Let

and

be energy curves for two different electronic states of a diatomic molecule, both computed within the Born–Oppenheimer approximation. If the two states belong to different symmetry species, say

and

,

and

, or singlet and triplet, there is no restriction on whether the curves can cross. If, however, the two states have the same symmetry, a non-crossing rule applies. Close approach of the two curves results in mutual repulsion, known as an anticrossing. For near degeneracy of

and

, a perturbation

, representing higher-order contributions in the Born–Oppenheimer approximation, becomes significant, giving mixed states that do not cross.

In this Demonstration, the lower energy state,

, is drawn in blue. It is assumed to be a bonding state, with dissociation energy

and equilibrium internuclear distance

, which can both be varied with sliders. The upper energy state,

, drawn in red, is assumed to be a repulsive state. The mixing parameter

can also be varied. In certain cases, the upper state can develop a minimum as a result of the

interaction. The dashed curves in the graphic pertain when

.