classical potential for UiO-66 to accurately model the framework–acetone hydrogen bonds, which are not accounted for in many MOF potentials. We find that hydrogen bonding decreases the diffusivity by about 1 order of magnitude at low loading and about a factor of 3 at high loading. Thus, proper accounting of hydrogen bonding and framework flexibility are both critical for obtaining physically realistic values of diffusivities for acetone and similar-sized polar molecules in UiO-66.

A note on Jacobi-type transitions in finite nuclei

The Jacobi-type transitions (JTTs) in nuclei and their connections with excite-state quantum phase transitions (ESQPTs) have been investigated within the framework of the interacting boson model (IBM) by both the semiclassical analysis and quantal calculations. The results indicate that the quadrupole deformation of a transitional system may change from γ rigid to γ soft as the angular momentum increases. This change may in turn drive the JTTs to occur around the saddle point of the corresponding classical potential, where the precursors of ESQPT can be also identified even for a realistic boson number. A further comparison between the experimental data and the model predictions confirms that the JTT phenomena may widely occur in the rare-earth isotopes associated with the 1st-order quantum phase transitions.

Artificial neural network potential for pure zinc

Zinc (Zn), because of its aberrant c/a ratio, has proven difficult to model using classical interatomic potentials such as the Modified Embedded Atom Method (MEAM). The limitations of existing formalisms in modeling Zn have been overcome here using a machine learned interatomic potential. This potential is trained using a database of density functional theory(DFT) calculations generated using the generalized gradient approximation. The resulting feedforward perceptron has a minimal architecture with a single hidden layer of 20 neurons. Validation of the network generated potential demonstrates that the potential correctly reproduced the training database while also predicting the experimentally observed c/a ratio as a function of temperature. The network is able to simultaneously predict the correct c/a ratio while also finding the hexagonally close packed structure as the ground state, which has not been previously demonstrated with semi-emprical potentials. This potential shows various results which are in good agreement with DFT and experimental calculation and will be a useful tool in the simulation of Zn at the molecular dynamics scale.

Accelerated Modeling of Lithium Diffusion in Solid State Electrolytes Using Artificial Neural Networks

There is great interest in solid state lithium electrolytes to replace the flammable organic electrolyte for an all solid state battery. Previous efforts trying to understand the structure-function relationships resulting in high ionic conductivity materials have mainly relied on ab initio molecular dynamics. Such simulations, however, are computationally demanding and cannot be reasonably applied to large systems containing more than a few hundred atoms. Herein, we investigate using artificial neural networks (ANN) to accelerate the calculation of high accuracy atomic forces and energies used during molecular dynamics (MD) simulations (Figure 1A), to eliminate the need for costly ab initio force and energy evaluation methods, such as density functional theory (DFT). After carefully training a robust ANN for four and five element systems, we obtain nearly identical lithium ion diffusivities for Li10GeP2S12 (LGPS) when benchmarking the ANN-MD results with DFT-MD. We find that the ANN generated potentials scale linearly with atomic system size, compared to cubically in DFT (Figure 1B). To demonstrate the power of the outlined ANN-MD approach we apply it to a doped LGPS system to calculate the effect of concentrations of chlorine on the lithium diffusivity at a resolution that would be unrealistic to model with DFT-MD. We find that there is an optimal chlorine doping concentration which is a result of competing electronic effects of the effective dielectric constant and effective ionic radius of chlorine. Such effects could not be adequately studied with classical potentials. We find that ANN-MD simulations can provide the framework to study systems that require a large number of atoms more efficiently while maintaining high accuracy. Figure 1

The influence of grain size on the hydrogen diffusion in bcc Fe

This work studies the diffusion of Hydrogen (H) in bcc Fe, containing a high-angle symmetric tilt grain boundary (GB), as a function of both the temperature and the average grain size. For this purpose, we propose a microscopic effective model which includes diffusion in bulk and in the GB. The model distinguishes between diffusion along the GB, in parallel with the bulk, while diffusion through the GB is to be considered in series. The bounding and migration energies of the H interstitial sites are derived through an extensive study of H atoms dissolved in a high-angle symmetric tilt GB. This is undertaken in the framework of a set of classical interatomic potentials, and partially from Density Functional Theory (DFT) calculations, in order to check the consistency of equilibrium atomic structures. We find that preferential trapping sites for H in the GB delay the H migration, thus enhancing its solubility. The derived H diffusion coefficients are in agreement with experimental evidence, however various kinds of GBs are present in real samples. In addition, we see that at high temperature, H diffusion does not depend on the grain size, as similar results than in bulk are found. In contrast, at room temperatures (290 K) and nano-sized grains (100 nm) the effective diffusion can slow down up to two orders of magnitude.

