Classical Interaction Potentials Research Articles

Accuracy, Performance, and Transferability of Interparticle Potentials for Al–Cu Alloys: Comparison of Embedded Atom and Deep Machine Learning Models

In several recent years, a significant progress has been made in atomistic simulation of materials, involving the application of machine learning methods to constructing classical interatomic interaction potentials. These potentials are many-body functions with a large number of variable parameters whose values are optimized with the use of energies and forces calculated for various atomic configurations by ab initio methods. In the present paper a machine learning potential is developed on the basis of deep neural networks (DP) for Al–Cu alloys, and the accuracy and performance of this potential is compared with the embedded atom potential. The analysis of the results obtained implies that the DP provides a sufficiently high accuracy of calculation of the structural, thermodynamic, and transport properties of Al–Cu alloys in both solid and liquid states over the entire range of compositions and a wide temperature interval. The accuracy of the embedded atom model (EAM) in calculating the same properties is noticeably lower on the whole. It is demonstrated that the application of the potentials based on neural networks to the simulation on modern graphic processors allows one to reach a computational efficiency on the same order of magnitude as those of the embedded atom calculations, which at least four orders of magnitude higher than the computational efficiency of ab initio calculations. The most important result is that about the possibility of application of DP parameterized with the use of configurations corresponding to melts and perfect crystals to the simulation of structural defects in crystals and interphase surfaces.

Accurate Calculation of Many-Body Energies in Water Clusters Using a Classical Geometry-Dependent Induction Model.

We incorporate geometry-dependent distributed multipole and polarizability surfaces into an induction model that is used to describe the 3- and 4-body terms of the interaction between water molecules. The moment expansion is carried out up to the hexadecapole with the multipoles distributed on the atom sites. Dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole distributed polarizabilities are used to represent the response of the multipoles to an electric field. We compare the model against two large databases consisting of 43,844 3-body terms and 3,603 4-body terms obtained from high level ab initio calculations previously used to fit the MB-pol and q-AQUA classical interaction potentials for water. The classical induction model with no adjustable parameters reproduces the ab initio 3-/4-body terms contained in these two databases with a root-mean-square error (RMSE) of 0.104/0.058 and a mean-absolute error (MAE) of 0.054/0.026 kcal/mol, respectively. These results are on par with the ones obtained by fitting the same data using over 14,000 (for the 3-body) and 200 (for the 4-body) parameters via Permutationally Invariant Polynomials (PIPs). This demonstrates the accuracy of this physically motivated model in describing the 3- and 4-body terms in the interactions between water molecules with no adjustable parameters. The triple-dipole-dispersion energy, included in the calculation of the 3-body energy, was found to be small but not quite negligible. The model represents a practical, efficient, and transferable approach for obtaining accurate nonadditive interactions for multicomponent systems without the need to perform tens of thousands of high level electronic structure calculations and fitting them with PIPs.

Existence of quasi-static crack evolution for atomistic systems

We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The interaction of the particles is modeled by classical interaction potentials where we implement a suitable irreversibility condition modeling the breaking of atomic bonding. This leads to a delay differential equation depending on the complete history of the deformation at previous times. We prove existence of solutions and provide numerical tests for the prediction of quasi-static crack growth in particle systems.

Fast quasi-centroid molecular dynamics.

We describe a fast implementation of the quasi-centroid molecular dynamics (QCMD) method in which the quasi-centroid potential of mean force is approximated as a separable correction to the classical interaction potential. This correction is obtained by first calculating quasi-centroid radial and angular distribution functions in a short path integral molecular dynamics simulation and then using iterative Boltzmann inversion to obtain an effective classical potential that reproduces these distribution functions in a classical NVT simulation. We illustrate this approach with example applications to the vibrational spectra of gas phase molecules, obtaining excellent agreement with QCMD reference calculations for water and ammonia and good agreement with the quantum mechanical vibrational spectrum of methane.

Topology and complexity of the hydrogen bond network in classical models of water

Over the years, plenty of classical interaction potentials for water have been developed and tested against structural, dynamical and thermodynamic properties. On the other hands, it has been recently observed (F. Martelli et al., ACS Nano, 14, 8616–8623, 2020) that the topology of the hydrogen bond network (HBN) is a very sensitive measure that should be considered when developing new interaction potentials. Here we report a thorough comparison of 11 popular non polarizable classical water models against their HBN, which is at the root of water properties. We probe the topology of the HBN using the ring statistics and we evaluate the quality of the network inspecting the percentage of broken and intact HBs. For each water model, we assess the tendency to develop hexagonal rings (that promote crystallization at low temperatures) and pentagonal rings (known to frustrate against crystallization at low temperatures). We then introduce the network complexity index, a general descriptor to quantify how much the topology of a given network deviates from that of the ground state, namely of hexagonal or cubic ice. Remarkably, we find that the network complexity index allows us to relate, for the first time, the dynamical properties of different water models with their underlying topology of the HBN. Our study provides a benchmark against which the performances of new models should be tested against, and introduces a general way to quantify the complexity of a network which can be transferred to other materials and that links the topology of the HBN with dynamical properties. Finally, our study introduces a new perspective that can help in rationalizing the transformations among the different phases of water and of other materials.

