Molecular Dynamics Simulations of a Siloxane-Based Liquid Crystal Using an Improved Fast Multipole Algorithm Implementat
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ABSTRACT In our continuing efforts towards designing materials with controlled optical properties, largescale molecular dynamics simulations of a molecular cluster of a liquid crystalline cyclic siloxane are still limited by the size of the molecular system. Such simulations enable evaluation of the orientation order parameter of the system, as well as modelling the behavior of the material in bulk. This study summarizes improvements in the implementation of the fast multipole algorithm for computing electrostatic interactions which is included in the molecular dynamics program PMD[7, 8], such as the elimination of computations for empty cells and the use of optimal interaction lists. Moreover, an improved implementation of a 3-D Fast Multipole Method (FMM3D) based on the algorithm previously proposed[1, 2] is described in detail. The structure of the module, details of the expansions, parallelization, and its integration with the molecular dynamics simulation code are explained in detail. Finally, the utility of this approach in the study of liquid crystalline materials is briefly illustrated.
INTRODUCTION The high cost of computing long-range electrostatic forces for molecular dynamics simulations has led to the use of simplified models for such forces, or even to neglecting them entirely. To calculate all interactions between n atoms in the obvious way requires 0(n 2) arithmetic operations, which is prohibitive for large molecules.
If interactions between atoms separated by more than a
certain cut-off radius rcutoff are ignored, the cost is 0(n) (for large n); such methods are called cutoff methods. However, this approximation is often inappropriate.[3] One approach to include long-range forces is to compute longer-range forces less frequently than short-range forces, as in the distance-class method described in[4]. The distance-class method has an asymtotic cost of O(nN) for N timesteps, as N gets large. A second approach (available as an option in CHARMm[5]) is to use a power series approximation for the long-range forces: the volume taken up by the molecule is divided into cubes, and a power series defined for each cube to describe the long-range forces. If the power series are computed directly from the charges, and the optimal number of cubes is chosen, the cost is 0(n 3/ 2). A refinement of the power-series approach is the fast multipole method[l, 6], which uses a hierarchy of partitions of the volume and a divide-and-conquer strategy to compute the power series in 0(n) operations. This makes it possible to recompute the electrostatic forces every timestep, even for very large systems. However, the cost of computing all electrostatic interactions remains high, even with the fast multipole method: with current implementations, one calculation of the electrostatic interactions requires several times as much computer time as the rest of the calculations for a timestep. For this reason, those codes which use the fast multipole method usually do not recompute all the interactions every timestep, which then n
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