The Non-Crossing Rule:

When we “mix” two wavefunctions to form a “better” wavefunction the new energies “repel” each other. The lower of the two new energies is lower than either of the original two energies while the higher one is higher than either of the original energies. A familiar example is the mixing of the two 1s atomic orbitals of the hydrogen atoms in H₂. They “mix” to form bonding and antibonding molecular orbitals:

e_A and e_B à energies of original wavefunctions before mixing.

E₁ and E₂à energies of new wavefunctions (molecular orbitals) after mixing.

We get a better wavefunction which is a combination of the two original wavefunctions.

Example of the non-crossing rule: HCl