Truly periodic boundary condition

Single-phase simulations in relatively small boxes (20 -30 sites) were performed after the determination of the surfactant/silica liquid crystal composition to generate model materials for adsorption simulation. The advantage of generating such materials is that they have truly periodic boundary conditions in the three directions. In contrast, extracted model materials obtained directly from the interfacial simulation will have periodic boundary conditions in two directions, but in the third direction (z-direction) there are two liquid-crystal/dilute phase interfaces. 

For moderately dense coulombic systems the use of Ewald potentials— that is, of truly periodic boundary conditions in the energy calculation—seems to have become almost routine in recent studies. It is also proposed for dipole systems. There seem, however, to be theoretical arguments for examining more critically the consequences of this approximation. These theoretical questions concern the physical realism of the approximation, and may be divided into those of long-range behavior and those of short-range behavior of the truly periodic model ... 

There are two issues that are relevant here. First, the adsorbates in a supercell calculation necessarily have a long-range pattern that is repeated exactly as the supercell is repeated. With periodic boundary conditions, it is impossible to model any kind of truly random arrangement of adsorbates. The good news is that in nature, it happens that adsorbates on crystal surfaces often do exhibit long-range ordering, especially at low temperatures, so it is possible for calculations to imitate real systems in many cases. 

In order to reproduce solution or crystal environments, it is necessary to define boundaries around the system. Several options are available to fix such boundaries. One of them is to place the system in a sufficiently large water droplet where the outer layer is restrained in order to prevent water molecules to evaporate . These methods are generally u.sed for simulating large systems such as nucleic acid/protein complexes for which the use of periodic boundaries would not allow to perform an MD simulation in a reasonable amount of time. For smaller systems, periodic boundary conditions can be routinely u.sed. In this method, the solute is placed in a box of solvent which is then replicated in all directions in order to mimic an infinite system. However, the use of truncation methods for the evaluation of electrostatic interactions restricts severely the infinite character of the system. The use of Ewald summation methods allows a simulation of truly infinite periodic conditions and is, therefore, the most adapted approach for simulations in a crystal environment, although it has been used efficiently for simulations of liquid phases. 

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