A variational path integral molecular dynamics study of a solid helium-4

In the present study, a variational path integral molecular dynamics method developed by the author [Chem. Phys. Lett. 482 (2009) 165] is applied to a solid helium-4 in the ground state. The method is a molecular dynamics algorithm for a variational path integral method which can be used to generate the exact ground state numerically. The solid state is shown to successfully be realized by the method, although a poor trial wavefunction that cannot describe the solid state is used.     

Towards Reduced Basis Approaches in ab initio Electronic Structure Computations

Due to the high dimensionality of the spaces where the problems are set, adapted discretization basis are often advocated in complex physical problems (Navier–Stokes equations, solid mecanics, ab initio electronic structure computations) to express the solution in terms of solution of similar (but easier to solve) problems. However, very few mathematical studies have been undertaken to asses the numerical properties of these approximations. Within this context, we will present in this paper an overview of the tools required to develop more rigorous reduced basis approaches for quantum chemistry: a posteriori numerical analysis and fast exponential decay of the n-width of the solution set.     

Fluctuations in molecular dynamics simulations

Statistical fluctuations of a system about its equilibrium state, monitored in a molecular dynamics simulation, are an effective means of computing the thermodynamic and kinetic properties of interfaces in metals and alloys. In this work, three applications of fluctuation analyses are reviewed. First, the capillary fluctuation method can be used to extract the stiffness of grain boundaries, as well as the solid–liquid interfacial free energy and its small anisotropy. Second, both a random walk analysis and a computation of a time correlation function involving the Fourier amplitudes of the interface height can be utilized to derive the mobility of grain boundaries and crystal–melt interfaces. Finally, the probability distribution of premelted grain boundary widths as a function of undercooling can be used to obtain the so-called disjoining potential, which is the thermodynamic driving force responsible for premelting.     

Phonon dispersion measured directly from molecular dynamics simulations

A method to measure the phonon dispersion of a crystal based on molecular dynamics simulation is proposed and implemented as an extension to an open source classical molecular dynamics simulation code LAMMPS. In the proposed method, the dynamical matrix is constructed by observing the displacements of atoms during molecular dynamics simulation, making use of the fluctuation–dissipation theory. The dynamical matrix can then be employed to compute the phonon spectra by evaluating its eigenvalues. It is found that the proposed method is capable of yielding the phonon dispersion accurately, while taking into account the anharmonic effect on phonons simultaneously. The implementation is done in the style of fix of LAMMPS, which is designed to run in parallel and to exploit the functions provided by LAMMPS; the measured dynamical matrices could be passed to an auxiliary postprocessing code to evaluate the phonons.

Program summary

Program title: FixPhonon, version 1.0Catalogue identifier: AEJB_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJB_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: GNU General Public licenseNo. of lines in distributed program, including test data, etc.: 105 393No. of bytes in distributed program, including test data, etc.: 3 231 800Distribution format: tar.gzProgramming language: C++Computer: AllOperating system: LinuxHas the code been vectorized or parallelized?: Yes. 1 to N processors may be usedRAM: Depends on problem, ≈1 kB to several MBClassification: 7.8External routines: MPI, FFT, LAMMPS version 15, January 2010 (http://lammps.sandia.gov/)Nature of problem: Atoms in solids make ceaseless vibrations about their equilibrium positions, and a collective vibration forms a wave of allowed wavelength and amplitude. The quantum of such lattice vibration is called the phonon, and the so-called “lattice dynamics” is the field of study to find the normal modes of these vibrations. In other words, lattice dynamics examines the relationship between the frequencies of phonons and the wave vectors, i.e., the phonon dispersion. The evaluation of the phonon dispersion requires the construction of the dynamical matrix. In atomic scale modeling, the dynamical matrices are usually constructed by deriving the derivatives of the force field employed, which cannot account for the effect of temperature on phonons, with an exception of the tedious “quasi-harmonic” procedure.Solution method: We propose here a method to construct the dynamical matrix directly from molecular dynamics simulations, simply by observing the displacements of atoms in the system thus making the constructing of the dynamical matrix a straightforward task. Moreover, the anharmonic effect was taken into account in molecular dynamics simulations naturally, the resultant phonons therefore reflect the finite temperature effect simultaneously.Restrictions: A well defined lattice is necessary to employ the proposed method as well as the implemented code to evaluate the phonon dispersion. In other words, the system under study should be in solid state where atoms vibrate about their equilibrium positions. Besides, no drifting of the lattice is expected. The method is best suited for periodic systems, although non-periodic system with a supercell approach is also possible, it will however become inefficient when the unit cell contains too many atoms.Additional comments: The readers are encouraged to visit http://code.google.com/p/fix-phonon for subsequent update of the code as well as the associated postprocessing code, so as to keep up with the latest version of LAMMPS.Running time: Running time depends on the system size, the numbers of processors used, and the complexity of the force field, like a typical molecular dynamics simulation. For the third example shown in this paper, it took about 2.5 hours on an Intel Xeon X3220 architecture (2.4G, quadcore).References:

• [1] 

  C. Campañá, M.H. Müser, Phys. Rev. B 74 (2006) 075420.

• [2] 

  L.T. Kong, G. Bartels, C. Campañá, C. Denniston, M.H. Müser, Comp. Phys. Commun. 180 (6) (2009) 1004–1010.

