Communication: On the origin of the surface term in the Ewald formula

Journal of Chemical Physics

Volumn 140, Issue 16, 2014, Pages

  Ballenegger, V ^a  

^a UNIVERSITÉ DE FRANCHE COMTÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

PHYSICS;

ELECTROSTATIC ENERGIES; GENERAL EXPRESSION; LATTICE SUM; POINT CHARGE; THREE DIMENSIONAL SYSTEMS;

PHYSICAL CHEMISTRY;

EID: 84899846836     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4872019     Document Type: Article

References (32)

1. C. Sagui and T. A. Darden, Annu. Rev. Biophys. Biomol. Struct. 28, 155 (1999). 10.1146/annurev.biophys.28.1.155
2. P. H. Hünenberger, in Simulation and Theory of Electrostatic Interactions in Solution: Computational Chemistry, Biophysics, and Aqueous Solutions, edited by L. R. Pratt and G. Hummer (AIP, New York, 1999), pp. 17-83.
3. A. Arnold and C. Holm, in Advanced Computer Simulation Approaches for Soft Matter Sciences II, Advances in Polymer Sciences Vol. II, edited by C. Holm and K. Kremer (Springer, Berlin, 2005), pp. 59-109.
4. M. Karttunen, J. Rottler, I. Vattulainen, and C. Sagui, in Computational Modeling of Membrane Bilayers, Current Topics in Membranes Vol. 60 (Elsevier Inc., 2008).
5. M. Mazars, Phys. Rep. 500, 43 (2011). 10.1016/j.physrep.2010.11.004
6. A. Arnold, F. Fahrenberger, C. Holm, O. Lenz, M. Bolten, H. Dachsel, R. Halver, I. Kabadshow, F. Gaehler, F. Heber, J. Iseringhausen, M. Hofmann, M. Pippig, D. Potts, and G. Sutmann, Phys. Rev. E 88, 063308 (2013). 10.1103/PhysRevE.88.063308
7. P. P. Ewald, Ann. Phys. 369, 253 (1921). 10.1002/andp.19213690304
8. A. Redlack and J. Grindlay, Can. J. Phys. 50, 2815 (1972); 10.1139/p72-375
9. A. Redlack and J. Grindlay, J. Phys. Chem. Solids 36, 73 (1975). 10.1016/0022-3697(75)90116-X
10. S. de Leeuw, J. Perram, and E. Smith, Proc. R. Soc. London A 373, 27 (1980); 10.1098/rspa.1980.0135
11. S. Deleeuw, J. Perram, and E. Smith, Proc. R. Soc. London A 373, 57 (1980); 10.1098/rspa.1980.0136
12. S. Deleeuw, J. Perram, and E. Smith, Proc. R. Soc. London A 388, 177 (1983). 10.1098/rspa.1983.0077
13. E. Smith, Proc. R. Soc. London, Ser. A 375, 475 (1981). 10.1098/rspa.1981.0064
14. L. Kantorovich and I. Tupitsyn, J. Phys.: Condens. Matter 11, 6159 (1999). 10.1088/0953-8984/11/32/307
15. E. R. Smith, J. Chem. Phys. 128, 174104 (2008). 10.1063/1.2908076
16. J.-P. Hansen, in Molecular Dynamics Simulation of Statistical Mechanical Systems, edited by G. Ciccotti and W. G. Hoover (North-Holland, Amsterdam, 1986).
17. L. Fraser, W. Foulkes, G. Rajagopal, R. Needs, S. Kenny, and A. Williamson, Phys. Rev. B 53, 1814 (1996). 10.1103/PhysRevB.53.1814
18. H. D. Herce, A. E. Garcia, and T. Darden, J. Chem. Phys. 126, 124106 (2007). 10.1063/1.2714527
19. R. N. Euwema and G. T. Surratt, J. Phys. Chem. Solids 36, 67 (1975). 10.1016/0022-3697(75)90115-8
20. M. Neumann, O. Steinhauser, and G. Pawley, Mol. Phys. 52, 97 (1984). 10.1080/00268978400101081
21. S. Boresch and O. Steinhauser, Berichte der Bunsen-Gesellschaft-Phys. Chem. Chem. Phys. 101, 1019 (1997). 10.1002/bbpc.19971010706
22. V. Ballenegger and J. P. Hansen, Mol. Phys. 102, 599 (2004). 10.1080/00268970410001675554
23. I. Yeh and M. Berkowitz, J. Chem. Phys. 111, 3155 (1999). 10.1063/1.479595
24. No non-analytic \documentclass[12pt]{minimal}\begin{document}\hat{\bm{\rm k}}= \bm{ \rm k}/k\end{document} k ̂ = k / k can survive in (17) because the summand in (16) is absolutely convergent.
25. The electric neutrality of the simulation cell is often invoked as the reason for the exclusion of the \documentclass[12pt]{minimal}\begin{document}\ bm{ \rm k}=0\end{document} k = 0 term in (18), but neutrality alone is not sufficient because that \documentclass[12pt]{minimal}\begin{document}\bm{ \rm k}=0\end{document} k = 0 term would still be plagued by an indeterminacy of the form 0 × ∞. That indeterminacy is intimately linked to how the long-range contributions in the lattice sum (1) are handled and it is resolved only by an adequate treatment of those contributions, performed here via the splitting (2).
26. One can show indeed that no term arises in (19), in the limit V → ∞, from the difference between the volume V and the crenelated volume made up of an integer number of cells.
27. J. A. Stratton, Electromagnetic Theory (IEEE Press, 2007).
28. D. R. Wheeler and J. Newman, Chem. Phys. Lett. 366, 537 (2002). 10.1016/S0009-2614(02)01644-5
29. J. Kolafa and J. Perram, Mol. Sim. 9, 351 (1992). 10.1080/ 08927029208049126
30. S. de Leeuw and J. Perram, Physica A 107, 179 (1981). 10.1016/0378-4371(81)90031-5
31. V. Ballenegger, A. Arnold, and J. J. Cerda, J. Chem. Phys. 131, 094107 (2009). 10.1063/1.3216473
32. V. Ballenegger, " On the electrostatic surface contributions to the Ewald potential in periodic charged systems " (unpublished).