# Non-Crossing Rule for Energy Curves in Diatomic Molecules

Non-Crossing Rule for Energy Curves in Diatomic Molecules

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.

E(R)

1

E(R)

2

Σ

Π

u

g

E(R)

1

E(R)

2

V(R)

12

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 .

E(R)

1

D

e

R

e

E(R)

2

V

12

V

12

V(R)=0

12