# Effect of Periodic Boundary condition in Pair Distribution function

When we simulate a bulk molecular system using molecular dynamics in (say) NVE ensemble (microcanonical), we apply some periodic boundary conditions (PBC) to avoid surface effects. What effect does this have on quantities like Pair Distribution function, since it so happens that part of a molecule is near one edge of the box and the other is in a different edge of the box. What effect does this have on PDF, MSD and other such thermodynamic quantities ?

PS : I am currently simulating SPC/E water molecules using cubic box, in some frames I find water molecules which are split apart, but connected by PBC.

• If the box is of dimensions (Dx, Dy, Dz), then an atom at (x, y, z) is also at (x + a Dx, y + b Dy, z + c Dz) for all integral a, b and c. So if one atom is at $\epsilon$ and another at Dx - $\epsilon'$ then you can say that the latter is at $-\epsilon'$ and the distance is $\epsilon + \epsilon'$. – Mathieu Bouville Apr 20 '19 at 11:22