Chemical bond effects in classical site density functional theory of inhomogeneous molecular liquids.

Intra-molecular interactions or chemical bonds represent one of the main distinguishing characteristics of molecular fluids. Development of accurate and practical methods to treat these effects is one of the long standing problems in classical site density functional theory (SDFT). One particular instance when these issues become particularly severe is the case of classical interaction potentials with auxiliary sites or dummy atoms. In this situation, current SDFT implementations, such as the three-dimensional reference interaction site model, lead to nonphysical results. We re-examine this issue in this work using our recent reformulation of SDFT (Valiev and Chuev, J. Stat. Mech.: Theory Exp. 2018, 093201). We put forward a simple practical solution to this problem and illustrate its utility for the case of spherical solutes in diatomic liquids.

Development of interatomic potentials for Fe-Cr-Al alloy with the particle swarm optimization method

Due to its potential application in nuclear cladding system, Fe-Cr-Al alloys have attracted significant interest recently. Thus, it is of importance to acquire the classical interatomic interaction potential in order to predict the mechanical behavior of FeCrAl structures at the microscopic scale. In this work, the particle swarm optimization method has been applied and improved to develop the interatomic potentials for Fe, Cr, Al unitary systems and Fe-Cr, Fe-Al binary systems. The potential parameters are fitted to experimental elastic constants, first principle calculated lattice information and defect formation energies with consideration of force matching. The developed Fe-Cr-Al ternary potentials are used to predict the phase stability region for FeCrAl ferrite alloys. The bulk modulus for the single crystal and the plastic behavior under grain boundary tensile stress are also modeled to find the influence of Cr and Al contents on the mechanical properties of FeCrAl alloys. The solutes Cr would improve the mechanical properties while high Al content would lead to poor elastic and plastic properties. The predictions from the newly developed potential are in good agreement with experimental results.

Comparison of 9 classical interaction potentials of liquid water: Simultaneous Reverse Monte Carlo modeling of X-ray and neutron diffraction results and partial radial distribution functions from computer simulations

Abstract Following preliminary studies on a few interaction potentials and at most two sets of diffraction data of liquid water (L. Pusztai et al., J. Chem. Phys. 129 (2008) 184103; Z. Steinczinger et al., Cond. Matt. Phys. 16 (2013) 43604), here an extended collection of water potentials is considered, along with four experimental total scattering structure factors. The basis of comparing interatomic potentials was the compatibility with results of neutron and X-ray diffraction experiments on pure water, using the scheme applied by Pusztai et al. (2008). The scheme combines experimental total scattering structure factors (TSSF) and partial radial distribution functions (PRDF) from molecular dynamics simulations in a single structural model. Goodness-of-fit values to the O-O, O-H and H-H simulated PRDF-s and to the experimental neutron and X-ray TSSF provided a measure that can characterize the level of consistency between interaction potentials and diffraction experiments. As an addition to classical water potentials, PRDF-s from one ‘ab initio’ molecular dynamics simulation have also been investigated. Out of the sets of partial RDF-s investigated here, the ones corresponding to the BK3 polarizable, and—somewhat surprisingly—to the simple 3-site TIP3P potentials have proven to be the most consistent with various combinations of diffraction results taken for the present study.

Role of nonlinearity in non-Hermitian quantum mechanics: Description of linear quantum electrodynamics from the nonlinear Schrödinger-Poisson equation

In this paper we consider a basic two-level nonlinear quantum model consisting in a two-particle interacting bound-state system. It is described by means of two different approaches: i) the mean-field stationary nonlinear Schrodinger-Poisson equation with classical Coulomb interaction and harmonic potential; ii) the linear quantum electrodynamics Hamiltonian of a quantized field coupled to two fixed charges. Computing numerically the ground state and the first excited state about the maximum eigenstate overlap (which is not zero because of eigenstate non-orthogonality), we numerically demonstrate that these two descriptions coincide at first order. As a consequence, a specific definition of the fine-structure constant \( \alpha\) is provided within 99.95% accuracy by the present first-order non-relativistic and nonlinear quantum description. This result also means that the internal Coulomb interaction commutes with external particle confinement for the calculation of the ground state. Consequently peculiar nonlinear quantum properties become observable (an experiment with GaAs quantum-dot helium is suggested).

