The equilibrium spacing will occur when the bond energy (Fn) is a minimum. This is when the net forces between the two atoms is zero: Fn=Fa+Fr=0.
Where:
Fa = attractive force.
Fr = repulsive force.
The force between atoms, F, is given as:
where U = bond energy and r = atomic separation.
Bond stiffness, S, is given by:
where U = bond energy and r = atomic separation.
When the stretching is small, S is constant and therefore the bond is linear-elastic. This means that as the interatomic distance increases, the force required increases linearly.
The shape of these curves changes for different bond types and materials. A number of material properties are influenced by this curve shape. The F vs. r curve for a flexible material will be shallower than one for a stiff material, at ro.