Interatomic Potential Energy Research Articles

DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models

In recent years, promising deep learning based interatomic potential energy surface (PES) models have been proposed that can potentially allow us to perform molecular dynamics simulations for large scale systems with quantum accuracy. However, making these models truly reliable and practically useful is still a very non-trivial task. A key component in this task is the generation of datasets used in model training. In this paper, we introduce the Deep Potential GENerator (DP-GEN), an open-source software platform that implements the recently proposed ”on-the-fly” learning procedure (Zhang et al. 2019) and is capable of generating uniformly accurate deep learning based PES models in a way that minimizes human intervention and the computational cost for data generation and model training. DP-GEN automatically and iteratively performs three steps: exploration, labeling, and training. It supports various popular packages for these three steps: LAMMPS for exploration, Quantum Espresso, VASP, CP2K, etc. for labeling, and DeePMD-kit for training. It also allows automatic job submission and result collection on different types of machines, such as high performance clusters and cloud machines, and is adaptive to different job management tools, including Slurm, PBS, and LSF. As a concrete example, we illustrate the details of the process for generating a general-purpose PES model for Cu using DP-GEN. Program summaryProgram Title: DP-GENProgram Files doi:http://dx.doi.org/10.17632/sxybkgc5xc.1Licensing provisions: LGPLProgramming language: PythonNature of problem: Generating reliable deep learning based potential energy models with minimal human intervention and computational cost.Solution method: The concurrent learning scheme is implemented. Supports for sampling configuration space with LAMMPS, generating ab initio data with Quantum Espresso, VASP, CP2K and training potential models with DeePMD-kit are provided. Supports for different machines including workstations, high performance clusters and cloud machines are provided. Supports for job management tools including Slurm, PBS, LSF are provided.

Modeling the Stretch Behavior of the Single-Crystal Ni–Al Alloy and Its Molecular Dynamics Simulation

Molecular dynamics simulation was employed in this study to investigate the atomistic mechanisms involved in the Ni–Al alloy homogeneous deformation and the mechanical properties of single-crystal Ni–Al under periodic boundary conditions (until the fracture begins). It is the objective of the present study to develop a simple mathematical model for calculating stress similar to molecular dynamics simulation while the effects of the components of the interatomic potential energy function and the different neighboring atomic shells are also determined on the total stress in the system. The model results show that the sixth nearest neighboring shell has the greatest effect on the stress-strain curve of the Ni–Al single crystal. The associated calculations in the model also show that, in the absence of the pair interaction type of the sixth nearest neighboring shell, the behavior of the material approaches a linear elastic one.

Calculation of scalar nuclear spin-spin coupling in a noble-gas mixture

Indirect spin-spin interactions between nuclei bound in a molecule are well-known in nuclear magnetic resonance, but such interactions between unbound atoms are less well studied and are often assumed to be zero. We present the first precision calculation of this interaction between 129Xe and 3He nuclei in a gas. Relativistic, state-of-the-art electronic structure theory is used to compute the scalar coupling constant J(R) and the interatomic potential energy function, V(R), as functions of the Xe-He internuclear distance R. Using virial expansion we find the nuclear spin enhancement factor kappa = -0.0105 +/- 0.0015 in excellent agreement with recent experiments. This interaction is particularly important for precision measurements using nuclear spin co-magnetometers.

Thermomechanics of Deformations in an Anharmonic Solid Body

The macroscopic laws determining the temperature and deformations of an anharmonic solid body in a given external temperature force field have been stated in the form of the first thermodynamics law supplemented by equations of state of the body. The internal and free energies necessary for it are found from the statistical sum in which some of degrees of freedom determining the body shape are discharged from statistical averaging. These functions of state have been calculated up to the first order of the perturbation theory in the anharmonicity for the microscopic dynamic model of the body with the interatomic interaction potential energy given as a series in powers of atom coordinates. The classical region of high temperatures is considered.

Термомеханика деформаций в ангармоническом твердом теле

AbstractThe macroscopic laws determining the temperature and deformations of an anharmonic solid body in a given external temperature force field have been stated in the form of the first thermodynamics law supplemented by equations of state of the body. The internal and free energies necessary for it are found from the statistical sum in which some of degrees of freedom determining the body shape are discharged from statistical averaging. These functions of state have been calculated up to the first order of the perturbation theory in the anharmonicity for the microscopic dynamic model of the body with the interatomic interaction potential energy given as a series in powers of atom coordinates. The classical region of high temperatures is considered.