Topologically derived dislocation theory for twist and stretch moiré superlattices in bilayer graphene

We develop a continuum dislocation description of twist and stretch moire superlattices in 2D material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moire structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints, and which minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer, and a Peierls-Nabarro like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result of the competition between the two contributions. The approach presented here captures the structure and energetics of twist and stretch moire superlattices of dislocations with arbitrary direction and character, without assuming an analytical solution a priori, with no adjustable parameters, while accounting naturally for dislocation-dislocation image interactions. In comparisons to atomistic simulations using classical potentials, the maximum structure deviation is 6%, while the maximum line energy deviation is 0.019 eV/Angstrom. Several applications of our model are shown, including predicting the variation of structure with twist angle, and describing dislocation line tension and junction energies.

Defects and Calcium Diffusion in Wollastonite

Wollastonite (CaSiO3) is an important mineral that is widely used in ceramics and polymer industries. Defect energetics, diffusion of Ca ions and a solution of dopants are studied using atomistic-scale simulation based on the classical pair potentials. The energetically favourable defect process is calculated to be the Ca-Si anti-site defect cluster in which both Ca and Si swap their atomic positions simultaneously. It is calculated that the Ca ion migrates in the ab plane with an activation energy of 1.59 eV, inferring its slow diffusion. Favourable isovalent dopants on the Ca and Si sites are Sr2+ and Ge4+, respectively. Subvalent doping by Al on the Si site is a favourable process to incorporate additional Ca in the form of interstitials in CaSiO3. This engineering strategy would increase the capacity of this material.

Comparative roles of charge, π, and hydrophobic interactions in sequence-dependent phase separation of intrinsically disordered proteins

Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS) of proteins, we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess roles of electrostatic, hydrophobic, cation-π, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated three different residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation-π interactions consistently accounted for available experimental LLPS data on the wild-type, a charge-scrambled, a phenylalanine-to-alanine (FtoA), and an arginine-to-lysine (RtoK) mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, important LLPS-driving π-related interactions are embodied in classical statistical potentials. Further elucidation is necessary, however, especially of phenylalanine's role in condensate assembly because experiments on FtoA and tyrosine-to-phenylalanine mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than posited by common statistical potentials. Protein-protein electrostatic interactions are modulated by relative permittivity, which in general depends on aqueous protein concentration. Analytical theory suggests that this dependence entails enhanced interprotein interactions in the condensed phase but more favorable protein-solvent interactions in the dilute phase. The opposing trends lead to only a modest overall impact on LLPS.

Equation of state for CO and CO2 fluids and their application on decarbonation reactions at high pressure and temperature

Ab initio molecular dynamics simulations were performed at pressures and temperatures up to 160 GPa and 4000 K, in order to obtain equations of state (EOS) for CO and CO2 fluids. We found that polymerisation of CO and CO2 fluids starts at low pressures, and that including the effect of polymerisation is essential for accurate EOS. EOSs for CO and CO2 determined from methods using experimental data, or classical potentials that ignore the changes in speciation, should be treated with caution when extrapolated beyond the examined pressures and temperatures. The obtained data was fitted to a modified Lee and Kesler EOS for both CO and CO2 fluids. The thermodynamic calculations for the decarbonation reactions of both MgCO3 and CaCO3 using the derived CO2 EOS reproduced the experimental data and theoretical calculations at low pressures. Both MgCO3 and CaCO3 pure phases are found to be stable in the upper mantle compared to CO2. However, they both become destabilised when approaching lower mantle conditions.

