Neighbour Lists Again

In a recent article, Thompson 1] described the use of neighbour lists in simulations, giving a detailed account of the implementation and the resulting economies. This note deals with a simple variant on the method, and discusses the choice of neighbour list technique, if any, to be used in various circumstances. The idea was originally introduced in the classic paper of Verlet 2] on the simulation of a dense Lennard-Jones uid. Using a cut-oo radius slightly greater than the truncation radius of the interaction potential 1], a list is made for each molecule of all other molecules which are, or could soon be, within interaction range. The lists are renewed at intervals 1], and during the intervening steps only the listed pairs are considered in calculating the pair interaction energies and forces. With a cut-oo radius equal to half the (cubic) box length only about half of the distinct pairs need be listed, and the resulting savings in computer time grows rapidly with N because the number of pairs is N(N-1)/2. However, the conventional method requires that an integer index be stored for every active pair, so that the list grows roughly as N 2 =4. This can quickly become burdensome in machines with limited storage, or where costs or priority depend on the amount of storage used. The alternative implementation described here combines the eeciency inherent in the use of neighbour lists with compact storage. For a given molecule, any other molecule is either within the cut-oo range, or it is not, and this situation is ideally suited to a binary representation. The rst form described here is particularly suitable for conventional Monte Carlo simulations, where the use of single particle moves requires that one be able to identify all neighbours of the molecule being moved. For molecular dynamics simulations, where all active pair interactions are required at each step, a simple and obvious modiication can be used to reduce the required storage by another factor of two, and the coding is even simpler. FORTRAN, still the dominant medium for simulation code, had no bit-handling facilities under the old standard, and rumour has it that the implementation of the new standard is not yet uniform. Many compilers ooer non-standard extensions for manipulating bit strings, but the details vary from site to site. For these reasons the code given here is more cumbersome than it need be, but it should …