My question is as follows. When (qualitatively at least) constructing molecular orbitals for a given molecule, a few "rules" are used to construct them. I'm wondering why the "rules" exist at all.
For example, it is given that orbitals must have "similar energies" (however one quantifies "similar") for them to interact. What is the justification for this? Why is it that in diatomic nitrogen the 2σ orbital is raised in energy above the π orbitals? I've been told it's due to s-p mixing because for nitrogen (compared to oxygen and fluorine) the energy gap between the 2s and 2p orbitals is smaller, thus the orbitals interact to a certain degree. But why is it the orbitals must be of similar energy to interact in the first place. I'd similarly like to know why it is that the HOMO-LUMO energy gap affects how fast reactions, such as nucleophilic addition the carbonyls, occur.
Related to this, I'd like to know why orbitals must have similar orientation to interact. I understand that if for example a 2pz and 2s orbital were to overlap on two different atoms, it would yield nothing due to a mixture of constructive and destructive overlap, but surely these are possible linear combinations of orbitals thus must still "happen" even if they only exist as virtual states.
Thank you all in advance