Multiscale Modeling of Defect Phenomena in Platinum Using Machine Learning of Force Fields

Computational methodologies have been critical to our understanding of defects at nanometer scales. These methodologies have been dominated by two classes: quantum mechanics (QM)-based methods and semiempirical/classical methods. The former, while accurate and versatile, are time consuming, while the latter are efficient but limited in versatility and transferability. Recently, machine learning (ML) methods have shown initial promise in bridging these two limitations due to their accuracy and flexibility. In this work, the true capability of ML methods is explored by simulating defects in platinum over several length/time scales. We compare our results with density functional theory (DFT) for atomic-level defect behavior and with experiments for nanolevel behavior. We also compare our predictions with several classical potentials. This work aims to showcase the length/time scales attainable using ML, as well as the complexity they are capable of capturing, demonstrating that these methodologies may be effectively used, in the future, to bridge experiments and QM methods.

A fully automated approach to calculate the melting temperature of elemental crystals

The interface method is a well established approach for predicting melting points of materials using interatomic potentials. However, applying the interface method is tedious and involves significant human intervention. The whole procedure involves several successive tasks: estimate a rough melting point, set up the interface structure, run molecular dynamic calculations and analyze the data. Loop calculations are necessary if the predicted melting point is different from the estimated one by more than a certain convergence criterion, or if full melting/solidification occurs. In this case monitoring the solid–liquid phase transition in the interface structure becomes critical. As different initial random seeds for the molecular dynamic simulations within the interface method induce slightly different melting points, a few ten or hundred interface method calculations with different random seeds are necessary for performing a statistical analysis on these melting points. Considering all these technical details, the work load for manually executing and combining the various involved scripts and programs quickly becomes prohibitive. To simplify and automatize the whole procedure, we have implemented the interface method into pyiron (http://pyiron.org). Our fully automatized procedure allows to efficiently and precisely predict melting points of stable unaries represented by arbitrary potentials with only two user-specified parameters (interatomic potential file and element). For metastable or dynamically unstable unary phases, the crystal structure needs to be provided as an additional parameter. We have applied our automatized approach on fcc Al, Ni, dynamically unstable bcc Ti and hcp Mg and employed a large set of available interatomic potentials. Melting points for classical interatomic potentials of these metals have been obtained with a numerical precision well below 1 K.

Differing preferential ion binding to the peptide bond in ionic environment from classical and first principles molecular dynamics simulations

The interactions of ions with N-methylacetamide (NMA) in hydrated ionic liquid (IL), methylammonium formate (MAF), with varying concentrations were studied by molecular dynamics simulations. As the interactions depend on the choice of potential, the current study aims to compare the preferential binding of cation and anion of MAF to peptide bond of NMA utilizing force field-based classical molecular dynamics (CMD) and first principles molecular dynamics (FPMD) simulations. NMA forms a stable hydrogen bonding network with anion. First principles molecular dynamics simulations predict hydrogen bonding interaction with both anion and cation in pure IL. In contrast, the classical molecular dynamics simulations provide evidence of the strong interaction of NMA with anion only. However, NMA interacts with cation in the presence of water as a co-solvent. Water molecules facilitate the more significant cation-anion distance, which decreases the electrostatic interaction between ions. In aqueous solutions, the self-diffusivity of the entities increases as compared to pure IL. The value of residence time rises with an increase in the concentration of IL. The analysis of hydrogen bond auto-correlation function reveals that with increasing IL concentration, the short-range force increases, and simultaneously, the lifetime of intermolecular hydrogen bonds increases. Between NMA-cation and NMA-anion, the strength of the NMA-anion hydrogen bond is stronger than the former. The preferential solvation is due to nature of predefined classical potential as compared to FPMD simulations.

Classical potential for general spinning bodies

In this paper we compute the spin-dependent terms of the gravitational potential for general spinning bodies at the leading Newton’s constant G and to all orders in spin. We utilize the on-shell approach, which extracts the classical potential directly from the scattering amplitude. For spinning particles, extra care is required due to the fact that the spin space of each particle is independent. Once the appropriate matching procedures are applied, taking the classical-spin limit we obtain the potential for general spinning bodies. When the Wilson coefficients are set to unity, we successfully reproduced the potential for the Kerr black hole. Interestingly, for finite spins, we find that the finite-spin deviations from Kerr Wilson coefficients cancel with that in the matching procedure, reproducing the Kerr potential without the need for taking the classical-spin limit. Finally, we find that when cast into the chiral basis, the spin-dependence of minimal coupling exhibits factorization, allowing us to take the classical-spin limit straight forwardly.