Effect of Ca addition on plastic flow in nanocrystalline magnesium by atomistic simulation

Atomistic simulations are used to study the effect of calcium (Ca) addition on plastic flow of nanocrystalline hexagonal close-packed (hcp) magnesium (Mg) under uniaxial tensile deformation. The nanostructure materials are constructed using the Voronoi tessellation method, and the plastic deformation behavior is studied by molecular dynamics simulation. A second nearest neighbor modified embedded atom method (2NN-MEAM) is applied to represent interatomic potential energy. Calcium atoms with different concentration of 0.0–1.3 wt% are randomly distributed in the magnesium nanocrystal with mean grain size of 8.5 nm as substitution atoms. Surprisingly, deformation twinning is not observed in the samples unlike the easy occurrence of twinning in Mg nanocrystal with coarse-grained structure. Structural analysis demonstrated that plastic deformation occurred in the studied Mg-Ca alloys via slip of partial dislocations, nucleation and growth of disordered atom segments (DAS) inside grains. The continuous accumulation of stacking faults induces hcp to fcc (face centered cubic) phase transformation. MD simulation results show that the tensile stress required for partial dislocation nucleation decreases with increasing Ca concentration. The presence of Ca atoms as solid solution in the structure of nanocrystalline Mg-Ca alloy influences the densities of stacking faults and DAS which promotes nucleation of partial dislocations and DAS.

Simulating electronically driven structural changes in silicon with two-temperature molecular dynamics

Radiation can drive the electrons in a material out of thermal equilibrium with the nuclei, producing hot, transient electronic states that modify the interatomic potential energy surface. We present a rigorous formulation of two-temperature molecular dynamics that can accommodate these electronic effects in the form of electronic-temperature-dependent force fields. Such a force field is presented for silicon, which has been constructed to reproduce the ab initio-derived thermodynamics of the diamond phase for electronic temperatures up to 2.5 eV, as well as the structural dynamics observed experimentally under nonequilibrium conditions in the femtosecond regime. This includes nonthermal melting on a subpicosecond timescale to a liquidlike state for electronic temperatures above ∼1 eV. The methods presented in this paper lay a rigorous foundation for the large-scale atomistic modeling of electronically driven structural dynamics with potential applications spanning the entire domain of radiation damage

Molecular simulations of hydrated phyllomanganates

Hydrated phyllomanganates are layered Mn-oxide minerals with interlayers that can possess variable water contents and react strongly with trace metals due to octahedral vacancies in the layer. The unique properties of phyllomanganates afford them a significant role in many environmental phenomena that affect soil and water composition mainly via cation exchange and adsorption of trace metals. Slight variations in the structural and chemical composition often result in a dramatic difference in the chemical reactivity of the minerals. Molecular simulations at the classical mechanical level of theory, which uses a simplified description of the interatomic potential energies, can provide an atomistic perspective of the relationship between the chemical composition and the bulk and interlayer structures. We introduce a set of interatomic potentials for hydrated phyllomanganates with variable vacancy and Mn3+ content and report the classical mechanical simulation results performed at standard temperature and pressure. The potentials we introduce provide not only a reasonable reproduction of the experimentally determined atomic structures of the chalcophanite group, but also new insights on similar phyllomanganate minerals with hexagonal symmetry and a range of vacancy contents. When a vacancy is protonated, Mn3+ is unstable in the hexagonal birnessite layer and occupies the interlayer as a cap on the associated vacancy. When a vacancy was charge-balanced by Mn3+ and Na+, considerable amounts of Mn3+ were incorporated into the hexagonal birnessite layer, but only at total Mn(III) contents greater than ∼10% and with disordered layer stacking. The potentials also predicted a vacancy-free, triclinic Na-birnessite structure with Mn(III)-rich rows in the layer which were arranged parallel to the b-axis and separated by two rows of Mn(IV) octahedra. The dominant interlayer Na complex at a water content ≥0.7 H2O/MnO2 was an octahedrally-coordinated, split interlayer site with two birnessite O atoms in the axial positions and four interlayer H2O in the equatorial positions. Other interlayer Na complexes including some edge- and face-sharing complexes existed in trace amounts (<10%). These classical mechanical simulations represent a successful first test of the introduced interatomic potentials, which can be used to further explore the interlayer and surface complexes of phyllomanganate and birnessite-group minerals.