Toward an Accurate Modeling of Ionic Liquid–TiO2 Interfaces

Structural properties of the ionic liquids 1-ethyl-3-methylimidazolium thiocyanate and tetracyanoborate at the anatase (101) surface are of crucial interest for energy harvesting and storage devices, but their investigation via molecular dynamics requires large simulation cells. Thus, two classical interaction potentials with and without polarization effects were parametrized in order to accurately model the interface between the liquid and solid. The parameters were fitted to match ab initio reference interaction energies. Application of the generated force field to model the interface is demonstrated. The adsorption profiles of the ionic liquid’s components reveal a very dense surface layer with an excess of cations, which has some possible implications for the use of the ionic liquids as electrolytes, for example in solar cells.

Modeling of structural, energetic, and dynamic properties of few-atom silver clusters embedded in polynucleotide strands by using molecular dynamics.

This work concerns the study of the structural, energetic, and dynamic properties of fluorescent systems composed of silver clusters stabilized by polynucleotide strands. To do so, classical interaction potentials relative to silver, neutral and cationic, were introduced in the AMBER force field. Molecular dynamics simulations allowed analysis of the nature and force of the interactions between the various parts of the nucleic oligomers and the silver clusters. Conformational analyses were necessary to explore the flexibility of the supramolecular assemblies, specifically by radial distribution functions and Ramachandran-type maps.

Role of diffusion in the violation of the long‐wave approximation in line wings

AbstractThe asymptotic line wing theory assumes the presence of two intermolecular interaction characteristics–quantum and classical intermolecular interaction potentials–in the expression of the absorption coefficient. The same classical potential enters into the expression for the second virial coefficient. The classical potential found from the second virial coefficient data is used for calculating of the temperature dependence of the absorption coefficient of water vapor line wings in the 8–12 μm transparency window. To obtain agreement between the calculated and experimental absorption coefficients at this point, it is necessary to refine the expression for the absorption coefficient by abandoning the longwave approximation in line wings. The calculation that meets this condition is performed in the framework of a diffusion model. The time between collisions of certain type giving rise to line wing absorption is estimated. © 2012 Wiley Periodicals, Inc.

Nonharmonic vibrational effects in HgClOH: An MP2 Born–Oppenheimer molecular dynamics study

AbstractWe report a Born–Oppenheimer molecular dynamics study of HgClOH to address the nonharmonic (NH) effects which are important in the development of classical interaction potentials. The electronic structure calculations were performed with the second order Möller–Plesset version of perturbation theory. For the Hg and Cl atoms, the Stuttgart–Dresden relativistic effective core potentials were used with extended‐optimized valence basis, while for O and H the aug‐cc‐pVnZ (n = D,T,Q) basis sets were used. Dynamic effects introduce non‐negligible changes to the equilibrium HgO distance and the ClHgO angle which shows rather large (but still harmonic) variations. The largest NH effects appear for the in‐molecular‐plane HOHg bending and the OH stretching modes. The results for the isolated molecule are relevant to compare the geometrical parameters with the water‐solvated species, both through cluster models or through condensed liquid phase studies. © 2012 Wiley Periodicals, Inc.

Low‐lying energy isomers and global minima of aqueous nanoclusters: Structures and spectroscopic features of the pentagonal dodecahedron (H2O)20 and (H3O)+(H2O)20

AbstractWe rely on a hierarchical approach to identify the low‐lying isomers and corresponding global minima of the pentagonal dodecahedron (H2O)20 and the H3O+(H2O)20 nanoclusters. Initial screening of the isomers is performed using classical interaction potentials, namely the Transferable Interaction 4‐site Potential (TIP4P), the Thole‐Type Flexible Model, versions 2.0 (TTM2‐F) and 2.1 (TTM2.1‐F) for (H2O)20 and the Anisotropic Site Potential (ASP) for H3O+(H2O)20. The nano‐networks obtained with those potentials were subsequently refined at the density functional theory (DFT) with the Becke‐3‐parameter Lee–Yang–Parr (B3LYP) functional and at the second order Møller–Plesset perturbation (MP2) levels of theory. For the pentagonal dodecahedron (H2O)20 it was found that DFT (B3LYP) and MP2 produced the same global minimum. However, this was not the case for the H3O+(H2O)20 cluster, for which MP2 produced a different network for the global minimum when compared to DFT (B3LYP). The low‐lying networks of H3O+(H2O)20 correspond to structures having 9 ‘free’ OH bonds and the hydronium ion on the surface of the nanocluster. The IR spectra of the various networks are further analysed in the OH stretching (‘fingerprint’) region and the various bands are assigned to structural arrangements of the underlying hydrogen bonding network. © 2012 Canadian Society for Chemical Engineering