On temperature effects on the structural phase transitions of GaP

In this presentation by employing a combination of calculations based on Density Functional Theory (DFT) and Molecular Dynamics simulations (MD), we show that temperature has an unquestionable role in the behavior of Gallium Phosphide under pressure, shedding a new light in the controversial interpretation of experimental results. For example, we justify the absence of some structures predicted by early theoretical works, which remained up to now misunderstood. Moreover, we predict transitions to new structures at high temperature that may encourage new experiments. The differences in the observed transition sequences at low and high temperatures indicate that the vibrational corrections we included in the DFT calculations are fundamental to the description of the stability of higher pressure structures, and may be employed on other materials. Additionally, the good agreement between DFT and MD shows the suitability of the classical effective many-body interaction potential used to describe the different high-pressure phases of GaP in the Molecular Dynamics simulations. Finally, we discuss the behavior of GaP under extreme conditions for temperatures up to 1400 K and pressures up to 50 GPa, predicting new phases.

Comparative study of Minnesota functionals performance on ferroelectric BaTiO3 and PbTiO3

Density-functional-theory-based simulations are the leading tool for the computational investigation of ferroelectrics and the parametrization of their classical potentials. However, the predictions often depend strongly on the exchange-correlation functional. The most popular choices, the LDA and GGA, tend to underestimate or overestimate some structural, electric, and energy properties. These impede the development of highly accurate classical potentials that extend the reach of first-principles simulations to finite temperatures and realistic sizes. In this work, we investigate the performance of recently developed Minnesota exchange-correlation functionals on the prototypical ferroelectrics ${\mathrm{BaTiO}}_{3}$ and ${\mathrm{PbTiO}}_{3}$ in comparison with some popular ones. We find that there exists a strong correlation between predictions for some properties (tetragonality, phase energy difference, and polarization) by different functionals. Along the correlation line, we find a range of functionals (including some from the Minnesota suite) whose predictions fall between those of the LDA and those of the GGA and, therefore, offer an improvement. A way to relatively rank functional performance with respect to chosen benchmarks is proposed and applied to identify the top performers for ${\mathrm{BaTiO}}_{3}$ and ${\mathrm{PbTiO}}_{3}$. The performance is found to be material dependent. Therefore, we propose that the performance assessment carried out in this work is employed to ``screen'' functionals prior to their use on ferroelectrics. Quick and computationally inexpensive, it is likely to lead to improved descriptions, especially for classical potential parametrization. The Minnesota functional suite is found to be suitable for this task.

Thermophysical properties of magnesium arsenide with atomistic simulation methods

A classical interionic potential for the Buckingham potential model was developed for magnesium arsenide (Mg3As2). Potential parameters were fitted to available experimental and first-principles data in the literature. They were implemented in classical molecular dynamics programs, and static properties such as lattice constant, bulk modulus, shear modulus, Young's modulus, elastic constants, Poisson's ratio and anisotropy factor were obtained at 0 K. Lattice constants, linear thermal expansion coefficients, heat capacities, self-diffusion coefficients for each axis, bulk moduli and radial distribution functions were calculated from room temperature up to the melting point. A superionic phase transition was observed. The superionic phase transition and the melting temperature points were found ~1505 K and ~1700 K by two-phase simulation box method, respectively. This method was used for the first time to determine the superionic phase transition temperature. Lattice parameter and bulk modulus were also calculated by the first-principles method. All the calculated data displayed an agreement with the available experimental and first-principles data in the literature. The present parameters of Buckingham potential provide a good description of magnesium arsenide (Mg3As2) crystal.

Numerical exploration of the pitching plate parameter space with application to thrust scaling

The thrust performance of a two-dimensional plate pitching harmonically in a uniform flow is assessed numerically using the OpenFOAM toolbox [1]. The mesh displacement vector associated with the rigid body motion is computed as the solution of a Laplace equation with variable diffusivity, using the appropriate mesh manipulation class of the toolbox. For a Reynolds number of 2000, the accuracy of the pressure and viscous stress distributions is assessed by comparison with reference data available for an equivalent fluid configuration. The efficiency and flexibility of the solver allows exploring large ranges of the pitching parameter space, that is the pitching frequency, amplitude and pivot-point location of the pitching plate. The forces induced by the pitching motion are computed for pitching amplitudes up to 15∘, for Strouhal numbers varying between 0.2 and 0.5 and for different pitch pivot points. Performing a thrust scaling analysis, a classical theoretical model for the swimming of a waving plate is reliably fitted to the numerical pressure force data. The dependence of the time averaged thrust with the pitching axis is shown to be predicted accurately by a classical potential flow formula (known as Garrick’s theory) for pivot points within the front quarter of the plate. The viscous drag is computed as well for the Reynolds number 2000. The time-averaged values are shown to depend on the pitching amplitude and frequency and for instance a Blasius-type scaling, sometimes used to model the viscous drag correction for oscillating two-dimensional foils in this Reynolds number range, is not reliable.

The mass scales of the Higgs field

In the first version of the theory, with a classical scalar potential, the sector inducing SSB was distinct from the Higgs field interactions induced through its gauge and Yukawa couplings. We have adopted a similar perspective but, following most recent lattice simulations, described SSB in [Formula: see text] theory as a weak first-order phase transition. In this case, the resulting effective potential has two mass scales: (i) a lower mass [Formula: see text], defined by its quadratic shape at the minima, and (ii) a larger mass [Formula: see text], defined by the zero-point energy. These refer to different momentum scales in the propagator and are related by [Formula: see text], where [Formula: see text] is the ultraviolet cutoff of the scalar sector. We have checked this two-scale structure with lattice simulations of the propagator and of the susceptibility in the 4D Ising limit of the theory. These indicate that, in a cutoff theory where both [Formula: see text] and [Formula: see text] are finite, by increasing the energy, there could be a transition from a relatively low value, e.g. [Formula: see text] GeV, to a much larger [Formula: see text]. The same lattice data give a final estimate [Formula: see text] GeV which induces to reconsider the experimental situation at Large Hadron Collider (LHC). In particular an independent analysis of the ATLAS[Formula: see text]+[Formula: see text]CMS data indicating an excess in the 4-lepton channel as if there were a new scalar resonance around 700 GeV. Finally, the presence of two vastly different mass scales, requiring an interpolating form for the Higgs field propagator also in loop corrections, could reduce the discrepancy with those precise measurements which still favor large values of the Higgs particle mass.

Second-order post-Minkowskian scattering in arbitrary dimensions

We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional case, in higher dimensions the classical potential receives contributions from box topologies. Moreover, the kinematical relation between momentum and position on the classical trajectory contains a new term which is quadratic in the tree-level amplitude. A precise interplay between this new relation and the formula for the scattering angle ensures that the latter is still linear in the classical part of the scattering amplitude, to this order, matching an earlier calculation in the eikonal approach. We point out that both the eikonal exponentiation and the reality of the potential to 2nd post-Minkowskian order can be seen as a consequence of unitarity. We finally present closed-form expressions for the scattering angle given by leading-order gravitational potentials for dimensions ranging from four to ten.

Bounds for lifespan of solutions to strongly damped semilinear wave equations with logarithmic sources and arbitrary initial energy

<p style='text-indent:20px;'>The main aim of this paper is to deal with the upper and lower bounds for blow-up time of solutions to the following equation: <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{tt}-\Delta u-\Delta u_{t} = |u|^{p-2}u\log|u|, $\end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>which has been studied in [<xref ref-type="bibr" rid="b5">5</xref>]. For high initial energy, it is well known that the classical potential well method is not effective. In order to overcome this difficulty, the authors apply the new energy estimate method to establish the lower bound of the <inline-formula><tex-math id="M1">\begin{document}$ L^{2}(\Omega) $\end{document}</tex-math></inline-formula> norm of the solution. Furthermore, the authors construct a new control functional and combine energy inequalities with the concavity argument to prove that the solution blows up in finite time for high initial energy. Meanwhile, an estimate of the upper bound of blow-up time is also obtained. Finally, a lower bound for blow-up time is obtained by introducing a new control functional. These results fill the gap of [<xref ref-type="bibr" rid="b5">5</xref>].