# What is the justification for the minimum image convention in periodic boundary condition?

As the distance between first particle-second particle and first particle-image of the second particle are not same. How is it justified to use the distance from the nearest image to compute potential and other properties? I think it has to do with the surface effects (?) but I need a clear justification.

## 1 Answer

This is because we want to avoid extensive mathematical calculations of pairwise interactions with all particle inside or outside the box. MIC is a way of providing a cutoff distance over which we are not calculating pairwise potential. The cutoff is usually half the box length. This means if distance between particle i and particle j is more than L/2, you will neglect the pairwise potential between i & j, instead you will consider potential between i & neareset image of j, hence the term Minimum Image.

• So for each particle $i$ in the cell we consider a sphere of a given radius, and we consider interactions between particle $i$ and $j$, for each $j$ inside this sphere? Commented Mar 27, 2023 at 14:25