Corrections of the periodic boundary conditions with rectangular simulation boxes on the diffusion coefficient,general aspects

It is generally known that the effect of the periodic boundary conditions using cubic boxes manifests itself as the underestimation for the self-diffusion coefficient and the difference between the experimental value and the simulation is proportional to the reciprocal of system size. Rather than the cubic boxes, the effect of the rectangular boxes, which has been normally ignored, however, exhibits some distinct features, according to the hydrodynamics theory on molecular diffusion. In particular, the diffusion coefficient along the direction of the short side length of the box is always larger than that along the larger side length. What’s unusual is that some components or even all three components of the diffusion coefficient may exceed that of an infinite system. Through the comparisons of the flow patterns excited by the diffusing particles, we find that the positive and negative corrections are linked to the local and global vortex of fluid, respectively. It appears that the box shape affects the diffusion by modifying the flow pattern. The theoretical predictions are further tested by molecular dynamics simulations.