Large Atomic Systems Research Articles

Linear Weak Scalability of Density Functional Theory Calculations without Imposing Electron Localization.

Linear scaling density functional theory (DFT) approaches to the electronic structure of materials are often based on the tendency of electrons to localize in large atomic and molecular systems. However, in many cases of actual interest, such as semiconductor nanocrystals, system sizes can reach a substantial extension before significant electron localization sets in, causing a considerable deviation from linear scaling. Herein, we address this class of systems by developing a massively parallel DFT approach which does not rely on electron localization and is formally quadratic scaling yet enables highly efficient linear wall-time complexity in the weak scalability regime. The method extends from the stochastic DFT approach described in Fabian et al. (WIRES: Comp. Mol. Sci.2019, e1412) but is entirely deterministic. It uses standard quantum chemical atom-centered Gaussian basis sets to represent the electronic wave functions combined with Cartesian real-space grids for some operators and enables a fast solver for the Poisson equation. Our main conclusion is that when a processor-abundant high-performance computing (HPC) infrastructure is available, this type of approach has the potential to allow the study of large systems in regimes where quantum confinement or electron delocalization prevents linear scaling.

(Invited) Machine Learned Deep Neural Networks to Simulate Raman Spectrum of Defective Graphene Systems

Raman spectrum is a common spectroscopic tool used in materials synthesis and characterization. The width and shift of Raman peaks are commonly used in characterization of graphene samples. In this presentation, I will highlight our efforts in using machine learned models to develop an efficient and accurate methodology for simulating accurate spectroscopic signatures in graphene. We are using deep neural networks trained with density functional theory calculations to take advantage of the accuracy of this approach while being able to simulate large atomic systems corresponding to doped graphene layers. We are then able to evaluate the empirical models presently used to assess the defect levels in graphene and compare them to state-of-the-art calculation on such systems.

Hierarchical, rotation-equivariant neural networks to select structural models of protein complexes.

Predicting the structure of multi-protein complexes is a grand challenge in biochemistry, with major implications for basic science and drug discovery. Computational structure prediction methods generally leverage predefined structural features to distinguish accurate structural models from less accurate ones. This raises the question of whether it is possible to learn characteristics of accurate models directly from atomic coordinates of protein complexes, with no prior assumptions. Here we introduce a machine learning method that learns directly from the 3D positions of all atoms to identify accurate models of protein complexes, without using any precomputed physics-inspired or statistical terms. Our neural network architecture combines multiple ingredients that together enable end-to-end learning from molecular structures containing tens of thousands of atoms: a point-based representation of atoms, equivariance with respect to rotation and translation, local convolutions, and hierarchical subsampling operations. When used in combination with previously developed scoring functions, our network substantially improves the identification of accurate structural models among a large set of possible models. Our network can also be used to predict the accuracy of a given structural model in absolute terms. The architecture we present is readily applicable to other tasks involving learning on 3D structures of large atomic systems.

Molecular Hyperdynamics Coupled with the Nonorthogonal Tight-Binding Approach: Implementation and Validation.

We present the molecular hyperdynamics algorithm and its implementation to the nonorthogonal tight-binding model NTBM and the corresponding software. Due to its multiscale structure, the proposed approach provides the long time scale simulations (more than 1 s), unavailable for conventional molecular dynamics. No preliminary information about the system's potential landscape is needed for the use of this technique. The optimal interatomic potential modification is automatically derived from the previous simulation steps. The average time between adjusted potential energy fluctuations provides an accurate evaluation of physical time during the hyperdynamics simulation. The main application of the presented hyperdynamics method is the study of thermal-induced defects arising in the middle-sized or relatively large atomic systems at low temperatures. To validate the presented method, we apply it to the C60 cage and its derivative C60NH2. Hyperdynamics leads to the same results as a conventional molecular dynamics, but the former possesses much higher performance and accuracy due to the wider temperature region. The coefficient of acceleration achieves 107 and more.

