Dynamics Simulations Of Large Systems Research Articles

A stochastic Schrödinger equation and matrix product state approach to carrier transport in organic semiconductors with nonlocal electron-phonon interaction.

Evaluation of the charge transport property of organic semiconductors requires exact quantum dynamics simulation of large systems. We present a numerically nearly exact approach to investigate carrier transport dynamics in organic semiconductors by extending the non-Markovian stochastic Schrödinger equation with complex frequency modes to a forward-backward scheme and by solving it using the matrix product state (MPS) approach. By utilizing the forward-backward formalism for noise generation, the bath correlation function can be effectively treated as a temperature-independent imaginary part, enabling a more accurate decomposition with fewer complex frequency modes. Using this approach, we study the carrier transport and mobility in the one-dimensional Peierls model, where the nonlocal electron-phonon interaction is taken into account. The reliability of this approach was validated by comparing carrier diffusion motion with those obtained from the hierarchical equations of motion method across various parameter regimes of the phonon bath. The efficiency was demonstrated by the modest virtual bond dimensions of MPS and the low scaling of the computational time with the system size.

Accelerated molecular dynamics simulation of large systems with parallel collective variable-driven hyperdynamics

The limitation in time and length scale is a major issue of molecular dynamics (MD) simulation. Although several methods have been developed to extend the MD time scale, their performance usually deteriorates with increasing system size. Therefore, an acceleration method which is applicable to large systems is required to bridge the gap between the MD simulations and target phenomena. In this study, an accelerated MD method for large system is developed based on the collective variable-driven hyperdynamics (CVHD) method [K.M. Bal and E.C. Neyts, 2015]. The key idea is to run CVHD in parallel with rate control and accelerate multiple possible events simultaneously. Using this novel method, carbon diffusion in bcc-iron bicrystal with grain boundary is examined as an application for practical materials. Carbon atoms reaching at the grain boundary are trapped whereas carbon atoms in the bulk region diffuse randomly, and both dynamic regimes can be simultaneously accelerated with the parallel CVHD technique.

Combining enhanced sampling with experiment-directed simulation of the GYG peptide

Experiment-directed simulation (EDS) is a technique to minimally bias molecular dynamics simulations to match experimentally observed results. The method improves accuracy but does not address the sampling problem of molecular dynamics simulations of large systems. This work combines EDS with both the parallel-tempering or parallel-tempering well-tempered ensemble replica-exchange methods to enhance sampling. These methods are demonstrated on the GYG tripeptide in explicit water. The collective variables biased by EDS are chemical shifts, where the set-points are determined by NMR experiments. The results show that it is possible to enhance sampling with either parallel-tempering and parallel-tempering well-tempered ensemble in the EDS method. This combination of methods provides a novel approach for both accurately and exhaustively simulating biological systems.

Physics-based potentials for the coupling between backbone- and side-chain-local conformational states in the UNited RESidue (UNRES) force field for protein simulations.

The UNited RESidue (UNRES) model of polypeptide chains is a coarse-grained model in which each amino-acid residue is reduced to two interaction sites, namely, a united peptide group (p) located halfway between the two neighboring α-carbon atoms (Cαs), which serve only as geometrical points, and a united side chain (SC) attached to the respective Cα. Owing to this simplification, millisecond molecular dynamics simulations of large systems can be performed. While UNRES predicts overall folds well, it reproduces the details of local chain conformation with lower accuracy. Recently, we implemented new knowledge-based torsional potentials (Krupa et al. J. Chem. Theory Comput. 2013, 9, 4620–4632) that depend on the virtual-bond dihedral angles involving side chains: Cα···Cα···Cα···SC (τ(1)), SC···Cα···Cα···Cα (τ(2)), and SC···Cα···Cα···SC (τ(3)) in the UNRES force field. These potentials resulted in significant improvement of the simulated structures, especially in the loop regions. In this work, we introduce the physics-based counterparts of these potentials, which we derived from the all-atom energy surfaces of terminally blocked amino-acid residues by Boltzmann integration over the angles λ(1) and λ(2) for rotation about the Cα···Cα virtual-bond angles and over the side-chain angles χ. The energy surfaces were, in turn, calculated by using the semiempirical AM1 method of molecular quantum mechanics. Entropy contribution was evaluated with use of the harmonic approximation from Hessian matrices. One-dimensional Fourier series in the respective virtual-bond-dihedral angles were fitted to the calculated potentials, and these expressions have been implemented in the UNRES force field. Basic calibration of the UNRES force field with the new potentials was carried out with eight training proteins, by selecting the optimal weight of the new energy terms and reducing the weight of the regular torsional terms. The force field was subsequently benchmarked with a set of 22 proteins not used in the calibration. The new potentials result in a decrease of the root-mean-square deviation of the average conformation from the respective experimental structure by 0.86 Å on average; however, improvement of up to 5 Å was observed for some proteins.

