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The truncated octahedron (TO) and the rhombic dodecahedron (RD) are two space filling shapes, which have special advantages as simulation cells for molecular dynamics [1, 2]. This article addresses the particular problem of how to incorporate the Ewald sum [3, 4] in simulations employing these unusual boundary conditions.

A systolic loop method for parallel molecular dynamics, previously written in Occam, is reimplemented in Fortran using a general message-passing library. The method is extended to include a conventional neighbour list, fully distributed over the processors. A modification of the systolic loop method, called systolic replication, permits a parallel implementation of the fastest known sequential algorithm, in which a link-cell spatial decomposition is used to form the distributed neighbour list. The performance of each method, for a liquid argon simulation, is measured on a Transputer system and analysed in terms of the concept of scaleability. Some measurements are also made using i860 processors. The best performance achieved is 5000 particle moves per second, using 28 Transputers.

Among several finite-difference algorithms which are used in MD simulation three popular ones are: the leapfrog, the Verlet and the Beeman. All three algorithms produce exactly the same particle trajectories, but they differ in terms of definition of the velocity and hence give different values of kinetic energy or temperature for the system. Evaluation of the temperature of a simulated system can be based on the Taylor expansion of coordinates, velocities or kinetic energies; leading to expressions which we characterise as being of the Verlet type, Beeman type or corrected-leapfrog type. Twelve different expressions for evaluation of the kinetic energy of a system are discussed and compared by means of a one-dimensional two-particle system and a liquid simulation. The results, consistent in both tests, show that the Verlet expressions underestimate the kinetic energy while the Beeman expressions overstimate it. In terms of conservation of total energy the corrected-leapfrog expressions prove to be superior. We have also been able to suggest some improved expressions which give the correct average kinetic energy with even smaller fluctuations in total energy.

Two new programs perform molecular dynamics simulations on molecular and ionic materials, respectively. The first simulates systems of small molecules, treated dynamically as rigid bodies, with interactions of the site-site Lennard-Jones form, plus point charges. The second simulates systems of point ions, which may be made polarizable by means of the shell model, treated by the method of adiabatic dynamics. Both programs handle Coulombic interactions in periodic boundaries by means of the Ewald sum. Force evaluations make use of efficient neighbor-search algorithms. The programs incorporate extensive analysis options in terms of structural and dynamic correlation functions. The programs are controlled by a command language, Dynamo, which provides a good environment for further development, as well as ease of use and flexibility in the choice of simulation protocol.

Parallel computers are a very cost-effective way of providing high performance computational power, though at present it is not always easy to use them effectively. Molecular dynamics simulation is intrinsically highly parallel in nature, both in the force evaluation phase of the timestep and in the motion integration phase. Methods are described which implement molecular dynamics simulation on two parallel computers: the Distributed Array Processor (DAP), and networks of Transputers. On the DAP, lattice dynamics can be studied by means of a geometrical decomposition which gives one processing element (PE) to each ion or molecule. The method can be modified for liquids by exchanging molecules between PEs when necessary. An alternative approach for molecular liquids maps pair interactions, rather than molecules, onto PEs. In the Transputer case, processors are connected in a ring and molecule data circulate in such a way that all required pair interactions may be evaluated. The data movements take place in parallel with the computation so little loss of efficiency arises from communication delays.

In molecular dynamics computer simulation of liquids it is important to use as large a timestep as possible in order to sample phase space rapidly and save on computer expense. The effect of the resulting algorithm errors in the trajectories of the molecules is not well understood. An empirical investigation into this question is reported. Several simulations differing only in the timestep used are compared. It is found that much larger timesteps than usual can be employed without producing significant errors in observed thermodynamic, structural or dynamic properties.

Algorithms are presented which enable molecular dynamics simulations of liquids to be performed most efficiently on the Cray-1 vector processing computer. For 256 atoms interacting via the Lennard-Jones potential the CPU time per step of the simulation is 22 ms.

The implementation of molecular dynamics simulation on parallel computers needs a method which distributes over the processors both the evaluation of pair interactions and the integration of particle motions. This paper introduces several ways to achieve this, all based on the systolic loop concept. Each particle has a home processor which integrates its motion. In the evaluation of the interactions, the particle data circulate around the ring of processors in such a way that every particle meets every other particle, enabling all the pair interactions to be evaluated. The methods are suitable for use with a spherical cut-off or with a neighbour list. Three possible sources of inefficiency are discussed in detail. These are: imperfect load balancing during the force evaluation; communication delays during the force evaluation; and communication delays in accumulating thermodynamic quantities. In each case the loss of efficiency is only significant if the number of processors approaches the number of particles, which is unlikely to be the case in practice. Also, if the parallel computer is constructed from transputers, their ability to simultaneously calculate and communicate can reduce communication delays in the force evaluation. The methods have been tested on systems of up to 130 transputers.