Temperature dependence of thermodynamic properties of MoS2 monolayer and single-wall nanotubes: Application of the developed three-body force field

MoS2 nanostructures, especially mono-, multilayer nanothin films as well as single- and multiwall nanotubes are rather interesting popular objects in nanomaterials chemistry. The thermodynamic properties of inorganic nanotubes, and the temperature dependence of their properties can be efficiently investigated by first-principles and molecular mechanics methods in the framework of harmonic approximation. At the same time, only thin single-wall nanotubes are available for the first-principles calculations. The classical mechanics is suitable to simulate very large atomic systems and their phonon frequencies, but developing sufficiently accurate force field is rather tedious work. Herein, we report the force field fitted to the experimental and first-principles data on the structure of 2H- and 3RMoS2 polytypes of bulk crystal, structure of monolayer and several bilayers, vibrational frequencies of 2HMoS2 bulk and monolayer, relative energetic stability of polytypes experimental and first-principles data, elastic constants, strain energy of a (12, 12) MoS2 nanotube. The thermodynamic functions and their temperature dependence for the armchair and zigzag nanotubes are calculated within the formalism of molecular mechanics using elaborated interatomic potential. The results of molecular mechanics and first-principles method application to the thinnest nanotubes are compared.

Breit and QED Effects in Spectra of the 4s2 1S0−4s4p 3P1,1P1 Transitions in the Zn Sequence

The 4s2–4s4p E1 transitions for Zn-like ions from Z in the range 30–92 are calculated using the multiconfi guration Dirac–Hartree–Fock (MCDHF) method. The results obtained are in good agreement with other theoretical and experimental data and demonstrate the applicability of this method to high-precision atomic structure calculations of both few-electron systems and large atomic systems, such as Zn-like ions, along the entire isoelectronic sequence. We also report herein the calculations of many-electron quantum electrodynamic (QED) and Breit effects for the 3P0, 3P1, 3P2, and 1P1 states for all Zn-like ions in the range 30 ≤ Z ≤ 100.

Reinforced dynamics for enhanced sampling in large atomic and molecular systems.

A new approach for efficiently exploring the configuration space and computing the free energy of large atomic and molecular systems is proposed, motivated by an analogy with reinforcement learning. There are two major components in this new approach. Like metadynamics, it allows for an efficient exploration of the configuration space by adding an adaptively computed biasing potential to the original dynamics. Like deep reinforcement learning, this biasing potential is trained on the fly using deep neural networks, with data collected judiciously from the exploration and an uncertainty indicator from the neural network model playing the role of the reward function. Parameterization using neural networks makes it feasible to handle cases with a large set of collective variables. This has the potential advantage that selecting precisely the right set of collective variables has now become less critical for capturing the structural transformations of the system. The method is illustrated by studying the full-atom explicit solvent models of alanine dipeptide and tripeptide, as well as the system of a polyalanine-10 molecule with 20 collective variables.

Modelling radiation effects in solids with two-temperature molecular dynamics

The ability to predict the structural modifications of materials resulting from a broad range of irradiation scenarios would have a positive impact on many fields of science and technology. Established techniques for modelling large atomic systems, such as classical molecular dynamics, are limited by the neglect of the electronic degrees of freedom which restricts their application to irradiation events that primarily interact with atomic nuclei. Ab initio methods, on the other hand, include electronic degrees of freedom, but the requisite computational costs restrict their application to relatively small systems. Recent methodological developments aimed at overcoming some of these limitations are based on methods that couple atomistic models to a continuum model for the electronic energy, where energy is exchanged between the nuclei and electrons via electronic stopping and electron-phonon coupling mechanisms. Such two-temperature molecular dynamics models, as they are known, make it practicable to simulate the effects of electronic excitations on systems with millions, or even hundreds of millions, of atoms. They have been used to study laser irradiation of metallic films, swift heavy ion irradiation of metals and semiconductors, and moderately high ion irradiation of metals.In this review we describe the two-temperature molecular dynamics methodology and the various practical considerations required for its implementation. We provide example applications of the model to multiple irradiation scenarios that accommodate electronic excitations. We also describe the challenges of including the effects of the modification of the interatomic interactions, due to the excitation of electrons, in the simulations and how these challenges can be overcome.