Combinedab initioand classical potential simulation study on silicon carbide precipitation in silicon

Atomistic simulations on the silicon carbide precipitation in bulk silicon employing both, classical potential and first-principles methods are presented. The calculations aim at a comprehensive, microscopic understanding of the precipitation mechanism in the context of controversial discussions in the literature. For the quantum-mechanical treatment, basic processes assumed in the precipitation process are calculated in feasible systems of small size. The migration mechanism of a carbon $\ensuremath{\langle}1\phantom{\rule{0.16em}{0ex}}0\phantom{\rule{0.16em}{0ex}}0\ensuremath{\rangle}$ interstitial and silicon $\ensuremath{\langle}11\phantom{\rule{0.16em}{0ex}}0\ensuremath{\rangle}$ self-interstitial in otherwise defect-free silicon are investigated using density functional theory calculations. The influence of a nearby vacancy, another carbon interstitial and a substitutional defect as well as a silicon self-interstitial has been investigated systematically. Interactions of various combinations of defects have been characterized including a couple of selected migration pathways within these configurations. Most of the investigated pairs of defects tend to agglomerate allowing for a reduction in strain. The formation of structures involving strong carbon--carbon bonds turns out to be very unlikely. In contrast, substitutional carbon occurs in all probability. A long range capture radius has been observed for pairs of interstitial carbon as well as interstitial carbon and vacancies. A rather small capture radius is predicted for substitutional carbon and silicon self-interstitials. Initial assumptions regarding the precipitation mechanism of silicon carbide in bulk silicon are established and conformability to experimental findings is discussed. Furthermore, results of the accurate first-principles calculations on defects and carbon diffusion in silicon are compared to results of classical potential simulations revealing significant limitations of the latter method. An approach to work around this problem is proposed. Finally, results of the classical potential molecular dynamics simulations of large systems are examined, which reinforce previous assumptions and give further insight into basic processes involved in the silicon carbide transition.

Atom-centered symmetry functions for constructing high-dimensional neural network potentials

Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calculations, and thus enable molecular dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the atomic positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as molecules, crystalline and amorphous solids, and liquids.

Structure and melting of two-dimensional dust crystals

Dust particles in plasmas confined near the boundary between the plasma bulk and the sheath form a two-dimensional system when appropriate conditions are satisfied. To keep dust particles from running away horizontally, the electrostatic potential is usually applied to the electrode surrounding these dusty plasmas and we have finite two-dimensional systems of dust particles. Adopting the Yukawa model for the interaction between dust particles, structures of finite two-dimensional Yukawa systems at low temperatures have been analyzed both by molecular dynamics simulations and variational methods. The effect of the correlation energy between dust particles is shown to play an important role in the formation of the one-body distribution in these systems. Molecular dynamics simulations of large systems typically with 103 to 104 particles have been performed and the behavior of the mean square displacement is obtained for various combinations of characteristic parameters. The results are discussed in relation to the melting transition on the basis of the theoretical analysis on static structures.

Block bond-order potential as a convergent moments-based method

The theory of a bond-order potential, which is based on the block Lanczos algorithm, is presented within an orthogonal tight-binding representation. The block scheme handles automatically the very different character of $\ensuremath{\sigma}$ and $\ensuremath{\pi}$ bonds by introducing block elements, which produces rapid convergence of the energies and forces within insulators, semiconductors, metals, and molecules. The method gives the first convergent results for vacancies in semiconductors using a moments-based method with a low number of moments. Our use of the Lanczos basis simplifies the calculations of the band energy and forces, which allows the application of the method to the molecular dynamics simulations of large systems. As an illustration of this convergent $\mathrm{O}(N)$ method we apply the block bond-order potential to the large-scale simulation of the deformation of a carbon nanotube.

An Algorithm with Logarithmic Time Complexity for Interactive Simulation of Hierarchically Articulated Bodies Using a Distributed-memory Architecture

The dynamic simulation of large systems of hierarchically articulated bodies is very time-consuming and cannot be done in real time using current one-processor workstations. This paper discusses the parallelization of dynamic simulation algorithms for such systems. First, the methods used in computer animation for solving initial-value problems are compared. Using test suites based on articulated bodies, the Gear method for non-stiff problems is identified as the solver with the least right-hand-side evaluations of the differential equations for the executed tests. On the basis of this method and the articulated-body method, a ‘simulation engine’ for distributed-memory architectures is presented. By reimplementing the Gear method and rearranging its parts, logarithmic time complexity is achieved for hierarchically articulated bodies. By using the simulation engine, interactive, physically based animation of large articulated figures is possible.

Dispersion curves from short-time molecular dynamics simulations. 1. Diatomic chain results

The multiple signal classification method (MUSIC) for frequency estimation is used to compute the frequency dispersion curves of a diatomic chain from the time-dependent structure factor. In this paper, the authors demonstrate that MUSIC can accurately determine the frequencies from very short time trajectories. MUSIC is also used to show how the frequencies can vary in time, i.e., along a trajectory. The method is ideally suited for analyzing molecular dynamics simulations of large systems.