Ewald summation dipole interaction

Pc- (c) Dipole density p. (d) Water contribution to the surface potential x calculated from the charge density Pc by means of Eq. (1). All data are taken from a 150 ps simulation of 252 water molecules between two mercury phases with (111) surface structure using Ewald summation in two dimensions for the long-range interactions. 

As a second application of the Ewald summation for systems with slab geometry we now consider strongly coupled confined dipolar liquids, that is, liquids where the dipolar interactions dominate the system s structure and phase behavior. Examples for sucli systems are ferrocolloidal films or confined molecular liquids with strong dipole moments and relatively weak van der Waals forces or hydrogen bonds [231]. 

The Hmit E exists, but differs by some multiple of the square of the dipole moment from the spherical limit as obtained by the Ewald summation [50]. From the physical point of view, the Coulomb interaction is replaced by a screened Coulomb interaction with screening length l/p. E is then the energy in the limit of infinite screening length. But because of the conditional convergence... 

In the case of polar liquids computer experiments whether by molecular dynamics or Monte Carlo methods present difficulties arising from the long range character of the dipole interaction energy and resolution of the problems for the modest sizes of systems in simulations is a task for statistical mechanics rather than ingenious computation methods. Vertheim (35) has summarized the results of the two main kinds of effort to improve on truncation, whether by cutoff of the potential or by periodic boundary conditions namely use of mean field approximations for longer distances and use of Ewald or other summation methods. There is much of interest and instruction value in comparison of results so far... 

However, the slow decay of the dipole-dipole interaction in (6) (proportional to r ) makes the use of Ewald summation techniques necessary when one uses (6) in a simulation. Thus, the computational effort of working with the full Stockmayer potential (6) is comparable to the effort needed for all-atom models with partial charges at the atoms. 

The preceding Ewald energy expressions have been written in a form corresponding to the so-called tin foil boimdary condition which supposes, when the summation of the pair interactions is performed, that, on a macroscopic scale, the system and its repUcas are surrounded by a conducting medium. If the latter mediiun is a dielectric with a dielectric constant e it will be polarized by the total dipole moment M = of the dipolar particles and a novel shape dependent contribution Ep resulting from this polarization effect should be added to E [ 18] ... 

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