Coulomb forces, long-range interactions

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]. 

If one or both of the particles are neutral, this Coulomb force is zero in the two-body approximation, and the long-range interaction is greatly reduced. 

Theories that account for the Coulomb forces among the ions are, e.g., provided by the work of Debye and Hiickel (DH) in 1923 [2] or by the Mean Spherical Approximation (MSA) introduced by Waisman and Lebowitz [3] in 1970. However, both, DH and MSA, only consider the Coulomb long-range interactions due to the ion charges. 

If you had substituted any attractive short-ranged potential (one that falls off more rapidly than r ) into Equation (24.17), it would have led to the pressure p oc y- , just as in Equation (24.22). For this reason, many different types of interaction are collectively called van der Waals forces. They all lead to the same contribution to p(V). For longer-ranged forces, such as coulombic interactions, the integral in Equation (24.17) becomes inhnite, and Equation (24.20) w ould not apply. For long-range interactions, you need to resort to the methods of Chapters 20 to 23, such as the Poisson equation. 

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