     

Generation of random non-overlapping dot patterns for light guides using molecular dynamics simulations with variable r-cut and reflective boundary techniques

This paper presents a molecular dynamics (MD) scheme for the automatic generation of dot patterns for the light guides used in LCD backlight modules. Several MD computational techniques are integrated with the conventional MD scheme to enable the adjustment of the dot density in specific regions of the light guide in order to create a dot distribution with a high dot density variation and a high spatial uniformity. These techniques include the cell division technique, the variable r-cut technique, the boundary smoothing technique and the reflective boundary condition. The reflective boundary condition enables a precise control of the dot density within each cell, and is instrumental in achieving a dot distribution with both a high dot density variation and a high spatial uniformity. The performance of the proposed dot generation scheme is verified by considering the practical example of the dot pattern design of a light guide with a single LED light source located in the lower-right corner. The numerical results confirm the ability of the proposed method to achieve an even luminance condition by establishing a dot pattern whose density increases concentrically with an increasing distance from the light source.     

A parallel multigrid accelerated Poisson solver for ab initio molecular dynamics applications

In this paper we present an application for a parallel multigrid solver in 3D to solve the Coulomb problem for the charge self interaction in a quantum-chemical program used to perform ab initio molecular dynamics. Techniques such as Mehrstellendiscretization and τ-extrapolation are used to improve the discretization error. The results show that the expected convergence rates and parallel performance of the multigrid solver are achieved. Within the applied Carr–Parrinello Molecular Dynamics scheme the quality of the solution also determines the accuracy in energy conservation. All forms of discretization employed lead to energy conserving dynamics. In order to test the applicability of our code to larger systems in a massively parallel environment, we investigated a 256 atom periodic supercell of bulk gallium nitride.     

Accelerating molecular dynamics simulations using Graphics Processing Units with CUDA

Molecular dynamics is an important computational tool to simulate and understand biochemical processes at the atomic level. However, accurate simulation of processes such as protein folding requires a large number of both atoms and time steps. This in turn leads to huge runtime requirements. Hence, finding fast solutions is of highest importance to research. In this paper we present a new approach to accelerate molecular dynamics simulations with inexpensive commodity graphics hardware. To derive an efficient mapping onto this type of computer architecture, we have used the new Compute Unified Device Architecture programming interface to implement a new parallel algorithm. Our experimental results show that the graphics card based approach allows speedups of up to factor nineteen compared to the corresponding sequential implementation.     

Hardware accelerator for molecular dynamics: MDGRAPE-2

We developed MDGRAPE-2, a hardware accelerator that calculates forces at high speed in molecular dynamics (MD) simulations. MDGRAPE-2 is connected to a PC or a workstation as an extension board. The sustained performance of one MDGRAPE-2 board is 15 Gflops, roughly equivalent to the peak performance of the fastest supercomputer processing element. One board is able to calculate all forces between 10 000 particles in 0.28 s (i.e. 310000 time steps per day). If 16 boards are connected to one computer and operated in parallel, this calculation speed becomes ∼10 times faster. In addition to MD, MDGRAPE-2 can be applied to gravitational N-body simulations, the vortex method and smoothed particle hydrodynamics in computational fluid dynamics.     

Explicit design of FPGA-based coprocessors for short-range force computations in molecular dynamics simulations

FPGA-based acceleration of molecular dynamics simulations (MD) has been the subject of several recent studies. The short-range force computation, which dominates the execution time, is the primary focus. Here we combine: a high level of FPGA-specific design including cell-lists, systematically determined interpolation and precision, handling of exclusion, and support for MD simulations of up to 256 K particles. The target system consists of a standard PC with a 2004-era COTS FPGA board. There are several innovations: new microarchitectures for several major components, including the cell-list processor and the off-chip memory controller; and a novel arithmetic mode. Extensive experimentation was required to optimize precision, interpolation order, interpolation mode, table sizes, and simulation quality. We obtain a substantial speed-up over a highly tuned production MD code.     