Crystal structure prediction supported by incomplete experimental data

The prediction of material structure from chemical composition has been a long-standing challenge in natural science. Although there have been various methodological developments and successes with computer simulations, the prediction of crystal structures comprising more than several tens of atoms in the unit cell still remains difficult due to the many degrees of freedom, which increase exponentially with the number of atoms. Here we show that when some experimental data is available, even if it is totally insufficient for conventional structure analysis, it can be utilized to support and substantially accelerate structure simulation. In particular, we formulate a cost function based on a weighted sum of interatomic potential energies and a penalty function referred to as "crystallinity", which is defined using limited X-ray diffraction data. This method is applied to well-known polymorphs of $\rm{SiO_2}$ with up to 96 atoms in the simulation cell to find that it reproduces the correct structures efficiently with a very limited number of diffraction peaks. The penalty function is confirmed to destabilize the local minima of the potential energy surface, which facilitates finding the correct structure. This method opens a new avenue for determining and predicting structures that are difficult to determine by conventional methods, such as surface, interface, glass, and amorphous structures.

DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

Recent developments in many-body potential energy representation via deep learning have brought new hopes to addressing the accuracy-versus-efficiency dilemma in molecular simulations. Here we describe DeePMD-kit, a package written in Python/C++ that has been designed to minimize the effort required to build deep learning based representation of potential energy and force field and to perform molecular dynamics. Potential applications of DeePMD-kit span from finite molecules to extended systems and from metallic systems to chemically bonded systems. DeePMD-kit is interfaced with TensorFlow, one of the most popular deep learning frameworks, making the training process highly automatic and efficient. On the other end, DeePMD-kit is interfaced with high-performance classical molecular dynamics and quantum (path-integral) molecular dynamics packages, i.e., LAMMPS and the i-PI, respectively. Thus, upon training, the potential energy and force field models can be used to perform efficient molecular simulations for different purposes. As an example of the many potential applications of the package, we use DeePMD-kit to learn the interatomic potential energy and forces of a water model using data obtained from density functional theory. We demonstrate that the resulted molecular dynamics model reproduces accurately the structural information contained in the original model. Program summaryProgram Title: DeePMD-kitProgram Files doi:http://dx.doi.org/10.17632/hvfh9yvncf.1Licensing provisions: LGPLProgramming language: Python/C++Nature of problem: Modeling the many-body atomic interactions by deep neural network models. Running molecular dynamics simulations with the models.Solution method: The Deep Potential for Molecular Dynamics (DeePMD) method is implemented based on the deep learning framework TensorFlow. Supports for using a DeePMD model in LAMMPS and i-PI, for classical and quantum (path integral) molecular dynamics are provided.Additional comments including Restrictions and Unusual features: The code defines a data protocol such that the energy, force, and virial calculated by different third-party molecular simulation packages can be easily processed and used as model training data.

Thermodynamically accessible titanium clusters TiN, N = 2-32.

We have performed a genetic algorithm search on the tight-binding interatomic potential energy surface (PES) for small TiN (N = 2-32) clusters. The low energy candidate clusters were further refined using density functional theory (DFT) calculations with the PBEsol exchange-correlation functional and evaluated with the PBEsol0 hybrid functional. The resulting clusters were analysed in terms of their structural features, growth mechanism and surface area. The results suggest a growth mechanism that is based on forming coordination centres by interpenetrating icosahedra, icositetrahedra and Frank-Kasper polyhedra. We identify centres of coordination, which act as centres of bulk nucleation in medium sized clusters and determine the morphological features of the cluster.

Excited interatomic potential energy surfaces of Rb + He that correlate with Rb terms 52S through 72S.

