Long-range coulomb interactions

Keywords Ewald methods Long-range interactions - Coulomb sum ... 

But the methods have not really changed. The Verlet algorithm to solve Newton s equations, introduced by Verlet in 1967 [7], and it s variants are still the most popular algorithms today, possibly because they are time-reversible and symplectic, but surely because they are simple. The force field description was then, and still is, a combination of Lennard-Jones and Coulombic terms, with (mostly) harmonic bonds and periodic dihedrals. Modern extensions have added many more parameters but only modestly more reliability. The now almost universal use of constraints for bonds (and sometimes bond angles) was already introduced in 1977 [8]. That polarisability would be necessary was realized then [9], but it is still not routinely implemented today. Long-range interactions are still troublesome, but the methods that now become popular date back to Ewald in 1921 [10] and Hockney and Eastwood in 1981 [11]. 

In an ionic material, the ions interact via long-range electrostatic (Coulombic) forces, as set out in the previous section. Instead of the simple expression used... 

Compared to all other types of intermolecular interactions, the Coulomb interaction is a very long ranged interaction. E.g., the interaction energy in water (e=80) between Na and Cl" at a distance 60-65 A from each other is roughly the same as between two Ne atoms in contact. 

If the defects can be considered point charges, localized on their own lattice sites, the polar electrostatic interaction between them is usually written as a long range monopolar Coulomb energy. If, on the other hand, for large concentrations of defects, local charge effects, as described in the introduction, are present, then AHjnter is much more difficult to write. 

In their considerations on the field generated by a single moving charged particle, Chubykalo and Smimov-Rueda [2,56,57] have claimed the Lienard-Wiechert potentials to be incomplete. These potentials are then not able to describe long-range instantaneous Coulomb interaction. However, in a modified theory by Chubykalo and Smimov-Rueda such interaction is included. The applicability of these potentials is, however, still under discussion [9]. 

In principle, such approximations may serve as a basis of the description of partially ionized plasmas, if we have to take into account ionization and recombination. However, because of the long range of Coulomb interaction, the Landau collision integral (3.110) and such integrals of type (3.119) are divergent. Such divergencies may be avoided by an appropriate screening. The simplest way to do this is to replace the... 

Let us now consider the problem of bound states in plasmas. The interaction between the plasma particles is given by the Coulomb force. A characteristic feature of this interaction is its long range. Therefore, Coulomb systems show a collective behavior, so we can observe, for instance, the dynamical screening of the Coulomb potential and plasma oscillations. 

This Hamiltonian is used usually only for the short-range part of Coulomb interaction. The long-range interactions can be better introduced through the self-consistent electrical potential Poisson equation with the average electron density. 

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