Static force fields simulations of reduced CeO2 (110) surface: Structure and adsorption of H2O molecule

The CeO2(110) surface properties are largely involved in the catalysis, energy and biological phenomenon. The Static Force Fields simulations are able to describe large atomic systems surface even if no information on the electronic structure can be obtained. We employ those simulations to study the formation of the neutral 2CeCe′VO•• cluster. We focus on seven different cluster configurations and find that the defect formation energy is the lower for the 1N-2N configurations. Two geometries are possible, as it is the case for the ab initio studies, the in plane and the more stable bridging one. We evidence the modifications of the surface energy and the Potential Energy Surface due to the presence of the 2CeCe′VO•• defect. The physical adsorption of a water molecule is calculated and the geometry described for all the cluster configurations. The H2O molecule physisorption stabilizes the Ce(110) surface and the presence of the 2CeCe′VO•• defect increases this effect.

A thermally driven differential mutation approach for the structural optimization of large atomic systems.

A computational method is presented which is capable to obtain low lying energy structures of topological amorphous systems. The method merges a differential mutation genetic algorithm with simulated annealing. This is done by incorporating a thermal selection criterion, which makes it possible to reliably obtain low lying minima with just a small population size and is suitable for multimodal structural optimization. The method is tested on the structural optimization of amorphous graphene from unbiased atomic starting configurations. With just a population size of six systems, energetically very low structures are obtained. While each of the structures represents a distinctly different arrangement of the atoms, their properties, such as energy, distribution of rings, radial distribution function, coordination number, and distribution of bond angles, are very similar.

Towards a Universal Embedded Atom Method Interatomic Potential for Pure Metals

A new interatomic potential for metals based on the embedded atom method is proposed in this paper. Some approximation of electron density distribution is suggested from the basic principles of quantum mechanics. The functional form of the electron density distribution includes two adjustable parameters. The form of this distribution defines the pair potential and, in part, the form of embedding energy function. The parameters are determined empirically by fitting to the equilibrium lattice constant, cohesion energy, vacancy formation energy, low index surface energy and elastic constants. Potential parameters for 27 metals (10 fcc metals, 9 bcc metals and 8 hcp metals) are presented. Potential is expressed by simple functions and can be used in molecular dynamics simulations of large atomic systems. PACS: 34.20.Cf, 61.50.Ah

Constrained density functional for noncollinear magnetism

Energies of arbitrary small- and large-angle noncollinear excited magnetic configurations are computed using a highly accurate constrained density functional theory approach. Numerical convergence and accuracy are controlled by the choice of Lagrange multipliers ${\ensuremath{\lambda}}_{I}$ entering the constraining conditions. The penalty part ${E}_{p}$ of the constrained energy functional at its minimum is shown to be inversely proportional to ${\ensuremath{\lambda}}_{I}$, enabling a simple, robust, and accurate iterative procedure to be followed to find a convergent solution. The method is implemented as a part of ab initio vasp package, and applied to the investigation of noncollinear B2-like and $\ensuremath{\langle}001\ensuremath{\rangle}$ double-layer antiferromagnetic configurations of bcc iron, ${\mathrm{Fe}}_{2}$ dimer, and amorphous iron. Forces acting on atoms depend on the orientations of magnetic moments, and the proposed approach enables constrained self-consistent noncollinear magnetic and structural relaxation of large atomic systems to be carried out.

Voxel based parallel post processor for void nucleation and growth analysis of atomistic simulations of material fracture

Molecular dynamics (MD) simulations are used in the study of void nucleation and growth in crystals that are subjected to tensile deformation. These simulations are run for typically several hundred thousand time steps depending on the problem. We output the atom positions at a required frequency for post processing to determine the void nucleation, growth and coalescence due to tensile deformation. The simulation volume is broken up into voxels of size equal to the unit cell size of crystal. In this paper, we present the algorithm to identify the empty unit cells (voids), their connections (void size) and dynamic changes (growth and coalescence of voids) for MD simulations of large atomic systems (multi-million atoms). We discuss the parallel algorithms that were implemented and discuss their relative applicability in terms of their speedup and scalability. We also present the results on scalability of our algorithm when it is incorporated into MD software LAMMPS.