MDWiZ: A platform for the automated translation of molecular dynamics simulations

A variety of popular molecular dynamics (MD) simulation packages were independently developed in the last decades to reach diverse scientific goals. However, such non-coordinated development of software, force fields, and analysis tools for molecular simulations gave rise to an array of software formats and arbitrary conventions for routine preparation and analysis of simulation input and output data. Different formats and/or parameter definitions are used at each stage of the modeling process despite largely contain redundant information between alternative software tools. Such Babel of languages that cannot be easily and univocally translated one into another poses one of the major technical obstacles to the preparation, translation, and comparison of molecular simulation data that users face on a daily basis. Here, we present the MDWiZ platform, a freely accessed online portal designed to aid the fast and reliable preparation and conversion of file formats that allows researchers to reproduce or generate data from MD simulations using different setups, including force fields and models with different underlying potential forms. The general structure of MDWiZ is presented, the features of version 1.0 are detailed, and an extensive validation based on GROMACS to LAMMPS conversion is presented. We believe that MDWiZ will be largely useful to the molecular dynamics community. Such fast format and force field exchange for a given system allows tailoring the chosen system to a given computer platform and/or taking advantage of a specific capabilities offered by different software engines.     

A parallel algorithm for molecular dynamics simulation of branched molecules

To get an insight into the effects of molecular architecture in the behaviour of thin lubricant films we have devised an algorithm for simulation of branched molecules. We have used this algorithm successfully to simulate branched isomers of C₃₀. However the algorithm is flexible enough to be used for the simulation of more complex branched molecules. The resulting algorithm can be used in molecular dynamics simulation of branched molecules and could be helpful in designing new materials at the molecular level.     

Nanosecond molecular dynamics simulations of Cdc25B and its complex with a 1,4-naphthoquinone inhibitor: implications for rational inhibitor design

Cdc25 phosphatases have been considered as attractive drug targets for anticancer therapies due to the correlation of their overexpression with a wide variety of cancers. To gain insight into designing new potent inhibitors, we investigate the dynamic properties of Cdc25B and its complex with a 1,4-naphtoquinone inhibitor NSC 95397 by means of molecular dynamics simulations in aqueous solution. It is shown from the calculated dynamic properties that the malleability of the residues 530–532 residing at the start of C-terminal region around the active site should be responsible for the catalytic action of Cdc25B. However, binding of the inhibitor in the active site leads to a substantial decrease in the motional amplitude of the flexible residues, due to the hydrophobic interactions with the side chain of Met531. The simulation results also indicate that at least four hydrogen bonds are involved in the enzyme-inhibitor complex. Among them, the hydrogen bond between the side chain carboxylate group of Glu478 and one of the hydroxyl groups of the inhibitor is found to be the most significant binding force stabilizing the inhibitor in the active site. This result supports the previous experimental implication that the possession of a single hydroxyl group is sufficient for the inhibitory activity of 1,4-naphthoquinone inhibitors.     

A web-deployed interface for performing ab initio molecular dynamics, optimization, and electronic structure in Fireball

Fireball is an ab initio technique for fast local orbital simulations of nanotechnological, solid state, and biological systems. We have implemented a convenient interface for new users and software architects in the platform-independent Java language to access Fireball's unique and powerful capabilities. The graphical user interface can be run directly from a web server or from within a larger framework such as the Computational Science and Engineering Online (CSE-Online) environment or the Distributed Analysis of Neutron Scattering Experiments (DANSE) framework. We demonstrate its use for high-throughput electronic structure calculations and a multi-100 atom quantum molecular dynamics (MD) simulation.

Program summary

Program title: FireballUICatalogue identifier: AECF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECF_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 279 784No. of bytes in distributed program, including test data, etc.: 12 836 145Distribution format: tar.gzProgramming language: JavaComputer: PC and workstationOperating system: The GUI will run under Windows, Mac and Linux. Executables for Mac and Linux are included in the package.RAM: 512 MBWord size: 32 or 64 bitsClassification: 4.14Nature of problem: The set up and running of many simulations (all of the same type), from the command line, is a slow process. But most research quality codes, including the ab initio tight-binding code FIREBALL, are designed to run from the command line. The desire is to have a method for quickly and efficiently setting up and running a host of simulations.Solution method: We have created a graphical user interface for use with the FIREBALL code. Once the user has created the files containing the atomic coordinates for each system that they are going to run a simulation on, the user can set up and start the computations of up to hundreds of simulations.Running time: 3 to 5 minutes on a 2 GHz Pentium IV processor.     

