[mmmcitrus]

There is something I have never understood about the molecular orbitals of diatomic molecules. I get that because electrons act as waves so the orbitals can be in phase or out of phase with each other and that the in phase orbitals combine to make bonding orbitals and the out of phase orbitals combine to make anti-bonding orbitals but in something like helium where each atom only has one 1s orbital filled each, how can the orbitals combine both as in phase and out of phase to create a bonding and anti-bonding orbitals and hence make the possibility of a diatomic helium impossible?

Surely if there are only two atomic orbitals at play there can only be one phase at play? Or is it the electrons themselves that are in phase and out of phase? but that still doesn't make sense to me. Or am I misunderstanding a basic quantum mechanical concept here? Or just misunderstanding this whole thing?

Help

[Corribus]

It's not so much combinations of phase that make a difference.  When you add two atomic orbital wavefunctions together, you take their linear combinations to arrive at new molecule orbital wavefunctions.

That is, if the 1SA is the AO on helium A and 1SB is the AO on helium B, then the MOs are 1SA + 1SB and 1SA - 1SB.  One of these is your bonding orbital and the other is your antibonding orbital.  In helium, both of these are completely filled, so the overall bonding order is zero.