Nearest image convention

Again the implementation of the nearest-image convention needs some care at each iteration both s,(7 + At) and s,(t) must be replaced by s, t + At) — U and s, f) — U where U is the integer part of 2 s,(f + At). Constant stress MD has been used by Tallon (1988) in a detailed study of the phase diagram of silver iodide. 

Except for the Coulombic contributions, which are computed by an Ewald-type summation, as described in Section 2.3, a potential cutoff distance is imposed to avoid unnecessary computing time calculating negligible contributions by short-range interactions from most of the V 2N N— 1) atom pairs in the system. In the commonly used nearest-image convention, if the cutoff obeys the condition re < VtJL, Then atom pair interactions included are between atom i in the central box and either atomj in the same box or one of its imagesf in an adjacent one, depending on whichever distance x/ - Xy or x/ - f is least (see Fig. 5.4). 

FIGURE 5.4. A two-dimensional projection of a symbolic cubic box used to simulate a system of particles in molecular dynamics with masses m/ and instantaneous velocities v/. At each of its faces, edges, and vertices the central cube is surrounded by a similar box, parts of which are shown here. In this way, if one particle exists the central box at a certain point it is simultaneously replaced by an identical particle entering the box from the opposite direction. The nearest image convention (see text) ensures that, for example, particle 6 (mass m6) in the central box in the system depicted here feels the presence of particle 8 by interacting with mg that is in the adjacent left hand box, but not the more distant mg in its own box. 

Noncubic boxes involve noncubic cells in the linked-cells algorithm. This makes the code very clumsy (especially in 3-D) due to greater number of walls, edges and vortices in noncubic cells than for cubic ones, thus involving complicated nearest image convention schemes [107]. 

The nearest image convention, (in which I include spherical... 

In this technique the nearest image convention is abandoned in favour of including all periodic images out to infinity. The simulation hamiltonian is. 

Fig. 2. (a) Periodic images surrounding the simulation box. Interactions are computed with respect to the nearest image which is indicated by the circle, (b) Violation of the minimum image convention resulting from the interaction of QM particle with point charge 1. 

A slightly more sophisticated method is the so-called minimum-image (MI) convention, in which all interactions between the central particle and its nearest image of all other particles are included. This is a significant improvement over a SC, since the central particle and its interacting particles constitute an electroneutral entity. The MI convention has frequently been appUed to simulate simple electrolytes and, to some extent, weakly asymmetric electrolytes. However, it suffers from the same principal deficiencies as a SC, and the MI convention becomes insufficient for higWy asymmetric electrolytes. 

Periodic boundary conditions refer to the simulation of structures consisting of a periodic lattice of identical subunits. Periodic boundaries help simulate bulk-material, solvent, and crystalline systems. Ideally, a periodic system infinitely replicates in all dimensions to form a periodic lattice. However, in practice, all periodic boundary algorithms imply a cutoff criterion for computational efficiency (Figure 1.1). In these cutoff schemes, each atom interacts with the nearest images of other N - I atoms (minimum-image convention) or only with the explicit images contained in a sphere... 

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