Estimate of the Cutoff Errors in the Ewald Summation for Dipolar Systems

Theoretical estimates for the cutoff errors in the Ewald summation method for dipolar systems are derived. Absolute errors in the total energy, forces and torques, both for the real and reciprocal space parts, are considered. The applicability of the estimates is tested and confirmed in several numerical examples. We demonstrate that these estimates can be used easily in determining the optimal parameters of the dipolar Ewald summation in the sense that they minimize the computation time for a predefined, user set, accuracy.

[1]  Christian Holm,et al.  Electrostatic effects in soft matter and biophysics , 2001 .

[2]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[3]  X. Daura,et al.  Peptide folding simulations: no solvent required? , 1999 .

[4]  J. Perram,et al.  Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  M. Deserno,et al.  HOW TO MESH UP EWALD SUMS. II. AN ACCURATE ERROR ESTIMATE FOR THE PARTICLE-PARTICLE-PARTICLE-MESH ALGORITHM , 1998, cond-mat/9807100.

[6]  H. G. Petersen,et al.  An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles , 1988 .

[7]  T. Darden,et al.  A smooth particle mesh Ewald method , 1995 .

[8]  H. Fang,et al.  Simulation of field-induced structural formation and transition in electromagnetorheological suspensions. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[10]  Philippe H. Hünenberger,et al.  Optimal charge-shaping functions for the particle–particle—particle–mesh (P3M) method for computing electrostatic interactions in molecular simulations , 2000 .

[11]  J. Perram,et al.  Cutoff Errors in the Ewald Summation Formulae for Point Charge Systems , 1992 .

[12]  Per Linse,et al.  Ewald summation and reaction field methods for potentials with atomic charges, dipoles, and polarizabilities , 2000 .

[13]  P. P. Ewald.  Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .

[14]  Christian Holm,et al.  How to mesh up Ewald sums. I. A theoretical and numerical comparison of various particle mesh routines , 1998 .

[15]  Herbert Morawetz.  Polyelectrolytes, science and technology, Hara Masanori, ed., Marcel Dekker, New York, 1993, 416 pp. price: $150.00 , 1993 .

[16]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[17]  H. G. Petersen.  Accuracy and efficiency of the particle mesh Ewald method , 1995 .

[18]  Christian Holm,et al.  How to Mesh up Ewald Sums , 2000 .