Simulations image convention

Both a uniform bulk fluid and an inhomogeneous fluid were simulated. The latter was in the form of a slit pore, terminated in the -direction by uniform Lennard-Jones walls. The distance between the walls for a given number of atoms was chosen so that the uniform density in the center of the cell was equal to the nominal bulk density. The effective width of the slit pore used to calculate the volume of the subsystem was taken as the region where the density was nonzero. For the bulk fluid in all directions, and for the slit pore in the lateral directions, periodic boundary conditions and the minimum image convention were used. 

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. 

In the simulations, the traditional algorithm was applied to an off-lattice at each step, and periodic boundary conditions were employed. The interactions were truncated using the minimum image convention, and the information was recorded every 50 cycles, after the system reached equilibrium 1000 samples were averaged in each simulation. 

Fock molecular orbital (HF-MO), Generalized Valence Bond (GVB) [49,50] and the Complete Active Space Self-consistent Filed (CASSCF) [50,51], and full Cl methods. [51] Density Functional Theory (DFT) calculations [52-54] are also incorporated into AIMD. One way to perform liquid-state AIMD simulations, is presented in the paper by Hedman and Laaksonen, [55], who simulated liquid water using a parallel computer. Each molecule and its neighbors, kept in the Verlet neighborlists, were treated as clusters and calculated simultaneously on different processors by invoking the standard periodic boundary conditions and minimum image convention. 

The inter-particle distance used in the simulation is calculated using the minimum image convention. It dictates that the distance between two particles m and k is the smallest of all the possible distances between particle m and k including all the replica images of particle k. 

When we solve the problem numerically, the number of surface elements, and consequently, the size of the dielectric boundary surfaces must be finite. This is in accordance with the practice in a simulation, where the simulation cell is also finite. To approximate an infinite system in a simulation, periodic boundary conditions are applied in the x and y directions. The closest image convention is used not only for the ionic distances but any distances between... 

However, because of periodic boundary conditions, one needs to make sure that as far as short-range interaction potentials are concerned, a molecule in the simulation cell interacts only with another peirticle in the simulation cell or one of its periodic images depending on which is closest. Tliis so-called minimum image convention can easily be implemented through the equations... 

Molecular dynamics simulations can be done on molecules in the gas phase (in vacuo), in the liquid phase as a pure liquid or dilute solution, and in the solid phase. In the simulation of molecules in the liquid and solid phase, periodic boundary conditions are used to reduce the surface effects because of the limited number of molecules that can reasonably be studied. The main principle is that as an atom or molecule leaves the main box, its image from one of the adjacent boxes enters. A natural consequence of periodic boundary conditions is the concept of minimum image convention. That is, a molecule will interact with all the N-1 molecules whose centers lie within a region of the same size and shape as that of the original box (see Figure 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. 

Smith, W., The minimum image convention in non-cubic MD cell, CCP5 Infotmation Quarterly for Computer Simulation of Condensed Phases, 30 35, Infomial Newsletter, Daresbury Laboratory, England, 1989. 

Moreover in stomach and esophagus, 3D imaging offers endoluminal projections (the so called virtual endoscopy ) able to generate images simulating a conventional endoscopy, moreover providing a complete evaluation of surrounding anatomical structures. 

The minimum image convention was used in all these simulations, and no tail corrections to the thermodynamic properties were applied, since we were investigating tte relative performance of various algorithms and did not concentrate on the precise values of thermodynamic properties. 

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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