PBC Requirements and Artifacts
Periodic boundary conditions are particularly useful for simulating a part of a bulk system with no surfaces present. Moreover, in simulations of planar surfaces, it is very often useful to simulate two dimensions (e.g. x and y) with periodic boundaries, while leaving the third (z) direction with different boundary conditions, such as remaining vacuum to infinity. This setup is known as slab boundary conditions.
PBC can be used in conjunction with Ewald summation methods (usually particle mesh Ewald) of accounting for electrostatic forces in the system. However, PBC also introduces correlational artifacts that do not respect the translational invariance of the system, and requires constraints on the composition and size of the simulation box.
In simulations of solid systems, the strain field arising from any inhomogenuity in the system will be artificially truncated and modified by the periodic boundary. Similarly, the wavelength of sound or shock waves and phonons in the system is limited by the box size.
In simulations containing ionic (Coulomb) interactions, the net electrostatic charge of the system must be zero to avoid summing to an infinite charge when PBC is applied. In some applications it is appropriate to obtain neutrality by adding ions such as sodium or chloride (as counterions) in appropriate numbers if the molecules of interest are charged. Sometimes ions are even added to a system in which the molecules of interest are neutral, to approximate the ionic strength of the solution in which the molecules naturally appear. Maintenance of the minimum-image convention also generally requires that a spherical cutoff radius for nonbonded forces be at most half the length of one side of a cubic box. Even in electrostatically neutral systems, a net dipole moment of the unit cell can introduce a spurious bulk-surface energy, equivalent to pyroelectricity in polar crystals.
The size of the simulation box must also be large enough to prevent periodic artifacts from occurring due to the unphysical topology of the simulation. In a box that is too small, a macromolecule may interact with its own image in a neighboring box, which is functionally equivalent to a molecule's "head" interacting with its own "tail". This produces highly unphysical dynamics in most macromolecules, although the magnitude of the consequences and thus the appropriate box size relative to the size of the macromolecules depends on the intended length of the simulation, the desired accuracy, and the anticipated dynamics. For example, simulations of protein folding that begin from the native state may undergo smaller fluctuations, and therefore may not require as large a box, as simulations that begin from a random coil conformation. However, the effects of solvation shells on the observed dynamics – in simulation or in experiment – are not well understood. A common recommendation based on simulations of DNA is to require at least 1 nm of solvent around the molecules of interest in every dimension.
Read more about this topic: Periodic Boundary Conditions