Ewald potential

Essmann U, Perera L, Berkowitz ML et al (1995) A smooth particle mesh Ewald potential. J Chem Phys 103 8577-8592... 

The alternative viewpoints here emphasize that the uniform neutralizing background for the individual contributions just permits the normal electric field to be zero on the boundary. These viewpoints avoid traditional (Valleau and Torrie, 1977) but inconclusive discussions of what periodic images might be doing when lattice sums are conceived with Ewald potentials. 

The Ewald potential traditionally includes an additive constant to achieve... 

The Ewald potential is traditionally implemented as a lattice sum (Ziman, 1972 Leeuw et al, 1980). We just outlined a conceptualization of electrostatic interactions in periodic boundary conditions that involved adding a uniform neutralizing background for each charge, and the subsequent solution of the Poisson equation in periodic boundary conditions. Here we discuss the interconnections between that conceptualization and the traditional lattice sums, as presented in many sources, e.g. (Allen and Tildesley, 1987 Frenkel and Smit, 2002 Leeuw et al, 1980). 

An exercise that follows requests utilization of the Poisson equation to evaluate the charge density implied by Eq. (5.37) the result of that calculation is the charge density in the Poisson equation of Eq. (5.26), p. 109. The potential in Eq. (5.37) is identical to traditional expressions for the Ewald potential (Leeuw et al, 1980) except for the final term that additive constant implies... 

To derive Eq. (6.8) for the real-space part of the Ewald potential, we start from Eq. (6.7) for the set of screened charges and apply Poisson s formula [see Eq. (6.3)]. This gives... 

For moderately dense coulombic systems the use of Ewald potentials— that is, of truly periodic boundary conditions in the energy calculation—seems to have become almost routine in recent studies. It is also proposed for dipole systems. There seem, however, to be theoretical arguments for examining more critically the consequences of this approximation. These theoretical questions concern the physical realism of the approximation, and may be divided into those of long-range behavior and those of short-range behavior of the truly periodic model ... 

The change in the right-hand side of (B8) as the result of a single particle displacement involves the interaction of the old and new coordinates of the moved particle only with each wave vector k[viz. sin(2irk r,), cos(2 irk ry), etc.]. This reduces the computation of this part of the Ewald potential to an amount comparable to that required for determining the energy change after a trial move in a system of 125 particles with a spherically s)mimetric potential. 

We are happy about many conversations with those who share our delight in the Monte Carlo game. We would like to thank Glenn Torrie for contributing the appendix on Ewald potentials. The financial assistance of the National Research Council of Canada is gratefully acknowledged. 

The Fourier transformations involved in Eqs. 9 and 17 are the most time-consuming part of the Ewald sum. Several methods have been proposed to address this problem, e.g., tabulation of the complete Ewald potential [37] or the use of polynomial approximations. A particularly successful approach for the latter is the expansion of the nonspherical contributions to the Ewald potential in cubic harmonics [37,38]. Apart from the difficulty of computational overheads which may strongly increase with the desired accuracy, these methods do not solve the additional problem of unfavorable scaling with particle number. At best they scale as which is more costly than a plain cutoff or reaction field approach. 

The determination of the properties of the 1-g interface of a dipolar fluid has been performed for a Stockmayer system and a system of diatomic particles which, in addition to the point dipole interaction, interact by site-site LJ potentials in [202]. The estimates of the surface tension are shown to be in reasonable agreement with experimental results for 1,1-difluoroethane when state variables are reduced by the critical temperature and density. The preferential orientation of the dipoles is parallel to the interface. This work also contains methodological aspects of the simulation of thin liquid films in equilibrium with their vapour. In particular, a comparison is made between the results obtained for the true (Eq. 25) and slab-adapted Ewald potentials. The agreement between the two numerical determinations of the dipolar energy is quite satisfactory asserting the validity of the use of the 3D Ewald approach for the simulation in a slab geometry. 

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