Filled molecular orbitals: Avoidance vs Mixing I am trying to figure out if the mixing of two filled orbitals requires some additional activation energy and, if it does, if there is some orbital avoidance area where the filled orbitals will not mix but rather repel each other, forming a 0-electron density barrier in between. 
Consider two helium atoms. Ultimately, when nuclei become close enough, the two 1S orbitals will become 1S and 2S, forming a single electronic system. The question is whether they will start forming this system right away as they start to feel each other - at a relatively large distance - or if they will first try to avoid each other, protecting the existent systems on each atom and only collapsing when the nuclei are brought very close.
 A: pushing together two helium atoms is an interesting thought. 
The 1s orbitals will for a $\sigma$ and $\sigma^*$ pair of molecular orbitals. 
The $\sigma$ is bonding (lower in energy) and the $\sigma^*$ is antibonding (higher in energy).

The same as in this diagram for hydrogen (diagram from wikipedia) (except the labels g for the lower MO and u upper MO are used instead of the * )
Now for Hydrogen each atom has one electron and the two electrons can fall down into the $\sigma$ (or 1$\sigma_g$) bonding orbital and the energy of the system is lower and we have a stable chemical bond.
For helium the diagram is the same but each atom has 2 electrons so in total we have 4 electrons so we fill both the $\sigma$ and $\sigma^*$ MOs (or 1$\sigma_g$ and 1$\sigma_u$) and as you can see from the diagram this will actually slightly raise the total energy and is unstable... so we don't get a bond and there is no He$_2$ molecule.... unless...
...unless we remover or excite one or both of the electrons out of the higher MO level.
For example, He$_2^{2+}$

Or finally, I can't find an image for this on the web so we will have to imagine it... as well as the 1s forming $\sigma$ and $\sigma^*$ MOs the 2s orbitals will also form $\sigma$ and $\sigma^*$ orbitals and we can excite electrons from the lower 1s  $\sigma^*$ into the upper 2s $\sigma$ to make a metastable excited state - I think it is sometimes called an exCimer and was often used in lasers, though not so much mow with solid state lasers being prevalent.  
Here is a diagram to show potential energy curves for the lower ground state - and upper excited state - note the ground state is not stable - the energy rises as the two atoms are pushed together. The upper states are 'metastable' the energy dips as the atoms approach and there is a potential well. Below Rg = rare gas.

