Ewald approach

The cell multipole method (also called the fast multipole method) is an algorithm that enables all N N — 1) pairwise non-bonded interactions to be enumerated in a time that scales linearly with N, rather than N, as in the standard Ewald approach [Greengard and Roklin 1987 Ding et al. 1992a, b Greengard 1994]. The cell multipole method can be used to evaluate interactions that can be expressed in the following general form ... 

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. 

Within the Ewald approach, the charge distribution is defined as a Gaussian function (see Eq. [8]), and the sum of the direct Coulomb force... 

Additional possibilities have focused on treatment of the long-range interactions that are neglected beyond the cutoff in SC. These include the implemention of full periodic boundary conditions through the Ewald method or supplementation of SC with a reaction field by imbedding the cutoff sphere in a polarizable continuum. The Ewald approach is certainly appropriate for perfect crystalline lattices and for systems such as molten salts. It has also received renewed attention... 

Gray C G, Sainger Y S, Joslin C G, Cummings P T and Goldman S 1986 Computer simulation of dipolar fluids. Dependence of the dielectric constant on system size a comparative study of Ewald sum and reaction field approaches J. Chem. Phys. 85 1502-4... 

Regardless of which algorithm is used for fast calculation of Ewald sums, the computational cost is now competitive with the cost of cutoff calculations, and there is no longer a need to employ cutoffs for purposes of efficiency. Since Ewald summation is the natural expression of Coulomb s law in periodic boundary conditions, it is the recommended approach if periodic boundary conditions are to be used in a simulation. 

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