A large-scale relativistic configuration-interaction approach: application to the 4s2–4s4p transition energies and E1 rates for Zn-like ions

Relativistic configuration-interaction calculations of the 4s4p excitation energies and 4s2–4s4p E1 transitions for Zn-like ions from Z = 30 to 92 are shown. B-spline basis functions are used for these large-scale calculations. QED corrections to the excitation energies are also calculated. Results are in good agreement with other theories and with experiment, and demonstrate the utility of this method for high-precision atomic structure calculations not just for few-electron systems but also for large atomic systems such as Zn-like ions along the entire isoelectronic sequence.

First-Principles Molecular Dynamics Simulations of Silicate Melts: Structural and Dynamical Properties

The study of silicate melts from first principles is computationally intensive due to the need of relatively large atomic systems and long simulation runs. Recent advances in hardware and software have made it possible to accurately simulate the liquid phase at pressures and temperatures that are geophysically relevant. This paper reports the details of the methodology used in the context of simulations and subsequent analysis of the output data. The simulations are performed using the parallel first-principles molecular dynamics (FPMD) technique within the framework of density functional theory. Various physical properties including the equation of state, thermodynamics, atomic and electronic structures, self-diffusion and viscosity are obtained from simulations. The position time series are visualized to gain insight into underlying physical mechanisms. We review the recent first-principles studies of three liquids along the MgO-SiO2 join including MgSiO3 melt to show that the structural and dynamical properties of these liquids are highly sensitive to pressure and temperature.

Molecular dynamics study of liquid iron under high pressure and high temperature

Unlike ab initio calculations, classical potentials in molecular dynamics (MD) allow the treatment of very large atomic systems. However, the quality of the potentials has to be carefully assessed, ...

Embedded atom potentials in fcc and bcc metals

A new embedded atom potential has been proposed in this paper. The potential is expressed by simple functions and is applicable to the molecular dynamics simulations of large atomic systems. The potential parameters are determined from the experimental data using the cohesive energy, Born stability, elastic constants, C 11, C 12 and C 44, the formation energy of a vacancy. In case of fcc the stacking fault energy is also used to fit parameters. The potential functions for copper, silver and gold for fcc metals and for bcc metals Nb, Ta and Va are presented.

Interatomic potential for silicon defects and disordered phases

We develop an empirical potential for silicon which represents a considerable improvement over existing models in describing local bonding for bulk defects and disordered phases. The model consists of two- and three-body interactions with theoretically motivated functional forms that capture chemical and physical trends as explained in a companion paper. The numerical parameters in the functional form are obtained by fitting to a set of ab initio results from quantum mechanical calculations based on density functional theory in the local density approximation, which include various bulk phases and defect structures. We test the potential by applying it to the relaxation of point defects, core properties of partial dislocations and the structure of disordered phases, none of which are included in the fitting procedure. For dislocations, our model makes predictions in excellent agreement with ab initio and tight-binding calculations. It is the only potential known to describe both the 30$^\circ$- and 90$^\circ$-partial dislocations in the glide set {111}. The structural and thermodynamic properties of the liquid and amorphous phases are also in good agreement with experimental and ab initio results. Our potential is the first capable of simulating a quench directly from the liquid to the amorphous phase, and the resulting amorphous structure is more realistic than with existing empirical preparation methods. These advances in transferability come with no extra computational cost, since force evaluation with our model is faster than with the popular potential of Stillinger-Weber, thus allowing reliable atomistic simulations of very large atomic systems.

Nonorthogonal tight-binding Hamiltonians for defects and interfaces in silicon

A computationally efficient and physically accurate method is desirable for simulation of solid-state phenomena that must be modeled by large atomic systems. To this end we present a nonorthogonal tight-binding model Hamiltonian based on the extended H\uckel approach. Tests of existing parametrizations of this type of model Hamiltonian on geometries including some low-energy crystal structures, point defects, and surfaces reveal important shortcomings. We develop an improved parametrization and test it extensively on a wide range of crystalline defects and surfaces, and an amorphous sample. Our model is well suited to capture the energetics of crystalline, defective crystalline, and amorphous silicon.

Embedded atom potentials in fcc metals

A new embedded atom potential has been proposed in this paper. The potential is expressed by simple functions and is applicable to the molecular dynamics simulations of large atomic systems. The potential parameters are determined from the experimental data using the cohesive energy, Born stability, elastic constants, C 11 C 12 and C 44, the formation energy of a vacancy and the stacking fault energy. The potential functions for copper, silver and gold are presented.