https://www.sandia.gov/~sjplimp/papers/jcompphys95.pdf

Fast parallel algorithms for short-range molecular dynamics

Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.

/pdf/quantum-espresso-a-modular-and-open-source-software-project-4t6vlupbeh.pdf

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials

http://www2.stat.duke.edu/~scs/Courses/Stat376/Papers/Constraints/Shake1977.pdf

Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes

The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less

A smooth particle mesh Ewald method

The equation of motion of a system of 864 particles interacting through a Lennard-Jones potential has been integrated for various values of the temperature and density, relative, generally, to a fluid state. The equilibrium properties have been calculated and are shown to agree very well with the corresponding properties of argon. It is concluded that, to a good approximation, the equilibrium state of argon can be described through a two-body potential.

Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules

The perturbation theory of liquids developed recently by Weeks, Chandler, and Andersen (WCA) is examined in detail: Each assumption introduced by these authors is tested by comparison with "exact" computer results. It is shown that the basic assumptions of WCA are justified. An improved expression for the radial distribution function of the hard-sphere gas enables us to correct for some further inconsistent assumptions of the WCA theory. We then succeed in giving simple analytical expressions for the thermodynamic functions of the Lennard-Jones fluid shown to be quite good at high density. We show that the remainder of the perturbation series, which converges slowly at lower density, can be evaluated with the help of the Percus-Yevick equation. We therefore possess a unified theory of liquids which is especially simple at high density. Finally we reexpress the original WCA theory in an analytical form.

Equilibrium Theory of Simple Liquids

Monte Carlo computations have been performed in order to determine the phase transitions of a system of particles interacting through a Lennard-Jones potential. The fluid-solid transition has been investigated using a method recently introduced by Hoover and Ree. For the liquid-gas transition a method has been devised which forces the system to remain always homogeneous. A comparison is made with experiment in the case of argon. An indirect determination of the phase transition of the hard-sphere gas is made which is essentially in agreement with the results of the more direct calculations.

Phase Transitions of the Lennard-Jones System

: Equilibrium correlation functions for a dense classical fluid are obtained by integrating the equation of motion of a system of 864 particles interacting through a Lennard-Jones potential. The behaviour of the correlation function at large distance, and that of its Fourier transform at large wave number are discussed in detail and shown to be related to the existence of a strong repulsion in the potential. A simple hard sphere model is shown to reproduce very well the Fourier transform of those correlations functions at high density, the only parameter of the model being the diameter a of the hard spheres. (Author)

Computer "Experiments" on Classical Fluids. II. Equilibrium Correlation Functions

A molecular-dynamics "experiment" was performed for a system of 864 particles interacting through a Lennard-Jones potential. The state considered was in the immediate neighborhood of the triple point. The total duration of the "experiment" was quite large: It corresponds to ${10}^{\ensuremath{-}9}$ sec in the case of argon. Transport coefficients were calculated using the standard Kubo formulas. They are compared with the prediction of a simple hard-sphere model. It is shown that, as in the case of the hard-sphere fluid near solidification, the Kubo-correlation function relative to the shear viscosity presents a tail extending at large time. The inclusion of this tail turns out to be essential in explaining the transverse-correlation function and the dynamical-structure factor, which shows, for the lowest wave vectors accessible in this study, a characteristic Brillouin doublet structure. Using the hydrodynamical model of Zwanzig and Bixon, it is shown that the introduction of the long-time tail in the Kubo-correlation function for the viscosity explains the negative plateau of the velocity-autocorrelation function observed near the triple point by Rahman and others.

Loup Verlet

Papers

Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules

Equilibrium Theory of Simple Liquids

Phase Transitions of the Lennard-Jones System

Computer "Experiments" on Classical Fluids. II. Equilibrium Correlation Functions

Computer "Experiments" on Classical Fluids. IV. Transport Properties and Time-Correlation Functions of the Lennard-Jones Liquid near Its Triple Point