Tuning the smooth particle mesh Ewald sum: Application on ionic solutions and dipolar fluids

Numerical properties of the smooth particle mesh Ewald (SPME) sum [U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen, J. Chem. Phys. 103, 8577 (1995)] have been investigated by molecular dynamics simulation of ionic solutions and dipolar fluids. Scaling dependence of execution time on the number of particles at optimal performance have been determined and compared with the corresponding data of the standard Ewald (SE) sum. For both types of systems and over the range from N = 103 to 105 particles, the SPME sum displays a sub $\mathscr{O}$O(N ln N) complexity, whereas the SE sum possesses an $\mathscr{O}$O(N3/2) complexity. The breakeven of the simulation times appears at $\mathscr{O}$O(103) particles, and the SPME sum is ≈20 times faster than the SE sum at 105 particles. Furthermore, energy truncation error and the energy and force execution time of the reciprocal space evaluation as function of the number of particles and the convergence parameters of the SPME sum have been determined for both types of systems containing up to 106 particles.