Unless we really want to simulate a cluster of atoms, this situation
is not realistic. No matter how large the simulated system is, its number of
atoms *N* would be negligible compared with the number of atoms
contained in a macroscopic piece of matter (of the order of 10^{23}),
and the ratio between the number of surface atoms and the total
number of atoms would be much larger than in reality, causing surface effects
to be much more important than what they should.

A solution to this problem is to use *periodic boundary conditions* (PBC).
When using PBC, particles are enclosed in a box, and we can imagine that
this box is replicated to infinity by rigid translation in all the three
cartesian directions, completely filling the space.
In other words, if one of our particles is located at position in the box, we assume that this particle really represents an infinite
set of particles located at

The key point is that now each particle *i* in the box should be thought
as interacting not only with other particles *j* in the box, but
also with their images in nearby boxes.
That is, interactions can ``go through'' box boundaries.
In fact, one can easily see that
*(a)* we have virtually eliminated surface effects from our system, and
*(b)* the position of the box boundaries has no effect (that is,
a translation of the box with respect to the particles leaves
the forces unchanged).

Apparently, the number of interacting pairs increases enormously
as an effect of PBC. In practice, this is not true because
potentials usually have a short interaction range.
The *minimum image criterion* discussed next simplifies
things further, reducing to a minimum the level of additional complexity
introduced in a program by the use of PBC.