The excited state interatomic potential energy surfaces for Rb + He are computed at the spin-orbit multi-reference configuration interaction level of theory using all-electron basis sets of triple and quadruple-zeta quality that have been contracted for Douglas-Kroll-Hess (DKH) Hamiltonian and includes core-valence correlation. Davidson-Silver corrections (MRCI+Q) are employed to ameliorate size consistency error. An extrapolation of CASSCF energies is performed using the procedure of Karton and Martin whereas extrapolation of correlation energy is performed using an expression involving the inverse powers of (lmax + 1/2), the highest angular momentum value present in the basis set. The spin-orbit energies in the limit of complete basis set are obtained by replacing the energy eigenvalues in the spin-orbit matrix by the relativistic-corrected MRCI+Q energies extrapolated to the complete basis set limit. MRCI diabatic potential energy surfaces for a few selected 2Σ states are calculated to study the general topology and avoided crossings and repulsive form of the 6s 2Σ+ state. Important features of the potential energy surfaces are discussed with implications for alkali laser spectroscopy.

State-of-the-art ab initio potential energy curve for the xenon atom pair and related spectroscopic and thermophysical properties.

A new ab initio interatomic potential energy curve for two ground-state xenon atoms is presented. It is based on supermolecular calculations at the coupled-cluster level with single, double, and perturbative triple excitations [CCSD(T)] employing basis sets up to sextuple-zeta quality, which were developed as part of this work. In addition, corrections were determined for higher coupled-cluster levels up to CCSDTQ as well as for scalar and spin-orbit relativistic effects at the CCSD(T) level. A physically motivated analytical function was fitted to the calculated interaction energies and used to compute the vibrational spectrum of the dimer, the second virial coefficient, and the dilute gas transport properties. The agreement with the best available experimental data for the investigated properties is excellent; the new potential function is superior not only to previous ab initio potentials but also to the most popular empirical ones.

A new determination method of interatomic potential for sodium silicate glass simulations

An interatomic potential for the classical molecular dynamics (MD) simulation of sodium silicate glasses was proposed. The ionic charges for this interatomic potential were determined by Mulliken population analysis via the density functional theory (DFT) calculation of alkali silicate crystals. The SiO interatomic potential energy curve was determined by molecular orbital (MO) calculation of SiO2+. The results of classical MD simulations using the new interatomic potential were consistent with the experimental trends in interatomic distance, thermal expansion coefficient, molar volume, SiOSi bond angle distribution, and Qn ratio with respect to the sodium composition of the silicate glass. The proposed interatomic potential improves the reproducibility of the ring size distribution in silicate glasses compared to conventional potentials.

Water self-diffusivity confined in graphene nanogap using molecular dynamics simulations

Fundamental understanding of water confined in graphene is crucial to optimally design and operate sustainable energy, water desalination, and bio-medical systems. However, the current understanding predominantly remains in the static properties near the graphene surfaces. In this paper, a key water transport property, i.e., self-diffusivity, is examined under confinement by various graphene nanogap sizes (Lz = 0.7–4.17 nm), using molecular dynamics simulations with various graphene-water interatomic potentials (Simple Point Charge (SPC/E) and TIP3P water models). It is found that the water self-diffusivity nearly linearly decreases as the graphene-water interatomic potential energy increases at a given nanogap size. It also decreases as the graphene nanogap size decreases down to Lz = 1.34 nm; however, it shows the peak water self-diffusivity at Lz = 0.8 nm and then continues to decrease. The peak water self-diffusivity is related to the significant change of the overlapping surface force, and associated, nonlinear local water density distribution. The in-plane water self-diffusivity is higher up to nearly an order of magnitude than that of the out-of-plane due to the geometrical confinement effect by the graphene nanogap. The obtained results provide a roadmap to fundamentally understand the water transport properties in the graphene geometries and surface interactions.

State-of-the-art ab initio potential energy curve for the krypton atom pair and thermophysical properties of dilute krypton gas.