A refined potential for hydroxylamine clusters and the liquid phase

A detailed study including ab initio calculations and classic Monte-Carlo simulations of hydroxylamine in the gas and liquid phases is presented. A classical interaction potential for hydroxylamine, which includes polarizability, many-body effects, and intramolecular relaxation, was constructed. The results of the simulation were compared to the available experimental data in order to validate the model. We conclude that liquid hydroxylamine has a multitude of hydrogen bonds leading to a large density where the existence of cis conformers and clusters of these conformers is possible. This explains the occurrence of the classical [R. Nast and I. Z. Foppl, Z. Anorg. Allg. Chem. 263, 310 (1950)] scheme for the molecule's decomposition at room temperature and its large exothermicity and instability.

Polarizable interaction potential for molecular dynamics simulations of actinoids(III) in liquid water

In this work, we have developed a polarizable classical interaction potential to study actinoids(III) in liquid water. This potential has the same analytical form as was recently used for lanthanoid(III) hydration [M. Duvail, P. Vitorge, and R. Spezia, J. Chem. Phys. 130, 104501 (2009)]. The hydration structure obtained with this potential is in good agreement with the experimentally measured ion-water distances and coordination numbers for the first half of the actinoid series. In particular, the almost linearly decreasing water-ion distance found experimentally is replicated within the calculations, in agreement with the actinoid contraction behavior. We also studied the hydration of the last part of the series, for which no structural experimental data are available, which allows us to provide some predictive insights on these ions. In particular we found that the ion-water distance decreases almost linearly across the series with a smooth decrease of coordination number from nine to eight at the end.

A powerful computational crystallography method to study ice polymorphism

Classical molecular dynamics (MD) simulations are employed as a tool to investigate structural properties of ice crystals under several temperature and pressure conditions. All ice crystal phases are analyzed by means of a computational protocol based on a clustering approach following standard MD simulations. The MD simulations are performed by using a recently published classical interaction potential for oxygen and hydrogen in bulk water, derived from neutron scattering data, able to successfully describe complex phenomena such as proton hopping and bond formation/breaking. The present study demonstrates the ability of the interaction potential model to well describe most ice structures found in the phase diagram of water and to estimate the relative stability of 16 known phases through a cluster analysis of simulated powder diagrams of polymorphs obtained from MD simulations. The proposed computational protocol is suited for automated crystal structure identification.

Morphological Transformations and Fusion of PbSe Nanocrystals Studied Using Atomistic Simulations

Molecular dynamics simulations are performed on capped and uncapped PbSe nanocrystals, employing newly developed classical interaction potentials. Here, we show that two uncapped nanocrystals fuse efficiently via direct surface attachment, even if they are initially misaligned. In sharp contrast to the general belief, interparticle dipole interactions do not play a significant role in this "oriented attachment" process. Furthermore, it is shown that presumably polar, capped PbSe{111} facets are never fully Pb- or Se-terminated.

Hydration Properties of the Bromide Aqua Ion: the Interplay of First Principle and Classical Molecular Dynamics, and X-ray Absorption Spectroscopy

The hydration properties of the bromide aqua ion have been investigated using state of the art density functional theory (DFT) based molecular dynamics with dispersion-corrected atom-centered pseudopotentials for water and classical molecular dynamics simulations. The reliability of the theoretical results has been assessed by comparing the attained structural results with the extended X-ray absorption fine structure (EXAFS) experimental data. The EXAFS technique is mainly sensitive to short distances around the bromine atom, and it is a direct probe of the local solvation structure. The comparison shows that the DFT simulation delivers a good description of the EXAFS experimental signal, while classical simulation performs poorly. The main reason behind this is the neglect of polarization effects in the classical ion-water interaction potentials. By taking advantage of the reliable information on the Br(-) local hydration structure it has been possible to highlight the contribution of hydrogen atoms to the EXAFS spectra of halide aqueous systems.

Identifying the most stable networks in polyhedral water clusters

We present a new discrete model to identify the most stable networks in polyhedral water clusters. The model relies on the screening of the energy of the local network based on the concept of ‘strong’/‘weak’ nearest neighbor interactions according to their ( trans/ cis) orientation and the connectivity of the respective pairs to neighbors. We apply this model to the pentagonal dodecahedron (H 2O) 20 cluster using a hierarchical description of the intermolecular interactions using classical interaction potentials and several levels of electronic structure methods. This study offers a practical and efficient approach for identifying stable networks in clathrate hydrate structures.