Carbon nanotube structures: molecular dynamics simulation at realistic limit

Single walled carbon nanotubes as all-carbon molecules of tubular form exemplify modern nanometre scale material structures, where the number of atoms range from less than a million up to few millions. Such system are quite ideal for computational studies like Molecular Dynamics simulations because the studies can be done at the realistic limit, rendering them in a way predictive. This point of view we try to explore through simulations of novel ring-like carbon nanotubes, observed experimentally. Whether these structures are toroidal or coiled is under debate. To this question we seek insight by studying the structure, the minimum energy configuration, and the thermal stability of large toroidal nanotubes of (n,n)- and (n,0)-helicity using large scale Molecular Dynamics simulations based on the interaction potential by Brenner. The system sizes of the studied tori range one and half orders of magnitude, in diameter from about 22 nm up to 700 nm, where the latter corresponds to the sizes of experimentally observed ring-like structures. Our simulations indicate that the toroidal form influences strongly the structure of the tubes for small tori while for the larger tori the structural changes are extremely small. We also find that there exists a critical tube radius dependent buckling radius at which the torus buckles. This was also found to be helicity dependent.     

MDMC: A molecular dynamics code for investigating the fragmentation dynamics of multiply charged clusters

MDMC² is a parallel code for performing molecular dynamics simulations on multiply charged clusters. It is a valuable complement to MCMC², a Monte Carlo program devoted to Monte Carlo simulations of multiply charged clusters in the NVT$NVT$ ensemble (Bonhommeau and Gaigeot, 2013). Both MCMC² and MDMC² codes employ a mesoscopic coarse-grained simplified representation of the clusters (or droplets): these clusters are composed of neutral and charged spherical particles/grains that may be polarisable. One grain can be either neutral or charged. The interaction potential is a sum of 2-body Lennard-Jones potentials (main cohesive contribution) and electrostatic terms (repulsive contribution), possibly supplemented by N$N$-body polarisation interactions. There is no restriction imposed on the values of the particle charges and/or polarisabilities. An external field can also be applied to the whole system. The derivatives of the potential energy-surface are determined analytically which ensures an accurate integration of classical equations of motion by a velocity Verlet algorithm. Conservation rules, such as energy conservation or centre-of-mass linear momentum conservation, can be steadily checked during the simulation. The program also provides some statistical information on the run and configuration files that can be used for data post-treatment. MDMC² is provided with a serial conjugate gradient program, called CGMC², that uses the same analytical derivatives as MDMC² and was found useful to probe the minima of the energy landscape explored during Monte Carlo or molecular dynamics simulations performed on multiply charged clusters.     

Exploiting hierarchy parallelism for molecular dynamics on a petascale heterogeneous system

Heterogeneous systems with nodes containing more than one type of computation units, e.g., central processing units (CPUs) and graphics processing units (GPUs), are becoming popular because of their low cost and high performance. In this paper, we have developed a Three-Level Parallelization Scheme (TLPS) for molecular dynamics (MD) simulation on heterogeneous systems. The scheme exploits multi-level parallelism combining (1) inter-node parallelism using spatial decomposition via message passing, (2) intra-node parallelism using spatial decomposition via dynamically scheduled multi-threading, and (3) intra-chip parallelism using multi-threading and short vector extension in CPUs, and employing multiple CUDA threads in GPUs. By using a hierarchy of parallelism with optimizations such as communication hiding intra-node, and memory optimizations in both CPUs and GPUs, we have implemented and evaluated a MD simulation on a petascale heterogeneous supercomputer TH-1A. The results show that MD simulations can be efficiently parallelized with our TLPS scheme and can benefit from the optimizations.     

Effect of allosteric molecules on structure and drug affinity of HIV-1 protease by molecular dynamics simulations

Recent experiments show that small molecules can bind onto the allosteric sites of HIV-1 protease (PR), which provides a starting point for developing allosteric inhibitors. However, the knowledge of the effect of such binding on the structural dynamics and binding free energy of the active site inhibitor and PR is still lacking. Here, we report 200 ns long molecular dynamics simulation results to gain insight into the influences of two allosteric molecules (1H-indole-6-carboxylic acid, 1F1 and 2-methylcyclohexano, 4D9). The simulations demonstrate that both allosteric molecules change the PR conformation and stabilize the structures of PR and the inhibitor; the residues of the flaps are sensitive to the allosteric molecules and the flexibility of the residues is pronouncedly suppressed; the additions of the small molecules to the allosteric sites strengthen the binding affinities of 3TL-PR by about 12–15 kal/mol in the binding free energy, which mainly arises from electrostatic term. Interestingly, it is found that the action mechanisms of 1F1 and 4D9 are different, the former behaviors like a doorman that keeps the inhibitor from escape and makes the flaps (door) partially open; the latter is like a wedge that expands the allosteric space and meanwhile closes the flaps. Our data provide a theoretical support for designing the allosteric inhibitor.