A new reference krypton-krypton interatomic potential energy curve was developed by means of quantum-chemical ab initio calculations for 36 interatomic separations. Highly accurate values for the interaction energies at the complete basis set limit were obtained using the coupled-cluster method with single, double, and perturbative triple excitations as well as t-aug-cc-pV5Z and t-aug-cc-pV6Z basis sets including mid-bond functions, with the 6Z basis set being newly constructed for this study. Higher orders of coupled-cluster terms were considered in a successive scheme up to full quadruple excitations. Core-core and core-valence correlation effects were included. Furthermore, relativistic effects were studied not only at a scalar relativistic level using second-order direct perturbation theory, but also utilizing full four-component and Gaunt-effect computations. An analytical pair potential function was fitted to the interaction energies, which is characterized by a depth of 200.88 K with an estimated standard uncertainty of 0.51 K. Thermophysical properties of low-density krypton were calculated for temperatures up to 5000 K. Second and third virial coefficients were obtained from statistical thermodynamics. Viscosity and thermal conductivity as well as the self-diffusion coefficient were computed using the kinetic theory of gases. The theoretical results are compared with experimental data and with results for other pair potential functions from the literature, especially with those calculated from the recently developed ab initio potential of Waldrop et al. [J. Chem. Phys. 142, 204307 (2015)]. Highly accurate experimental viscosity data indicate that both the present ab initio pair potential and the one of Waldrop et al. can be regarded as reference potentials, even though the quantum-chemical methods and basis sets differ. However, the uncertainties of the present potential and of the derived properties are estimated to be considerably lower.

High temperature Raman investigation of few-layer MoTe2

We present a Raman investigation of the temperature effect of single and few layer MoTe2 at an electronic device working temperature range from 300 K to 500 K. We observe linear frequency red-shifts with increasing temperature for the first order Raman active E12g, A1g, Raman inactive B12g mode, and the second order ω2 mode, which can be attributed to the anharmonic effect of the interatomic potential energy. The temperature coefficients of the out-of-plane vibrational B12g modes and inplane vibrational E12g modes are similarly around −0.013 cm−1/K, while lower than that of out-of-plane vibration A1g mode at −0.009 cm−1/K. The temperature coefficient of ω2 mode is −0.00521 cm−1/K, approximately half of those of the first order modes, and the temperature coefficient of transverse acoustic TA (M) mode is indirectly deduced as −0.0102 cm−1/K, which shows the corresponding Mo-Te stretching bonds of TA (M) mode behavior similarly to those of optical Raman vibrations. Our work thus provides temperature dependent lattice vibration information of MoTe2 and could be potentially useful in future optoelectronic devices based on MoTe2 related two dimensional materials.

Work conjugate strain of virial stress

ABSTRACTCertain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the strain tensor. Virial stress is widely accepted as the stress measurement in molecular dynamics (MD). However, its conjugate strain is not yet identified. An atomic logarithmic strain is proposed and numerically verified as the conjugate strain of virial stress at temperature. The strain energy is calculated by virial stress and the proposed atomic logarithmic strain equals to the interatomic potential energy density. This conclusion is numerically verified with (1) Coulomb-Buckingham potential, Lenard-Jones potential, or arbitrary nonlinear pair potential and (2) randomly generated atomic configurations and deformation gradients. Examples are given in determining the stress–strain relation for magnesium oxide with MD simulation. The result shows that the atomic logarithmic strain is identical to engineering strain when deformation is small.

Effect of O2 + O ab initio and Morse additive pairwise potentials on dissociation and relaxation rates for nonequilibrium flow calculations

This work quantifies the sensitivity of O2 + O dissociation rates and relaxation to interatomic potential energy surfaces at high-enthalpy, nonequilibrium flow conditions. State-to-state cross sections are obtained by quasi-classical trajectory (QCT) calculations with two potential surfaces. The first is a Morse additive pairwise potential for O3 that is constructed based on O2(3Σg−) spectroscopic measurements and the second is a double many-body expansion potential by Varandas and Pais [Mol. Phys. 65, 843–860 (1988)]. The QCT calculations of cross sections and rates with the two surfaces are compared to each other and shock tube measurements. It is found that, at temperatures between 2500 K and 20 000 K, the equilibrium dissociation rates predicted by the two potentials agree within 12%, and they are bound by experimental dissociation measurements. In contrast, above 10 000 K, ab initio based equilibrium dissociation rates are about a factor of two higher than the widely used Park’s model. The nonequilibrium dissociation rates calculated by the two potentials are within 70% while phenomenological models differ by two orders of magnitude for vibrationally cold conditions of shocks. The analyses provide an approach for improving accuracy of nonequilibrium high-enthalpy flow modeling when ab initio potentials are not available.

An atomic finite element model for biodegradable polymers. Part 1. Formulation of the finite elements

Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young׳s modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide).