Long ranged interactions in computer simulations and for quasi-2D systems

Taking correctly into account long ranged interactions in molecular simulations of molecular models based on classical atomistic representations are essential to obtain reliable results on model systems and in simulations of biological systems. A lot of numerical methods have been developed to this end; the most important of them are reviewed in this paper. Particular attention is paid to the analytical relations between the methods, this allows comparisons on efficiency and accuracy between them and also to proceed to precise implementations of these techniques. While most of the methods have been developed for Coulomb interactions, we give also some analytical details to apply these methods to screened Coulomb (Yukawa interactions), inverse power law and dipolar interactions. Particular types of systems, the quasi-2D systems, are also considered in this paper. Quasi-2D systems represent a large class of physical systems where the spatial extension in one direction of the space is very small by comparison to the other two. These representations are very useful to describe the properties of interfaces, surfaces, fluids confined in slab geometry, etc. In computer simulations, these systems are studied with partial periodic boundary conditions: periodic boundary conditions are taken in directions where spatial extensions are large and some other boundary conditions are taken in directions with smaller extensions. In this review, we describe also the numerical methods developed to handle long ranged interactions in numerical simulations of quasi-2D systems. The properties of quasi-2D systems depend strongly on interactions between components; more specifically electrostatic and magnetic interactions and interactions with external fields are of particular interest in these systems.